The fundamental surface science of wurtzite gallium nitride

Surface Science Reports ∎ (∎∎∎∎) ∎∎∎–∎∎∎

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Surface Science Reports journal homepage: www.elsevier.com/locate/surfrep

The fundamental surface science of wurtzite gallium nitride$ V.M. Bermudez 1 Electronics Science and Technology Division, Naval Research Laboratory, Washington, DC 20375, USA

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Article history: Received 27 December 2016 Received in revised form 30 April 2017 Accepted 30 April 2017

A review is presented that covers the experimental and theoretical literature relating to the preparation, electronic structure and chemical and physical properties of the surfaces of the wurtzite form of GaN. The discussion includes the adsorption of various chemical elements and of inorganic, organometallic and organic species. The focus is on work that contributes to a microscopic, atomistic understanding of GaN surfaces and interfaces, and the review concludes with an assessment of possible future directions. & 2017 Elsevier B.V. All rights reserved.

Contents 1. 2. 3.

Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 The ideally-terminated surfaces . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 Preparation of clean surfaces (ex-situ growth / in-situ cleaning). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 3.1. Ex-situ wet-chemical pre-treatment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 3.2. In-situ chemical cleaning . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11 3.2.1. Ga deposition and desorption . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11 3.2.2. Annealing in NH3 vapor . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13 3.3. In-situ ion bombardment and annealing and related topics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14 3.3.1. Faceting . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14 3.3.2. Annealing only . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15 3.3.3. Ion-beam damage . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15 3.3.4. Ion bombardment and annealing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16 3.4. Other methods. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17

Abbreviations: 2D, Two-Dimensional; 2DEG, Two-Dimensional Electron Gas; 2DPS, Two-Dimensionally-Periodic Slab; 3D, Three-Dimensional; AES, Auger Electron Spectroscopy; AFM, Atomic Force Microscopy; ARUPS, Angle-Resolved Ultraviolet Photoemission Spectroscopy; B3LYP, Becke-3 Lee-Yang-Parr; BB, Band Bending; BE, Binding Energy; BEP, Beam-Equivalent Pressure; BZ, Brillouin Zone; CBED, Convergent-Beam Electron Diffraction; CBM, Conduction Band Minimum; CMP, Chemo-Mechanical Polishing; C-V, Capacitance-Voltage; CVD, Chemical Vapor Deposition; DB, Dangling Bond; DFT, Density Functional Theory; DFTB, Density Functional Tight Binding; DI, Deionized (H2O); DOS, Density of States; ECR, Electron Counting Rule; EDAX, Energy-Dispersive Analysis by X-rays; ELS, (Electron) Energy Loss Spectroscopy; ESD, ElectronStimulated Desorption; FCC, Face-Centered Cubic; FK, Fuchs-Kliewer; FLAPW, Full-Potential Linearized Augmented Plane Wave; GGA, Generalized Gradient Approximation; HCP, Hexagonal Close-Packed; HOMO, Highest Occupied Molecular Orbital; HREELS, High-Resolution Electron Energy Loss Spectroscopy; HRTEM, High-Resolution Transmission Electron Microscopy; HSE, Heyd-Scuseria-Ernzerhoff; IBA, Ion Bombardment and Annealing; IPES, Inverse Photoemission Spectroscopy; ISS, Ion-Scattering Spectroscopy; I-V, Current-Voltage; KE, Kinetic Energy; LDA, Local Density Approximation; LEED, Low-Energy Electron Diffraction; LEEM, Low-Energy Electron Microscopy; MBE, Molecular Beam Epitaxy; MD, Molecular Dynamics; MIGS, Metal-Induced Gap States; ML, Monolayer; MOCVD, Metal-Organic Chemical Vapor Deposition; MOVPE, MetalOrganic Vapor-Phase Epitaxy; NBLP, Non-Bonding Lone Pair (Orbital); NCPP, Norm-Conserving Pseudopotential; NEA, Negative Electron Affinity; NEB, Nudged Elastic Band; NLCC, Non-Linear Core Correction; PAW, Projector Augmented Wave; PBE, Perdew-Burke-Ernzerhoff; PED, Photoelectron Diffraction; PH, Pseudo-Hydrogen; PL, Photoluminescence (Spectroscopy); PP, Pseudopotential; PW, Plane Wave; PW-91, Perdew-Wang 1991; QCO, Quartz Crystal Oscillator; RAS, Reflection-Absorption Spectroscopy; RBS, Rutherford Backscattering; RHEED, Reflection High-Energy Electron Diffraction; RHF, Restricted Hartree Fock; RMS, Root Mean Square; RPES, Resonant Photoemission Spectroscopy; RT, Room Temperature; SAM, Self-Assembled Monolayer; SBH, Schottky Barrier Height; SCL, Space-Charge Layer; SCLS, Surface Core-Level Shift; SE, Spectroscopic Ellipsometry; SIMS, Secondary-Ion Mass Spectroscopy; SPV, Surface Photovoltage (or Surface Photovoltaic); STM, Scanning Tunneling Microscopy; STS, Scanning Tunneling Spectroscopy; SUC, Surface Unit Cell; TEG, Triethylgallium; TEM, Transmission Electron Microscopy; TCE, Trichloroethylene; TMG, Trimethylgallium; TOF-SARS, Time-of-Flight Scattering and Recoil Spectroscopy; TPD, Temperature-Programmed Desorption; UHV, Ultra-High Vacuum; UPS, Ultraviolet Photoemission Spectroscopy; USPP, Ultra-Soft Pseudopotential; UV, Ultraviolet; VBM, Valence Band Maximum; VPE, Vapor-Phase Epitaxy; XAES, X-ray-(Excited) Auger Electron Spectroscopy; XPS, X-ray Photoemission Spectroscopy; XRD, X-ray Diffraction. ☆ The views presented are those of the author and do not necessarily represent the views of the Department of Defense or its Components. E-mail address: [email protected] 1 Retired (Volunteer Emeritus). http://dx.doi.org/10.1016/j.surfrep.2017.05.001 0167-5729/& 2017 Elsevier B.V. All rights reserved.

V.M. Bermudez / Surface Science Reports ∎ (∎∎∎∎) ∎∎∎–∎∎∎

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3.5. Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17 Structure and properties of clean surfaces . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18 4.1. Theoretical background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18 4.1.1. Calculations at T = 0 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18 4.1.2. Calculations at finite temperature. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21 4.2. Polarity and polarization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22 4.2.1. Polarity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22 4.2.2. Polarization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23 4.3. Surface morphology. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24 4.4. Defects, strain and other imperfections . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27 4.5. Thermal stability and decomposition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28 4.6. Stoichiometry and reconstruction (AES, ISS, XPS, LEED, RHEED, STM) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29 4.6.1. The (0001) surface. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29 4.6.2. The (0001̄ ) surface. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35 4.6.3. The (101̄0) and (112̄ 0) surfaces . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37 4.6.4. Semi-polar surfaces . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39 4.7. Spectroscopy and surface electronic structure (UPS, ELS, STS) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42 4.7.1. Ultraviolet photoemission spectroscopy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42 4.7.2. Electron Energy Loss Spectroscopy and related methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56 4.7.3. Band bending and surface photovoltage. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58 4.8. Vibrational properties and free-electron excitation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65 The chemical elements - adsorption and interfaces . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65 5.1. Aluminum . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66 5.2. Antimony . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70 5.3. Arsenic . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71 5.4. Barium . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72 5.5. Beryllium . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73 5.6. Bismuth . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73 5.7. Boron . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73 5.8. Carbon . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73 5.9. Cerium . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75 5.10. Cesium . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75 5.11. Chlorine . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77 5.12. Chromium . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 78 5.13. Cobalt . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 78 5.14. Copper . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 80 5.15. Europium . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 80 5.16. Fluorine . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 80 5.17. Gadolinium . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81 5.18. Gallium. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81 5.19. Germanium . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 86 5.20. Gold . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 86 5.21. Hafnium . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 89 5.22. Indium . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 89 5.23. Iron. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 91 5.24. Lead . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93 5.25. Magnesium . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93 5.26. Manganese . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 99 5.27. Nickel . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 102 5.28. Niobium . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 106 5.29. Palladium . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 106 5.30. Platinum. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 107 5.31. Ruthenium . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 108 5.32. Samarium. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 109 5.33. Scandium . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 109 5.34. Silicon. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 110 5.35. Silver . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 113 5.36. Sulfur . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 114 5.37. Titanium. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 115 5.38. Vanadium. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 116 5.39. Zirconium. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 116 Metal contacts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 117 Adsorption of inorganic and organometallic molecules. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 120 7.1. Ammonia (NH3) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 120 7.2. Hydrazine (N2H4). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 125 7.3. Hydrogen (H and H2) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 125 7.4. Hydrogen chloride (HCl) and gallium monochloride (GaCl) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 133 7.5. Nitric oxide (NO) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 134 7.6. Nitrogen (N and N2) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 134 7.7. Nitrous oxide (N2O) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 137 7.8. Oxygen (O and O2) and ozone (O3). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 137 7.9. Trimethylgallium (Ga(CH3)3), triethylgallium (Ga(C2H5)3), etc . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 143

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7.10. Water (H2O and OH) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Adsorption of organic molecules . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8.1. Alcohols . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8.2. Alkanes. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8.3. Alkenes and alkynes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8.4. Amines . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8.5. Grignard reagents . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8.6. Peptides . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8.7. Phosphonic acids . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8.8. Silanes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8.9. Thiols . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9. Concluding remarks and future prospects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Acknowledgments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Note Added in Proof . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8.

1. Introduction The surface science of the wurtzite form of GaN has reached a level of maturity that justifies a review of the field. It is, furthermore, possible that the award of the 2014 Nobel Prize in Physics to I. Akasaki, H. Amano and S. Nakamura for their pioneering work on the blue light-emitting diode will trigger a resurgence of interest in GaN surfaces and interfaces, leading to further progress that might be aided to some extent by a review of this nature. There have previously been important reviews in this general area. Neugebauer [1], Feenstra et al. [2,3] and Bakhtizin et al. [4] have discussed theoretical and experimental results pertaining to the structure and properties of surfaces prepared using MBE and studied in situ using LEED, RHEED and STM. The adsorption of several elements has also been examined in detail [2,3]. The review by Eller et al. [5] deals primarily with the preparation, characterization and properties of GaN surfaces and interfaces as they relate to electronic devices. These reviews have been concerned mainly with the polar (0001) and (0001¯ ) surfaces. Eisele and Ebert [6] have also reviewed some aspects of the non-polar ¯ ) and (1120 ¯ ) surfaces. Very recently, as the present work was (1010 nearing completion, a review by Zúñiga-Pérez et al. [7] appeared that provides an in-depth discussion of polarity and polarization in relation to surface structure, material growth and device applications. Of necessity, the present work addresses the same subjects as these earlier reviews but also includes a more extensive array of adsorbed species. It is useful at this point to indicate those subjects that are not covered in this review. Such topics include the growth of the material and anything having to do with device fabrication or processing. Studies relating to metal contacts are also omitted unless they include an atomistic description of the basic properties of the interface. Likewise, etching via wet-chemical, electrochemical, plasma-enhanced, etc. methods are not discussed unless, again, there is a fundamental atomistic component to the work. These exclusions are not in any way intended to be pejorative. Rather the goal is to limit the scope of the review to a tractable amount of material that falls within the author's general range of experience. Another reason for limiting the range of topics is that there are already many excellent reviews [8-42], a few of which are listed in Table 1, that cover subjects not treated here. An examination of some of these will provide insight into the technological considerations that drive much of the basic research in GaN. Recently it has been found [43] that wurtzite GaN can exhibit a high degree of resistance to mechanical wear and abrasion. This opens a new range of applications, beyond the use of GaN as an electronic material, that may also relate to surface properties.

3

144 151 151 151 151 152 154 154 154 155 155 155 159 159 159

As suggested by the title, there will be no discussion of the cubic, or zinc blende, form of GaN. Substantially less work has been done on the surface science of this material, probably as a result of the relative difficulty in obtaining suitable samples and the greater technological importance of wurtzite GaN. It was, furthermore, thought that attempting to combine both in the same review would be disruptive. There will also be no discussion of nano-wires or related structures nor of the growth and surface properties of GaN formed by nitridation of GaAs or other Ga-based materials. The list of references included in this review is believed to be complete through mid-2015; although, several 2016 and a few 2017 publications have also been cited. Every effort has been made to avoid overlooking any relevant work, and no such publication has been intentionally omitted. However in cases where virtuallyidentical papers have been presented at different conferences only one is cited, usually the one that is most easily obtained. A few references are not available in English or in any other language that the author of this review can read at the technical level, in which case only the information contained in the English-language abstract (if available) is included. When this occurs, a notation will be added at the appropriate point in the text. In cases where not even an English-language abstract is available, the work will be included in the list of references but not otherwise discussed. Typically there are several references for a given topic, in which case the various publications will be discussed as follows. Experiments will be described first, followed by theoretical work. Within each of these groups, the (0001) surface will be discussed first, followed by the (0001¯ ) and then by other surfaces as needed. Within each of these subgroups, references are discussed in approximate chronological order based on publication date. Often the chronological order does not correspond to that of the reference numbering, which occurs when the same publication is cited under more than one topic. There are quite a few references to papers published in the Materials Research Society Internet Journal of Nitride Semiconductor Research. This was an on-line journal that operated from 1996 through 2005, and papers published therein can be obtained on an open-access basis [44]. There are also numerous references to papers published in Materials Research Society Symposium Proceedings, which can be obtained on a subscription basis [45]. Many papers describe the substrate as "GaN (0001)", which implies that the Ga-polar surface (Section 4.2) is under study. Usually no reference is made to any specific test of polarity; hence, it is assumed in the present review that the polarity has been independently established by the growth conditions or by some other means. Therefore, unless otherwise noted, "GaN (0001)" will

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List of Symbols

χ D

ΔEa ΔEads ΔEf ΔHf ΔH0 ΔN(E)

EF Eg Ep

ϕS

Electron affinity Dipole moment in Debyes (1 D ¼ 10
18 esu cm) Activation energy (or energy barrier) Adsorption energy (Defect) Formation energy Heat of formation Heat of reaction at 0 K Difference spectrum (N(E) after treatment minus N (E) before) Fermi energy (or Fermi level) Band gap Primary-beam energy Sample work function

be taken literally to mean "Ga polar". The convention for units (eV vs. kcal mol
1, K vs. °C, etc.) will follow that used by the authors of the paper being discussed rather than being converted to a common set of units. The one exception will be in the case of pressure, for which millibar (mbar) or Pascal (Pa) will be converted to Torr. Adsorbate coverages are typically given in MLs, where 1 ML means one adsorbed species per surface lattice site (2/(√3a2) ¼ 1.135x1015 cm
2 for GaN (0001) or (0001̄ ), given a basal-plane lattice constant of a ¼ 3.190 Å). In general, little or no attempt is made to reinterpret the data in a particular study or to offer criticism of the analysis put forth by the authors of a paper under discussion. Deviations from this practice will be labeled as "speculation" or otherwise noted to indicate that the opinions presented are those of the reviewer and not of the original authors. However, points of agreement or disagreement among results and interpretations in different studies will be noted. Hopefully, when presented with all the relevant results on a given topic, the reader can formulate his/her own conclusions. In an effort to make the material more accessible to the general reader, brief summaries (highlighted with italics for easy location) are provided at appropriate points in the longer sections that cover many references. It is assumed that the reader is familiar with the experimental techniques discussed; hence, little or no explanation of these is provided. There is, however, a somewhat cursory description of theoretical methods given in Section 4.1 in order to make the reviews of computational results more accessible to the experimentalist. The overwhelming majority of surface-science studies of wurtzite GaN have been performed on thin films grown by MOCVD or MBE on single-crystal sapphire or SiC substrates or by MOVPE. The latter is essentially the same process as MOCVD except that the growth is epitaxial [46]. However, the terms "MOCVD" and "MOVPE" appear to be used interchangeably in the GaN surface-science literature, and that practice will be followed here. A number of studies have also been carried out on synthetic single crystals, which in the past have been more difficult to obtain with a size and quality comparable to that of thin-film samples. To our knowledge, GaN does not occur naturally as a mineral; although, there is one report [47] of wurtzite GaN crystals having been found in sediment from the bottom of the eastern Pacific Ocean retrieved from a depth of 5.17 km.

HeI HeII hν ip L

μB μX

N(E) Pa Ry sb

θX

VGa VN

Atomic He (21.2 eV emission line) Singly-ionized He (40.8 eV emission line) Photon energy Primary-beam current Langmuir (1 L ¼ 1  10
6 Torr sec) Bohr magneton Chemical potential of species "X" Intensity (or counts) vs. energy Pascal (133.3 Pa ¼ 1 Torr) Rydbergs (1 Ry ¼ 13.606 eV) Areal density of bound surface polarization charges Coverage of adsorbate species "X" (in monolayers) Gallium vacancy Nitrogen vacancy

projection of the c-axis on the surface normal, which in turn fixes the magnitude of the surface-normal lattice polarization (discussed in Section 4.2.2). These categories are the polar [(0001), ¯ ) , (1120 ¯ )] (Fig. 2) and the (0001̄ )] (Fig. 1), the non-polar [ (1010 ¯ ¯ semi-polar [ (1122), (1011)] (Figs. 3) and [(101̄3), (202̄1)] (Fig. 4) surfaces [48]. The (0001) and (0001̄ ) surfaces are sometimes labeled "+c-plane" and "−c-plane", and the (101̄0), (112̄ 0) and (101̄2) surfaces are termed "m-plane", "a-plane" and "r-plane" respectively. Here we discuss only those surfaces that are most commonly treated in the fundamental surface-science literature. Other

Table 1 A sampling of GaN review articles dealing with some of the topics not included in the present review. This tabulation is not intended to be either exhaustive or completely up-to-date with regard to either the subjects or the references. Topic

Authors [Ref.]

Bio-functionalization

Stutzmann et al. [8] Bain et al. [9] O'Leary et al. [10] Meyer et al. [11] Van de Walle et al. [12] Reshchikov et al. [13] Yam et al. [14] Orton et al. [15] Pearton et al. [16] Zhang et al. [17] Khan et al. [18] Roccaforte et al. [19] Zhu et al. [20] Eddy [21] Pearton et al. [22] Zhuang et al. [23] Strite et al. [24] Jain et al. [25] Paskova [26] Zhuang [27] Keller et al. [28] Liu et al. [29] Kukushkin et al. [30] Wang et al. [31] Liu et al. [32] Chen et al. [33] Greco et al. [34] Oon et al. [35] Pearton et al. [36] Cao et al. [37] Polyakov et al. [38] Pearton et al. [39] Anderson et al. [40] Irokawa [41] Ren et al. [42]

Carrier Dynamics Defects (Point)

Defects (Extended) Devices

Doping Etching

General Properties

Growth Growth Substrates

Metal Contact Technology

Oxidation Processing Radiation Damage

2. The ideally-terminated surfaces Sensors

Wurtzite GaN surfaces are divided into three categories, depending on crystallographic orientation. This determines the

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Fig. 1. Schematic diagram (not to scale) showing the unrelaxed, ideally-terminated (0001) surface with various adsorption sites indicated. (a) and (b) are side and top-down views respectively. The same diagram applies to the (0001̄ ) with Ga and N interchanged. Light green (gray) spheres are Ga (N), and surface Ga atoms in (b) are marked with small dark-green spheres for emphasis. In (b) the solid lines indicate the (1  1) SUC. An adsorbate in a T4 (or HCP) site is back-bonded to three surface Ga atoms and lies above a first-underlayer N. An adsorbate in an H3 (or FCC) site is similarly back-bonded but lies above an empty first-underlayer site. A Br site bridges two surface Ga atoms, and a T1 lies directly above a Ga. This figure and others like it were prepared using the VESTA program [48].

Fig. 2. Similar to Fig. 1 but showing the unrelaxed, ideally-terminated non-polar (a),(b) (101̄0) and (c),(d) (112̄ 0) surfaces. The side views, (a) and (c) each show four planes in the surface-normal direction. In the top-down views, (b) and (d), the bonds between coordinatively-unsaturated Ga and N atoms in the surface plane are emphasized with black lines. These surface Ga-N bonds are often termed "dimer bonds" or "Ga-N dimers". Atoms not so joined are in the first underlayer. The red dashed lines show the surface unit cells.

semi-polar surfaces have been studied in this context but only rarely and mainly theoretically. As an explanatory note, the basalplane hexagonal lattice vectors are related via a3 = −(a1+a2) so

that for a plane designated as (xyzc) one has x+y+z = 0. On rare occasions one sees a wurtzite plane designated as (xyc) or (xy•c) in which case (xy−(x+y)c) is understood. The general characteristics

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̄ surfaces. The black dashed lines show the primitive surface Fig. 3. Similar to Fig. 1 but showing the unrelaxed, ideally-terminated semi-polar (a),(b) (112̄ 2) and (c),(d) (1011) unit cells. The (112̄ 2) is terminated in 2-fold-coordinated Ga and 3-fold-coordinated N (two each per unit cell), which are circled in red in the top-down view for clarity. In ̄ is N-terminated with one 3-fold and one the (112̄ 2) side view, all surface Ga atoms are two-fold-coordinated, and all surface N atoms are three-fold coordinated. The (1011) 2-fold N per primitive unit cell and with the latter lying slightly higher along the surface normal. The violet dashed line in (d) shows the non-primitive cell that is used in some calculations.

and applications of semi-polar and non-polar GaN surfaces are reviewed in Refs. [49–52] and [6,26,50,51] respectively, with emphasis on fundamental surface properties given in Ref. [6]. Due to the availability of samples in the form of heteroepitaxial thin films on sapphire or hexagonal SiC, the vast majority of experimental work focuses on the (0001) and (0001̄ ) surfaces. Of

these, the former has been given more emphasis as a result of its greater technological significance. However, bulk single crystals can be cleaved on the non-polar surfaces, and the increasing availability of crystals of sufficient size and quality presents the possibility of preparing atomically-clean and well-ordered nonpolar surfaces by in-situ cleaving in UHV [6].

̄ and (c),(d) (202̄1) surfaces. In (a),(b), "T" and "D" indicate equal numbers of Fig. 4. Similar to Fig. 1 but showing the unrelaxed, ideally-terminated semi-polar (a),(b) (1013) triply (3-fold-) and doubly (2-fold-) coordinated N atoms, and, for clarity, only atoms in the uppermost 2 Ga-N bilayers are shown above the shaded plane. All Ga atoms on the (101̄3) surface are 3-fold coordinated. In (c),(d), only the uppermost surface atoms are shown above the shaded plane. The black dashed lines show the (1  1) primitive surface unit cells. In (b) the violet dashed lines show the non-primitive unit cell employed in a theoretical model. In (c) the dashed lines show nano-facets (F1, F2) that are ̄ surfaces respectively. On the (202̄1), all N are 2-fold- or 3-fold coordinated in equal numbers. There is one 3-foldused in a theoretical model. These are (101̄0) and (1011) coordinated Ga per primitive SUC, which lies on the F1 ((101̄0)) nano-facet.

V.M. Bermudez / Surface Science Reports ∎ (∎∎∎∎) ∎∎∎–∎∎∎ Table 2 Surface energies (meV Å
2) computed for different relaxed wurtzite GaN planes. Surface Planea

Rapcewicz et al. [53]b

Dreyer et al. [54]c

Li et al. [55]d Zhang et al. [56]e

(0001) ( þc) (0001̄ ) (
c) (101̄0) (m) (112̄ 0) (a) ̄ (1011) (101̄2) (r) (112̄ 2)

165 41.6

159 239 122 125

o209 4 124 132 o249 4 o208 4 o223 4

169.5 (201.5) 202.1 (265.6) 102.1 106.0

a

For convenience, the commonly-used plane designations (m, a, etc.) are given. Energies were extracted from graphical results and converted from eV per (1  1) SUC to meV Å
2 using a SUC area of √3a2/2 ¼ 8.813 Å2 where a ¼ 3.190 Å is the GaN basal-plane lattice constant. The results are for the lowest-energy surfaces predicted in LDA calculations, which are the N-adatom (2x2) for (0001) and the N-vacancy (2  2) for the (0001̄ ). c Energies were obtained using the HSE hybrid functional and were extracted from graphical data for N-rich conditions, under which they are independent of μN. All values decrease toward the high-μGa limit when Ga adlayers form. The predicted lowest-energy surfaces for high μN are the N-adatom (2  2) for (0001) and the Gaadatom (2  2) for (0001̄ ). d Results were obtained using the LDA for unreconstructed surfaces. Quantities in brackets o... 4 are averages for opposing polar or semi-polar surfaces. For the polar and semi-polar surfaces the values are for the lower-energy of the two possible terminations. For example, Ga-terminated (0001) and N-terminated (0001̄ ) is more stable than the reverse. e Results obtained for unreconstructed surfaces under N-rich conditions using a GGA functional. Quantities in parentheses were obtained using the hybrid HSE functional and are thought to be more reliable. b

Theoretical surface energies for the different planes have been reported [53–56] and are summarized in Table 2. These are valuable for an understanding of the relative stability of different surfaces and also in the formulation of Wulff constructions [51,55,57]. A Wulff construction derives the lowest-energy shape of a bulk single crystal using the area of each plane on the crystal surface and the surface energy of the plane, which can vary according to growth conditions. This is very useful in understanding growth, which is beyond the scope of the present review, but Wulff constructions are mentioned here as an illustration of the practical significance of surface-energy considerations. It should also be noted that, with the exception of the non-polar surfaces, all the GaN surfaces considered here exhibit some form of reconstruction in experiment and/or in theory, which can significantly affect surface energies. Of those works cited here that focus specifically on surface energies, only those of Rapcewicz et al. [53] and Dreyer et al. [54] consider such effects. For a two-dimensionally-periodic slab with a thickness of N unit cells in the surface-normal direction, the total energy per slab unit cell is E = (σA+σB)·A + N·EB, where σA and σB are the energies of the two surfaces, A is the area of the surface unit cell and EB is the energy of the corresponding bulk unit cell. The accepted approach [58,59] to obtaining σ is to compute E vs. N for increasing values of N until the behavior becomes linear and then to determine the N = 0 intercept. Simply using EB obtained in a 3D-periodic calculation for a bulk crystal can lead to erroneous results. The theoretical methods employed in these calculations will be described briefly in Section 4.1. The result is simple only in the case of non-polar surfaces (σA = σB), for which an absolute surface energy is obtained. Applying the same approach without modification to polar or semipolar surfaces, for which the two opposing crystal faces are different, gives only the average (σav) or total surface energy for the two faces. Alternative methods have been developed [53,54,56] that permit absolute σ-values to be obtained for polar and semi-polar surfaces and the dependence on surface stoichiometry and reconstruction to be determined. Some of these results will be examined in Section 4.6 in the discussion of surface composition and

7

reconstruction. Here we are concerned mainly with the general structural features of ideally-terminated surfaces. Fig. 1 shows a schematic structure for the ideally-terminated (0001) and (0001̄ ) surfaces, which are terminated in a layer of Ga and N respectively, for which the relaxed σav is 209 meV Å−2 [55]. Dreyer et al. [54] find that σ is higher for the (0001̄ ) than the (0001) for any reconstruction of either surface. Also shown are high-symmetry surface sites that figure prominently in adsorption studies. These are the T4 (or HCP), H3 (or FCC), bridge and T1 sites. An adsorbate in a T4 site is back-bonded to three surface Ga sites (or three N sites on the (0001̄ )) and sits above a first-underlayer N (or Ga on the (0001̄ )). In the case of the H3 the first-underlayer site is vacant. An adsorbate in a bridge site is back-bonded to two surface atoms, while in the T1 it sits directly above a surface atom. Fig. 2 shows the non-polar (101̄0) and (112̄ 0) surfaces for which σ = 124 and 132 meV Å−2 respectively [55] when relaxed but ideally terminated. Here the two slab faces are identical, which enables an absolute value of σ to be obtained. Only a few of the many possible semi-polar surface orientations are described here, focusing on those that that have received the most attention in the surface-science literature. Fig. 3 shows models for the (112̄ 2) and ̄ surfaces, for which σav = 223 and 249 meV Å−2 respectively (1011) [55]. In each case the top-down view shows only one of the two — opposing surfaces (e.g., (112̄ 2) and not (1122)), and the composition of the terminating layer shown is that which gives the lowest σav as found in Ref. [55]. For example, Ga-terminated (112̄ 2) (Ga — outermost) and N-terminated (1122) (N outermost) gives a lower σav than the reverse. Likewise, Fig. 4 shows the ideally-terminated (101̄3) and (202̄1) surfaces, but to our knowledge there are no surface-energy results available for these in the relaxed, ideallyterminated state. As expected, the non-polar surfaces are lower in energy than the others, which results from there being equal numbers of threefold-coordinated Ga and N atoms. The greater stability is a consequence of the electron counting rule, which will be discussed in Section 4.1. Briefly, the excess electron density in the dangling bond on the electropositive Ga atom before electronic relaxation equals the deficiency in density in the dangling bond on the electronegative N atom. Electronic relaxation leads to an autocompensation process that transfers electron density from Ga to N to yield a passivated surface with empty Ga and doubly-occupied N dangling bonds.

3. Preparation of clean surfaces (ex-situ growth / in-situ cleaning) The first issue to consider is the preparation of atomicallyclean, well-ordered and well-characterized surfaces. The first two topics are discussed in this section. Section 4 will deal with the characterization and properties of such surfaces; although, there will necessarily be some overlap between the two sections. In an ideal situation, clean surfaces are grown in situ at the start of each experiment and the properties of interest studied in the same chamber without the need for any surface-cleaning procedure. This can be accomplished, for example, with the use of a so-called "MBE cluster tool". When this is either not feasible or not desirable (as in more-practical and applied studies) the surface-cleaning method and its effects on surface properties become integral parts of the experiment. This is particularly the case when studying reactive metal adsorbates, which require aggressive methods such as IBA for removal. Both types of studies are relevant to a complete understanding of GaN surface phenomena. Clean-surface preparation using in-situ growth requires no further comment here; hence, the following subsections will focus on cleaning after exsitu growth (i.e., growth in a different chamber and transport

V.M. Bermudez / Surface Science Reports ∎ (∎∎∎∎) ∎∎∎–∎∎∎

8

through room air to the analysis chamber). Key issues include contamination (principally C and O), stoichiometry (the Ga/N atomic ratio), the degree of ordering and the surface roughness. As a general comment, one difficulty in comparing surfacecleaning and other results from different laboratories is the uncertainty in temperature measurement. Typically the GaN sample is grown as a thin film on a ∼0.3 mm-thick insulating Al2O3 wafer that is then pressed against a heated mounting stage in UHV, and the reported temperature is that of the stage measured using a thermocouple. Due to finite thermal contact, this temperature may be 100 °C or more above that of the GaN itself at high temperature (∼700 °C and above). In such cases the error in temperature measurement can be estimated by replacing the sample with a thin Si wafer and using an IR pyrometer to compare the sample reading with that of the mounting stage. Most experimental studies do not discuss the details of temperature measurement. 3.1. Ex-situ wet-chemical pre-treatment This section reviews surface cleaning of GaN using chemical reagents beyond simple organic solvents. Almost without exception, cleaning begins with immersion in a series of solvents, often warmed and in an ultrasonic bath, which is sometimes referred to

as "degreasing". Typically this series, which is commonly used in the semiconductor industry to remove polar and non-polar organic species, consists of TCE, acetone and methanol in the order given. This section deals with the next step, in which more-aggressive reagents are used to reduce further the level of contamination. There have been many studies [60–106] of different wet-chemical cleaning procedures for GaN, some of which have been reviewed by Eller et al. [5] and by Long and McIntyre [107], and a summary is given in Table 3. The publication dates of the most recent papers show that this is still an active area of research. In the vast majority of these studies, the sample is assessed for contamination after cleaning using AES or XPS, and a truly atomically-clean surface is never observed unless additional in-situ processing is performed. It is not clear whether this results from a deficiency in the chemical process or from recontamination of the clean surface caused by exposure to room air. In principle this could be circumvented by carrying out the cleaning in a controlled-atmosphere environment attached to the UHV chamber such that air exposure is avoided. To our knowledge, this has not been done in AES or XPS experiments on GaN. Many other such studies focus on optimizing the surface preparation prior to depositing metal contacts, and the results are evaluated largely on

Table 3 Summary of wet-chemical cleaning methods for GaN, arranged in approximately chronological order. Only the first author is named, and an italicized name indicates that the work is discussed further in Section 3.1. Due to space limitations, "Method" describes only the nominal best wet-chemical procedure reported in the study. "Analysis" refers to the technique(s) used to assess the surface condition after cleaning. In some cases electrical measurements were also used to evaluate metal contact properties. "ALD", "BOE", "IPA", "MeOH" and "soln." refer to "atomic layer deposition", "buffered oxide etchant", "isopropanol", "methanol" and "solution" (typically in H2O). A mixture of H2SO4 and H2O2 is commonly referred to as a "piranha solution" and a mixture of HNO3 and HCl as aqua regia. Piranha solutions are exceedingly dangerous to use, and appropriate safety precautions should be observed. In many cases, wet-chemical cleaning is followed by additional in-situ cleaning in UHV, but the present tabulation deals only with the wet-chemical step. In almost all cases, the cleaning is preceded by "degreasing" in organic solvents as described in Section 3.1. Author [Ref.]

Method

Analysis

Comments

Edwards [61] Smith [62] Ishikawa [63] King [60,64] Kim [65,67] Lee [68,73] Koyama [70] Kim [71,80] Waki [72] Lee [74,75] Sun [76] Kim [78] Lee [66,77] Kim [69,79] Chung [81] Shalish [82] Rickert [84] Tripathy [85] Zhou [86] Jang [87] Machuca [83] Liu [88] Kim [89] Tereshchenko [90] Tang [91] Selvanathan [92] Diale [93] Uhlrich [94] Hattori [95] Shah [96] Nepal [97] Al Alam [98] Kalaitzakis [99] Tsuji [100] English [101] Yang [102] Kerr [103] Mishra [104,105] Hossain [106]

MeOH þ NH4OH þ NaOH HF or HCl soln. buffered HF soln. UV/O3 þ HF or HCl soln. boiling aqua regia

SE AES XPS AES, XPS, TPD XPS

warm NH4OH soln. boiling aqua regia HCl soln.; H2SO4 þ H2O2 UV/O3 þ HCl soln. KOH soln. boiling aqua regia aqua regia þ (NH4)2S soln.

XPS XPS XPS AES XPS XPS XPS

in-situ analysis HF better for C desorption rapid C, O uptake in air halogens remain before anneal better than HCl for C, O; small increase in roughness good oxide removal surface termination changes improved by UHV anneal UV/O3 for C; HCl for O lower p-type BB than HCl lower BB and O than HCl S residue impedes oxidation in air

KOH soln. HCl soln. HCl for n-; KOH for p-GaN HCl soln. or KOH soln. HF or HCl soln. BOE þ HCl H2SO4 þ H2O2

XPS PL,SPV,AES,XPS XPS XPS,AFM XPS, STM XPS UPS, XPS

better for O than C; slight roughening effective for removing O but not C vacancies cause lower BB little cleaning; increased roughness HF removes more O but causes pits effective for removing O on p-GaN removes O; UHV anneal to remove C

boiling aqua regia HCl soln. in IPA HCl soln. in ethanol BOE aqua regia þ (NH4)2S soln. HCl soln. HF soln. molten KOH at 215 °C H2SO4 þ H2O2 UV/O3 þ BOE boiling aqua regia H2SO4 þ H2O2/HF/(NH4)2S H2SO4 þ H2O2 NH4OH soln. HCl /NH4OH /(NH4)2S HCl soln. H2SO4 þ H2O2

XPS XPS, ELS XPS XPS AES, AFM XPS, UPS XPS, LEED, STM XPS AFM, XPS XPS XPS XPS AFM, XPS XPS, UPS XPS XPS, UPS AFM

low p-type BB; good contacts 450 °C UHV anneal for further clean data look same as for KOH good for O; maybe not for C smooth surface; S blocks oxidation adsorbed Cl impedes oxidation in air UHV anneal for (2x2) reconstruct. removes oxide good preparation for ALD of Al2O3 rougher p- vs. n-GaN differs for MBE vs. CVD GaN C, O and S remain good C, O removal; low roughness O reduced; Ga- and N-faces studied C, O reduced; no S; mild anneal helps nearly clean after 750 °C UHV anneal relatively smooth with low C, O

V.M. Bermudez / Surface Science Reports ∎ (∎∎∎∎) ∎∎∎–∎∎∎

the basis of electrical characteristics such as contact resistance. Here we will include only those studies for which some form of surface analysis was performed (using, e.g., AES, XPS or AFM) in order to assess surface quality while omitting those involving only electrical measurements. Likewise, the many works dealing with wet-chemical or photochemical etching, polishing or "planarization" of GaN, as distinct from just surface cleaning, are also excluded. These issues are relevant to the preparation of bulk singlecrystal surfaces but less so in the case of thin-film samples grown by MBE or MOCVD, which have been used in the vast majority of fundamental GaN surface experiments. Also excluded from the present discussion are various forms of ex-situ "dry" processing involving plasma treatments. These do not preclude the need for additional in-situ surface cleaning and are unnecessarily complicated and aggressive for the goal of simply reducing the contamination level on the as-received surface to a level sufficiently low for successful in-situ cleaning. For the purpose of the present review, the interest is in wetchemical procedures that minimize surface contamination without also adversely affecting surface morphology and stoichiometry. For the work of interest here, this will always be followed by an in-situ surface cleaning in UHV; hence, the requirements for the wetchemical cleaning are not as stringent as they might be otherwise. The purpose of the ex-situ pre-treatment is simply to reduce gross contamination to a level where the remainder can be removed fairly easily by in-situ cleaning. In some of the studies discussed here, ex-situ wet-chemical cleaning is followed by in-situ annealing in UHV as the primary cleaning method. Other studies using annealing without ex-situ cleaning, other than "degreasing", will be mentioned in Section 3.3.2. At this point a brief comment on the subject of XPS quantification is needed. Many studies of GaN cleaning report C and O coverages as an atomic percentage or an atomic concentration ratio relative to Ga. This is found using a formalism that applies when the analyte is uniformly distributed throughout the XPS sampling depth, dXPS. This is given, for example, by dXPS ≈ 2λEAL ≈ 5 nm for the Al Kα-excited Ga 3d where λEAL is the effective electron attenuation length and the collected photoelectrons exit along the surface normal. The expression used for an analyte X in this case takes the form NX/NGa = (IXSGa)/(IGaSX) where N, I and S are the atomic concentration, XPS peak area and sensitivity factor respectively. If X is instead concentrated at the immediate surface as an adsorbate (e.g., as a residual impurity after cleaning) then it is more meaningful to quantify the coverage either as a fraction of an ML, if θX o 1 ML, or as a layer thickness in the case of heavier contamination. The standard procedure for accomplishing this is described in many papers (for example, in Ref. [108] (Supplementary Material) in the context of O adsorbed on GaSb (100)) and can be carried over easily to the case of C or O on GaN. As an example of the effect of a more-accurate procedure on quantification, NO/NGa = 0.02 is obtained in the homogeneousmixture model for I(O 1s)/I(Ga 3d) = 0.0426 using the S values given by Wagner et al. [109], which are appropriate to a cylindrical-mirror analyzer in the retard mode. The experimental conditions here are assumed to involve Al Kα excitation, photoelectron collection along the surface normal and the standard angle of 54.7° between the x-ray and photoelectron paths. This value of I(O 1s)/I(Ga 3d) then gives θO ≈ 0.15 ML when the O is modeled as an adsorbate, where 1 ML means 1 O per surface lattice site. While NO/NGa = 0.02 might be perceived as indicating an almost-perfect surface, this is less so for θO = 0.15 ML. Similarly, for C, NC/NGa = 0.02 in the homogeneous-mixture model gives θC ≈ 0.17 ML. In evaluating coverages the photoionization cross-sections for each element given by Scofield [110] are used. Similar considerations apply in the case of surface analysis using AES, and further details on XPS and AES quantification are provided by Seah [111].

9

As a final introductory comment, most of the wet-chemical studies either fail to specify the surface under study or else focus on the (0001), while only a few include the (0001̄ ) and none, to our knowledge, address other surfaces. It cannot be assumed a priori that the same method is suitable for all surfaces. However, studies that include both polar surfaces [101,102] find that the wet-chemical treatments under investigation do, in fact, work equally well for both. One study is particularly noteworthy in that surface contamination was monitored while maintaining the sample in an N2 atmosphere, which constitutes an approach to in-situ analysis of wet-chemical cleaning. Edwards et al. [61] used SE to observe the complex pseudo-dielectric constant, oε 4 = oε1 4 + io ε2 4, of GaN at intervals during cleaning. Here one records the ellipsometric angles ψ and Δ vs. photon energy in the 1.5 to 6 eV range for a substrate covered by a thin film and from these computes a dielectric constant using the Fresnel relations for polarized reflection from the bare substrate, neglecting the presence of the film. The quantity thus determined is referred to as a "pseudodielectric constant". For the case of a very thin transparent film on an absorbing substrate, the real component oε1 4 will always be less than ε1, the real component of the true dielectric constant of the bare substrate, and conversely for the imaginary component, oε2 4. This applies specifically in a situation where |εs| 4 4 |εo| 4 4 |εa|, where εx refers respectively to the real (not pseudo) complex dielectric constant of the substrate (GaN), the overlayer film and the ambient (air). The thin film can take the form of a contamination layer or one with a density less than that of the bulk material as a result of roughness. Hence, the best treatment is one that simultaneously maximizes oε1 4 and minimizes oε2 4; although, chemical identification of the species involved can be problematic. On this basis it was found that the best process involves the following sequence: methanol (MeOH), H2O rinse, 1:1 NH4OH:H2O, H2O rinse, 1:1 (by weight) NaOH:H2O, H2O rinse, 0.01% (by volume) Br2:MeOH, MeOH rinse. The last step, using Br2:MeOH, can be omitted since it appears to have little or no effect. The use of optical techniques for the in-situ (or almost so) study of wet-chemical cleaning of GaN, first demonstrated by Edwards et al. [61], is potentially valuable in the systematic investigation of such processes. Another method, which is perhaps easier to instrument than SE, is PL, the application of which to GaN surface diagnostics has been discussed in a UHV study by Hattori et al. [112]. This has been shown to be sensitive to the presence of surface oxide and also to BB (Section 4.7.3), which is an indicator of electrically-active surface defects. When using laser excitation in PL, some care must be exercised to test for and avoid possible photochemical effects particularly for above-Eg photon energies in a wet-chemical medium. It should also be possible to apply PL in a so-called "cook-and-look" approach, as was done by Edwards et al. for SE, in which processing is periodically interrupted, the cell purged of reagent with dry N2 and data recorded. Contactless electroreflectance [113] is yet another technique based on optical spectroscopy that has been shown to be useful in evaluating GaN surface quality after processing, in this case after polishing of bulk crystals. Other groups have either reported very detailed comparisons among several different wet-chemical cleaning procedures or else have found that clean (or nearly so) surfaces can be obtained simply by annealing in UHV following ex-situ wet-chemical treatment. These will be briefly summarized here. King et al. [60,64] used UV/O3 treatment to reduce C contamination. This typically involves exposing the sample to O2 in the presence of near-UV radiation from a Hg arc source, which generates highly-reactive O3 (ozone). The surface is converted to a mixture of GaOx and Ga(OH)x with some residual C, and the oxide

10

V.M. Bermudez / Surface Science Reports ∎ (∎∎∎∎) ∎∎∎–∎∎∎

can be removed in an aqueous solution of either HCl or HF. Both give the lowest C and O coverages compared to other methods of oxide removal, with HF being better than HCl for C elimination. Furthermore, HCl leaves a Cl residue, which may actually be beneficial in that it impedes re-oxidation during subsequent air exposure; whereas, HF leaves no F that is detectable in XPS. Samples thus cleaned show a (1×1) LEED pattern (from the bulk substrate) after removal of the amorphous oxide layer, and AFM indicates no significant increase in surface roughness relative to the as-received material. Other methods of oxide removal following UV/O3 treatment are less effective and/or leave some form of unwanted residue. Complete removal of C and O by annealing in UHV cannot be achieved at temperatures below which (∼800 °C) decomposition of the GaN begins, which is indicated by the appearance of Ga in mass spectrometry. However, changes in the C 1s and O 1s XPS with annealing indicate that C–O and Ga–OH bonds are eliminated at much lower temperatures, in the range of 400–600 °C. The authors also present an extensive discussion of the nature of the oxides formed during exposure to air or to UV/O3. It is suggested that HF treatment facilitates thermal desorption of C via the formation of more C–O species than is the case for oxide removal in HCl. Lee et al. [74,75] also employed UV/O3 exposure followed by immersion in aqueous HF or HCl solutions and obtained results qualitatively similar to those of King et al. [60,64]. The C coverage could be completely eliminated by UV/O3, and removal of the oxide in acid solution left small O and Cl residues with no significant increase in surface roughness relative to the as-received material. Shalish et al. [82] used SPV and PL together with AES and XPS to characterize the state of GaN (0001) after oxide removal in HCl solution. The XPS data show little or no change in C coverage, which consists mainly of hydrocarbons with additional satellite features due to C–O and C–Cl bonding. There is a large decrease in O coverage resulting from the complete elimination of Ga–O bonds and a small decrease in that of C–O species. The SPV data, which are obtained in a dry-N2 ambient but after exposure of the HCltreated surface to room air, show a decrease in the concentration of defects that are localized either in the oxide or at the oxide/GaN interface. Machuca et al. [83] and Liu et al. [88] reported a nearly-complete removal of C and O using 4:1 H2SO4:H2O2 (termed a "piranha solution") at 90 °C followed by annealing in UHV at 700 °C, after which XPS indicates C and O coverages of 0.01 and 0.08 ML respectively. (The method used to quantify surface coverage was not described.) The loss of C is attributed to the partial oxidation of hydrocarbons to more-volatile C-O containing species, as noted above [60,64]. Prior to annealing, N-O as well as Ga-O and C-O bonds are detected in XPS. The nearly-clean, annealed surface shows a sharp, low-background (1×1) LEED pattern, and the Ga/N atomic ratio is 1.0, indicating a stoichiometric surface. Piranha solutions are exceedingly dangerous to use, and appropriate safety precautions should be observed. Rickert et al. [84] used XPS, excited by photons of various energies provided by synchrotron radiation, to study the effects of different wet-chemical treatments on surface contamination and BB. Treatment of n-type GaN in aqueous ∼6 M HCl solution led to a 0.9 eV reduction in upward BB, and immersion of p-type GaN in boiling 24 M aqueous KOH solution reduced the downward BB by 0.3 eV. In either case these changes can potentially lead to lower resistance for deposited metal contacts. The BB changes are ascribed to the introduction of defects, e.g., VN donors for n-type and VGa acceptors for p-type material. This is supported by changes in the Ga/N atomic ratio for the two treatments. In the case of HCl, the reduced upward BB coincides with the presence of Cl, the thermal desorption of which is complete at 500 °C and

accompanies a reversal of the 0.9 eV BB shift. These results are helpful in establishing the desorption temperature for adsorbed Cl remaining from wet-chemical cleaning in Cl-containing reagents. Zhou et al. [86] compared the effects of aqueous solutions of HCl, HF and NaOH on surface morphology and contamination. The original MOCVD surfaces, after cleaning in organic solvents, were relatively smooth with visible steps and terraces; although, the surface contamination precluded high-quality AFM imaging. After treatment in a 1:1 HCl:H2O solution at 70 °C, a low density of pits (6.3x108 cm-2) was seen at step edges, but the surface remained relatively smooth (0.5 nm RMS roughness). On the other hand, 2:1 HF:H2O and 2 M NaOH solutions at RT caused an increase in pitting and other features that suggested an etching effect. Solutions of HF and HCl were more effective in removing O but increased the level of C, while NaOH solutions were better able to remove C but had little effect on O. All cleaning solutions resulted in a sharp (1×1) LEED pattern, which one assumes is a result of diffraction from the bulk. Tereshchenko et al. [90] described a cleaning procedure consisting of immersion in a solution of HCl in isopropanol followed by annealing in UHV at 400–450 °C. The residual C and O contaminations seen in XPS are at a level of 0.03–0.05 ML, and a sharp, low-background (1×1) LEED pattern is observed. The relative ease in reducing the C coverage via UHV annealing, in contrast to the situation following immersion in aqueous HCl solution [60,64], is attributed to some effect of the isopropanol solvent. In light of previous work, this might possibly be the formation of a lower density of hydrocarbons vs. more-volatile C-O containing species. Diale et al. [93] used AES and AFM to study the effects of several wet-chemical procedures, in conjunction with UHV annealing, on the contamination level and surface roughness. Aqua regia (3:1 HCl:HNO3) gives the smoothest surface of all the cleaning methods studied. Subsequent immersion in an aqueous solution of (NH4)2S (sometimes described as (NH4)2Sx) increases the roughness somewhat, but the adsorbed S then impedes the uptake of C and O contamination during exposure to room air. After treatment in aqua regia but before sulfide treatment the Ga/N atomic ratio is well above unity; whereas, after (NH4)2S it is close to stoichiometric. Hattori et al. [95] used LEED, AFM and XPS to evaluate a cleaning method consisting of immersion in HF solution (0.5% by weight in H2O, 100 s at 18 °C) followed by annealing in UHV in stages up to a final temperature of 550 °C. The HF treatment was found to be more effective than immersion in solutions of HCl, HNO3 or NaOH, and the wet cleaning was performed under a fluorescent light, which might have introduced a photoassisted effect. After HF treatment of samples grown by hydride vaporphase epitaxy, the C and O concentrations were about 9 and 3 at% respectively, assuming a uniform distribution of impurities within the XPS sampling depth, and were reduced to about 20% of these values after annealing. The HF-treated surface appeared to be slightly N-rich both before and after annealing. The roughness of the final surface was found to be less than that of the as-received sample, and the LEED pattern after annealing was a low-background (2x2) with sharp spots. To our knowledge this is the only instance of a reconstructed GaN (0001) surface having been reported after simple wet-chemical cleaning and annealing. The appearance of a (2x2) LEED pattern is thought to result from adsorbed N (with θN = 0.25 ML, Section 4.6.1), and it was also noted that smoother surfaces tended to give higher intensity in the integral-order LEED spots, which indicates better ordering. A detailed discussion was given of the composition of the Ga-H2O system vs. pH as it relates to the solubility of GaOx, which provides insight into oxide removal by acidic and basic solutions. English et al. [101] used XPS and AFM to evaluate a wide variety of wet-chemical treatments for both (0001) and (0001̄ ) surfaces.

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For either surface the best, both in terms of residual contamination and roughness, was determined to be a piranha solution (5:1 H2SO4:H2O2) at 80 °C. Furthermore, the O 1s and Ga 2p3/2 XPS data show that a large fraction of the O is bound to C and not Ga, which should make it relatively easy to remove by thermal desorption in UHV; although, this was not specifically investigated. Kerr et al. [103] used a process consisting of first "degreasing" in organic solvents followed by immersion in 6% HCl and 7% NH4OH aqueous solutions and finally in 5% (NH4)2S aqueous solution. Relative to just degreasing, this reduced the C and O coverages by factors of 3.3 and 5 respectively as seen using XPS. A subsequent UHV anneal at 200 °C had no significant effect on C but reduced the O coverage by an additional factor of 2. The final carbon coverage was ∼0.5 ML while that of O was near the detection limit. Significantly, S remaining from the (NH4)2S treatment was found to protect the surface from further contamination during exposure to ambient air and also to desorb at RT in UHV leaving no S residue detectable in XPS. This contrasts with the case of GaAs after similar treatment, which shows a stable surface sulfide. Mishra et al. [104,105] used XPS and UPS to study a cleaning procedure involving immersion in aqueous HCl solution followed by outgassing and annealing in UHV in stages over a range of 650– 750 °C. After cleaning, the C 1s XPS peak was below the detection limit, and the Ga/N atomic ratio was 1.0. Some O remained, at a concentration estimated to be ∼4 at% using a formalism that applies to O uniformly distributed throughout the XPS sampling depth. However, the electron affinity (χ) measured in UPS after cleaning (3.9 eV) is higher than the typical value (χ ≈ 3.3 eV, Section 5.10) for atomically-clean (0001) surfaces, which could represent the effect of a dipole layer (negatively-charged side outward) formed by adsorbed O. This suggests that the residual O was localized at the surface rather than being uniformly distributed. A further discussion of χ is given in Section 5.10, which deals with NEA and the adsorption of Cs. In summary, a few general conclusions can be drawn from the work summarized in Table 3; although, claims about the efficacy of various methods are somewhat conflicting. None of these treatments have been shown to yield, on their own, an atomicallyclean surface. Processes involving HF, HCl or sulfur-containing reagents tend to leave (in addition to C and O) a residue of halogen or sulfur, which may be beneficial in that these species can impede the regeneration of oxide when the treated surface is exposed to air. In cases where AES is used for surface analysis, F might not be easily observable due to the rapid ESD of F under typical AES conditions [114]. The presence of halogens or sulfur is not a problem if they can be easily removed by subsequent in-situ cleaning. It appears that O is more easily removed by wet-chemical treatments, particularly in HCl or KOH solutions, than is C and that C is more susceptible to thermal desorption during UHV anneals if it is bonded to O. Some wet-chemical treatments appear to give a nearly-clean surface after a subsequent low-temperature UHV anneal. Surface roughness, in addition to contamination, is also a consideration. Based on the above discussion, a reasonable approach would appear to be "degreasing" in a series of organic solvents, as described at the start of this section, followed by immersion in either aqua regia or a piranha solution. Of the two, aqua regia is less dangerous for routine laboratory use; however, there is a report [71,80] of the (0001) surface termination being changed by aqua regia. This suggested recipe is based on a few reports of surfaces that are both smooth and fairly clean; although, no one procedure stands out as being clearly superior to all others. Of course, with a sufficiently-effective in-situ cleaning method it may be feasible to omit wet-chemical cleaning (other than "degreasing"). However, the reported smoothing effect of aqua regia and

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piranha solutions, which is thought to result from the etching of surface protrusions, could still be beneficial. 3.2. In-situ chemical cleaning In-situ chemical cleaning generally encompasses two methods, which will be discussed in the following two subsections. The first consists of either depositing a thick layer of Ga metal followed by thermal desorption or else heating in a flux of Ga vapor. The latter is sometimes termed "Ga flux-annealing". The second involves annealing in a low-pressure ambient of NH3 vapor. These are useful when removing adventitious C and O from a GaN surface that has been exposed to room air, but they are usually not sufficient for restoring a surface on which a reactive metal has been deposited. In that case a more-aggressive process (namely IBA) is needed, and this will be reviewed in Section 3.3. The studies to be discussed in Sections 3.2–3.4 are those that focus mainly or entirely on the cleaning process itself and on its effects on surface quality, e.g., LEED pattern, stoichiometry, roughness, etc. In many of the publications dealing with adsorption and/or interface formation, which are described in later sections, useful comments are given under the heading of "experimental details" that relate to the efficacy of different cleaning procedures. The information contained in these studies is not included here but is mentioned later, at the point where these results are described. The interested reader is encouraged at least to skim the later sections on adsorption of elements and molecules for further insight into surface preparation methods. 3.2.1. Ga deposition and desorption This technique (henceforth abbreviated as "Ga-cleaning") was originally developed for the low-temperature cleaning of vicinal Si surfaces [115]. These are unstable and cannot be subjected to the procedure normally used to clean Si (100) and (111) (flashing to ∼1250 °C in UHV, Ref. [116]) without incurring faceting. It is important to note here that Ga-cleaning will not easily eliminate a thick oxide or carbon layer from GaN, which must first be removed to the extent possible by one of the ex-situ wet-chemical methods described in Section 3.1. To our knowledge, there has never been a detailed experimental study of the actual mechanism involved in the Ga-cleaning of GaN; although, Foxon et al. [117] have observed this effect under MBE conditions. It has been suggested [117,118] that Ga reacts with chemisorbed O to make volatile GaOx and somehow also displaces elemental C from the surface, which is then removed along with the Ga being desorbed. Gallium is not known to form a stable carbide under "normal" conditions of temperature and pressure. There is also the possibility that exposure to Ga at elevated temperature might reduce a thin Ga oxide layer to a more-volatile suboxide as suggested in recent work [119] on Ga-cleaning applied to the GaSb (100) surface. Furthermore, a theoretical study [120,121] of Ga-cleaning of α-Al2O3 (0001) has been performed. The adsorbate being removed was H, but the results might also apply to other species and substrates. Briefly, Ga is seen to weaken the bonding of chemisorbed H and also to bond directly to less-strongly-adsorbed H. The Ga-cleaning approach has been discussed in Refs. [122– 133] as it applies to GaN. Again, only works specifically focused on this method and the resulting surface quality are mentioned here. Other studies, which employ Ga-cleaning as part of a larger investigation, will be described in Sections 4–8 as appropriate. The treatment conditions (e.g., the sample temperature during exposure to and/or desorption of Ga and the processing of the sample before Ga-cleaning) vary among different studies. However, the general result is that C and O coverages are significantly reduced, sometimes to near or below the AES and XPS detection limits, and that a sharp, low-background (1×1) LEED pattern

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appears. In some cases the LEED pattern shows evidence of faceting (Section 3.3.1). One study [131] has applied this technique to the (112̄ 0) surface; whereas, the others have been confined to the (0001) or to surfaces of undetermined polarity. The work of Schulz et al. [131] on the (112̄ 0) surface also noted a significant reduction in roughness after Ga-cleaning as well as a clear (1×1) LEED pattern. Widstrand et al. [127–129] reported an extensive study of insitu chemical cleaning methods for GaN (0001) including Gacleaning. The sample was first outgassed by annealing in UHV at 500–550 °C, followed by further annealing at 800 °C in UHV [128] or in NH3 vapor [127,129]. These steps led to a moderate decrease in surface contamination and improvement in the (1×1) LEED pattern. The next step involved Ga deposition at RT followed by annealing either in UHV [127,129] or in NH3 [128]. The Ga depositions at this stage were in the range of 1.3 to 1.7 ML (where 1 ML = 1.135x1015 Ga cm-2), and significant amounts of residual C and O remained following the UHV anneal. An impurity analysis was not provided in the case of the NH3 anneal, but a reasonably good (1×1) LEED pattern was obtained. In some cases [127,129] a final step was performed in which the sample was heated in a flux of Ga, with a total exposure of ∼3.4 ML, followed by further heating in NH3. Smaller but still-significant (∼0.1 ML) coverages of C and O remained, and XPS indicated a complex chemical mixture of residual C- and O-containing species [129]. In the work of Widstrand et al., Ga-cleaning by itself was found not to be very effective. However, it appears that the process consisted of at most only a few deposit/anneal cycles with a thin Ga layer. For a surface properly prepared ex situ, repeated cycles and thicker Ga layers (thick enough to appear metallic to the unaided eye) result in a more-thorough cleaning (Ref. [123] and works cited). One might speculate that the value of a thick layer is that, due to the finite evaporation rate, there is still metallic Ga on the surface when the sample has reached an elevated temperature, which should accelerate whatever reactions occur during cleaning. On the other hand, for a very thin layer, most of the Ga may evaporate before a temperature sufficiently high for cleaning has been reached. In support of this suggestion, one study [122], in which a sample at 620 °C was exposed to a Ga flux, showed (in AES) a stoichiometric surface with no detectable O and only a slight amount of C with a sharp, low-background (1×1) LEED pattern. Schulz et al. [130] investigated Ga-cleaning of the (0001) surface of MOVPE material using XPS. The sample was stored under dry N2 immediately after growth, and no ex-situ cleaning was performed. Outgassing for 14 h in UHV at 650 °C removed a suboxide feature from the O 1s XPS leaving only a peak assigned to Ga2O3. Subsequent outgassing for 62 h at 700 °C had no significant effect on the O 1s but eliminated the C 1s peak entirely. The sample was then subjected to two cycles of deposition of a few ML of Ga at RT followed by annealing at 650 °C, which reduced the O content to one-third of what it was after outgassing. A subsequent Ga deposition at 650 °C followed by desorption at 650 °C had only a slight additional effect on θO. In later work Schulz et al. [131] also studied Ga-cleaning of the (112̄ 0) surface, using methods similar to those described above, for a sample grown by MOVPE on r-plane sapphire. Outgassing in UHV for 14 h at 750 °C reduced the O content by a factor of ∼2 relative to the as-inserted sample and the C content by a factor of ∼4. Several different chemical species or functional groups were identified in the C 1s and O 1s spectra including OH, Ga suboxide, C=O, C-O and possibly C incorporated into the surface. One cycle of deposition of a few ML of Ga at RT followed by annealing at 750 °C reduced the C and O levels by another factor of almost 2, but subsequent cycles resulted in little additional cleaning. Falta et al. [132] first annealed a GaN (0001) sample in UHV at

650–750 °C, which resulted in a significant reduction in the level of C and O contamination, and then performed three cycles consisting of deposition of ∼1 ML of Ga followed by desorption at 650 °C. The first cycle lead to a significant further reduction in C and O with additional small decreases after each succeeding cycle. After the last step, a sharp (1×1) LEED pattern with no evidence of faceting was seen, but C and O were still detectable in XPS. Storm et al. [133] studied the effect of Ga-cleaning, in conjunction with other methods, on the (0001) surface of freestanding wafers grown by hydride VPE with an interest in optimizing the procedure for preparing substrates for MBE homoepitaxy. The samples were characterized before MBE growth using RHEED and after via AFM, TEM and SIMS. It was found, using SIMS, that C and O at the interface could be minimized by a procedure consisting of ex-situ treatment in acid and in base followed by insitu outgassing at 600 °C and then two cycles of Ga deposition at 750 °C (with 45 ML of Ga per cycle) followed by desorption at 920 °C. However, RHEED indicated significant roughening when the clean sample was maintained at the MBE growth temperature of 860 °C. The authors note that temperature measurements were obtained using a thermocouple mounted behind the sample but not in direct contact with it. It is speculated here that the actual sample temperatures might have been significantly higher than the stated values, which could contribute to decomposition and roughening. The authors also note, with reference to earlier work in the same series of studies, that roughening appears to be much less pronounced for (0001̄ ) surfaces following a similar cleaning procedure. There is a reason why annealing in a Ga flux might be preferable to depositing a thick Ga layer at RT and then desorbing at elevated temperature. L'vov [134] found, in agreement with earlier work cited in Ref. [134], that liquid Ga in contact with GaN catalyzes thermal decomposition. The threshold temperature at which this catalytic process occurs is not known with certainty. For example, the discussion given by L'vov involves temperatures of 1100 K or more. It is also noteworthy that, in the discussion of the Au/GaN interface in Section 5.20, it will be seen that the contact properties are adversely affected when the GaN surface has been cleaned by Ga metal deposition and desorption. It is possible that this may be a consequence of Ga-enhanced surface decomposition prior to in-situ Au deposition. An issue that arises in Ga-cleaning is the removal of any and all excess Ga. This also applies to IBA (Section 3.3), which generally produces excess Ga due to preferential removal of N. This in turn raises the question of what is meant by "excess Ga". As will be seen in Sections 4.6.1 and 4.6.2, which address the structure and stoichiometry of the (0001) and (0001̄ ) surfaces, a Ga adatom coverage of 0.25 ML leads to a stable semiconducting surface; whereas, an ideally-terminated surface with no "excess Ga" is metallic as a result of the presence of partially-filled DBs on surface atoms. Such Ga adatoms are distinct from bulk metallic Ga as seen in, e.g., the Ga 3d XPS. In principle, excess Ga adatoms (beyond 0.25 ML) and metallic Ga can be desorbed at a sufficientlyhigh temperature, but precise end-point detection is difficult, which means that VGa and/or VN defects are difficult to avoid. It will be seen, for example, that removing 0.25 ML of Ga from the ideally-terminated (0001) also gives a stable semiconducting surface. The standard approach to the removal of excess Ga is to anneal until the intensity of the low-BE Ga 3d satellite in XPS (BE = 18.7 eV), which is associated with metallic Ga, has been minimized. This is not entirely straightforward since other factors contribute intensity near this peak (Section 4.7). A novel method has been demonstrated by Agnarsson et al. [135], which involves the in-situ deposition of In metal. Subsequent desorption of the resulting In-Ga alloy, which can be done at 550 °C, then removes

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free Ga. This was demonstrated for a surface bombarded with 0.5 keV Ar+ ions but should work equally well after Ga-cleaning. Presumably the last 0.25 ML of Ga, which is strongly adsorbed, remains; although, this was not investigated in detail. The use of more-energetic (1 keV) Ar+ is more damaging, and in this case reaction occurs to form InN, which is then difficult to remove. It was also noted that, although C was eliminated, a finite amount of O of undetermined origin was always present on the cleaned surfaces. In closing this section it is noted that Section 5.18 discusses certain aspects of the adsorption of Ga on GaN. There it will be seen that, at a given temperature, there are ranges of increasing Ga flux within which a single layer of Ga, a bilayer or a bilayer plus droplets are stable on the surface. It is possible that a careful consideration of such effects might help to optimize cleaning via annealing in a Ga flux. 3.2.2. Annealing in NH3 vapor Cleaning GaN surfaces by annealing in a flux of NH3 vapor offers distinct advantages, as well as disadvantages, in comparison to other methods. The reaction 4NH3 + 3C → 3CH4 + 2N2 is very exothermic, which results in the rapid removal of C at low temperature. Also, at a sufficiently high NH3 flux, the more-rapid loss of N than Ga during annealing above ∼760 °C (Section 4.5) can be compensated, which can result in better surface ordering and stoichiometry. On the other hand the reaction 2NH3 + 3Oads → 3H2O + N2 is less rapid, which means that a higher temperature and NH3 pressure are needed for removal of adsorbed O vs. C. Also, NH3 adsorbs strongly on the internal surfaces of a typical UHV chamber (including on GaN itself), and recovering a sufficientlyclean vacuum is therefore difficult after a large NH3 exposure. This issue will be discussed further in Section 7.1, which addresses NH3 adsorption. As a result, the use of this method in actual practice may require an isolable side-chamber with independent pumping and an in-situ sample transfer capability. In-situ cleaning of GaN by annealing in NH3 vapor has been described in Refs. [60,64,83,123,127–129,136–141]. In other studies, Uhlrich et al. [94] investigated ex-situ NH3 cleaning in a tube furnace and analyzed the thermochemistry of this process theoretically, and their results provide insight into the difficulty in removing all O vs. all C by this means. Reitmeier et al. [142] reported the use of NH3 to clean GaN templates in an MOCVD environment prior to homoepitaxial growth. As before, this section will review only those studies that focus specifically on NH3 vapor-cleaning and the quality of the resulting surface. Other work, where this technique is used to prepare surfaces for further experimentation, will be discussed in Sections 4–8 as appropriate. The subject of GaN thermal decomposition will be examined in Section 4.5; however, it is worth noting in the present context that Grandjean et al. [143] found that an NH3 flux inhibits GaN decomposition at ≥825 °C. For example, 5x1016 NH3 cm-2 s-1 (equivalent to an ambient pressure of ∼1×10-4 Torr [144]) reduces the rate by a factor of ∼100 at 825 °C and 30 at 875 °C. To our knowledge, King et al. [60,64] were the first to report a successful application of this technique. Annealing in 5×10-6 Torr of NH3 for 25 min at 800 °C (following ex situ UV/O3 cleaning) gave a surface with 0.1 ML of O and no detectable C. The removal of C was complete at only 600 °C, and apparently no wet-chemical treatment was performed to remove the UV/O3 oxide, which might have then given a more-complete removal of O during NH3 exposure. The resulting LEED pattern was (2x2), which indicates a reconstructed (and therefore well-ordered) surface. Similar results, obtained under similar conditions, were reported by Bermudez et al. [123] for samples with no ex-situ cleaning, except that the LEED pattern was a (1×1) with sharp spots but a high background due, presumably, to the residual O contamination.

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Machuca et al. [83], on the other hand, found that a sample that had been treated ex situ in "piranha solution" (Section 3.1) was more effectively freed of O by annealing in UHV than in 2×10-6 Torr of NH3. A possible complication is the purity of the NH3, which can contain H2O as a contaminant either in the supply or by displacement from internal surfaces. In the author's own work [123], for example, ultra-high purity NH3 was transferred under vacuum on a so-called "Schlenk line" into a stainless-steel cylinder containing Na metal as a drying agent. This then served as the NH3 supply for surface cleaning. Uhlrich et al. [94], in a somewhat different approach, annealed GaN (after wet-chemical cleaning in aqueous HCl) in NH3 using a tube furnace rather than in situ in a UHV chamber. Subsequent XPS analysis showed that all C had been removed; although, O was still detected. This confirms the easy removal of C by reaction with NH3 and shows that a C-free surface does not necessarily reacquire strongly-adsorbed carbonaceous species during a brief exposure to room air. As described in the previous section, Widstrand et al. [127–129] combined Ga-cleaning with annealing in NH3. Detailed studies of in-situ NH3 cleaning were performed by McGinnis et al. [136], Hartlieb et al. [137], Oliver et al. [138,139], Tracy et al. [140] and Grabow et al. [141] and are briefly summarized here. The work of Reitmeier et al. [142] on NH3 cleaning in an MOCVD environment is also very relevant here. McGinnis et al. [136] reduced the C and O levels to about 2 atomic-% (assuming a uniform distribution of contaminants within the XPS sampling depth) by annealing first in UHV and then in NH3. No ex-situ wetchemical cleaning was mentioned (other than immersion in TCE) which potentially might have led to a more-complete cleaning in situ. Decomposition at 800 °C is inhibited by NH3 if the BEP is at least 1.5x10-5 Torr; whereas, below this BEP, surface roughening is seen. In a case such as this, where the NH3 is introduced as a directed molecular beam, the BEP is the ambient pressure at which the random flux (NH3 cm-2 s-1) would equal that arriving in the beam. Hartlieb et al. [137] performed a three-step "degreasing" procedure in organic solvents followed by wet-chemical cleaning in aqueous HCl solution. Heating at 830 °C in 9x10-5 Torr of NH3 removed C to below the XPS detection limit (∼0.3 atomic-%) and reduced the O to about 2 atomic-% (assuming that the impurities are uniformly distributed within the XPS sampling depth). Oliver et al. [138,139] cleaned GaN first in organic solvents and then in situ in 2x10-5 Pa (1.5x10-7 Torr) NH3 at ∼820 °C or lower. With increasing temperature, RHEED and STM show a gradual loss of contaminants, changes in surface morphology (associated with islands and pits and with terraces having both smooth and jagged edges) and a (3×1) reconstruction that transitions to a Ga-rich (2×2) at the highest temperatures. Significant surface roughening is also observed at the highest temperatures, which is consistent with the results of McGinnis et al. regarding the correlation between roughness and the BEP during annealing. This study also demonstrated a novel approach to clean-surface preparation in which a thin GaN layer is grown in situ on a GaN template cleaned in situ by annealing in NH3 vapor. It was shown that sufficient growth for this purpose can be achieved under conditions that are compatible with a conventional UHV surface-science chamber using thermal decomposition of NH3 on the substrate as the Natom source together with Ga from a Knudsen cell. Tracy et al. [140] cleaned n- and p-type GaN (0001) ex situ in a series of organic solvents and then in aqueous HCl, after which the sample was quickly mounted in a UHV preparation chamber where it was annealed at 865 °C in 1×10-4 Torr of NH3. Following this the chamber was evacuated to o2.5x10-8 Torr and the sample transferred in vacuo into the surface-analysis chamber. No C or O was detectable in XPS data for the clean surface, which also indicated a stoichiometric surface. The LEED pattern was a lowbackground (1×1) with sharp spots, and AFM showed a slight

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decrease in surface roughness vs. that seen before NH3 treatment. It is noteworthy that, of all the surface-cleaning studies reviewed thus far, this is the only one that resulted in a sample demonstrated to be free of both C and O down to the XPS detection limit and to show a LEED pattern with no indication of faceting (Section 3.3.1). However, the presence of NH3 adsorbed from the background is likely, as mentioned at the start of this subsection, and has not been excluded. Comparable results (i.e., no detectable C or O and no faceting) have been obtained by methods described in later sections. Reitmeier et al. [142] grew GaN on GaN (0001) templates that had been cleaned first by immersion in 1:1 HCl:H2O at 75 °C and then by heating in the growth chamber to 1020 °C in a flowing mixture of H2 and NH3 at a total pressure of 20 Torr prior to MOCVD. After growth, SIMS profiling showed no accumulation of C or O at the interface, in contrast to the situation when the template had been heated similarly in mixed H2 and N2. Also, AFM showed no significant increase in the surface roughness of the template, which would indicate decomposition, again in contrast to the result for H2+N2. Grabow et al. [141] cleaned samples by "degreasing" in the solvent series TCE, acetone and methanol followed by concentrated HCl and then DI H2O. In-situ cleaning involved heating to 900 °C in 1×10-4 Torr of purified anhydrous NH3 in a turbopumped appendage chamber attached to the surface-analysis chamber. After treatment the sample was cooled to 500 °C before stopping the flow of NH3. The XPS data showed a Ga/N atomic ratio that was close to unity and an almost-complete removal of C but a persistent low level of O impurity. This is consistent with other results, mentioned above, showing that heating in NH3 removes C more easily than O. 3.3. In-situ ion bombardment and annealing and related topics In the case of tenaciously-adsorbed species such as reactive metals, surface cleaning requires the use of IBA, which has been the subject of numerous studies in the context of GaN. In this section we will discuss cleaning by IBA as well as by simple annealing in UHV, since these topics are closely related. However, the latter procedure will not by itself easily remove reactive metals. Any discussion of the annealing of GaN must include the subjects of faceting and thermal decomposition. The former will be considered here, since it relates directly to surface preparation, while the latter, which is more general in nature, will be discussed in Section 4.5. Another topic that is closely related to IBA is that of ion-beam damage. This will also be reviewed here subject to the restriction that only nitrogen and rare-gas ions of ≤5 keV kinetic energy will be considered, since these are most relevant to cleaning by IBA. In the following, since the relative amounts of N+ and N2+ are unknown, reference will be made only to "nitrogen ions". 3.3.1. Faceting Faceting of the GaN (0001) and (0001̄ ) surfaces is a recurring issue when annealing at high temperature, either with or without prior ion bombardment. As noted in the previous two subsections, faceting can also occur during in-situ chemical cleaning at elevated temperature. Faceting has been discussed in several works [145– 148], and the effect appears to be sample dependent. This will be evident when examining experimental results given later in this section and in Secs. 4-8. For nominally-similar annealing conditions, some authors report a sharp (1×1) LEED pattern with either no mention of faceting or else an explicit statement that none was seen, while others observe this effect with varying degrees of severity. It must be kept in mind, when reading the literature, that the intensity of the facet features in LEED depends strongly on Ep

Fig. 5. LEED patterns exhibiting faceting. Each set (a) and (b) shows patterns at Ep ¼ 50 and 70 eV. Upper: (a) (1  1) phase observed immediately after introduction of a fresh (0001̄ ) sample; (b) (1  1) phase with horseshoe facets developing after nitrogen-ion bombardment and subsequent annealing to 1050 K. Lower: Model of a groove formed by opposing facet orientations. The facet surfaces are displayed in bulk truncated geometry with each plane representing one of the two terminations. From Starke et al. [148] (Copyright Wiley-VCH Verlag GmbH & Co. KGaA. Reproduced with permission.).

and can be made to disappear at certain beam energies as shown in, e.g., Ref. [145]. It has also been shown [147,148] that facets may contribute substantially to surface reactivity. Fig. 5 shows an example of LEED patterns from a faceted (0001̄ ) surface together with a model that has been developed [148] to account for these results. The model is based on an analysis of the tilt angle between the local surface normal at the facet and that of the macroscopic surface that is needed to explain the dependence of the facet beams on the incident electron energy. The proposed model involves "grooves" with the indicated semi-polar side walls, but similarly-oriented pyramids or depressions with a triangular or hexagonal shape are also feasible. It was also found that faceting could be avoided by annealing a nitrogen-ion-bombarded surface in a flux of Ga at 850 K rather than in UHV at 1050 K. This results in the (3×3) LEED pattern characteristic of an ordered (0001̄ ) surface with a Ga "adlayer+adatom" reconstruction (Section 4.6.2). Here the Ga flux is acting to promote the repair of ion-beam damage rather than as a cleaning agent. It was also shown using HREELS that the IBA treatment virtually eliminates O–H and C–H vibrations and reduces the FWHM of the intrinsic GaN phonon loss features, from which it is inferred that O and C (and not just H) have been removed. The mechanism is unknown whereby the presence of a Ga flux permits the restoration of order, following ion bombardment of

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the (0001̄ ) surface, at a lower annealing temperature than in UHV. The driving force for facet formation also has not been conclusively identified, and one might speculate that it possibly constitutes a mechanism for relieving stress in the GaN film. This could explain the fact that faceting appears to be sample-dependent since stress might depend on the details of sample growth and processing and on the rate of cooling following in-situ cleaning at elevated temperature. One study [123], in which little faceting was seen, suggested that the lateral uniformity of the sample temperature during annealing is important in avoiding this effect. If true, this could be related to stress due to the mismatch in thermal expansion between GaN and a sapphire substrate. There is also the implication that slow heating and cooling rates in annealing might be beneficial in avoiding faceting. Other observations regarding faceting are very significant. Exposing a faceted (0001̄ ) surface to a sufficiently-large dose of atomic H removes the faceting [147], which suggests an etching effect that smoothes the surface. In Section 7.3, which discusses the interaction of H with GaN surfaces, it will be seen that some studies find H to be more reactive with the (0001̄ ) than with the (0001). Hence, this smoothing effect might not occur as readily on the (0001). Another observation is that annealing an as-received (0001̄ ) surface in UHV at 950 K does not result in faceting [146]; whereas, a similar anneal after bombardment with 1 keV nitrogen ions does give a faceted surface. This suggests that adsorbed C and/ or O might somehow stabilize the surface against this effect. Since faceting is often seen for other cleaning methods (Section 3.2) it is unlikely that it is solely a consequence of ion bombardment itself. Janzen et al. [145] studied faceting on surfaces of unknown polarity (designated "{0001}") for three different in-situ cleaning methods: (a) annealing in a Ga flux and then in UHV; (b) deposition of 10 nm of Ga at RT followed by thermal desorption and (c) IBA (1 keV nitrogen ions). All samples were first cleaned ex situ in HF solution before mounting in UHV, and all three methods resulted in C and O levels that were at or below the AES detection limits. Facet features in the (1×1) LEED patterns were first detectable after annealing at 830 °C and became more pronounced with small increases in temperature. 3.3.2. Annealing only Several studies [130–132,136,146–151] report the effects of cleaning simply by annealing in UHV with no ex-situ treatment other than perhaps "degreasing" in organic solvents. This is generally not sufficient to obtain an atomically-clean surface at temperatures (o900 °C) low enough to avoid rapid decomposition of the GaN; although, contamination levels can sometimes be significantly reduced. In Section 4.5, results will be examined that show ∼800 °C to be the "safe" upper limit on the annealing temperature in UHV to avoid damage to the GaN (0001) surface. As noted in Section 3.2.2, higher temperatures can be used [143] when annealing in a background of NH3. A few authors have reported surfaces that were nearly atomically-clean after ex-situ wet-chemical cleaning with aggressive reagents (e.g., acids) followed by annealing in UHV. These studies were discussed in Section 3.1. A related topic is that of the effect of annealing on surface morphology. This will be discussed in Section 4.3, which deals with surface morphology in general. Schulz et al. [130,131] were able to remove a large fraction of the detectable (via XPS) C and O from GaN (112̄ 0) by annealing in UHV for 14 h at 750 °C. For the (0001), all the C was eliminated after 62 h at 700 °C; although, a significant O coverage remained. Similar results were obtained by Falta et al. [132] for the (0001) surface after an unspecified time at 650–750 °C and by McGinnis et al. [136] for the (0001) after 30 min at 730 °C. Suto et al. [149] used a form of ISS to study the effects of annealing on surface contamination for two types of GaN (0001) samples, one grown by

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liquid-phase epitaxy and the other by MOCVD. The former was etched in an unspecified medium to remove a defective surface layer remaining from growth, after which annealing at 900 °C reduced the O coverage to a level near the detection limit and improved the degree of crystalline order. On the other hand, the MOCVD sample showed a significant amount of O after a 900 °C anneal, which was attributed to O strongly retained at dislocations. Hattori et al. [150] reported extensive studies of cleaning using only annealing. A three-step process was used that consists of outgassing at 200 °C for 12 h and at 400 °C for 1 h, followed by 5 min at 500 °C. This reduced the level of C and O contamination to ∼20% of what it was on the as-inserted surface (for which no exsitu cleaning was described). It was important to maintain good UHV conditions (o 5x10-7 Pa or o4x10-9 Torr) during the highertemperature stages in order to avoid surface roughening, which presumably results from reaction with H2O in the UHV background. For MOCVD material, the resulting LEED pattern was a superposition of (3×3) and a stronger (1×1), which became faceted for annealing temperatures of 600 °C and above. The (3×3), which is typically found only on (0001̄ ) and not on (0001) surfaces, was attributed to the presence of dislocations and/or to defects related to N depletion. Qualitatively-similar results were obtained for hydride VPE material that had been mechanically polished; although, cleaning was less effective, due to a higher level of surface contamination, and only a (1×1) LEED pattern was seen after annealing. This work is important in that it indicates the best procedure for outgassing a new sample prior to in-situ cleaning. 3.3.3. Ion-beam damage Many studies [63,152–175] have addressed the effects on GaN surfaces of low-energy (≤5 keV) rare-gas- or nitrogen-ion beams, which are typically used in IBA. Damage takes the form of ion implantation, disordering, surface roughening, creation of defects and DBs and changes in stoichiometry as a result of preferential sputtering of N. A brief review of this subject in reference to GaN has been given by Finzel et al. [174] who also discuss at length the effect of hyperthermal nitrogen ions (KE o 25 eV) on GaN (0001). It is, however, not clear whether a beam of this low an energy would be effective in surface cleaning. Some early work [153] found that a 0.1–0.5 keV Ar+-ion beam did not roughen a GaN surface, make it amorphous or lead to preferential sputtering. However, other experimental studies of Ar+-ion bombardment [152,155,156,159,172–175] have found that preferential sputtering of N occurs at all beam energies down to ~300 eV; although, the effect is less pronounced at lower energies and at a high angle of incidence relative to the surface normal. The greater damage caused by 1 keV vs. 0.5 keV Ar+ was already noted in Ref. [135] (Section 3.2.1). Several MD simulations of Ar+-ion bombardment of GaN have been performed [154,158,166,169–171] using force-field models, and these are generally in qualitative agreement with experiment. In particular, Elovikov et al. [158] performed an MD study of the dependence of sputtering on ion mass and energy for a normally-incident beam, focusing on the yield and energy of sputtered atoms and on the depth from which ejected atoms originate. This depth, which may be representative of the extent of the damage, decreases with increasing ion mass and decreasing ion energy. For energies of 0.5 keV or less, however, the mass dependence is small above about 20 atomic mass units. The effect of nitrogen ions vs. Ar+ has been studied. Ishikawa et al. [63] compared the effects of the two ions at 200 eV using XPS and found that for nitrogen ions the N/Ga atomic ratio initially decreases slightly and then increases to unity or perhaps higher with increasing bombardment time while for Ar+ the ratio decreases monotonically. No annealing was done to drive out implanted nitrogen, and it appears that both implanted and lattice N

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were included in the total N 1s intensity. Lai et al. [155], using XPS, found that nitrogen ions are less damaging for an equivalent energy and angle of incidence. Many spectroscopic studies of the implanted nitrogen and of defects created by nitrogen-ion bombardment have been reported [157,160–165,167,168] for GaN, but these are beyond the scope of the present review. Further insight into the effects of ion bombardment will be provided in the following subsection, which discusses cleaning by IBA. From the work presented in this subsection it appears that a 0.5 keV nitrogen-ion beam incident at a high (~60–70°) angle relative to the surface normal is the most favorable for use in IBA. A beam energy of less than 0.5 keV would perhaps be even better if the removal rate for surface contaminants is sufficiently high. The obvious principle here is that the less the damage done, the less that has to be repaired by annealing. 3.3.4. Ion bombardment and annealing It is, in principle, always possible to obtain a surface completely free of adsorbed contaminants using ion bombardment, assuming a sufficiently-clean UHV environment and sputtering-gas supply. It is assumed that contaminants are located entirely on, or very close to, the surface and not distributed throughout the bulk. The issue then becomes one of how best to minimize surface damage and to restore order without causing further damage. The cleaning of GaN by IBA has been investigated in Refs. [123,135,138,139,145– 150,155,176,177]. A force-field MD study of the crystallization via annealing of a disordered GaN thin film on sapphire, which may be relevant to the healing of surfaces damaged by ion bombardment, was reported by Onozu et al. [178]. It was found in this study that annealing in the 1100–1200 K range is optimal in terms of crystallinity and surface smoothness but that higher temperature (1300 K) causes damage. One of the first studies of this nature and, to our knowledge, the first to demonstrate the advantages of nitrogen ions vs. Ar+ or Xe+ was that of Hunt et al. [176]. Unfortunately, the ion energy in each case was 5 keV, and it is known from later work (discussed in the previous subsection) that much lower energies are needed in order to minimize damage. After a few minutes of ion bombardment followed by a 30-min anneal at 500–600 °C, the N/Ga atomic ratio observed via AES is much closer to unity for nitrogen ions (0.80) than for Ar+ or Xe+ (0.50). The C signal is below the AES detection limit, but a significant amount of O remains. Ishikawa et al. [63] compared the effects of 200 eV nitrogen and Ar+ ions using XPS and found that both types of ions greatly reduced, but did not eliminate, the C and O levels relative to the untreated samples. Bermudez et al. [123] performed ion bombardment with 1 keV nitrogen ions incident at ∼45° relative to the surface normal, after which no contaminants appeared above the AES detection limits. Annealing in stages beginning at 600 °C led to a gradually-improving (1×1) LEED pattern. For an 850 °C anneal the LEED pattern appeared reasonably good with bright spots, a low background intensity and no indication of pronounced faceting. However, deliberately-overexposed LEED photographs all showed weak indications of imperfections. Lai et al. [155] compared IBA results for 1 keV nitrogen and Ar+ ions and found much better behavior in the case of nitrogen. Similar results were obtained for Ne+ and Ar+, which indicates that the differences between nitrogen and Ar+ ions are due to chemical effects and not to the ion masses. After nitrogen-ion bombardment and annealing at 823 K, the N/Ga atomic ratio is higher, the coverage of free Ga lower and the (1×1) LEED pattern better than for an equivalent treatment using Ar+. The LEED in either case shows no clear indication of faceting; however, significant surface degradation is seen in LEED and XPS following a 970 K anneal. This study also shows that the N 1s feature due to implanted nitrogen disappears at ∼623 K.

Oliver et al. [138,139] performed IBA with 200 eV nitrogen ions at a sample temperature of ∼250–300 °C and annealing at ∼820 °C. (The temperatures were estimates based on that of a resistivelyheated Si wafer pressed against the back of the sample.) The resulting surface showed a (√3×√3)R30° RHEED pattern and a Garich stoichiometry. Butcher et al. [177] carried out IBA using 2.5 or 5 keV Ar+ ions, with annealing up to 650 °C, and observed severe depletion of N as well as difficulties in eliminating surface O. Hattori et al. [150] used IBA with 0.5 keV Ar+ ions incident at an angle of 50°. Sputtering for ∼20 min reduced the C coverage to below the XPS detection limit and the O concentration to ∼2 atomic-% (assuming a uniform distribution of O within the XPS sampling depth). For MOCVD material, a three-step annealing sequence up to 500 °C, as described above in Section 3.3.2, gave a RHEED pattern dominated by sharp (1×1) spots with additional weak (3×3) spots while higher temperatures resulted in faceting. Further reports of IBA will be reviewed in later sections in connection with adsorption and interface studies. A variation of the conventional IBA approach that has proven effective involves annealing in a flux of NH3 vapor [123] or Ga [148], after nitrogen-ion bombardment, rather than in UHV. The effect of an NH3 flux in reducing the GaN thermal decomposition rate [143] has been noted above (Section 3.2.2), and the use of a Ga flux permits annealing at a lower temperature in order to avoid faceting. In either case the resulting surface exhibits no detectable C or O, and the LEED pattern is a sharp (1×1) with no evidence of faceting. The exact mechanisms involved are not clearly established at this point. However, in the case of NH3, it is likely that thermal decomposition of NH3 releases NHx (x o3), which reacts with the surface to compensate for the loss of N caused by ion bombardment and/or annealing. In view of the results of Tautz et al. [147] on the effects of atomic H on faceting, it is also possible that H atoms released in the decomposition of NH3 may act to etch away facet features as they form. Widstrand et al. [128] have suggested that direct reaction with NH3 at elevated temperature can remove excess Ga, and Moon et al. [179] have shown that GaN surface damage resulting from plasma etching can be repaired by annealing in NH3 vapor. An advantage of nitrogen-ion bombardment followed by annealing in NH3 is that the NH3 pressure needed is substantially lower than that required for the chemical removal of adsorbed O via reaction with NH3 without prior ion bombardment. There is also the possibility that hydrazine (N2H4) might be a more effective reagent than NH3 in this application since it decomposes easily [180] to form NH2. However, this is contingent on being able to obtain N2H4 that is highly pure and free of H2O. It is worth noting yet another IBA approach in which the annealing is performed in N2 at ∼10-7 Torr. To our knowledge, this has been employed in only two GaN studies, those of Wu et al. [181] and Zhang and Ptasinska [182]. Both report a good (1×1) LEED pattern with little or no C or O contamination. Since groundstate N2 is relatively inert, one assumes that the process involves dissociation and/or electronic excitation mediated by a hot ionization gauge filament and/or hot metallic parts of the sample holder, as suggested by Wu et al. Atomic N or excited N2 could then be effective in maintaining a nearly-ideal GaN stoichiometry during annealing at temperatures at which desorption of N is rapid. Previous work (on cubic SiC) has shown that N adsorption can be promoted by a hot W filament [183] as is commonly done for atomic H adsorption; although, the "cracking" efficiency of N2 appears to be quite low. Although this method has yet to be thoroughly evaluated, it appears to offer two advantages over annealing in NH3 following ion bombardment. One is that complete evacuation to UHV conditions is much easier for N2 than for NH3, and there is no concern about reagent adsorption on the clean surface. The other is that obtaining ultra-high-purity

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anhydrous material is easier for N2 than for NH3. One aspect that has not been widely studied is the possible importance of the sample temperature during ion bombardment. With few exceptions [138,139], this is normally done at RT. It is possible, for example, that an elevated temperature might increase the rate of impurity removal and thus minimize the required ion dose. 3.4. Other methods Here we briefly mention other methods for in-situ cleaning that do not fit easily into any of the above categories and are not often employed in fundamental surface studies of GaN. The use of a hydrogen plasma has been discussed in Refs. [60,64,74,75], and cleaning via a nitrogen or NH3 plasma is described in Refs. [74,75,102,130–132,151,184–186]. The conditions employed, such as the sample temperature, vary among the different studies, and the treatment is sometimes not in situ in the surface analysis chamber. Plasmas are generally effective in reducing the C and O coverages but are potentially damaging to the GaN surface [187], and many references make no mention of LEED, AFM, etc. results for structural order and morphology after plasma treatment. However, Schulz et al. [131] and Gangopadhyay et al. [151] have reported results for the (112̄ 0) and (0001) surfaces respectively after in-situ cleaning in a nitrogen plasma. For the former, the surface is smoother than as-received, and a good (1×1) LEED pattern is seen. For the latter, significant surface roughening occurs during plasma treatment for 30 min at 700 °C; however, this can be avoided and a smooth surface obtained via treatment at 375 °C for 30 min followed by 750 °C for 10 min. A clear (1×1) LEED pattern is observed for this smooth surface. Similarly, Hashizume et al. [184,185] found only a small degree of roughening due to exposure of a (0001) surface to a nitrogen plasma. The substrate in this case was not explicitly identified as (0001), but one infers this polarity from the appearance of a (2×2) RHEED pattern during MBE growth (Section 4.6.1). The removal of oxide was particularly effective when the plasma exposure was preceded by immersion in organic solvents and then in NH4OH solution at 50 °C. However, the level of C contamination on the treated surfaces was not indicated. Cleaning by exposure to atomic H, formed by dissociating H2 on hot (∼1800 °C) tungsten, has been widely used for other III–V materials (e.g., Ref. [188] and works cited). Such "H-atom cleaning" does not seem to have been applied to GaN to any great extent but is probably worth further consideration. An issue in any GaN cleaning method involving H atoms is the possibility of etching to form volatile GaH3 and/or NH3. If NH3 production is dominant then a Ga-rich surface is a likely outcome. The interaction of H and H2 with GaN surfaces will be discussed at length in Section 7.3. Annealing ex situ in a tube furnace in first NH3 vapor and then in HCl vapor, followed by an in-situ anneal at 550 °C has also been examined [94] as a cleaning method, but this appears to be less effective for removing O than immersion in aqueous HCl solution followed by annealing. Another, more-general, study that must be noted is that of Bartoš et al. [189] (note the Erratum) that applied a variety of insitu cleaning methods to polar, non-polar and semi-polar surfaces of free-standing wafers grown using hydride VPE and polished to give an RMS roughness, as seen using AFM, of ~1 nm. The approaches included combinations of annealing in UHV, annealing in 1.8x10-6 mbar (1.3x10-6 Torr) of NH3 vapor and 5 keV nitrogen-ion bombardment followed by annealing either in UHV or in NH3. For each surface the as-received sample was first cleaned ex situ in 1:1 HCl:H2O at 75 °C. The main focus of this study was on the dependence of BB (Section 4.7.3.1) on surface orientation and treatment, but detailed surface characterizations were also performed. The optimum cleaning procedure, in terms of surface order and

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reduced contamination, consisted of cycles of nitrogen-ion bombardment and annealing in NH3 (at a different temperature for each orientation), which removed all C and O except for a trace of O remaining on the semi-polar surfaces. A (1×1) LEED pattern was seen for all samples, and faceting was observed only for the semipolar surfaces, which is expected as a result of the relatively-high surface energy of the semi-polar surfaces (Section 2). However, there was a significant variation in the (Ga 3d)/(N 1s) XPS intensity ratio for different treatments of the same surface, and the Ga/N atomic concentration ratio for the non-polar (101̄0) and (112̄ 0) surfaces differed from the expected value of unity. The XPS data were obtained with Mg Kα excitation (hν = 1253.6 eV) and were therefore largely bulk sensitive. For surfaces containing coordinatively-unsaturated Ga atoms, an apparent decrease in the Ga/N atomic ratio that occurs in some cases might arise from adsorbed NH3 remaining from cleaning (Section 7.1). 3.5. Summary We conclude this section with a "best-practices" recommendation for GaN surface preparation. This applies specifically to the (0001) surface and may be useful at least as a starting point for other surfaces, aided perhaps by additional experimental details given in works cited in Secs. 4-8. It should be kept in mind that the following procedure has not been tested in its entirety but is instead a synthesis based on results described above. (1) Immerse for a few minutes in warm TCE, then warm acetone, then warm methanol. Blow dry in N2. Ultrasonic agitation may help, but its effect (if any) on surface condition has not been investigated. (2) Immerse for several minutes in boiling aqua regia or in hot "piranha solution", then rinse in DI H2O. Blow dry in N2. (3) Load into UHV as quickly as possible, then outgas in stages from about 200 to 500 °C while maintaining the pressure in the low-10-9 Torr range or below. (4) If C and O are the only contaminants, anneal in flux of either Ga or NH3 vapor as detailed in references discussed in Section 3.2. Repeat as needed for a clean surface. (5) As an alternative, especially for strongly-adsorbed contaminants, sputter with ≤0.5 keV nitrogen ions at a high (≥60°) angle of incidence relative to the surface normal. Anneal in a flux of Ga or NH3 vapor as detailed in references discussed in Section 3.3.4. Repeat as needed for a clean surface. Simply annealing an ion-bombarded surface in UHV may also give good results if conditions (i.e., time and temperature) can be found such that a well-ordered and unfaceted surface can be produced. It is desirable to keep the annealing temperature as low as possible in order to avoid faceting and decomposition. Optimizing the annealing process depends on a number of variables and, hence, will require a certain amount of "trial-and-error". However, there have been a sufficient number of reports, discussed above, of wellordered surfaces having been prepared to establish that this is possible. Two other approaches should be noted that can eliminate the need for IBA in the case of strongly-bound adsorbates. If one has an adequate supply of samples and a UHV chamber with a loadlock sample transfer capability, it is reasonable to consider simply using a new sample for every experiment. An ex-situ wet-chemical cleaning procedure, such as immersion in a strong acid, could then be used to remove the adsorbate and the sample then subsequently reused. Another course might be to regrow a clean surface in situ, as has been done by Falta et al. [132] and by Oliver et al. [138,139], using homoepitaxial MBE to form a very thin fresh layer

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on a previously-used sample. It should also be mentioned here that the electronic structures of surfaces prepared by annealing in Ga vs. in NH3 may be fundamentally different. Annealing in UHV is probably similar to annealing in Ga in that Ga adatoms can be expected on the clean surface. This will become evident in Section 4.6 when discussing the appearance of surface states near the VBM. The source of this potential difference lies in how the polar surfaces, which are metallic when ideally terminated, are stabilized in the observed semiconducting state by the presence of adsorbates or defects. On the subject of the removal of O impurities from GaN surfaces by whatever means, three points should be mentioned that could contribute to the difficulty in preparing and maintaining a completely O-free surface. The first is that the clean surfaces are highly reactive with H2O, which is present in the UHV background and is often generated as a by-product of in-situ experiments (e.g., in the outgassing of filaments). The topic of H2O adsorption will be examined at length in Section 7.10. The second point is that Si and Mg, which are common dopants in n- and p-type GaN respectively, have been found to segregate to the (0001) surface in heavilydoped material (Sections 5.25 and 5.34). The oxides of both elements are refractory and are unlikely to be thermally desorbed at temperatures below which GaN decomposes. This means that they will be difficult to remove by any of the in-situ chemical procedures described above if the bulk behaves like an infinite source of surface Si or Mg. It is possible that persistent low levels of O contamination on GaN could actually represent oxides of trace quantities of surface-segregated Si or Mg, which may be difficult to detect in AES and XPS and are not looked for in typical experiments. A similar effect in Pt metal is well known [190] as the source of a spurious "Pt oxide" that is stable at anomalously-high temperatures. One study [140], however, did specifically look in XPS for Mg surface segregation in a typical p-GaN sample (not heavily doped) and did not find any. The third point is that both experiment [149,191,192] and theory [193] indicate that O can be readily adsorbed on GaN at macroscopic defects such as pits, dislocations and micropipes. Impurities bound at such sites might not be easily accessible to the in-situ cleaning methods described above. The subject of surface morphology and its dependence on sample preparation will be examined briefly in Section 4.3. In a more-positive view, contamination that is localized in small areas of the surface might not severely affect most types of experiments.

4. Structure and properties of clean surfaces This section deals with experimental and theoretical approaches to characterizing the properties of clean GaN surfaces. 4.1. Theoretical background Since this is the first section in which computational results are discussed in any detail, a few brief comments regarding theoretical methods are in order. This review is written by, and primarily for, an experimentalist, and the goal here is only to provide such readers with enough background information to make understandable the descriptions of computational results given in later sections. As such, the topics described are those that will appear frequently in discussions of computational results for GaN surfaces. 4.1.1. Calculations at T = 0 Except where noted, all calculations employ density functional theory (DFT), and more details can be found in any text on solidstate DFT (e.g., Ref. [194]). Nearly all calculations use plane waves (PWs) and pseudopotentials (PPs). The all-electron wavefunctions

describing valence states must be orthogonal to those for core states, which introduces rapidly-varying structure in the radial components Rn,l(r) of the valence wavefunctions in the region of small r, i.e., close to the nucleus. Accurate representation of this sharp structure in Rn,l(r) using PWs then requires very high PW cut-off energies, which leads to a computationally-intractable situation. In a standard PW-PP calculation, the Rn,l(r) component of a valence-electron wavefunction is "pseudized", i.e., replaced with a smoothly-varying function that matches the true, all-electron function beyond a cut-off radius, rc, and that can then be expanded in terms of PWs. For r o rc, the "frozen" core electrons together with the nucleus are treated as a rigid, non-polarizable ionic core and replaced with a PP that is consistent with the pseudized wavefunction for r 4 rc. Many of the calculations reviewed here use the projector augmented wave (PAW) method [195,196]. This is, in effect, a way to make the pseudized Rn,l(r) "look like" the corresponding allelectron function without adversely affecting the PW representation. A transformation operator T is defined such that |Ψ4 = T | Ψ'4 where |Ψ4 and |Ψ' 4 are respectively the all-electron and pseudized wavefunctions. The operator T then has the effect of projecting out of |Ψ'4 the pseudized component for r o rc and replacing it with the all-electron function. The PAW approach is considered to be more accurate than standard methods with little additional computational cost. The PP is termed "hard" or "soft" depending on rc. Norm-conserving pseudopotentials (NCPPs), which are "hard", are more easily transferable between different materials because the small rc renders them less sensitive to the chemical environment. However, because of the small rc, NCPPs require PWs up to high energies (typically several hundred Ry) for convergence in order to accommodate the strongly-varying radial potential for small rc. Hence such calculations can be computationally expensive. On the other hand soft pseudopotentials involve a larger rc and usually require much lower PW cut-off energies. Ultra-soft pseudopotentials (USPPs), which are used in the majority of GaN surface studies, represent a further development. The USPP relaxes the NCPP requirement that the norm of the pseudo-wavefunction equal that of the all-electron wavefunction for r o rc. This enables rc to be increased to the maximum possible extent, further reducing the necessary cut-off values for the PW energies to a few tens of Ry; although, much higher cut-off energies are typically needed for the charge density. It is now widely recognized that the Ga 3d orbitals have a significant degree of valence character in GaN and, therefore, must be treated explicitly rather than being included in the PP. Unless otherwise stated, it can be assumed that this is the case when discussing computational results. In some studies, explicit treatment of the Ga 3d orbitals is avoided through the use of a method known as non-linear core correction (NLCC) developed by Louie et al. [197]. In calculations that focus on the reconstruction and electronic structure of the clean surface, the tendency is to use the local density approximation (LDA) since this appears to give generallyreliable results. However, in studies of adsorption, it is recognized that the generalized gradient approximation (GGA) typically yields better agreement with experiment. In the LDA, the exchangecorrelation functional is that of a uniform electron gas; whereas, in the GGA, the gradient in electron density near an atom is taken into account. The most widely-used pure-GGA functional, at least in the work reviewed here, is the PBE; although, the closely-related PW-91 functional is also frequently employed in GaN surface studies. Usman et al. [198] have demonstrated the use of the PW91 functional together with the PW-PP approach to compute a range of different bulk properties of GaN. Other functionals that are used less often in the work described here are the B3LYP and

V.M. Bermudez / Surface Science Reports ∎ (∎∎∎∎) ∎∎∎–∎∎∎

the HSE06. These are hybrid-GGA functionals that include a contribution from Hartree-Fock exchange and are thus computationally expensive. However they give more accurate results for band gaps than do pure LDA or GGA [199,200]. This is an important issue when attempting to determine accurately the position of surface states in the gap relative to the band edges, which is in turn a critical factor when applying theoretical results to the interpretation of UPS experiments. Another approach that has sometimes been employed in GaN studies is called "DFT+U" or sometimes "LDA+U", which has been reviewed by Kulik [201]. This is a method for treating stronglycorrelated systems with localized electrons, such as transitionmetal ions with partially-filled d-orbitals, and can also overcome the problem of band-gap underestimation that is typical in DFT with "pure" functionals that are based on an electron gas. Such "standard" DFT treatments tend toward excessive electron delocalization, which in the extreme can cause an insulating material to appear metallic as a result of the underestimation of Eg. In DFT +U, the energy is given in the form

EDFT + U = EDFT +

∑ a

Ueff 2

Tr ( ρa − ρa ρa )

(1)

where Ueff is a parameter determined semi-empirically, "Tr" means "trace (of a matrix)" and ρa is an atomic-orbital occupancy matrix. This in effect introduces a "penalty function" that forces orbitals to be either fully occupied or completely empty. Another technique that has sometimes been used in theoretical studies of GaN is density functional tight binding (DFTB), a tutorial review of which has been given by Koskinen and Mäkinen [202]. This is a parameterized method that is much less computationallyintensive than fully ab-initio DFT and is therefore more-readily applicable to very large systems or to MD calculations involving long elapsed times. Here each atom in the unit cell is treated exactly, within the limits of DFT, while interactions between nearestneighbor atoms are included as perturbations using parameters obtained by fitting to ab-initio DFT results. The nudged elastic band (NEB) method [203,204] is commonly used to locate the transition state (TS) in computational studies of chemical reactions as well as physical processes such as diffusion. The TS is the highest-energy point in the lowest-energy path, i.e., the path that involves the least "climbing" in crossing between the initial-state and final-state "valleys". The NEB calculation starts with models for the initial and final states and an estimate for the TS configuration. A series of steps, or "images", is then defined in terms of atomic displacements leading from the initial to the final state via the estimated TS. Each image is imagined to be joined by mechanical springs to its neighbors, and the object is then to find a path the minimizes the elastic force parallel to the path (i.e., the amount of "climbing") while at the same time also minimizing the DFT force perpendicular to the path. The latter assures that any deviation from the path, in a direction perpendicular to the path, costs energy (i.e., is up-hill). The atomic positions for each image are iteratively refined until these conditions are satisfied, which is often a very computationally-intensive process. The TS can then be located precisely by interpolating between images along the path to either side of the peak energy. In a variation of this method, called "Climbing Image NEB" (CINEB), the TS is located by "sliding" the image closest to the TS along the reaction path until the energy is maximized. The software used in this work is complex and highly developed. The PW-PP calculations typically use program suites named "VASP" (Vienna Ab-Initio Simulation Package) and "Quantum ESPRESSO" (Quantum opEn Source Package for Research in Electronic Structure, Simulation and Optimization). Some calculations use PPs to replace inner core levels and Bloch functions

19

constructed from localized Gaussian or Slater-type basis sets to treat valence electrons. These offer certain advantages, such as speed in some cases and the relative ease (vs. PW calculations) in obtaining properties such as atomic charges and molecular orbitals. Such calculations typically make use of programs named "SIESTA" (Spanish Initiative for Electronic Simulations with Thousands of Atoms) and "Crystal". More information about these programs is available at the appropriate websites, and many other DFT packages are also widely used. Surface calculations typically employ two-dimensionally periodic slab (2DPS) models, which are constructed from a finite number of Ga-N bilayers (typically four to eight) stacked in the surface-normal direction with periodic boundary conditions applied within the plane. Usually geometry optimization involves only the uppermost few bilayers and the adsorbates, if any, while the rest of the slab is fixed in the configuration of the relaxed bulk lattice. Ideally, the number of layers allowed to vary during optimization is chosen such that atomic displacements due to surface relaxation, which decrease in magnitude with increasing distance from the surface, have decayed essentially to zero before the first fixed layer is encountered. However, most computational studies of GaN make no mention of having tested the convergence of the results with respect to the slab thickness. Typically calculations involve the use of supercells, which are constructed using an integer number of unit cells. A unit cell is (1×1) in the surface plane and comprises the full thickness of the 2DPS. A widely-used supercell for the (0001) and (0001̄ ) surfaces consists of four (1×1) unit cells and is thus designated a (2×2) surface unit cell (SUC). The larger the SUC the lower the adsorbate coverage that can be modeled but the greater the computational cost. For example, the lowest coverage attainable for a (2×2) cell is 0.25 ML. In modeling the (0001) surface covered with a metallic Ga bilayer, which is discussed in Section 4.6.1, the typical SUC is a (√3×√3)R30°, which is sometimes termed simply (√3×√3). Another issue concerns the lateral size of the SUC and the separability of adsorbed species. Consider a single adsorbate within a SUC of finite size, and suppose that lattice atoms in the vicinity of this species undergo displacement in response to adsorption. Suppose further that these displacements are still significant at a distance from the adsorbate such that the SUC boundary is encountered. In this case the adsorbate is said to be interacting with its translational image so that complete relaxation to the true energy minimum is inhibited, and adsorption will be less energetically favorable (or more unfavorable) than it is in the true low-coverage limit wherein adsorbates do not interact with each other. This is one mechanism that can lead to a coverage-dependent ΔEads, both in theory and experiment. Thus some caution must be applied when identifying a given ΔEads with the lowcoverage limit, and specific examples will be seen in later sections. An often-encountered effect in 2DPS calculations is a dependence of the computed band gap on slab thickness. This results from quantum confinement (QC), which is nicely illustrated in the work of Santosh et al. [205] on the InP (100) surface. Conventional DFT calculations using "pure" (not hybrid) LDA or GGA functionals typically underestimate Eg by as much as 50%, but for a "too-thin" slab QC can counteract this effect and result in an apparent Eg that is larger than in experiment. However, as a qualitative observation, QC does not appear to be very significant in the case of wurtzite GaN and is typically ignored. The 2DPS calculations for this material typically involve four, or a few more, Ga-N bilayers and give an uncorrected Eg in the range of 1.5 to 2 eV vs. the RT experimental value of 3.39 eV (3.50 eV at T = 1.6 K) [24]. Since Eg is underestimated to about the same degree in comparable bulk calculations, one concludes that the effect of QC on GaN slab calculations is fairly small. Nevertheless, Lymperakis et al. [206] found it necessary to use a slab with at least 24 atomic layers to

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describe correctly the CBM on the (101̄0) surface and to locate accurately the empty surface state that appears below the CBM. The electron-counting rule (ECR) [207–209] will appear frequently in discussions of adsorption and surface reconstruction. For a compound semiconductor, the rule states that the most stable surface structure is one in which cation (e.g., Ga) dangling bonds (DBs) are all empty and anion (e.g., N) DBs are all doublyoccupied. The empty cation (filled anion) DBs then form surface states near the CBM (VBM), and adding an electron to the cation DB or removing one from the anion DB raises the total energy. In a 2DPS model, the ECR dictates the proper termination of DBs at the "bottom" layer. In the ECR formalism, Ga (N) has three (five) valence electrons and forms four two-electron bonds in the bulk. Hence, Ga (N) contributes an electron density equivalent to 3/4 (5/ 4) |e| to each bond. At the ideally-terminated (0001) surface the electropositive Ga atom then has 3/4 |e| of excess electron density in the DB while on the (0001̄ ) the DB on the electronegative N is missing the 3/4 |e| needed to form a doubly-occupied non-bonding lone-pair (NBLP) orbital. If left unpassivated, such partially-filled DBs result in energetically-unfavorable metallic surfaces. There are several types of reconstructions that, in theory and/or experiment, are known to make the GaN surface semiconducting by satisfying the ECR, and these will be discussed in Sections 4.6 and 4.7. Here the goal is simply to make deeper-lying layers of the slab appear bulk-like. This is typically done using pseudo-hydrogens (PHs), which are fictitious H atoms with a fractional nuclear charge and electron occupancy. For example, 1 ML of PHs with 3/4 |e| can be used to saturate N DBs on the (0001̄ ) bottom surface when studying the (0001). Likewise, a 1 ML of PHs with 5/4 |e| is used to saturate a Ga DB on the (0001) surface when studying the (0001̄ ). Most of the calculations for (0001) and (0001̄ ) surfaces use a (2×2) SUC, which is a consequence of the ECR. On the ideallyterminated (0001), a (2×2) SUC cell contains four surface Ga atoms, each with 3/4 |e| in a DB; hence, the SUC involves a total unpaired electron density of 3 |e|. This can be passivated, in principle, by any mechanism that either removes 3 |e| to empty all Ga DBs or else adds 3 |e| to form three two-electron bonds while leaving the fourth DB empty. Creating a VGa on the (0001) surface would be an example of the former. The vacancy involves three N atoms each with 5/4 |e| in a DB that is then filled with the 3/4 |e| in DBs on each of the three remaining Ga atoms. The end result is three N atoms with NBLP orbitals and three Ga atoms with empty DBs. Adding a Ga adatom to form 3 Ga-Ga back bonds or 3/4 ML of H to form 3 Ga-H bonds would be examples of passivation by adsorption. Similar considerations apply to the (0001̄ ), with 5 |e| per (2×2) SUC. For example, a Ga adatom can add 3 |e| to form 3 Ga-N bonds while leaving the fourth N with a doubly-occupied NBLP orbital. For a (2×2) SUC, the lowest non-zero adsorbate coverage that can be studied is 0.25 ML, and some calculations use SUCs larger than (2×2) in order to study lower coverages. The majority of stable structures formed on GaN surfaces will be seen to obey the ECR. However, the rule is not completely rigid, and the following discussions will on occasion provide examples of structures that violate the ECR and yet are theoretically stable under certain conditions. Another issue concerns the effect of the polarization of the 2DPS on PW-PP calculations. When PWs are used to represent valence electrons, the model must be periodic in all directions including along the surface normal. This is accomplished by repeating the slab with a large surface-normal translation vector so as to produce a vacuum gap of typically ∼10–20 Å between slabs such that there is no interaction between adjacent slabs. When the slab unit cell has a surface-normal dipole moment, which is the case for GaN in the [0001] direction, for example, the potential diverges as shown schematically in Fig. 6. Imposing periodic boundary conditions then results in a spurious electric field in the

Fig. 6. (a) Schematic diagram (not to scale) showing the diverging potential (red lines) when a 2DPS with a surface-normal polarization is periodically repeated. A spurious, linearly-varying potential (blue lines) in the vacuum gap results from the imposition of periodic boundary conditions on what is actually a non-periodic system. This linearly-varying potential then corresponds to a finite electric field. (b) Shows the removal of this field at the surface (Ref. [210]) by a dipole correction layer (green lines) near the middle of the vacuum gap. The black lines show the periodically-repeated 2DPS (n, n þ1, ...), and the orange spheres represent a layer of adatoms on the "active" surface.

vacuum gap, which can affect calculations of surface properties. This can be eliminated, following Bengtsson [210], by inserting a thin dipole layer near the middle of the vacuum gap. The electric field is then confined to this narrow region, where it has no effect near the surface. This approach, or some variation thereof, is used in many GaN calculations and is termed a "dipole correction". Some calculations make use of a free-standing cluster, rather than a 2DPS, with DBs at the edge of the cluster terminated with real (not pseudo) H atoms. Cluster calculations are considerably less demanding in terms of computational resources than are those for a 2DPS. A typical cluster, with a stoichiometry such as Ga13N13H24, is designed to be a closed-shell system with no partially-filled DBs. Thus, cluster models generally do not correctly describe the occupancy of DBs on the bare, ideally-terminated polar GaN surfaces. Pragmatically, whether or not this causes difficulties is best determined by comparing the results with experimental and/or 2DPS results. The most widely-used program suite for cluster calculations is named "Gaussian". This program, in the latest release at the time of this writing (vers. G16/rev. A.03), does not permit the use of PHs. However another program, named "ADF" (Amsterdam Density Functional), is also widely used for cluster calculations, although apparently not yet for GaN. This does include a PH capability and, therefore, should permit cluster calculations to be done that approximate surface DB occupancies. A topic that arises occasionally in theoretical discussions of GaN surface reconstructions is the Peierls distortion [211]. Within this context, consider for example a periodic row of evenly-spaced Ga atoms each with one electron in a DB. This constitutes a metallic system with a half-filled band of states at EF. The total energy can be lowered by a Peierls distortion in which two Ga atoms move toward each other to form a dimer pair with a doubly-occupied bonding and an empty anti-bonding orbital. This doubles the lattice constant and results in a semiconducting surface with no bands that cross EF. The Peierls distortion is thus analogous to the Jahn-Teller reduction in symmetry in an electronically-degenerate molecular system. Two further brief comments are useful at this point. One concerns spin-restricted vs. unrestricted (or spin-polarized) calculations. Many of the theoretical studies reviewed here make no explicit mention of this issue; although, one assumes that

V.M. Bermudez / Surface Science Reports ∎ (∎∎∎∎) ∎∎∎–∎∎∎

treatment of, e.g., an adsorbed transition-metal atom would be spin-unrestricted. Some studies provide a magnetic moment per SUC or a spin-polarized DOS, which means that a spin-unrestricted calculation must have been performed. In the case of spin-restricted calculations for molecular systems that are not obviously closed-shell, it is usual to test the electronic stability of the final result by relaxing the spin constraint to see if a lower-energy open-shell configuration is obtained. Another common practice in molecular systems is to check for mechanical stability by computing the 3N-6 vibrational modes to test for the absence of large (several meV) imaginary frequencies. These occur when the geometry optimization has converged to a metastable structure rather than a true minimum-energy state. In the case of a periodic structure this would be done by computing the Γ-point phonon frequencies. We are unaware of any GaN surface study in which either of these tests was performed; although, the former is needed only for a calculation that is not already spin-polarized. Finally, the sign convention for computed adsorption energies (ΔEads) should be mentioned. For a reaction A+B→AB, some authors define the reaction energy as E(AB)−[E(A) + E(B)] where E refers to the relaxed total energy and is a negative quantity. Hence, the reaction energy is negative for an exothermic process. Other authors use the reverse definition, [E(A) + E(B)]−E(AB). Henceforth we will use the former definition, so that a negative ΔEads corresponds to an exothermic adsorption. This is done to avoid confusion when discussing diffusion barriers or defect formation energies, which are typically endothermic and given as positive quantities. 4.1.2. Calculations at finite temperature In many of the calculations discussed in the following sections the atoms are "static", meaning that the temperature is effectively 0 K with nuclear motion (even zero-point motion) making no contribution. In this case only the total energy is considered. These are useful in understanding experiments done with samples at RT in UHV. However, to address chemical processes occurring under equilibrium conditions at elevated temperature or pressure, such as the growth or thermal oxidation of GaN, it is necessary to take free energy into account, i.e., to include thermodynamics. Calculations of this type often a yield an understanding of surface reactions that differs significantly from that obtained in a static calculation. To our knowledge, Northrup et al. [212] and Van de Walle and Neugebauer [213,214] were the first to apply this approach to GaN surfaces, using it to construct phase diagrams for NH2+H on the (101̄0) surface and for H on the (0001) and to understand the surface stoichiometry and structure under equilibrium growth conditions. The same basic procedure has been employed in many of the theoretical studies mentioned later in this review. The Gibbs free energy change for a chemical process at constant temperature (T) and pressure (P) is ΔG = ΔH−TΔS = ΔE + PΔV −TΔS where H, S, E and V are enthalpy, entropy, energy and volume. For the formation of a surface with some number of adsorbed Ga, N and/or H atoms, ΔG is given by

ΔG = Etot (ads ) − Etot (bare) + ΔFvib − nGaμGa − nN μN − nH μH

(2)

where the first two terms are the total energies per SUC of the relaxed surface with and without the adsorbate(s), which are obtained in static DFT calculations. An explanation is given in Ref. [213] for why the total pressure, and therefore the PΔV, term can be omitted in Eq. (2). Explicit dependence on T can also be omitted so that T enters only through the effects on ΔFvib and on μX. ΔFvib is the change in vibrational free energy caused by adsorption, nX is the number of adsorbed atoms per SUC of type X and μX is the corresponding chemical potential.

21

In a static calculation, the ΔFvib term would be absent, and μX would be replaced by the DFT total energy of the free atom. For a solid there is of course no translational or rotational contribution of the substrate to ΔG. With the zero of energy at the bottom of the potential well, the vibrational partition function for each oscillator is given by [217]

Z vib =

e−hν /2kT 1 − e−hν / kT

(3)

where h (k) is Planck's (Boltzmann's) constant, and ν is the vibrational frequency. With Fvib = −kT ln(Zvib) this leads to

Fvib =

∑ i

hνi + kT ∑ ln 1 − e−hνi/ kT 2 i

(

)

(4)

summed over all oscillators, where the vibrational energies of the adsorbates can be obtained from experimental data. It is assumed that the lattice modes are essentially unaffected by adsorption and therefore make no significant contribution to ΔFvib, which then depends only on adsorbate normal modes. At T = 0, ΔFvib is then just the change in zero-point energy. In equilibrium, μGa + μN = E(GaN), which is the DFT total energy per two-atom unit cell of the optimized bulk GaN lattice. Thus μGa and μN are not independent variables, which simplifies the application of Eq. (2). Choosing μGa as the active variable, an upper limit of μGa = μ(bulk Ga) can be established for Ga-rich conditions. Likewise, under N-rich conditions one has μN = μ(N2), which fixes the lower limit on μGa. Since the heat of formation (negative for a stable compound) can be written as ΔHf = E(GaN)−μ(bulk Ga)−μ (N2), we have μGa varying between a maximum of μ(bulk Ga) and a minimum of μ(bulk Ga) − |ΔHf| (which corresponds to μN = μ(N2)). Since only the change in μ is significant, it is usual to set μ(bulk Ga) = 0 and to use the computed value of ΔHf, which is typically in the range of −1.1 to −1.2 eV for wurtzite GaN. Thus −|ΔHf| ≤ μGa ≤ 0 with the upper (lower) limit corresponding to very Ga-rich (Nrich) conditions. Finite-temperature effects in calculations involving H2, as an example, are incorporated largely through μH, which is given by [217]

(

)

2μH = E(H2) − kT ln Ztrans⋅Z rot ⋅Z vib

(5)

where E(H2) is the DFT total energy of static H2 and the next three terms are the translational, rotational and vibrational contributions with Z being the respective partition function. This can be recast into the form given in Ref. [214] as ⎞ ⎛⎛ ⎞ 2 ⎞3/2⎟ ⎜ ⎜ P ⎟⎛ h ⎟⎟ ⎟ − kT ln(Z rot ) − kT ln(Z vib ) 2μH = E(H2) + kT ln⎜ ⎜ ⎟⎜⎜ ⎜ ⎜ kT ⎟⎝ 2π m kT ⎠ ⎟ ⎠ ⎝⎝ ⎠

(6)

where P is the pressure and m the mass of H2, and the term in large parentheses is 1/Ztrans. If one were instead dealing with, for example, a flux of metal atoms rather than a background pressure of H2, P would be the BEP, which is the pressure of metal vapor at which the random flux of atoms striking the surface would equal that from the directed beam. For a homonuclear diatomic molecule, Zrot = 4π2IkT/h2, where I is the moment of inertia, and Zvib is given in Eq. (3). Eq. (6) can then be used to determine μ of the reagent species for a given choice of T and BEP; although, in the case of an atomic beam there would of course be no Zrot or Zvib terms. The same basic approach can be applied to determining the thermodynamic stability of adatom structures under conditions of varying reagent "richness" in the vapor phase. It should be noted that somewhat different expressions [217] for Zrot apply in the case of polyatomic or heteronuclear diatomic molecules. For a system with degenerate ground and/or low-lying

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appropriate to MBE and MOCVD growth [215,216]. The purpose here is only to describe the computational method. These results, and others like them, will be discussed in more detail in the appropriate sections. Another type of finite-temperature calculation that has sometimes been done for GaN surfaces is molecular dynamics (MD). Here the force acting on each atom in the system at a given time is used to predict the position of each atom at a time δt in the future. In one approach, termed "Born-Oppenheimer MD", one commonly uses the Verlet algorithm ri(t+δt) = ri(t) + vi(t)·δt + 1/2ai(t)·(δt)2 + 1/6bi(t)·(δt)3 + O(δt4) + H.O.T 2

3

(7a) 4

ri(t-δt) = ri(t) − vi(t)·δt + 1/2ai(t)·(δt) − 1/6bi(t)·(δt) + O(δt ) + H.O.T

(7b)

to obtain ri(t+δt) = 2ri(t) − ri(t−δt) + ai(t)·(δt)2 + O(δt4) + H.O.T Fig. 7. (a) Phase diagram for the GaN (0001) surface in the presence of H, as a function of μGa and μH. The diagram was computed for T ¼ 950 K, but the important qualitative features are independent of temperature and pressure. μH ¼ 0 corresponds to H2 molecules at T ¼ 0, and μGa ¼ 0 corresponds to bulk Ga. These are the H-rich and Ga-rich limits respectively. Dots indicate experimental MOCVD data, which, within the error bars, agree with the calculated (NH3 þ3Ga-H)-(3Ga-H) phase boundary highlighted by the thicker line. "VGa" is a Ga vacancy, and "Nad-H" is an N-H group adsorbed in an H3 site. (b) Temperature dependence of μH for two different pressures. From Van de Walle and Neugebauer [213,214]. (Copyright 2002, American Physical Society. Reprinted with permission.).

excited electronic states, the electronic partition function should be included in Eq. (6) as −kT·ln(Zel) where Zel = Σ[giexp(−ΔEi/kT)] summed over all electronic states (i) with degeneracy gi at an energy of ΔEi relative to the ground state. This is generally a relatively small effect. For example, the Ga atom, with a 3d104s24p1 electronic configuration, has a 2P1/2 ground state and a 2P3/2 excited state at ΔE = 0.1024 eV, which at 1000 K gives kT·ln(Zel) = 0.101 eV. With these results the phase diagram shown in Fig. 7 can be constructed, where μH = 0 corresponds to Eq. (5) at T = 0 K with E (H2) set to zero. The left-hand panel shows the most stable structure, in terms of ΔG, for any allowed value of μH and μGa, and the right-hand panel shows, for a given pressure, the temperature that corresponds to a particular value of μH. Fig. 8 shows μH vs. temperature for various pressures and indicates typical values

(7c)

where ri(t), vi(t) and ai(t) are vectors giving respectively the position, velocity and acceleration of atom i at time t and H.O.T. means "higher-order terms". If the time step δt is much smaller than the period of the fastest oscillatory motion in the system then the higher-order terms (O(δt4) and beyond) in Eq. (7c) can be ignored. For GaN (0001) with adsorbed H, for example, the period of the Ga-H stretch is about 18 fsec. In ab-initio MD, the force on each atom at each point in time (fi(t)) is computed "on the fly" using DFT and the acceleration obtained via ai(t) = fi(t)/mi where mi is the mass. In force-field MD the forces are instead obtained from some form of semi-empirical "balls-and-springs" potential function. This is much faster than AIMD, but the reliability depends critically on the accuracy of the parameterization. Various "thermostats" have been developed to fix the temperature of the system, the simplest of which is velocity scaling. Here vi(t) = [ri(t +δt)-ri(t−δt)]/2·δt is used to obtain the total kinetic energy (Ekin) and from that the system temperature as

⎛ 3 ⎞ N 3NkT Ekin = 1/2 ∑ mi ⎜⎜ ∑ vi2, j⎟⎟ = 2 ⎝ j=1 ⎠ i=1

(8)

where N is the total number of atoms and j = x,y,z are the velocity components. The velocities are then scaled by a factor of √(TD/T) where TD is the desired temperature. An alternative to the BornOppenheimer method in AIMD is the Car-Parrinello approach, which projects the electron density, rather than the atom positions, forward in time. This will not be described here. Using MD, the evolution of the structure of a system (termed the "trajectory") can be followed over time as it approaches thermal equilibrium. As will be seen later, MD has been used to model, among other effects, the crystallization of disordered GaN films at elevated temperature, the adsorption of NHx (x≤3) species and the structure of the interface with liquid H2O at RT. 4.2. Polarity and polarization

Fig. 8. Temperature dependence of μH for various H2 pressures (given in atmospheres on the right). Typical values for MBE and MOCVD growth are indicated. From Northrup and Neugebauer [215] (reproduced with the permission of AIP Publishing).

4.2.1. Polarity The wurtzite structure of GaN can be viewed as being formed from Ga-N bilayers stacked in the c-axis direction, and the term "polarity", as it applies to the (0001) and (0001̄ ) surfaces, refers to whether the bulk lattice ends in a Ga or an N layer. In principle, the (0001)-oriented substrate could be terminated in N simply by removing the uppermost Ga layer (Fig. 1). However, this would result in a highly-unstable surface consisting of N atoms with one back-bond and three dangling bonds. Similar considerations apply to the semi-polar surfaces, as noted in Section 2. Stated differently, when considering the structure of GaN in the [0001] direction, the

V.M. Bermudez / Surface Science Reports ∎ (∎∎∎∎) ∎∎∎–∎∎∎

lattice should be envisioned as a stack of Ga-N bilayers rather than alternating Ga and N layers. "Polarity" is distinct from "termination", which refers to the chemical composition of the surface. For example, as will be seen later, it is possible under some conditions for a (0001̄ ) (N-polar) substrate to be terminated in an ML of adsorbed Ga. In this case, the sample would be described as "N-polar and Ga-terminated". In any study of polar or semi-polar GaN surfaces it is very desirable to know the substrate polarity. Specific structural models for ideallyterminated polar, semi-polar and non-polar surfaces of wurtzite GaN were given in Section 2. Here we are concerned mainly with different experimental techniques for determining polarity. The situation is simplified by the fact that the c-axis growth of thin-film GaN is now sufficiently well understood that the polarity can be predicted from a knowledge of the growth conditions. Thus, at the present stage of development, growers are able to produce material of known c-axis polarity "on demand". This however was not the case in the mid 1990s and before, when the surface science of GaN was in its infancy, and most of the work at that time was done with samples of uncertain polarity. In some cases it has been possible, with hindsight, to determine what the polarity was, based on the current knowledge of the connection between growth conditions and polarity. The determination of GaN polarity has been reviewed elsewhere [7,218,219]. Here we will briefly note the different methods that can be used, some of which are reported in publications that have appeared since the review by Sumiya and Fuke [219]. The methods used or proposed [220–262] are listed in Table 4, and other methods involving ELS, ISS, LEED/RHEED and transient piezoelectric response are also known. These are described in earlier reviews [218,219] together with references to previous work, which will not be repeated here. Given that the polarity of thinfilm samples is usually already known at the time of growth, what the experimentalist needs is a relatively-simple method that can be used to verify the polarity should questions arise. The need is greater in the case of bulk single-crystals, for which polarity may not be known a priori but can be determined using XRD. Most of the studies noted above concern only the polar (0001) and (0001̄ ) surfaces, but some [236,238,240,242,260] also address semi-polar surfaces. Some methods, such as CBED, ELS, ISS, PED or XRD, require a considerable amount of specialized apparatus, expertise and/or data analysis when applied to GaN, while others are destructive (i. e., etching or thermal stability measurement). Still others are surface-sensitive (e.g., AES, work-function measurement and XPS) and may be complicated by the effects of adsorbed contaminants, Table 4 Summary of methods proposed or demonstrated for determining GaN surface polarity. Most of these apply specifically to the (0001) and (0001̄ ) surfaces. Additional methods and references are given in the reviews by Zúñiga-Pérez et al. [7], Hellman [218] and Sumiya and Fuke [219]. Method

References

Auger Electron Spectroscopy Atomic Force Microscopy Convergent-Beam Electron Diffraction Hydrogen Plasma Etching Kelvin-Probe Microscopy Optical Spectroscopy Photoelectron Diffraction Secondary-Ion Mass Spectroscopy Transmission Electron Microscopy Thermal Stability Wet-Chemical Etching Work Function X-ray Photoemission Spectroscopy X-ray Diffraction

[220,221] [222,223] [224–227] [228,229] [222,223,230] [222,231–234] [235–243] [244] [245] [246–249] [250–257] [221] [258–261] [262]

23

non-ideal stoichiometry, faceting, etc. For in-situ MBE growth, the polarity can be easily found by observing the surface reconstruction using RHEED or LEED (Section 4.6). For bulk single crystals, for which etching and polishing are usually needed in any case for sample preparation, wet-chemical etching methods are convenient for determining polarity. For thin-film samples grown ex situ, wet-chemical etching techniques are the most widely used and are considered reliable and relatively simple. If the test can be performed on a small piece cut from the sample of interest then the destructive nature of the etching does not present a major problem. There are, to our knowledge, no relatively-simple methods for polarity determination in the case of thin-film, semipolar substrates other than perhaps angle-resolved XPS of the VB [260]. However, XRD can be used for this purpose in the case of bulk single crystals [189]. There is one other issue worth mentioning that is peripherally related to polarity. This concerns methods for distinguishing cubic from hexagonal GaN. The obvious technique for accomplishing this is XRD. However, Xu et al. [263] have shown that there are subtle differences in the N KLL AES lineshapes of the two materials, which arise from differences in the VB electronic structure. Since the N L-shell forms the major part of the GaN VB, the N KLL lineshape is, to a first approximation, given by a self-convolution of the VB DOS [264]. Hence, differences in the VB DOS for the two forms of GaN are detectable as subtle variations in the N KLL lineshape. 4.2.2. Polarization Polarization is an electrostatic effect that occurs in two forms; namely, spontaneous and piezoelectric. The former results from the static dipole moment of the unperturbed wurtzite unit cell in the c-axis direction and the latter from distortion of the unit cell by strain. This subject is discussed in the context of GaN surface science in the reviews by Eller et al. [5] and by Zúñiga-Pérez et al. [7] as well as in other, more-general reviews [265–267]. Typically the piezoelectric effect is important only in heterostructures and interfaces, e.g., between GaN and AlxGa1−xN (x ≤ 1), or in metal contacts. An example of the latter is given by Karrer et al. [268] for Pt/GaN, which has also been discussed by Rizzi [269]. However, Bridger et al. [270,271] have observed a piezoelectric effect in bare GaN caused by the strain field surrounding extended defects. In the present discussion we are concerned with spontaneous polarization and its manifestations in surface-science experiments. Fig. 9 illustrates, in schematic form, spontaneous polarization as it applies to n-GaN. Following the discussion given by Eller et al. [5], experiment [272] indicates a bound surface polarization charge density of σb = −1.37×1013 cm-2 on the (0001) surface with an equal density of positive charges on the (0001̄ ). This value is close to that found in ab-initio theory. The exact value of σb depends sensitively on the Ga and N partial ionic charges and on the crystallographic parameter u, which is the length of the Ga-N bond parallel to the c-axis expressed as a fraction of the c-axis unit cell distance. In principle, ionization of donors can compensate the polarization charges to achieve charge neutrality at either surface. This is an internal mechanism that gives rise to an SCL with trapped positive charges (ionized donors) at the Ga-face and CB electrons at the Nface. The band bending (δΦs) at the Ga-polar surface can be obtained by solving the Poisson equation d2Φ/dx2 = −ρ(x)/ε0εs subject to the boundary conditions that dΦ/dx = 0 at the bottom of the SCL (x = 0) and Φ = δΦs + V0 at the surface (x = W) where V0 is the potential in the bulk. Here ε0 and εs are the vacuum permittivity and the static dielectric constant of GaN, and all donors (with density ND) are assumed to be ionized. This gives a constant ρ(x) = qeND, with qe the electron charge, and an SCL width of W = Nss/ND where Nss is the areal density of polarization charges that need to be compensated.

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order of magnitude greater than Eg. In experiment, |δΦs| o 1 eV is typical at the clean n-type Gapolar surface, which for GaN corresponds to Nss o 2.3×1012 cm-2 for ND = 5×1017 cm-3. Therefore, most of the compensation of σb can be attributed to external sources such as charges trapped in surface states, defects or adsorbates. In particular, Van de Walle and Neugebauer [12] and Reshchikov and Morkoç [13] have extensively reviewed the structure and properties of various point defects in GaN, and VGa and VN are the most easily-formed such species. The density of external charges necessary to compensate σb is on the order of 1×1013 cm-2, or ∼0.01 ML, which means that the species involved will be difficult to detect using conventional techniques for surface spectroscopy. Different types of external charge-compensation mechanisms are discussed by Eller et al. [5], and similar considerations apply to the N-face. If the compensation were due entirely to donor ionization, free electrons would move to the N-polar surface and form a 2DEG with downward BB. However, in practice, the density of negative external charges on the N-face exceeds the positive σb so that some density of ionized donors is needed, as on the Ga-face, to achieve charge compensation. This results in a small upward BB as observed experimentally. For example, Jang et al. [258] observed a larger (by 1.40 eV) upward BB on the (0001) Ga- vs. the N-face, as expected from consideration of the spontaneous polarization, and also observed the effects of piezoelectric polarization on BB by applying tensile and compressive strains to the samples. A further discussion of BB is given in Section 4.7.3. 4.3. Surface morphology

Fig. 9. (A): Crystal structure and orientation of the c-axis as well as of the macroscopic spontaneous polarization P and the corresponding electric field E for Gaface and N-face GaN grown on a heterosubstrate. Also shown are the polarizationinduced terminating fixed charges at the substrate interface and the sample surface and the compensating surface charges due to adsorbed ions. For purposes of illustration the two polarities are shown in the form of an inversion domain. From Stutzman et al. [265] (Copyright Wiley-VCH Verlag GmbH & Co. KGaA. Reproduced with permission.). (B): Band bending schematic for Ga- and N-face GaN showing both the theoretical and the experimental situations. Both surfaces are screened by ∼1013 charges/cm2. (NOTE: the position of the ionized donors and electrons in the material corresponds to their physical position rather than their energy level within the band gap.) From Eller et al. [5] (reproduced with the permission of the American Vacuum Society).

The result is δΦs = −qeNss2/(2ε0εsND). With εs = 9.5 [24], Nss = σb = −1.37×1013 cm-2 and ND = 5×1017 cm-3 (a typical value) one obtains δΦs = −35.6 eV. This result applies if the charge compensation were entirely by internal means and is unreasonably large, being about an

The term "morphology" as used here refers to macroscopic surface features such as steps, pits, hillocks, etc. and is distinct from "reconstruction" (Section 4.6), which relates to ordering on an atomic level. Faceting, which is one aspect of morphology, was discussed in Section 3.3.1. Morphology is a complex issue since it depends on the growth method, surface polarity, surface cleaning technique, thermal history, etc. Information concerning surface morphology is obtained largely from AFM and STM data, and most surface-science studies of adsorption and interface formation on GaN give few if any such details unless there is a specific interest in this topic. Hence, it is difficult to determine from the available data the extent to which surface morphology influences these sorts of experiments. However, there is experimental evidence [147,148] suggesting that features such as facets and step edges can be reactive sites on GaN surfaces, which might have a significant effect on studies of adsorption. There is also the point, mentioned in Section 3.5, that experiment [149,191,192] and theory [193] reveal a tendency for impurity O to accumulate at macroscopic defects such as pits. Thus it is potentially useful to have some understanding of the range of different morphologies that may be encountered in typical experiments. The goal with respect to morphology is to obtain surfaces that are as smooth, flat and featureless as possible. It appears that steps are unavoidable, but in an ideal situation these are of a height equal to the spacing between Ga-N bilayers (~2.6 Å) and are far apart and separated by smooth flat terraces. Surface morphology of bulk crystals has been studied in Refs. [95,150,222,225,273–279], and that of thin films grown by MBE and studied (usually) in situ has been reported in Refs. [280–288]. The surface morphology of GaN grown ex situ by MBE or MOCVD and cleaned either wet-chemically or in situ has been studied in Refs. [86,132,138,139,289–291]. In this case, several different methods of surface processing have been employed; hence, some of this discussion overlaps that in Section 3. The present section is by no means a thorough review of the effects of growth conditions on surface morphology, and additional references to some earlier

V.M. Bermudez / Surface Science Reports ∎ (∎∎∎∎) ∎∎∎–∎∎∎

studies are found in Ref. [292]. For single crystals, the (0001) and (0001̄ ) surfaces differ significantly. Using TEM, Liliental-Weber et al. [225,226,273] studied bulk GaN crystals grown from a solution of atomic N in liquid Ga at high pressure. One of the as-grown polar surfaces is smooth and the other rough with stacking faults and with pyramidal structures sometimes as high as 100 nm. Using CBED, the smooth face was identified as the (0001̄ ). As described in the original references, CBED shows that, for the Ga-N bond lying along the c-axis (Fig. 1), N lies closer to the rough surface, i.e., the (0001). Both sides are damaged when subjected to mechanical polishing followed by CMP, but only the (0001̄ ) is chemically active during etching in aqueous NaOH or KOH solutions and becomes smooth again. Nowak et al. [274] studied similar samples using AFM and also observed one face to be rough and the other smooth. However, annealing in a mixture of H2 and NH3 in the 600–900 °C range smoothes the rough surface and roughens the smooth face. Various possible mechanisms were suggested for this affect. Qhalid Fareed et al. [275] used AFM to study crystals grown by sublimation and found that the non-polar (112̄ 0) surface is flat with step growth in the (0001) direction. Zhou et al. [276] grew thick layers of unspecified orientation using hydride VPE and found the asgrown surfaces to be rough with pits and pyramids. Oh et al. [277] also grew single crystals via hydride VPE and produced smooth (0001) surfaces, with an RMS roughness of 0.096 nm, using CMP followed by annealing in air at 900 °C. It is speculated here that perhaps the growth of volatile GaOx contributed to the observed smoothing effect. Hattori et al. [95] studied the effects of various wet-chemical cleaning methods, followed by annealing in UHV, on the morphology of (0001) surfaces of wafers that were polished by CMP after being cut from crystals grown by hydride VPE or by Na-flux liquid-phase epitaxy (LPE). The best surfaces, in terms of the quality of the LEED pattern and of the RMS surface roughness, were obtained by immersion in a dilute aqueous HF solution followed by a 3-step annealing treatment in UHV (described below). The LPE sample exhibits a flatter surface (0.08 nm RMS roughness) than does the VPE material, with small clusters that are 0.6-1.2 nm in diameter. Hattori et al. [150] performed detailed studies of GaN (0001) surface morphologies for different in-situ surface treatments using wafers cut from crystals grown by hydride VPE and subsequently polished via CMP and also samples grown homoepitaxially on these wafers using MOCVD. For VPE samples, a three-step annealing process (12 h. at 200 °C; 1 h at 400 °C; 5 min at 500 °C) results in a sharp (1×1) LEED pattern and a surface with flat ∼10 nm terraces having an RMS roughness of 0.39 nm. Successful treatment requires that the vacuum be maintained at o5×10-7 Pa (4×10-9 Torr) during the second and third annealing stages. As noted in Section 3.3.2, this study indicates the best procedure for outgassing a new sample in UHV prior to in-situ cleaning. Somewhat different results (e.g., evidence of a higher defect density in one case) were found for VPE material obtained from different suppliers that had been grown and polished using different procedures. For the VPE samples used here, the onset of faceting in LEED and RHEED occurs at 550 °C, accompanied by the appearance of hillocks in STM and an increased Ga/N atomic ratio in XPS. In Section 4.5, which examines the thermal stability of GaN surfaces, it will be seen that 550 °C is well below the temperature at which the bulk decomposition rate is significant, which suggests that the faceting seen here is not directly related to decomposition. The species desorbed during annealing were also investigated using TPD, which showed H2, CH4, NH3, H2O, N2, CO, HCl, Ga and GaCl as the major desorption products. The presence of the Cl-containing species is thought to result from incomplete reaction in the VPE

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growth. It is noted here that the variety of species seen in TPD suggests a complex surface chemistry that might be related in some way to the observed low-temperature onset of faceting and decomposition. The effect of IBA on VPE samples was studied using a 0.5 keV Ar+-ion beam incident at 50° (presumably relative to the surface normal) followed by the 3-step annealing process described above. A (1×1) LEED pattern is observed that is inferior to that seen for annealing only, and STM shows the presence of islands and increased roughness. It is concluded that, after ion bombardment under these conditions, it is not possible to recover a flat surface via annealing at temperatures below which faceting occurs. Foussekis et al. [222] grew crystals using halide VPE, polished the (0001) and (0001̄ ) surfaces either mechanically or via CMP and studied the morphology using AFM and Kelvin-probe microscopy. In this case the (0001) surface is the smoother of the two for the as-grown material and, after CMP, exhibits an RMS roughness of o1 nm. McNamara et al. [278] extended this work, using PL and SPV to show the presence of a damaged surface layer following mechanical polishing. The work of Załuska-Kotur et al. [279] includes a simulation, based on a Monte-Carlo technique, of the evolution of the GaN (0001) surface morphology during annealing, which is compared to AFM data. The results show the growth and bunching of steps over time during annealing and identify the conditions required for the formation of uniform steps. As a general comment, the works cited above suggest the optimum procedures for preparing cut-and-polished (0001) and (0001̄ ) surfaces of bulk single crystals; although, the most suitable approach may depend on the method used in crystal growth. These studies also provide information (not described in detail here) as to the nature of the surface imperfections to be expected. Attention is now focused on the surface morphology of GaN grown by MBE and studied (usually) in situ. It is assumed here that exposure to the ambient atmosphere after growth does not greatly influence surface morphology and that, therefore, ex-situ structural results are indicative of the in-situ surface condition. As a practical matter, the issues involved here are well understood by the MBE community, and the surface-science experimentalist perhaps needs only a basic awareness of the subject. Piquette et al. [281] grew GaN (0001) and (0001̄ ) on sapphire and studied the surfaces ex-situ using AFM. Growth under conditions with a slight excess of Ga is mainly 2D and leads to flat surfaces with a relatively low density of shallow pits. On the other hand, stoichiometric growth is 3D and results in a higher density of deeper pits, and N-rich growth yields a highly-defected surface. Xie et al. [282] grew GaN (0001) under Ga-rich conditions on 6HSiC (0001) and on vicinal 4H-SiC (0001), the latter being 3.5° offaxis in the [1̄010] direction. Spiral mounds, but no pits, are seen for growth on the (0001) surface but not on the vicinal substrate, which shows only well-defined steps. Feenstra et al. [283] grew GaN (0001) on sapphire and observed smoother surfaces, with some pits and trenches, for Ga-rich vs. N-rich growth. Vézian et al. [284] grew GaN (0001) on Si (111) and observed spiral mounds under stoichiometric conditions (Ga/N flux ratio ≈ 1) but truncated pyramidal mounds for N-rich growth. Jeganathan et al. [285] found smooth (0001) surfaces, with steps having heights of atomic dimensions, for growth on SiC (0001) under slightly Ga-rich conditions. It was also found, using XRD, that the bulk crystallinity of the GaN is significantly improved for growth on atomically-clean SiC surfaces prepared by Ga cleaning (Section 3.2.1). Lee et al. [286,287] grew GaN (101̄0) on ZnO (101̄0) that was unintentionally cut several degrees off-axis in the [0001] direction. For thin layers (o1 μm thick), large flat terraces are seen for Ga-rich conditions with steps resulting from the miscut of the substrate; whereas, ̄ rough surfaces result from N-rich growth. For thicker layers, (1011) — or (1011) facets occur, which complicate the MBE growth of

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smooth non-polar surfaces. Heying et al. [280] used ex-situ AFM to compare the morphologies of (0001) samples grown by MBE vs. MOCVD. The MOCVD samples were grown on sapphire (0001) surfaces and were also used as templates for the MBE material. Both types of growth gave high dislocation densities (∼108 cm-2) which resulted in dislocation-mediated steps, hillocks and depressions. The shapes, sizes and distributions of the different defects, which depend on the growth conditions, were analyzed in terms of a theoretical description of the growth dynamics. Shen et al. [288] also used ex-situ AFM to compare the morphologies of (0001) samples grown by MBE vs. MOCVD. Two types of vicinal sapphire substrates having inclination angles in the range of 0.5° to 1.0° were used. One was off-axis in the mplane ([101̄0]) direction and the other in the a-plane ([112̄ 0]) direction. For substrates off-axis in the m-plane direction, MBE produces monolayer-high steps with "zigzag" edges for a 0.5° tilt angle, but step bunching occurs for greater angles and results in higher steps (3.6 nm high). For MOCVD growth, step bunching on a 1.0° off-axis substrate yields much higher steps (20 nm high) that are, however, much farther apart than for MBE. Still different behavior is seen for MBE growth on a GaN MOCVD template grown on a vicinal substrate, leading to the conclusion that morphology depends on both the vicinal angle and the growth technique. For substrates off-axis in the a-plane direction, similar behavior is seen for MBE except that the step edges are essentially straight rather than "zigzag". On the other hand, MOCVD growth shows essentially no dependence on the off-axis direction. Very flat surfaces were obtained by MBE on an MOCVD template grown on a substrate that was 1.0° off-axis in the a-plane direction. In summary, MBE growth under typical slightly Ga-rich conditions yields relatively smooth surfaces with steps and with some presence of pits or spiral mounds. This is consistent with the wellknown (Section 4.6) surfactant effect of a metallic-Ga bilayer that promotes 2D growth. Further improvement is possible using vicinal SiC (0001) or vicinal sapphire (0001) substrates or by MBE on an appropriately-grown MOCVD template. There is also evidence that, at least in the case of SiC (0001), the details of the substrate surface preparation can influence the morphology of the resulting GaN surface. For GaN grown ex situ and cleaned in situ prior to AFM or STM, surface morphology is closely linked to the cleaning method. Therefore, attention will now focus mainly on those studies that were conducted after some form of cleaning, either in situ or wetchemical. These are more relevant to the subject of the present review than are structural studies of the as-grown surfaces themselves. However, in the case of MOCVD, the surface morphology of the as-grown surface is also known [293] to depend strongly on several growth parameters. Maxson et al. [289] used LEEM to image atomically-flat terraces, separated by bilayer steps, on the (0001) surface of MOCVD material after cleaning in organic solvents and heating to 400 °C in UHV. However, the coverage of impurity C and O was not determined. Zhou et al. [86] studied GaN (0001) grown by MOCVD on sapphire (0001) and found that good STM imaging was possible only after cleaning in an aqueous solution of HCl, HF or NaOH at 70 °C. Cleaning in HCl gives an RMS roughness of 0.5 nm with terraces having a height and width of 1.2 ±0.5 and 224±84 nm respectively. Pits are seen clearly but only at step edges. These have a depth, width and density of 2.1±0.6 nm, 68±18 nm and 6.3x108 cm-2 respectively. Cleaning in HF yields pitting on terraces as well as at step edges, and NaOH leads to cleaning (with terrace pitting) followed by etching. Manske et al. [290] used in-situ STM to study GaN (0001) and (0001̄ ) surfaces grown by MBE or MOCVD and prepared by different methods. These included annealing in UHV, IBA (1 keV nitrogen ions) and reaction with Br2 generated in situ by electrolysis

of AgBr. For MOCVD (0001) surfaces, annealing in UHV yields a (1×1) LEED pattern (of unspecified quality) with the onset of faceting at ∼1050 K. A mild IBA treatment, with annealing up to 850 K, gives a sharp (1×1) LEED pattern with no faceting, but STM reveals the presence of nanoscale clusters. More-extensive IBA, with annealing up to 1050 K, gives a faceted LEED pattern with crystallites and the continued presence of clusters visible in STM. Exposure to Br2 at high temperature also results in nanoscale clusters and faceting. For MBE (0001̄ ) surfaces grown with a protective InN cap to permit transport in ambient air, desorption of this cap at 750 K results in a weak (1×1) LEED pattern and, again, clusters of various sizes in STM. Higher-temperature anneals improve the LEED pattern, in some cases giving a weak (2×2) reconstruction, but have little or no effect on morphology. Different treatments involving IBA or Br2 exposure at high temperature in general lead to textured surfaces with crystallites and clusters in STM and faceting in LEED. It was suggested that the clusters constitute Ga-rich GaN or GaN with a Ga adlayer. Oliver et al. [138,139] performed in-situ STM studies on (0001) MOCVD samples after in-situ cleaning and also on MBE samples grown in situ on MOCVD templates. The cleaning procedure consisted of either annealing at 770–870 °C in 2×10-5 Pa (1.5×10-7 Torr) of NH3 or IBA (200 eV nitrogen ions at 250–300 °C, annealing at 820 °C). Exposure to NH3 above 800 °C leads to the appearance of islands and steps, with alternating jagged and smooth edges, and a (3×1) RHEED pattern. The steps are 0.25±0.1 nm high, i.e., about half the c-axis length of the unit cell, which is equivalent to the spacing between Ga-N bilayers. With increasing temperature the islands become more ordered and then at 840 °C are replaced by a high density (1.45×1012 cm-2) of small triangular pits on flat terraces. At this point a (2×2) RHEED pattern appears; however, at 850 °C surface roughening is apparent in RHEED, and XPS (after sample transfer in air) indicates a Ga-rich surface. For samples cleaned by IBA, a (3×1) RHEED pattern appears, but the morphology is different from that seen after the NH3 treatment. The steps, which are again 0.26±0.1 nm high, do not have well-defined edges, and a few irregular holes, but no triangular pits, are observed. However, small bright features with a density of 3.1×1012 cm-2 are found in STM and are ascribed to N vacancies. Growth via MBE of GaN at 750 °C on an MOCVD template cleaned in NH3 at 840 °C gives a surface with a smaller pit density than on the template and with well-defined step edges. A detailed discussion of the possible mechanisms involved in the various structural changes was presented, leading to the conclusion that the best surface morphology, in terms of reduced defect density, results from MBE growth of a thin GaN layer on a template cleaned in-situ by annealing in NH3. A similar conclusion was reached by Reitmeier et al. [142] (Section 3.2.2) for MOCVD growth on a GaN template cleaned by annealing in NH3. It was further shown by Oliver at al. that sufficient MBE growth for this purpose can be achieved under conditions that are compatible with a conventional UHV surface-science chamber using thermal decomposition of NH3 on the substrate as the N-atom source together with Ga from a Knudsen cell. Hattori et al. [150] investigated the surface morphology of GaN (0001) MOCVD films grown homoepitaxially on substrates that were grown by hydride VPE. The preparation and characterization of the VPE substrates prior to MOCVD was discussed earlier in this section. The as-inserted samples showed a (1×1) LEED pattern even before cleaning, and the three-step annealing process described above led to a sharper (1×1) LEED with a weak additional (3×3) pattern. Annealing at 600 °C and above led to faceting and to an increased Ga/N atomic ratio indicating decomposition. As noted in the above discussion of the VPE substrates, this temperature is well below that at which rapid decomposition of GaN is thought to occur.

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Falta et al. [132] reported the (0001) surface morphology for MOCVD samples after annealing in UHV at 750 °C for 28 h. followed by in-situ cleaning by Ga deposition and desorption. Cleaning leads to a significant decrease in roughness on the terraces between steps vs. that seen for the as-grown sample. A fairly smooth (and presumably atomically-clean) surface could also be obtained by first cleaning in an N-atom plasma and then growing a few MLs of GaN in situ under Ga-rich conditions in an approach similar to that of Oliver et al. [138,139]. Strawbridge et al. [291] demonstrated a correlation between surface roughness and the energy of the plasmon loss peak in ELS (Section 4.7.2) for GaN as well as for AlN and InN. The primary beam energy in these experiments was Ep = 20 keV, and the beam was incident at a near-grazing angle of 2° relative to the surface. The loss peak comprises unresolved contributions from surface and bulk valence plasmons with the former occurring lower in energy by a factor of √2. For rough surfaces the bulk plasmon dominates, leading to an energy difference of ∼4 eV between smooth and rough samples. The effect arises from the fact that, although the beam is incident at a grazing angle relative to the macroscopic surface plane, the direction of impact on a microscopic roughness feature is closer to the local surface normal. Due to the high Ep, any small deviation from grazing incidence leads to a significant loss of surface sensitivity and therefore of surfaceplasmon intensity. Correlation with AFM data shows that the effect does not scale with conventional RMS roughness values but rather with the nature of the roughness. Surfaces with small, sharplypeaked grains exhibit bulk-like plasmons; whereas, those which large, flat-topped grains show predominantly surface plasmons. In summary, obtaining a reproducibly good surface morphology appears to difficult for in-situ cleaning of polar GaN surfaces. "Good" in this context means large, flat terraces with a minimal coverage of extraneous features such as pits or protrusions. Homoepitaxial growth of a thin MBE layer after in-situ cleaning appears to be a viable (and perhaps the only) approach to obtaining a good morphology after in-situ cleaning, at least for the polar surfaces. However, many of the in-situ cleaning procedures described in Section 3 have not yet been studied in detail from the perspective of morphological effects. Schulz et al. [131] used STM to observe the effects of Gacleaning and exposure to a nitrogen plasma on the morphology of the (112̄ 0) (a-plane) surface of samples grown by MOVPE on rplane sapphire. The initial surface exhibited many small and large pits with depths in the range of 30–60 Å, a corrugation of 10–15 Å in the area between pits and an RMS roughness of 2.6 nm. After outgassing and Ga-cleaning, as described in Section 3.2.1, a good (1×1) LEED pattern is seen, and the surface is much smoother with a roughness of 1-2 Å in the area between pits and an RMS roughness of 0.3 nm. It was suggested that surface protrusions, because of a higher surface energy, might evaporate faster than smooth (112̄ 0) terraces. It is further speculated here that in-situ cleaning appears to give better results for the (112̄ 0) than for the (0001) because of the greater stability (Table 2) of the non-polar surfaces. Exposure to the nitrogen plasma also results in a significant improvement in surface quality, relative to the as-inserted sample, but with a larger RMS roughness (1.1 nm) as well as shallow grooves of uncertain origin. 4.4. Defects, strain and other imperfections In this section various issues concerning sample imperfections, as they relate to surface-science experiments, will be discussed. Point defects (i.e., vacancies, interstitials and antisite species) in bulk GaN have been studied extensively, and this topic has been reviewed from both theoretical [12] and experimental perspectives [13]. However, bulk properties lie outside the scope of the

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present review. One manifestation of bulk defects that is familiar in surface-science experiments is the yellow luminescence [294] that appears when MOCVD GaN is exposed to a typical AES primary electron beam. Charge trapping by defects is a critical factor in determining BB (Section 4.7.3), which has an impact on many types of surface experiments. There is, however, only a relativelysmall body of work that deals directly with the possible consequences of point defects in GaN surface-science experiments. Here we are neglecting the substantial literature on the production and subsequent passivation of defects in plasma processing and other treatments relating to device fabrication, which lie outside the scope of the present review. Theoretical results [295] indicate that the diffusion of a wide variety of GaN bulk defects is isotropic, which suggests the absence of any significant tendency toward surface accumulation. However, the possible formation of complexes involving defects and H or O, which are common impurities in GaN, was not specifically considered. Experiment [296,297] indicates that under certain conditions an increased density (relative to the bulk) of some types of defects can be found near the GaN surface, and Packard et al. [298,299] have, using STM, observed a high density of N vacancies that aggregate into various ordered arrays on GaN (0001) or (0001̄ ) cleaned by annealing in UHV at 900 °C. Of somewhat more-immediate concern is the possibility of defect production or surface modification resulting from experimental probes themselves. Myers et al. [300], Wang et al. [301] and Nykänen et al. [302,303] have documented the effects on GaN of the several-keV electron beams typically used in AES and RHEED, which take the form either of ESD of surface species, defect creation or enhanced defect mobility. However, for the kinds of experiments of interest here, only AES measurements would potentially be affected, and these are typically confined to a small area of the sample surface. Auret et al. [304,305] have observed damage during deposition of refractory metals on GaN via electron-beam evaporation when stray electrons from the source are allowed to impinge on the sample. This effect is detected in the form of a degradation of the resulting contact properties but can be minimized with proper shielding. Due to lattice mismatch, differential thermal expansion and the presence of point defects, thin GaN films grown on sapphire are inherently strained, which has been shown to affect bulk properties (e.g., Refs. [306–309]) as well as various surface characteristics. The first two effects contribute to axial strain, while point defects generate hydrostatic strain. Cai et al. [310,311] and Palisaitis et al. [312] reported strain-induced shifts in, respectively, AES and ELS transition energies, and Ritchie et al. [313] found similar effects in the N 1s near-edge x-ray absorption fine structure. In a complementary study, Xu et al. [314] observed a shift of the Ga MVV AES transition to lower KE with increasing temperature, which was explained in terms of thermal expansion of the lattice. All these studies were supported by ab-initio theoretical analyses, which show that the effects arise from structural perturbations; namely, changes in lattice constants and interatomic distances. Florescu et al. [315] have used AFM to observe the effect of strain on GaN surface morphology. Interestingly, an increase in roughness appears to correlate with a decrease in compressive strain. However, to our knowledge there have been no data documenting strain effects on GaN surface reconstruction, which is consistent with theoretical results [316] indicating the absence of such phenomena. However, other theoretical work [317] finds that adatom diffusion can be significantly affected by the presence of strain. Although to our knowledge there has been no experimental demonstration of such an effect, it is possible that strain might play a role in the sample-dependent faceting of GaN surfaces noted in Section 3.3.1. One might speculate that facet formation could provide a mechanism for the relief of strain during high-

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Fig. 10. N (solid line) and Ga (dashed line) desorption fluxes (left hand axis) plotted as a function of temperature. The dotted line is the flux for 1 ML desorption per second. The calculated surface residence time, τs, for N and Ga is also plotted (right hand axis). The open-circle datum point is the GaN decomposition rate estimated from heating GaN in 50 Torr of H2 for 10 min. The data shown are for cubic GaN but have been used in reference to the growth of wurtzite GaN. From Koleske et al. [324] (reproduced with the permission of AIP Publishing).

temperature annealing. A strain-induced polarization field (Section 4.2.2) could also be a source of line broadening and/or shifting in XPS core-level data, which could arise from local strain-induced variations in BB. For example, Jang et al. [258] have shown that tensile or compressive strain can cause a significant change in BB through a piezoelectric polarization effect. As a practical note this indicates that some care should be applied in designing the sample mounting in surface-science experiments so as to avoid strain. 4.5. Thermal stability and decomposition The thermal stability of GaN surfaces is a significant issue both in surface cleaning and in many experiments. In keeping with the main focus of this review, the discussion here is limited to studies performed in UHV while omitting the many works that deal with stability in growth environments or in high (several Torr or more) pressures of H2, N2, etc. The thermal decomposition of GaN in vacuo has been studied using several techniques [134,143,318–328] including thermogravimetric analysis (i.e., mass loss vs. temperature), gas-phase mass spectrometry, RHEED intensity oscillations, film thickness measurement and XPS. Many of these works include detailed discussions of kinetics and mechanisms; however, here the main interest is in the effect on surface stoichiometry. Fig. 10 summarizes the essential results, which show that congruent evaporation (i.e., equal rates for Ga and N) occurs at 780 °C, above which the loss of N is more rapid than that of Ga. The data shown are for cubic GaN but have been used [324] in reference to the growth of wurtzite GaN. This supports the empirical observations discussed in Sections 3.2–3.4, which indicate that an N-deficient surface results from annealing in vacuo at temperatures (800–900 °C) often used for in-situ preparation of clean GaN surfaces. Below 780 °C the loss of Ga is faster, but at still-lower temperatures the absolute rate of loss of either species may be so slow as to be inconsequential. In Sections 3.2.1 and 3.2.2, the effects of liquid Ga [134] and of NH3 vapor [143] in, respectively, promoting or inhibiting thermal decomposition have already been noted. A similar inhibition effect has been observed [328] for "active nitrogen", which is essentially a mixture of atomic N and electronically-excited N2 produced by a plasma source. Early studies in vacuo by Groh et al. [318], using

thermogravimetric analysis, found that decomposition was not clearly evident below 980 °C. However, the sensitivity limit of the measurement (10-5 gm) corresponds to ∼63 GaN bilayers over an area of 1 cm2. In TPD, effusion of N from MOCVD GaN, marking the onset of decomposition, is first detectable [319] at 850±20 °C. On the other hand, for samples grown at typical MOCVD growth temperatures, effusion of hydrocarbon impurities is complete by ∼550 °C. Freundt et al. [322] grew GaN (0001)−(1×1) surfaces by in-situ MBE and observed the N 1s XPS peak and also a Ga LMM XAES peak of nearly the same KE (and, therefore, surface sensitivity). Little change is seen up to 850 °C, but pronounced decomposition is observed at 900 °C. Benemanskaya et al. [326] found the thermal stability of the (0001) surface in vacuo in the 700–950 °C range to increase with decreasing mosaic spread as seen in AFM, which suggests that the boundaries between mosaic domains are inherently unstable and that the stability should increase with the degree of crystal perfection. Fernández-Garrido et al. [328] observed RHEED intensity oscillations for the (0001) surface in the 740–805 °C range, within which the decomposition is nearly congruent. This indicates a layer-by-layer process, and the continued presence of a streaky RHEED pattern suggests the absence of significant roughening. Such a congruent process is not expected to have a significant effect on surface stoichiometry, and these results therefore suggest that 800 °C is a safe upper limit on the temperature for annealing GaN (0001) in UHV. An activation energy of 3.1±0.1 eV was obtained from the kinetic data, which is in good agreement with the value of 3.24 eV reported by Groh et al. [318] using thermogravimetric results in the 900–1250 °C range. To our knowledge, there have been no studies under UHV conditions that compare the relative thermal stabilities of the (0001) and (0001̄ ) surfaces; although, distinct differences have been seen (e.g., Ref. [249]) in various gas ambients. Some caution should be applied in considering thermal decomposition. As is evident from the results discussed, the estimate for the maximum sustainable temperature depends on the method used to detect decomposition and on the criteria for what constitutes a "significant" effect. A possible complication in interpreting decomposition experiments is that some measurements, such as mass loss, are primarily bulk-sensitive while others (e.g., XPS) are surface-sensitive. Quantitative differences could result depending on whether diffusion from the bulk or desorption from the surface is rate limiting. The studies discussed here are largely concerned with macroscopic decomposition at elevated temperature and not with microscopic effects, such as the formation or diffusion of pointdefects, that can occur at lower temperatures. A classic example is the work of Proix et al. [329] in which a GaAs (110) surface was formed by cleaving in UHV, after which annealing-induced changes in work function were studied. Defect formation was detected beginning at ~350 °C, well below the onset of rapid macroscopic decomposition (∼580 °C). Similarly, Bermudez et al. [123] observed an irreversible increase in upward BB on n-type MOCVD GaN (0001) when an as-received sample was heated for the first time in the 300–700 °C range in UHV. It was suggested that the effect might result from the diffusion to the surface of acceptor-like defects remaining from growth. As noted by Rickert et al. [84], Ga vacancies are potential acceptors, and these are expected to occur under MOCVD conditions, which are typically N-rich (i.e., Ga-deficient). Similar BB increases were seen for ntype MOCVD material by Uhlrich et al. [94], Maffeis et al. [330] and Kim et al. [331] after annealing an as-inserted sample for the first time in UHV at 550, 600 and 500 °C respectively and by Bartoš et al. [189] for different surface orientations of n-type GaN grown via hydride VPE either as a film or as a single crystal. It should be noted that Uhlrich et al. [94] and Kim et al. [331] also

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found an increase in downward BB after annealing p-type material, which suggests the possible involvement of a donor-like defect. The essential point is that "thermally stable" on a macroscopic level does not necessarily mean "unaffected by heating" on a microscopic level. 4.6. Stoichiometry and reconstruction (AES, ISS, XPS, LEED, RHEED, STM) In this section, studies addressing the chemical and physical structure of various GaN surfaces will be reviewed including both experimental and theoretical work. The focus here is mainly on stoichiometry and reconstruction. The following section (Section 4.7) will then discuss surface electronic structure as determined using spectroscopic methods supported by ab initio theory. There will, of necessity, be some overlap between the two sections with regard to subject matter and references cited. In keeping with the focus of this review, studies dealing mainly with growth issues will be omitted. Sections 4.6–4.8 will review only those studies that are directly concerned with clean surfaces. "Clean" in this context includes surfaces with adsorbed Ga or N but with no foreign atoms. Many references that focus on adsorption and interface formation, which are discussed in Secs. 5–8, also provide information about the clean surface as a preliminary to analyzing adsorbate effects. In discussing adsorption in these later sections, notice will be taken as appropriate of such additional results. Similarly, references that relate to structure and stoichiometry but deal mainly with surface cleaning, morphology, etc. have already been discussed, and this material will not be repeated here. As an historical note, one of the earliest XPS studies of GaN was the work of Carin et al. [152] on films grown by reactive sputtering onto Si and GaAs substrates. Changes in the XPS and XAES structure due to preferential sputtering of light elements (N and impurity O) by a 2 keV Ar+ beam were analyzed, and sputtering yields were determined. In both Sections (4.6 and 4.7) a distinction is made between surfaces formed using MBE and studied in situ and those for which the sample was grown ex situ, by whatever means, and then cleaned in situ. These are really two different material systems, and an understanding of both is important for a complete appreciation of GaN surface properties. This is already evident from the discussion of morphology given in Section 4.3 and will become more so in the following descriptions of reconstruction and electronic structure. Some introductory remarks on this subject, which anticipate the following discussion, are helpful in providing context for Sections 4.6 and 4.7. For MBE growth combined with in-situ experimental study, it will be seen that the surface composition and structure can be reproducibly controlled by varying the growth temperature and μGa (or equivalently μN), which is accomplished by adjusting the relative fluxes of Ga and atomic N. The concomitant changes in surface morphology (Section 4.3) are by now well understood, and it is generally agreed that a small excess of Ga leads to a smoother surface due to the surfactant effect of a metallic Ga layer in promoting 2D growth. Several different reconstructions have been found, which are characteristic of the surface polarity and growth conditions. On the other hand, for surfaces cleaned in situ by any of the methods discussed in Section 3, the typical LEED pattern is (1×1) for both (0001) and (0001̄ ). This pattern can vary significantly in quality depending on the methods employed for substrate growth and surface cleaning, and the exact nature of these (1×1) surfaces is not well understood. A bare (0001) surface (with no Ga or N adatoms) is found theoretically to be unstable, and one possibility is that the LEED pattern arises simply from bulk diffraction with a disordered surface layer. This might apply in some cases; however,

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in others the pattern appears with sharp spots and a low background, which suggests a well-ordered surface. Furthermore, theory shows that a bare and unreconstructed (0001) or (0001̄ ) surface is metallic, with a finite density of states at EF, as a consequence of the partially-filled Ga or N DBs. However, UPS data typically show the (1×1) surface after in-situ cleaning to be semiconducting. The lack of an atomic-level understanding of such (1×1) surfaces is a major impediment to progress in the fundamental surface science of this material. Some studies do observe a reconstructed surface after in-situ cleaning. In the few cases where this occurs, it is most often a (2×2) structure [64,95,139]; although, (√3×√3)R30°, (3×1) and (3×3) have also been reported [139,150]. These may not be related in any simple way to those observed for in-situ MBE growth and analysis. In principle, the (2×2) is easily understandable in terms of the ECR through a mechanism that was described in Section 4.1.1. Since in-situ cleaning frequently involves annealing at temperatures above ~800 °C, for which N is lost more quickly than Ga (Section 4.5), one might suppose that Ga adatoms or N vacancies at a coverage of 0.25 ML could be the means for stabilizing a (2×2) structure. There is theoretical and experimental support for this view, which will be presented for the (0001) surface in Section 4.7. Since there is more than one equivalent location for the adatom or vacancy within the (2×2) SUC, this structure could appear as a (1×1) (perhaps with an elevated background intensity) if the adatoms or vacancies are randomly placed within the cell. Another possible mechanism, according to the ECR, for stabilizing a (0001)- or (0001̄ )−(2×2) surface is the adsorption of 3/ 4 ML of H, which has been the subject of numerous theoretical studies. Since H is a poor scatterer of electrons, such a surface might be difficult to distinguish in LEED from a (1×1) if the positions of surface Ga or N atoms are not greatly affected by Ga-H or N-H bond formation. However, experiment (Section 7.3) shows that the ESD of H from the (0001) surface is very efficient under typical LEED conditions for the primary electron beam energy and current density, which means that any such stabilizing effect of adsorbed H would be rapidly lost in a LEED experiment. It is not known, however, if the (0001̄ ) surface behaves similarly with regard to ESD of H. Furthermore, ISS and HREELS data (Section 7.3) show the (0001), although not the (0001̄ ), to be relatively free of H for n-type MOCVD material after in-situ cleaning. Thus it is possible that the (0001̄ )−(1×1) surface might, in some cases, actually be the H-stabilized (2×2), at least for material with a high concentration of bulk H. Evidence that this is indeed the case will be given in the following discussion of the (0001̄ )−(1×1); although, this does not appear to be likely for the (0001)−(1×1). It also may not be likely in the case of MBE material or bulk single crystals, which generally contain less bulk H than MOCVD material grown in an H2-rich environment. To our knowledge, no specific atomistic models have been proposed for the (√3×√3)R30°, (3×1) or (3×3) reconstructions sometimes seen for the in-situ-cleaned (0001). A further novel (0001) structure, a (√3×2√3)R30°, has been observed by Munkholm et al. [332] during MOCVD growth using in-situ grazing-incidence x-ray scattering. This is believed to arise from 1/3 ML of VGa in the lattice-terminating layer, and the transition between this and the bare (1×1) was studied as a function of temperature and NH3 pressure. To our knowledge, this structure has not been observed other than under MOCVD conditions. As a final introductory remark, many of the MBE surface structures discussed here involve Ga adlayers. Independent studies of Ga adsorption and desorption described in Section 5.18 provide additional useful information regarding the composition and structure of such adlayers. 4.6.1. The (0001) surface We will begin with a discussion of the chemical and physical

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structure of the (0001) surface for samples grown via MBE and studied in situ. Some of these results have been reviewed already in Refs. [1–4], which also consider other surface orientations. Experimental data are presented in Refs. [117,333–362] and theoretical work in Refs. [53–55,351,363–380]. Some studies (e.g., Ref. [357]) also address the effects on GaN (0001) surface reconstruction of As contamination, which can occur when the MBE chamber has been used previously to grow As-containing materials. This aspect will be discussed in Section 5.3, which deals with the adsorption of As. Most experimental work in this area employs RHEED during MBE, and some studies also make use of LEED after growth. Other investigations also include AFM [337,339,348], STM [340– 346,348,350–352], LEED I–V analysis [358,359], standing wave measurements [360,362] and/or in-situ AES or XPS [349,355,356]. An early study of (0001) surface reconstruction during MBE was that of Iwata et al. [333] who reported transitions between (1×1), (2x2) and (4×4) RHEED patterns depending on temperature and on whether the N plasma source was on or off. Subsequent work [334–339,347–349,353–356] established correlations between growth conditions, stoichiometry, substrate polarity, etc. and the appearance of the (2×2) and other structures. In particular, King et al. [349] applied a variety of techniques, including LEED and XPS, to the study of MBE using NH3 as the source of N (referred to as "gas-source MBE"). Experimental work to identify the atomic arrangements of the different (0001) MBE structures began with that of Smith et al. [339–344,350] and continued with that of Xue et al. [345,346,351,352], Xu et al. [358], Yu et al. [359], Harland and Li [360], Wang et al. [361] and Sun et al. [362]. Fig. 11 summarizes the results of Smith et al. [339–344,350], which were obtained using a combination of AES, LEED, RHEED and STM supported by ab-initio computational modeling (described in more detail below). A (0001) surface was first grown via MBE on a GaN/sapphire substrate prepared using MOCVD [344]. The (2×2) structure is formed by exposing this surface to atomic N at about 600 °C. The (5×5) is prepared by annealing the as-grown surface at 750 °C, depositing 0.5 ML of Ga and then annealing again at 700 °C and the (6×4) by depositing 0.5 ML of Ga on the (5×5) followed by annealing at 700 °C. The "(1×1)" can be formed by depositing 1 ML of Ga on the (6×4) and then annealing rapidly at 700 °C or by terminating the original MBE growth under Ga-rich conditions. The surfaces are atomically flat with the (5×5) and (6×4) typically coexisting in well-ordered domains under conditions for which either is present. A (2×2) surface can also be prepared by slowly heating the (5×5), to desorb Ga, until the fifth-order diffraction features disappear. It is not known whether this is the same structure as that formed in the procedure described above, and neither (2×2) surface appears to be well ordered although both are semiconducting. The structure was thought to correspond to 0.25 ML of either N adatoms in H3 sites or Ga adatoms in T4 sites, either of which satisfies the ECR (Section 4.1.1). These (2×2) structures are believed [341] to be distinct from that reported to occur during MBE growth, which may instead arise from As contamination. The (5×5) is also semiconducting, and the model proposed [344] on the basis of experimental and theoretical results is illustrated in Fig. 12. This consists of 1 Ga adatom per SUC in a T4 site, 2 N adatoms in H3 sites and 3 VGa in the lattice terminating layer (not shown in Fig. 12), which nearly satisfies the ECR. With 25×3/4 |e| per SUC in Ga DBs on the bare (0001) surface, 9 |e| are removed by the 3 VGa, and 9 |e| are used to make 6 N-Ga and 3 Ga-Ga adatom back-bonds, which leaves only 3/4 |e| in a Ga DB. The site labeled "DB" is a particular rest-atom (i.e., a terminating-layer Ga) that could possibly bond to another adatom. The (6×4), which is also semiconducting, exhibits complex characteristics in STM, and possible interpretations of this structure were presented.

Fig. 11. Upper: Schematic phase diagrams illustrating the coverage and temperature dependence of the reconstructions on the (a) (0001̄ ) N face and (b) (0001) Ga face. Ga coverage increases from left to right in both diagrams, and the temperatures given correspond to either order-disorder phase transitions or annealing transitions. Cross-hatched regions indicate either mixed or intermediate phases. RHEED patterns for both faces, as viewed along the [112̄ 0] azimuth, are also shown. The '1  1' label across the top of either panel indicates the RHEED pattern seen during growth. From Smith et al. [339] (reproduced with the permission of AIP Publishing). Lower: Ga/N Auger intensity ratios for various reconstructions on the Ga face. The scale on the right shows the corresponding number of Ga adlayers, derived from a numerical simulation of Auger intensities. From Smith et al. [344] (Copyright 1999, reproduced with permission from Elsevier).

The "(1×1)" or pseudo-(1×1) structure, which figures prominently in much of the fundamental science of the GaN (0001) surface, has been described in detail by Smith et al. [340]. The RHEED and LEED patterns for this surface are (1×1) with additional satellite features indicating a structure that is not truly (1×1), whence the designation "(1×1)" or pseudo-(1×1). Careful observation of the LEED temperature dependence indicates an incommensurate fluidGa phase that transitions to a disordered fluid phase as the temperature increases from RT to 350 °C. The metallic-Ga layer represents a coverage of 2-3 ML (Fig. 11) and lies on top of the Ga

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Fig. 12. Simultaneously-acquired dual bias images of the (5  5) reconstruction. Sample biases are þ2.0 and
2.0 V with gray scale ranges of 0.5 and 0.6 Å for (a) and (b) respectively. A 5x5 grid is superimposed on each image with the corners located on the bright features seen in (a). Shown in (c) is the same 5x5 grid where the underlying primitive lattice is shown in empty circles. Black circles are T4 adatom sites. Dark-gray circles are H3 adatom sites. Light-gray circles are DB (dangling bond) sites. The small diamond shapes represent the basic structural unit for the (5x5), which is found in three possible orientations throughout the surface. The heavy black line shows the (5x5) SUC. The three VGa per SUC are not shown. From Smith et al. [344] (Copyright 1999, reproduced with permission from Elsevier).

terminating layer of the substrate as illustrated in Fig. 13a. Furthermore, the metallic-Ga layer is laterally contracted relative to the Ga-Ga nearest-neighbor distance in GaN (3.19 Å), which is greater than in bulk Ga (2.7 Å). This model for the "(1×1)" is then generally termed the "laterally-contracted bilayer" structure. A further aspect [340] of the "(1×1)" is the appearance of RHEED satellites, with a spacing of either 0.16 or 0.08 k1 relative to the (1×1) spacing of k1 = 2.28 Å−1, that appear when cooling to below 350 °C after growth. These structures, the difference between which is not well understood, are labeled "(1+1/6)" and "(1 +1/12)" respectively. The former can exist down to RT for a narrow range of θGa, but for higher θGa conversion to the (1+1/12) occurs below 200 °C. Upon raising the temperature above 200 °C the structure converts back to the (1+1/6). No difference between the two structures is seen in STM, and they are labeled collectively as "(1×1)". Xue et al. [345] grew GaN (0001) on atomically-clean and flat Si-terminated SiC (0001)−(3×3) substrates on which 150 Å of AlN had first been deposited as a buffer layer. Using STM and RHEED, the authors observed (2× 2), (4×4) and (5×5) reconstructions. A (2×2) was also observed during growth at 650 °C under Ga-rich conditions, and some controversy exists (see Ref. [345] and Section 5.3) as to whether this structure and also the (4×4) and (5×5) seen in this study are the result of As contamination. Terminating the growth by turning off the supply of N atoms and then depositing 2 ML of Ga at 650 °C, followed by cooling rapidly to RT

("quenching"), gave a bare surface with a (1×1) structure and θGa slightly less than 1 ML. A second (2×2) phase was then prepared by depositing 1 ML of Ga on the (1×1) at RT and annealing at 200 ° C, with higher-temperature anneals giving a mix of (4x4) and (5x5) structures. This second (2x2) was suggested to result from 0.25 ML of Ga in T4 sites, which satisfies the ECR. The (4x4) was ascribed to the desorption of one-fourth of the Ga from the (2x2), and both models were supported by ab-initio computational models giving the total energy vs. μGa. However, islands comprising Ga multilayers are also observed, which makes it difficult to obtain meaningful coverage estimates using AES. On the basis of STM data, the (5x5) is proposed to represent a variation of the (4x4) that consists of parallel rows of Ga adatoms in T4 sites running along the [112̄ 0] direction. The stability of this structure was attributed to a Peierls distortion (Section 4.1.1) as a result of which the metallic band of half-filled states splits into filled and empty bands to give a semiconducting system. However, this distortion was not clearly illustrated or described in terms of the (5x5) structure. Returning to the (1×1) surface after growth, further deposition of Ga at RT led to (√7x√7), (5√3x2√13) and (10x10) structures in STM in order of increasing θGa. Xue et al. [346,351,352] later extended this work to include further analyses of the more-complex reconstructions. The asgrown (1x1) is further described as the bare Ga-terminated surface with θGa o 1 ML, which is smooth but shows poor ordering. One might speculate that the surface is stabilized by 1/4 ML of VGa, as

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Fig. 13. (a) Side view of possible structural model for the ‘‘(1  1)’’ surface (at a given instant in time) consisting of 2.7 ML of Ga sitting on top of the Ga-terminated bilayer. The open circles represent the various possible positions of first-layer Ga atoms plotted with respect to each of several GaN unit cells and illustrate the timeaveraged height of the first-layer Ga atoms and thus the 1  1 contour which the STM tip will follow. At a given instant in time, however, this incommensurate structure will manifest itself in diffraction as satellites surrounding the integral order peaks. From Smith et al. [340] (reproduced with the permission of the American Vacuum Society). (b) Formation energies for various reconstructions of the GaN (0001) surface as a function of Ga chemical potential μGa. All lowest-energy structures except the Ga double layer exhibit (2  2) periodicity, but energies are expressed in eV per 1  1 cell relative to that of the relaxed bare (1  1) surface. "Ga adlayer" means a full ML of Ga in T1(atop), T4 or H3 sites. From Segev and Van de Walle [375] (Copyright 2007 by the American Physical Society).

suggested by the ECR, that is not arranged in a well-ordered pattern and thus results in a (1×1) rather than a (2x2) LEED pattern. The (4x4) structure described above, with the Ga adatom coverage reduced to 3/16 ML from the 1/4 ML of the second (2x2) structure discussed by Xue et al., does not satisfy the ECR since there are then three "extra" electrons per (4x4) cell. The authors suggest that each occupies a Ga DB and that the structure is stabilized by a repulsive interaction between these negatively-charged Ga atoms. A theoretical analysis [351] indicates that the (4x4) is only slightly less stable than the parent (2x2) at intermediate values of μGa. With reference to the controversy regarding As contamination [345] that was mentioned above, one notes that addition of 1/16 ML of As to the (4x4), to form three As-Ga back-bonds, should give a stable surface with no unpaired electrons. This low a θAs might be difficult to detect in AES. It was also possible to form what might be an N-adatom (2x2) structure by exposing the (1×1) to the nitrogen plasma and then annealing, but the surface was rough and not well ordered. A more-extensive study of the (5x5), which coexists with the (4x4), was performed, and further STM data were obtained for the (√7×√7), (5√3×2√13) and (10×10) structures. Specific models were also proposed for these complex structures, which have been reviewed by Bakhtizin et al. [4]. Foxon et al. [117] and Hughes et al. [336,347] performed RHEED studies of a (2x2) reconstruction for GaN (0001) grown homoepitaxially by MBE on hydride VPE substrates that were in turn

grown on SiC (0001). It was determined that the structure arises from Ga adatoms on top of an ML of adsorbed Ga, and a thermallyreversible order-disorder transition was observed in which the (2x2) converts to a (1×1) upon heating above 750 °C and returns when cooled to 400–500 °C or below. The (1×1) was suggested [117] to result from the single adlayer of Ga on top of the Ga lattice-termination layer. The (2x2) is also removed by deposition of excess Ga or by adsorption of O. In the former case the (2x2) returns when the excess Ga is desorbed and in the latter when the sample is heated to 4600 °C and exposed to a Ga flux equivalent to ≥3 ML, which removes the adsorbed O. Different results were obtained in this work for GaN growth on sapphire (0001) substrates that were first nitrided (exposed to the N plasma at high temperature). It is now known (Ref. [7] and works cited) that this process leads to N-polar GaN (0001̄ ); whereas, Ga-polar (0001) material is formed when a thin AlN or GaN buffer layer is deposited at low temperature (550–650 °C) prior to growth. Xu et al. [358] and Yu et al. [359] performed quantitative LEED analyses of a (1×1) structure grown by MBE on an atomically-clean Si-terminated SiC (0001)-(√3x√3)R30° substrate with no buffer layer or pre-growth nitridation. Growth was performed at 650 °C with a Ga/N flux ratio of 2, after which the Ga and N sources were extinguished and the sample quenched to RT, which gave a (1×1) RHEED pattern. The best fit to the data is obtained for a true (1×1) model with 1 ML of Ga adatoms in T1 sites above the Ga terminating layer of the substrate with a Ga-Ga bond length between layers of 2.51 Å. This differs significantly from the (1×1) model described by Xue et al. [345,346,351], which consists of a somewhat Ga-deficient bare surface; however, the growth conditions were not identical in the two studies. Most theoretical studies of the (0001) surface (described below) find a Ga ML to be unfavorable under equilibrium growth conditions; however, such a structure may be achievable in UHV. Harland and Li [360] used standing waves in an STS experiment to study the "(1×1)" surface described by Smith et al. [340]; although, the reported lateral contraction of the outer-most Ga layer was not observed. The results indicate free-electron-like behavior in the surface layer, which is consistent with the metallic character. Wang et al. [361] reported a (√3x√3)R30° reconstruction for a (0001) surface grown by MBE on an atomically-clean, Si-terminated SiC (0001)-(√3x√3)R30° substrate. Growth was performed at 650 °C with no buffer layer or pre-growth nitridation, after which annealing was carried out at 620 °C while continuing to flow N2 through the plasma source with the discharge extinguished. No impurities were detected in AES after cooling to RT. An analysis of the LEED pattern was done that included I–V measurements and the observation of LEED intensity vs. the angle of incidence of the primary beam. The result, which was supported by ab-initio modeling, indicates a two-phase structure consisting of bare (1×1) regions mixed with areas having a (√3x√3)R30° structure with Ga adatoms in T4 sites. The latter regions cover a slightly larger fraction of the sample surface and lie higher than the (1×1) by a distance equal to a single Ga-N bilayer thickness. Sun et al. [362] performed standing-wave STM studies of the "(1×1)" structure and compared the results with those from a band-structure calculation for the bilayer. They observed effects due to electron scattering at dislocation-induced steps and at structurally-transformed areas, the latter being associated with deliberately-deposited InN islands. It appears, from the results discussed above, that the (0001) reconstructions obtained in MBE are very sensitive to the growth conditions and to the nature of the substrate. A summary of results that illustrate this point is given by Wang et al. [361]. In particular there are different understandings of what constitutes the (1×1) and (2×2) surfaces, and it is possible that there may be more than one structure for each, depending on substrate, growth conditions,

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etc. There is, however, general agreement that Ga-rich conditions (Ga/N flux 4 1) are needed in order to obtain 2D growth and smooth surfaces and that the observed reconstructions are all related in some way to adsorbed Ga or N. Moving now to the subject of theory, most studies [53–55,363– 380] find the bare, relaxed (0001) surface to be without reconstruction. However, a few groups [381–383] have reported a (2×1) structure consisting of an inward displacement of half the Ga atoms. This lowers the energy by about 0.07 eV per Ga atom, relative to the (1×1) surface, and the difference in vertical positions between the two sets of Ga atoms is about 0.6 Å. Finding such an effect, which was first reported in the theoretical study of Kempisty et al. [381], requires the use of a larger SUC than the (1×1) normally employed in modeling the bare (0001) surface. The up (down) Ga atoms are sp3 (sp2) hybridized, and the DOS shows a

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difference from the (1×1) surface with respect to the Ga DB surface states. However, no magnetic moment (μ o 0.005 μB per SUC) is found [382] for either the (1×1) or (2×1) surface. In Section 5.18, which deals with Ga adsorption, other theoretical studies will be described that also identify a (2×1) reconstruction of the bare (0001) surface. It is possible that beginning the geometry optimization from a distorted, rather than planar, (0001) surface may assist the process of relaxing into the slightly more stable (2×1) structure if there is a significant energy barrier between the (1×1) and (2×1). To our knowledge, this (2×1) reconstruction has not been conclusively observed experimentally. However, Smith et al. [340,343] observed a (1×1) RHEED pattern during growth that changed to a (1×2) when the sample was annealed at 800 °C and then cooled to RT. The (1×2) surface thus formed was described

̄ and (d) semi-polar (112̄ 2) orientations as functions of Fig. 14. Calculated phase diagrams for surfaces with (a) polar (0001), (b) non-polar (112̄ 0), (c) semi-polar (1011) temperature and Ga BEP. The stable reconstructions on these surfaces are also schematically shown in top-down views. From Ito et al. [380] (© IOP Publishing. Reproduced with permission. All rights reserved.).

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[340] as being disordered, but no further details were given. Shen et al. [354] observed a (1×2) RHEED structure, and also (2x2) and (5x5) structures, after cooling below 400 °C following MBE growth at 700 °C under Ga-rich conditions. These authors also found that which structure forms depends sensitively on the Ga flux during growth and that samples exhibiting the (1×2) also show the best properties in terms of XRD, low-temperature PL and Hall mobility. The predicted small stabilization energy of the (2x1) (or (1×2)) relative to the (1×1) might mean that it is sensitive to perturbation by defects, adsorbates, strain, etc. Thus, the appearance of the (1×2) structure would be consistent with a higher material quality. This suggestion is reminiscent of the situation that pertains to the cubic SiC (100) surface, for which one finds a higher-order c(4x2) reconstruction for a very clean and defect-free surface but a lowerorder (2×1) when there is any small imperfection [384,385]. However, it is not known if these (1×2) GaN structures are the same as that found theoretically for the bare (0001) surface. There have been many theoretical studies that address the physical and chemical structure of the (0001) surface reconstructions as part of a larger study of other surfaces or of adsorption or interface formation. These will be noted in subsequent discussions dealing with these topics. Here we consider only those studies that are largely or entirely focused on the (0001) reconstructions in particular. Generally, those theoretical studies that treat the (0001) in passing arrive at essentially the same description as do those that investigate this surface in detail. Fig. 13b summarizes the theoretical results for in-situ preparation of the (0001) surface under thermodynamic equilibrium, which have been observed in numerous computational studies [54,371–375]. Under N-rich conditions a (2x2) structure with 0.25 ML of N in H3 sites is the most stable. The H3 is preferred over the T4 because it avoids a repulsive interaction between the adatom and N in the first underlayer. Moderately Ga-rich conditions favor a (2x2) with 0.25 ML of Ga in T4 sites, which is facilitated by an attractive interaction between the adatom and the first-underlayer N. Both these (2x2) structures satisfy the ECR and result in a semiconducting surface. A (2x2) structure with 0.25 ML of Ga vacancies, which also satisfies the ECR, is slightly less stable than the N-adatom (2×2), but other structures involving a laterallycontracted ML of Ga in T1, T4 or H3 sites are all unfavorable under equilibrium conditions. Very Ga-rich conditions lead to the "(1×1)", also known as the pseudo-(1×1) or laterally-contracted Ga bilayer structure. The Ga coverage is 4/3 ML in the outer-most (first) layer and 1 ML is the second, giving a net metallic-Ga coverage of 2.33 ML. The driving force for the contraction derives from the fact that the Ga-Ga distance in bulk Ga (~2.7 Å) is smaller than in the GaN (0001) surface (~3.2 Å). Only the outermost Ga layer is contracted; whereas, the lower layer is not. It is also found that the relaxed, ideally-terminated surface is never the most stable structure. Earlier theoretical studies [363–369], reviewed by Neugebauer [1], obtained somewhat different results, in some cases possibly as a result of including the Ga 3d electrons in the PP rather than as valence states (Section 4.1.1). Similar theoretical results for the (2x2) N-adatom and Ga-adatom structures were obtained by Xue et al. [351]. Rinehimer et al. [376] studied Ga adlayers on GaN (0001) using force-field MD and ab-initio DFT methods for the purpose of formulating an accurate model for the laterally-contracted bilayer. Normally computational models for this structure employ a (√3x√3)R30° SUC, in which the top layer of the Ga bilayer is rotated relative to the underlying layer. This is done in order to make the calculation tractable by minimizing the required size of the SUC. However, if this rotation were real it would lead to a similar rotation of the 1/6 and 1/12 satellites [340] discussed above, which is not seen in LEED or RHEED. It was found that a multi-domain structure consisting of (1×6) unit cells can explain the appearance

of the 1/6 satellites in LEED. The domains form an hexagonal pattern, and the lateral contraction is uniaxial along the x6-direction rather than being isotropic as in the simpler model. However, the ab-initio total energy is very close to that of the (√3×√3)R30° model. Ito et al. [377–380] have computed phase diagrams, shown in Fig. 14, for the (0001) and other surfaces that give the stability of different surface structures as a function of temperature and Ga BEP. Although this work is concerned largely with MBE growth issues, the results are nevertheless valuable in understanding surface reconstructions. The results for the (0001) surface are similar to those in Fig. 13 except that there is narrow band of temperature (~100 K wide) over which another (1×1) Ga bilayer phase, different from the pseudo-(1×1) bilayer, is predicted to be stable. This new (1×1) bilayer structure, described in Ref. [379], arises from the desorption of a fraction of the Ga in the outermost layer of the pseudo-(1×1) bilayer. Notice should also be taken of earlier work by Elsner et al. [365,366] using the DFTB approach with Ga 3d electrons included in the valence states and a (4x4) SUC. It is found that the (0001) surface with a single ML of adsorbed Ga is a stable structure under moderately to very Ga-rich conditions, in contrast to the studies described above that find this to be less stable than the "(1×1)" laterally-contracted Ga bilayer (Fig. 13). It was suggested that the difference might be explained by the fact that a (2×4) SUC is the minimum-size cell that contains an even number of DB electrons for 1 ML of Ga adatoms on the (0001) surface. With 3/4 |e| in each Ga DB on the ideal (0001) surface, a Ga adatom in a T1 site uses 5/ 4 |e| to form a Ga-Ga back-bond, which leaves 7/4 |e| per adatom or 14 |e| per (2×4) cell. An even number of adatom DB electrons permits pairs of adatoms to form Ga-Ga dimers via a Peierls distortion, which uses 8 |e| per (2×4) cell while leaving no unpaired electrons. Elsner et al. suggest that the dimers lack any long-range order, which would be consistent with a (1×1) RHEED or LEED pattern, but the Peierls distortion was not clearly described or illustrated. However, there will necessarily be doubly-occupied NBLP orbitals on three Ga adatoms per (2x4) cell, in violation of the ECR. To our knowledge, later theoretical work (except for that of Xue et al. [345,351], described above) has not pursued the suggestion of larger SUCs to include the possibility of Peierls distortion. It is also recalled from the discussion above that the LEED I-V studies of Xu et al. [358] and Yu et al. [359] for a (1×1) surface supported the existence of a single ML of Ga adatoms in T1 sites. However, there was no suggestion in this work of a significant Peierls distortion. Next we consider studies of the chemical and physical structure of the (0001) surface that focus on material grown ex situ and subsequently cleaned in situ using one or more of the methods discussed in Section 3. Some of this work has been discussed already in Section 3, in connection with surface cleaning, and in the introduction to Section 4. Here we will consider further aspects of these studies and also additional work [129,139,189,290,298,299,386,387] that focuses more directly on surface composition and structure. Most studies [129,139,290] (see also Section 3.3.4) find evidence for excess Ga on the (0001) surface after in-situ cleaning, which typically involves heating in UHV to temperatures above ~800 °C, and Packard et al. [298,299] have observed ordered arrays of N vacancies using STM on such surfaces after heating to 900 °C. (There was some uncertainty in this study as to whether the surface was (0001) or (0001̄ ).) As discussed in Section 4.5, loss of N becomes increasingly rapid at temperatures above 800 °C. However, using XPS, Bartoš et al. [189] (note the Erratum) found an essentially-stoichiometric (0001) surface (Ga/N atomic ratio = 1.03) after heating to 910 °C in 1.8x10-6 mbar (1.4x10-6 Torr) of NH3, which suggests that annealing in NH3 restores N lost by annealing in UHV. However,

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other surfaces [189] showed an apparent Ga deficiency, and one might speculate that a Ga/N atomic ratio of less than unity could result from adsorbed NH3 remaining from cleaning. Mori et al. [386] compared n- and p-type GaN surfaces of unspecified orientation using AES and XPS and found the former to be enriched in N and the latter in Ga. This was ascribed to the existence of different types of vacancies for the two materials. No cleaning was done other than rinsing in organic solvents, but the contamination layer was taken into account in the analysis. Ahn et al. [387] reported detailed ISS studies of the (0001) surface of MOCVD material cleaned by IBA (1 keV nitrogen ions, annealing at 920 °C). To our knowledge, this is the most extensive study of the atomic structure of such surfaces, and results are also given for the (0001̄ ) that will be discussed in the following section. Immediately after cleaning the surface exhibits a diffuse (1×1) LEED pattern that becomes sharp upon standing for an hour in UHV. The clean surface is highly reactive, and ISS shows the accumulation of H (and probably also C and O) during the first hour after cleaning but little or no further change for an additional 11 hours. The sharpening of the LEED pattern with increased contamination, which is counter-intuitive, is attributed to a stabilization of the unreconstructed surface by adsorbed species, which leads to better ordering. The coverage of adsorbed H is low, and, therefore, the effect is ascribed to C and/or O. Applying the ECR, one finds for example that 8 Ga atoms on the ideally-terminated (1×1) surface involve a total electron density of 6 |e| in DBs, which

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is sufficient to adsorb 3 O atoms to produce a surface with θO = 3/ 8 ML and no occupied Ga DBs. Within the precision of ISS (±0.2 Å) the contaminated surface appears to be bulk terminated with no detectable relaxation or reconstruction; however, the status of the atomically-clean surface in this regard is unknown. There are very few theoretical works that relate specifically to surfaces of material grown ex situ and cleaned in situ. This is a consequence of the fact that the structure of such surfaces is not as well characterized, and therefore not as amenable to theoretical modeling, as in the case of in-situ growth. As noted above, surfaces cleaned in situ often involve excess Ga, which appears in both experiment (UPS) and theory as a feature above the bulk VBM. This aspect will be discussed in Section 4.7, which deals with electronic structure. A summary of this section is given at the end of Section 4.7.1.1, which deals with the electronic structure of the (0001) surface. 4.6.2. The (0001̄ ) surface The chemical and physical structure of the (0001̄ ) surface grown via MBE and studied in situ has been discussed experimentally in Refs. [339,340,342,343,348,350,352,388–397] and theoretically in Refs. [53–55,363,365,366,368–370,389]. Some of this work has been reviewed previously in Refs. [1,2,4]. Fig. 11 and Fig. 15 summarize results of Smith et al. [339,340,342,343,350,389,390] for in-situ studies of the (0001̄ ) surface following MBE growth. The results were obtained using

Fig. 15. Models for the various (0001̄ ) surface reconstructions: (a) the (1  1); (b) the (3x3), showing the lateral relaxation in the (1  1) adlayer; (c) the (6x6); (d) the c (6x12). In (c), Ga adatoms are shown by dark-gray circles with ellipses illustrating two-atom dimerization. Locations of inequivalent corrugation minima are indicated by M1, M2, and M3. (d) Shows a schematic model consisting of a slightly rearranged (6x6) model plus four additional adatoms per SUC, indicated by the large, light-gray circles. These additional adatoms form bridges between the rearranged (6x6) adatoms, shown as smaller black spheres. In each case, heavy black lines show the SUC. From Smith et al. [390] (with the permission of Springer).

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AES, LEED, RHEED and STM supported by ab-initio computational modeling (described in more detail below). A solvent-cleaned sapphire (0001) surface is first heated to 1000 °C and exposed to a nitrogen plasma after which it is cooled to 685 °C and growth initiated. The temperature is gradually raised to 775 °C during growth, after which annealing is performed at 800 °C to desorb excess Ga. The resulting surface exhibits a (1×1) RHEED pattern and consists of an ML of Ga in T1 sites on the N lattice-terminating layer with steps and with terraces up to 1 μm wide. The existence of this Ga adlayer for both Ga- and N-rich growth conditions has been confirmed in ISS experiments by Shimizu et al. [391]. The adlayer is under tensile stress since the Ga-Ga distance in bulk Ga (~2.7 Å) is less than the N-N distance on the (0001̄ ) surface (~3.2 Å); however, the strong Ga-N back-bond and the Ga-Ga interactions within the adlayer maintain the Ga in the T1 position. With successive depositions of sub-ML quantities of Ga on the (1×1), one observes first a (3x3), then a (6x6) and finally a c(6x12) reconstruction. Deposition of still more Ga does not lead to any further reconstructions. The (3x3), (6x6) and c(6x12) are estimated to involve about 1/9, 3/9 and 4/9 ML, respectively, of Ga adatoms on top of the Ga adlayer that defines the (1×1) structure. However, the latter two estimates are only upper limits since they are based on an assumption that the Ga sticking coefficient is independent of coverage. These structures relieve the stress in the (1×1) but are stable only up to at most 300 °C, above which disordering occurs with a return to a (1×1) RHEED pattern. The disordering at low temperature indicates a high adatom mobility; however, the (1×1) itself persists in a well-ordered state up to the decomposition temperature of 850 °C. Fig. 15 shows models for the (1×1) Ga adlayer and (3×3) adlayer +adatom structures based on STM data and on ab-initio modeling (described below). In the (3x3) structure, the Ga adatoms adsorb in 3-fold-coordinated sites and "sink into" the adlayer, thereby forcing the adlayer Ga atoms closer together and relieving the tensile stress noted above. The total Ga coverage of 1.11 ML required by this model has been confirmed by the Ga 3d XPS results of Beach et al. [388]. The (6×6) model involves dimerized pairs of Ga adatoms, with a coverage of 1/6 ML, that are arranged in different orientations. The tentative c(6x12) model is obtained by rearranging the Ga-Ga adatom dimers in the (6x6) model into rows in the [11̄00] direction and adding four more adatoms per SUC in bridge sites between (6×6) adatoms, giving a net coverage of 2/9 ML. Foxon et al. [392,393] observed a (0001̄ )-(2×2) reconstruction for homoepitaxial MBE growth on a single-crystal substrate prepared by CMP. Growth is performed at about 750 °C under slightly Ga-rich conditions and leads to a (1×1) RHEED pattern that transitions to a stable (2×2) structure when the Ga and N supplies are simultaneously shut off. Somewhat different behaviors are observed when only one source or the other is terminated. The (1×1) structure is believed to correspond to the adlayer consisting of 1 ML of adsorbed Ga, described above, and the (2×2) to the presence of Ga adatoms strongly adsorbed on the adlayer. Xue et al. [352,394,395] grew N-polar GaN on atomically-clean C-polar SiC (0001̄ ) substrates on which an AlN buffer layer was deposited before MBE. Growth at 700 °C under Ga-rich conditions [394,395] leads to a (1×1) RHEED pattern. Subsequent deposition of Ga at 250 °C followed by annealing at the same temperature results in (2×3), (2×4) and (6×6) structures with the (6x6) being identical in STM to that reported by Smith et al. Other work [352] found, in order of increasing θGa, (2×3), (2×4), (√7×√7), (2√7×2√7), (6x6) and (6x8) structures in STM. However, the (3×3) was not observed under these conditions, and no specific models were proposed for the other reconstructions. Wang et al. [396] grew on Si (111) that was first nitrided by exposure to the nitrogen plasma. The GaN layers showed, in STM,

Fig. 16. The relative energies calculated for possible models of the GaN (0001̄ ) surface are shown as a function of the Ga chemical potential. The energy zero is arbitrary. AOA (adatom on adlayer) denotes a Ga adatom on a Ga adlayer. There is a typographical error in the labeling of the most-stable N-rich structure, which should be "(2x2) Ga adatom (H3)" according to the text accompanying this figure and also Ref. [389]. From Neugebauer [1] (Copyright Wiley-VCH Verlag GmbH & Co. KGaA. Reproduced with permission.).

well-ordered (1×1), (3×3), (6×6) and c(6×12) structures as reported previously by Smith et al., provided that specific conditions on substrate temperature and Ga BEP were met. (The BEP is the Ga pressure at which the random flux impacting the surface would equal that from the directed molecular-beam source.) Alhashem et al. [397] performed further STM studies of the c(6×12) surface that examined the effects of annealing at 800 °C followed by quenching to RT. This forms a so-called "trench line" structure, which consists of parallel lines (trenches) separating strips of atomically-ordered regions. The trenches involve Ga adlayer atoms that are devoid of adatoms, while the ordered strips comprise different arrangements of the c(6×12) adatoms described above. Theoretical results for the (0001̄ ) surface structure, based on those in Refs. [1,370,389], are summarized in Fig. 16, and earlier results have been reviewed by Neugebauer [1]. Formation of a (2×2) Ga-adatom structure, which is consistent with the ECR, is predicted for growth under N-rich conditions. This structure, which consists of 0.25 ML of Ga in H3 sites, is generally not observed experimentally due to the need to avoid N-rich conditions and the attendant surface roughening that results from 3D growth. A (2×2) structure has been seen experimentally in Refs. [392,393], as discussed above, but it is unknown whether this corresponds to the theoretically-predicted (2×2), and the authors proposed a different (adlayer+adatom) model for the observed (2×2). Another (2×2) structure, with 0.25 ML of VN in the bare N termination layer, is also possible and satisfies the ECR. This has been considered in Refs. [363,365,366,368,369]. The results vary somewhat, but the (2×2)-VN appears not to be the most stable structure for any value of μGa. Fritsch et al. [368,369] proposed a (2×2) vacancy complex involving two VN in the surface layer and one VGa in the first underlayer on the basis of a DFTB calculation. This is somewhat more stable than the (2×2) with a single VN and is found in this study to be the most stable structure for the full range of μGa. The (1×1) adlayer structure consists of a full ML of Ga in T1 sites with a Ga-N back-bond distance of 1.97 Å (slightly larger than the bulk bond length of 1.95 Å) and a Ga-Ga distance of 3.19 Å, which is larger than the value for bulk Ga (2.7 Å). As noted above, other reconstructions occur when small amounts of Ga are deposited on the (1×1) adlayer. Of these, the (3×3) has been studied theoretically by Smith et al. [389] who found the structure shown in Fig. 15b. The Ga adatom is only 0.9 Å above the adlayer plane, which leads to a 0.5 Å lateral relaxation within the plane and gives an in-

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plane Ga-Ga distance much closer to that in bulk Ga. Experimental results for the chemical and physical structure of the (0001̄ ) surface for samples grown ex situ and subsequently cleaned in situ using one or more of the methods described in Section 3 have been presented in Refs. [189,238,239,387,398–400]. Ahn et al. [387] and Sung et al. [398] performed detailed ISS studies of the structure and composition of n-type MOCVD GaN (0001̄ ) cleaned by IBA (1 keV nitrogen ions, annealing at various temperatures). The LEED pattern, which is a faint (1×1) after annealing at 815 °C, becomes a sharp (1×1) after treatment at 920 °C and then develops a diffuse background and faceting features after heating to 1000 °C. Significantly, H is always detected in ISS at a coverage of about 3/4 ML whenever LEED shows a sharp (1×1) pattern. The ISS angular dependence is consistent with a (2×2) model with each SUC having 3 N-H bonds and one N with a doubly-occupied NBLP orbital, which satisfies the ECR. The absence of fractional-order spots in LEED can be explained by the fact that H is a poor scatter of electrons and by the probable presence of mixed (2x2) domains. The appearance of a (1×1) LEED pattern also suggests that the position of a surface N atom is not very dependent on the presence or absence of an N-H bond so that all N atoms appear to be equivalent. The bulk of MOCVD material contains a high concentration of H as a residue from growth and appears to function as a reservoir that maintains a stable coverage of θH = 3/4 ML on the (0001̄ ), but not the (0001), even at elevated temperature. Sung et al. suggest that this is consistent with the dominant mobile species being H+, which has an affinity for N in the bulk [401]. However, for the ntype GaN used by Sung et al., H− has a lower formation energy [401] than H+ (Fig. 17) and is expected to be present in greater abundance. Also, H− is found to have an affinity for Ga in the bulk and to have a much higher ΔEa for diffusion than H+. A possible explanation for the accumulation of H− on the N-polar surface might be the presence of positive bound polarization charges on this surface, which was discussed in Section 4.2.2. Diffusion of H− to this surface at high temperature could be a mechanism for compensating such charges. Another contributing effect is the fact that N atoms on the ideally-terminated (0001̄ ) surface are electron deficient and might thus be expected to adsorb H− strongly. To our knowledge, there has been no similar ISS study using MBE or single-crystal material (grown ex situ and cleaned in situ), which is expected to contain a lower density of bulk H.

Fig. 17. Formation energy vs. EF for H þ , H0, and H
(solid lines), for H2 (long-dashed line) and for an Mg-H complex (short-dashed line). The formation energy is referenced to the energy of a free H atom, and EF ¼ 0 corresponds to the VBM. E0/
and E þ /0 indicate the EF positions where H0 is isoenergetic with H
or H þ . From Neugebauer and van de Walle [401] (Copyright 1995 by the American Physical Society).

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Romanyuk et al. [238,239,399,400] performed PED and LEED IV studies of the (0001̄ ) surface of a free-standing wafer grown by hydride VPE. In the LEED study the material was doped with Fe during growth to compensate the unintentional donor impurities, which resulted in a free-carrier concentration of 1013 cm-3. Charging of the semi-insulating sample when exposed to the LEED primary beam prevented data acquisition at low Ep. The sample was treated ex situ using CMP and immersion in 1:1 HCl:H2O at 75 °C. In-situ cleaning consisted of flashing to 1000 °C for outgassing followed by repeated anneals at 1000 °C in 2.6×10-6 mbar (2.0×10-6 Torr) of NH3, which resulted in a (1×1) LEED pattern. No evidence of faceting was noted in this study. Of the models considered, the best fit to the LEED data [400] was obtained for a bare surface with a spacing of 0.52±0.11 Å between the N surface layer and the Ga first-underlayer. This is 18% smaller than the bulk interplanar spacing, which indicates a significant inward contraction. It was noted that a bare (0001̄ ) surface violates the ECR and should be unstable, and it was suggested that adsorbed H, which cannot be directly detected in LEED, might produce the stabilization. This proposal is in agreement with the ISS results of Ahn et al. [387] and Sung et al. [398]; however, it is not known whether H was present on the surface studied by Romanyuk et al. In later work, Bartoš et al. [189] (note the Erratum) cleaned the (0001̄ ) surfaces of free-standing wafers by 5 keV nitrogen-ion bombardment followed by annealing at 910 °C in 1.8×10-6 mbar (1.4×10-6 Torr) of NH3. The resulting LEED pattern was a (1×1) without faceting, and AES and XPS showed no C and only a slight amount of O. A summary of this section is given at the end of Section 4.7.1.2, which deals with the electronic structure of the (0001̄ ) surface. 4.6.3. The (101̄0) and (112̄ 0) surfaces Experimental work on the chemical and physical structure of the (101̄0), or m-plane, surface has been described in Refs. [3,238,286,287,402–405] and for the (112̄ 0), or a-plane, in Refs. [131,238,406]. Theoretical results for these surfaces have been reported in, respectively, Refs. [54–56,286,287,374,375,402,407– 417] and [54–56,374,380,407,409,415,416]. A review of these topics has been given by Eisele and Ebert [6]. Beginning with experimental work on the (101̄0), Lee et al. [286,287] and Feenstra et al. [3] used STM and RHEED to study GaN (101̄0) layers grown in situ by MBE on a ZnO (101̄0) substrate, which lattice-matches GaN better than either sapphire or hexagonal SiC. The substrates were unintentionally miscut by several degrees in mainly the [0001] direction, which leads to steps in the GaN layer. Ga-rich conditions result in 2D growth and smoother terraces than are seen for N-rich conditions, which leads to 3D growth (i.e., islands). For film thicknesses up to 0.5 μm the terraces — ̄ or (1011 are flat; whereas, (1011) ) facets occur for thicknesses of 1 μm or more. For the flat terraces under Ga-rich conditions, a nominal "(4×5)" (or pseudo-(4×5)) reconstruction is observed that exhibits metallic properties in STS and comprises 21 (1×1) unit cells. Theoretical results, obtained using methods described in more detail below [286,409], indicate that the bare, unreconstructed surface is the lowest in energy except under very Ga-rich conditions. In this case, a surface with ≥2 ML of Ga on top of the lattice termination layer, which can be modeled on the basis of the pseudo-(4x5) structure, is lowest in energy. Brandt et al. [404,405] used MBE to grow GaN (101̄0) on γLiAlO2 (100) substrates, which were chosen because of the good lattice match. The smoothest surfaces give a complex RHEED pattern when the N source is extinguished immediately after growth and the sample cooled rapidly to ∼150 °C. The pattern is a (4×4) that is not identical to the pseudo-(4x5) seen by Lee et al. [286,287]. On the other hand a (1×1) pattern is seen during growth, with an intensity that depends on the coverage of

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unreacted Ga, and persists when the sample is cooled gradually to 100 °C. A series of Ga depositions and anneals, starting with the (1×1) surface and monitored using RHEED, shows that a bilayer of adsorbed Ga gives a stable (1×2) phase and that a trilayer results in a well-ordered (4×4) structure. The (1×2) bilayer RHEED also exhibits features related to a (4x2) structure that is ascribed to a chain-like ordering of (1×2) domains. The outer layer of the bilayer is not incommensurate, as is the case for the laterally-contracted bilayer on (0001), which suggests a stronger bonding within the layer. Bertelli et al. [402] and Eisele et al. [403] performed STM and STS studies of (101̄0) surfaces prepared by cleaving crystals in UHV. Theoretical results [402] obtained as part of this work and also the STS data will be summarized in Section 4.7.1.3, which deals with electronic structure. The STM results indicate an unreconstructed (1×1) surface consistent with theoretical results showing this to be the most stable structure. Flat terraces are seen with steps running parallel to the [0001] direction. The step spacing is found in one study [403] to vary laterally across the surface and from one cleave to another. Romanyuk et al. [238] studied this surface using LEED, STM and PED. The samples were cut from single crystals followed by mechanical polishing and CMP. In-situ cleaning was accomplished by flashing to 900 °C for outgassing followed by heating at 750 °C in 2×10-6 Torr of NH3 after which no C or O was detected in AES or XPS. The LEED pattern is (1×1) but indicates a higher degree of order parallel vs. perpendicular to the [0001] direction (see Fig. 2). The PED data reveal the presence of two faulted domains that are 180° apart; however, the nature of the faults was not described in detail. For the (112̄ 0) surface, Krüger et al. [406] reported STM results for surfaces prepared by cleaving a single crystal in UHV. The crystal does not cleave easily on this plane, which leads to a somewhat poor surface morphology; however, a (1×1) LEED pattern with no reconstruction is observed. Schulz et al. [131] studied the effects of annealing in UHV, Ga-cleaning and exposure to a nitrogen plasma on the composition and morphology of the (112̄ 0) surface, as described in Sections 3.2.1 and 4.3. The samples were grown by MOVPE on r-plane sapphire and exhibited a good (1×1) LEED pattern when clean. Romanyuk et al. [238] studied this surface using methods and sample preparation methods similar to those described in connection with their work on the (101̄0) surface. A (1×1) LEED pattern is seen with indications of steps and of some degree of disorder of an uncertain origin. Moving on now to theoretical work on the (101̄0) surface, there is general agreement that a bare, unreconstructed (1×1) structure is the lowest in energy under most conditions. The Ga-N surface dimers (Fig. 2) are buckled with the Ga (N) end down (up) relative to the bulk position and an interatomic distance that is a few percent shorter than in the bulk. The buckling is a consequence of the rehybridization that occurs when the unpaired electron density in the Ga DB on the ideally-terminated surface is transferred to the N neighbor to form an empty Ga DB and a filled N DB, as required by the ECR. This results in an sp3-hybridized N and an sp2-hybridized Ga. The exact structural results depend somewhat on the computational approach, and, in the most recent study, Landmann et al. [417] used different DFT techniques in order to evaluate the extent of this method dependence. These include pure-GGA (PBE) and hybrid-GGA (HSE) functionals and also selfenergy-corrected LDA and PBE+U to overcome the DFT underestimation of the band gap. These were implemented using the PAW approach and a symmetric 2DPS with between 16 and 48 atomic layers. The outermost 1/4-th of the slab on either side was free to relax, with the inner part being fixed in the relaxed bulklattice configuration. The Ga-N surface dimer distance is found to be 7-8% shorter than in the bulk, and the buckling is such that the

dimer makes an angle of 8° with the ideal surface plane. These results agree with those of previous studies [409,416]. The relaxation is not entirely confined to the surface since smaller dimer bucklings (1-2° angles) are seen in the first through third underlayers. González-Hernández et al. [416] previously studied this surface also using different DFT methods including LDA and various pure-, hybrid- and meta-GGA functionals together with the PAW approach. The symmetric 2DPS comprised 16 GaN layers with the outermost few layers on either side being free to relax. The results obtained for the surface dimer are very similar to those described above. This study finds that overall the best agreement with experimental bulk and surface properties for GaN is obtained with the PBEsol functional, which is the original PBE modified for solidstate applications. Some groups have studied the stability of the (101̄0) surface as a function of μGa under equilibrium conditions. Lee et al. [286,287] and Northrup and Neugebauer [409] found that the bare, stoichiometric (1×1) surface is lowest in energy except under very Garich conditions. Here a more-stable structure can be formed by substituting Ga for N in the surface layer, leading to Ga-Ga dimers. A bilayer of metallic Ga can then form, and the three different surfaces (Ga dimers only, Ga bilayer only and Ga dimers+Ga bilayer) are all close in energy. Segev and Van de Walle [374] obtained qualitatively-similar results except that the Ga dimer structure is less stable than the bare stoichiometric surface (termed the "Ga-N dimer surface" in this study) even at the highest μGa, and the Ga dimers+Ga bilayer structure is significantly more stable (by 0.27 eV per (1×1) SUC) at the highest μGa. This surface shows a (1×2) reconstruction, and over a narrow range of μGa another (1×2) structure is favored that consists of 1 Ga adatom per SUC on top of a single Ga adlayer. It is possible that one or both of these (1×2) structures might correspond to that observed experimentally by Brandt et al. [404,405] for ̄ a Ga bilayer on the (1010). This study also identified a so-called inverted-polarity structure (IPS), which is only a little less stable than the bare Ga-N dimer surface. Here the polarity of the upper̄ layer is reversed in the [0001] direction (in other words most (1010) rotated by 180° about the surface normal). The reader is referred to the original paper for a diagram of this structure. In more-recent work by Dreyer et al. [54] both (1×2) structures appear to be close in energy at the highest μGa. The study by Dreyer et al. used the HSE hybrid functional, which is found to give more-accurate surface energy results than can be obtained with pure GGA. Mutombo and Romanyuk [415], on the other hand, find that the Ga dimer structure is stable only at the highest μGa and that other non-stoichiō surfaces are unfavorable at any μGa. metric (1010) For the (112̄ 0) surface, the most recent theoretical results pertaining to structure and stoichiometry are those of GonzálezHernández et al. [416], which were obtained using methods similar to those described above in connection with their results for the (101̄0) surface except that the 2DPS in this case comprised 7 GaN layers. The stable surface is a stoichiometric (1×1) with shortened (by about 6% relative to the bulk) and buckled (7-8° tilt angle) Ga-N dimers with the Ga (N) down (up) as for the (101̄0). These results agree well with those obtained previously by Northrup and Neugebauer [409]. Several groups have investigated the stability of the (112̄ 0) surface as a function of μGa. All agree that the bare surface is the most stable except possibly at very high μGa. Northrup and Neugebauer [409] found that, unlike in the case of the (101̄0), replacing N with Ga and forming Ga-Ga dimers leads to an unstable surface at any μGa. However, Segev and Van de Walle [374] found that adding a Ga bilayer on top of the Ga-Ga dimer surface leads to a stable (1×1) structure at a high μGa. Ito et al. [380] found that a single Ga adlayer on the otherwise-bare surface was the most

V.M. Bermudez / Surface Science Reports ∎ (∎∎∎∎) ∎∎∎–∎∎∎

stable structure but only at lower temperatures (below ~750– 1050 K, depending on the Ga BEP). The adsorption site was not clearly specified, but close examination of the structure shown in Fig. 14b suggests that the adatom lies above surface Ga sites. Dreyer et al. [54] also found the Ga bilayer to be stable at high μGa, but it is not clear whether this model also includes the Ga-Ga dimer layer as in Ref. [374]. Mutombo and Romanyuk [415], on the other hand, find that non-stoichiometric (112̄ 0) surfaces are unstable for any μGa. 4.6.4. Semi-polar surfaces Fundamental studies of the chemical and physical structure of GaN surfaces other than those discussed in the previous sections are relatively few in number. As noted in Section 2, Li et al. [55] have given theoretical values for the average surface energies of ̄ and (101̄2) surfaces, where "average" refers to the (112̄ 2), (1011) the average energies for the two dissimilar, ideally-terminated — surfaces (e.g., (112̄ 2) and (1122)) with each having the lowest-energy configuration. For example, (112̄ 2) with Ga in the outer-most — layer and (1122) with N outer-most is more stable than the reverse. ̄ surface. The (1011) ̄ surface (Fig. 3c,d) has been 4.6.4.1. The (1011) studied experimentally by Romanyuk et al. [240,242] using PED and LEED and theoretically by Ito et al. [380], Northrup et al. [418],

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Akiyama et al. [419], Lee and Kim [420] and Zhu et al. [421]. — Akiyama et al. [422] have also investigated the (1011) surface. In the experimental work, samples were cut from single-crystal — ̄ or (1011 boules, grown by hydride VPE, so as to expose the (1011) ) surface. The identity of the surface plane was determined using XRD to orient the crystal before cutting, and after mechanical ̄ surface was found to be smoother polishing and CMP the (1011) — than the (1011). The samples were cleaned in organic solvents and in situ by 1-hr periods of annealing in NH3 vapor (2x10-6 mbar ≈ 1.2x10-6 Torr) at ∼800 °C, after which no O was detected in XPS and a faceted (1×1) LEED was obtained that showed both polar (0001) and non-polar (1̄010) facets. It was also demonstrated that — ̄ and (1011 PED can be used to distinguish the (1011) ) surfaces. ̄ Northrup et al. [418] studied the (1011) surface theoretically as a function of μGa. Under Ga-rich conditions the most stable surface is a (1×1) consisting of a Ga adlayer with two types of sites, labeled T1 and B2. In the former, Ga back-bonds to a three-fold-coordinated N while in the latter a bridge is formed between two two-fold-coordinated N atoms. This structure is stabilized by strong Ga-Ga interaction within the adlayer. From N-rich to moderately Ga-rich conditions a (1×1) Ga adatom structure is the most stable. Here a single Ga back-bonds to one three-fold- and two two-fold-coordinated N atoms. ̄ Lee and Kim [420] investigated reconstructions of the (1011)

̄ surface. (a) (1x1) unreconstructed, (b) (2x1) dimerized and (c) (2x1) dimer-vacancy (DV) reconstructed GaN(1011) ̄ surfaces. The Fig. 18. Atomic structures of the (1011) dashed lines indicate the unit cells, and N1 and N2 are the three- and two-fold-coordinated atoms respectively. Large (small) circles represent Ga (N). The (4x2) DV reconstruction is shown in (d), where the dashed lines indicate the unit cells, and the cyan-shaded areas are the cells where the dimer vacancies are located. In (d), the red numbers indicate the DB electron density donated (negative) or gained (positive) by each (2x1) section of the (4x2) SUC. From Lee and Kim [420] (Copyright 2011 by the American Physical Society).

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surface theoretically using the PAW approach with a GGA functional (presumably the PBE) and with the Ga 3d levels included in the valence states. Due to the complexity of the surface, large SUCs are needed to describe the reconstructions accurately. A 2DPS with 10 Ga-N bilayers was used for the smaller SUCs (up to (2×2) and (4×1)), and a 5-bilayer slab was employed for the larger cells (up to (6x2), (4x3) and (12x1)). Dangling bonds on the bottom surface were terminated with PHs, and the lowermost 2 Ga-N bilayers were fixed in the ideal bulk geometry during relaxation. The ideally-terminated surface (Fig. 18a) is N-terminated with one twofold- and one three-fold-coordinated N per (1x1) SUC. Electron counting (Section 4.1.1) indicates densities of 5/4 |e| and 5/2 |e| in the DBs on the three-fold and two-fold N atoms respectively, which yields a highly-unstable surface. Alternatively, this could be described as a system with a total DB hole density of 9/4 |e| per (1x1) cell, since adding the equivalent electron density would then give a total of 6 |e|, which is sufficient to form 3 doubly-occupied NBLP orbitals on the surface N atoms and satisfy the ECR. A (2x1) reconstruction (Fig. 18b), in which an N-N dimer bond forms between the two-fold atoms lowers the energy by 2.6 eV per (1x1) SUC. The resulting surface is almost fully passivated. With 15/2 |e| per (2x1) cell in DBs, 2 |e| go to forming the N-N σ-bond and 4 |e| to filling the DBs on the 2 three-fold N atoms with the remaining 3/2 | e| going to the N-N dimer π orbital. Results obtained for the DOS (discussed in Section 4.7.1.4) show the effects of the reconstruction and the associated redistribution of unpaired electron density on states in the band gap. This structure, because of the unpaired electron density, is not the lowest in energy but serves as a framework for describing other, more-stable surfaces. Several other reconstructions involving N-N dimers, N vacancies and/or Ga adatoms were evaluated in terms of total energy and the ECR. The result is that, under intermediate conditions (neither Ga- nor N-rich), the most stable structure is the (2x1)DV shown in Fig. 18c with all two-fold N sites vacant. Under N-rich conditions, the (4x2)DV (Fig. 18d), with three N-N dimers and one dimer vacancy (DV) per (4x2) SUC, is lowest in energy. It is shown that this structure satisfies the ECR, i.e., that the excess-hole density is zero. Finally, under Ga-rich conditions the most stable surface (not shown) is a (1x1) consisting of Ga adatoms in twofold bridge sites between two-fold-coordinated N atoms. It is noted that none of these structures were observed experimentally by Romanyuk et al. [240,242]; however, it is quite possible that they might be produced in situ during MBE homoepitaxial growth on a ̄ (1011)-oriented substrate. ̄ Akiyama et al. [419], and later Ito et al. [380], studied the (1011) surface theoretically using a 2DPS with 8 atomic layers (4 Ga-N bilayers) for which the bottom surface was terminated with PHs and the lowermost 4 atomic layers fixed in the ideal bulk geometry. The PW method was used together with the GGA and USPPs. The study by Akiyama et al. preceded that by Lee and Kim [420], which was described first for convenience. The ideally-terminated surface is stable only under extremely N-rich conditions. Under less N-rich to moderately Ga-rich conditions, the two-foldcoordinated N atoms in the ideally-terminated surface are unstable and desorb leading to Ga-Ga dimers. This is similar to the (2x1)DV structure (Fig. 18c) except that Ga-Ga interaction occurs across the VN; although, the strength of the bonding (e.g., the relaxed Ga-Ga distance) was not described. Under more Ga-rich conditions, the two-fold N atoms are stable in the presence of an ML of adsorbed Ga or, at very high μGa, a Ga bilayer. Overall, the results are similar to those of Lee and Kim [420] except that the more-recent study finds the (4x2)DV to be more stable than the (2x1)DV under N-rich conditions. ̄ surface Zhu et al. [421] studied reconstructions on the (1011) theoretically using an evolutionary algorithm to search systematically and automatically for the lowest-energy structure at a

given μGa. This was coupled with DFT total-energy calculations using the GGA and the PAW method with a SUC of (2x2) or smaller. Except under N-rich conditions, the results are similar to those of Akiyama et al. [419] and Lee and Kim [420] described above. For very high μN (low μGa) this study finds a (2x1) N trimer structure, with an N adatom bridging the two-fold-coordinated N sites, to be the lowest in energy. However, since larger SUCs were not considered, the (4x2)DV structure found by Lee and Kim under N-rich conditions cannot be excluded. Akiyama et al. [422] have reported theoretical results for the — ̄ shown in Fig. 3c,d ex(1011) surface. This is similar to the (1011) cept that it consists of one two-fold- and one three-fold-coordinated Ga per (1x1) primitive SUC. From N-rich to somewhat Ga-rich conditions the lowest-energy structure has a (1x2) cell constructed from two of the non-primitive cells shown in Fig. 3d. Within each (1x2) cell, two of the four two-fold Ga atoms are missing and the other two form a Ga-Ga dimer. Moderately Garich conditions favor a stoichiometric surface with the four twofold Ga atoms per non-primitive (1x2) forming two Ga-Ga dimers. At higher μGa the Ga-Ga dimers break, and a Ga bilayer forms on top of the stoichiometric surface. ̄ surface. The (101̄3) surface (Fig. 4a,b) has been 4.6.4.2. The (1013) studied experimentally by Romanyuk et al. [423]. The procedures for sample preparation (cutting an x-ray-oriented single-crystal boule) and cleaning were similar to those described in the preceding subsection except that the temperature for annealing in NH3 vapor was somewhat higher (1000 °C). A (101̄3)-(1x1) LEED pattern was seen with, however, certain spots missing, which was attributed to some form of disorder. The main focus of this study was on ELS, which will be discussed below in Section 4.7.2. — ̄ and (1013 The (1013) ) surfaces have been studied theoretically by Kioseoglou et al. [424] using a 2DPS with a (1x1) or (2x1) SUC and 9 Ga-N bilayers terminated on the bottom with PHs. The GGA (presumably implemented in the PBE functional) was employed together with PAW PPs. The ideal surfaces of either polarity are ̄ each Ga terminated with equal numbers of Ga and N. On the (1013), is three-fold coordinated and has one DB. Half the N atoms are also three-fold-coordinated (NT), and the others are two-fold co— ordinated (ND) with two DBs. The situation is reversed on the (1013) where all N have one DB and Ga atoms have either one or two DBs. ̄ On the (1013), the most stable structure (Fig. 19) under any conditions from very N-rich to very Ga-rich has a layer of Ga adatoms that bond to one NT or to two ND. The former adatoms also interact weakly with two Ga atoms in the surface layer (Ga-Ga distance of 2.94 Å), and in this case the surface-layer Ga appears to be approximately five-fold coordinated in the model. Those Ga adatoms bonded to two ND also form one stronger bond (Ga-Ga distance of — 2.55 Å) to a single surface Ga. The behavior of the (1013) is more complex. Here, under N-rich conditions, the bare surface is the most stable but with a (2x1) reconstruction in which the 2-fold-coordinated Ga atoms form Ga-Ga dimers (Fig. 19). Under moderately Ga-rich conditions a Ga adlayer forms with each Ga bonded to a single surface N atom such that the local configuration of the now4-fold-coordinated N appears to be approximately tetrahedral. In this case the 2-fold Ga atoms in the surface layer are not dimerized. Under very Ga rich conditions, a metallic Ga bilayer forms as the most stable structure. The DOS of some structures was also obtained and will be discussed in Section 4.7.1.4. 4.6.4.3. The (112̄ 2) surface. The (112̄ 2) surface (Fig. 3a,b) has been studied experimentally by Bartoš et al. [189] and by Romanyuk et al. [242]. The procedures for sample preparation and cleaning were similar to those described above in connection with the — ̄ and (1011 (1011) ) surfaces. Single-crystal boules grown by hydride — VPE were x-ray oriented and wafers sliced on the (112̄ 2) and (1122)

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Fig. 19. Left: (a) Cleaved, relaxed (101̄3) GaN surface. T, D indicate triply and doubly coordinated N atoms. In (b) the Ga adlayer is shown. Reconstructions are presented in top view (upper images), normal to (101̄3), and in cross section view along [112̄ 0] (lower images). In all cases, the (2x1) periodicity is given for higher clarity. The (1x1) cell is indicated by a dotted rectangle in (a). (Note that, in the (a) top-down view, there appears to be an inconsistency in the coloration of one of the NT rows.) In (b), dashed bonds denote interactions between neighboring Ga adatom and Ga surface atoms. Large/small spheres correspond to Ga/N atoms. Darker spheres designate top-most surface — atoms. Right: (a) Cleaved, relaxed (1013) surface. The bond formation between the triply coordinated Ga atoms in the relaxed model (doubly coordinated in the unrelaxed), denoted as T (D), is evidenced. In (b) the Ga adlayer structure is shown. From Kioseoglou et al. [424] (© IOP Publishing. Reproduced with permission. All rights reserved.).

planes. Surfaces were cleaned ex situ in 1:1 HCl:H2O at 75 °C and in situ by cycles of 5 keV nitrogen-ion bombardment and annealing in NH3 vapor (560 °C, 1.8x10-6 mbar). Following this process, XPS showed no C and only a trace amount of O, and a faceted (1x1) LEED pattern was observed. It was shown that PED can be used to — distinguish between the (112̄ 2) and (1122) surfaces. Yamashita et al. [425,426] studied this surface theoretically using a 2DPS with 14 atomic layers for which the bottom surface was terminated with PHs and the lowermost 4 layers fixed in the ideal bulk-lattice configuration. The PW method was used with the GGA and with the Ga 3d states treated via NLCC [197]. The ideallyterminated surface (Fig. 20a) consists of 2-fold-coordinated Ga and 3-fold-coordinated N atoms (2 each per primitive SUC). For conditions ranging from N-rich to moderately Ga-rich, the most stable surface is the c(2x2) Ga adatom structure shown in Fig. 20c, which satisfies the ECR. The c(2x2) primitive unit cell is the (√2x√2) R45° (Fig. 20c). Here dimers form between the 2-fold Ga atoms on the bare surface, and a Ga adatom (one per primitive cell) bonds to one of the dimerized Ga atoms and to two 3-fold N atoms. Per (√2x√2)R45° SUC, the bare surface has 8 Ga DBs with 3/4 |e| each and 4 N DBs with 5/4 |e| each that, together with the 3 |e| from the Ga adatom, make a total of 14 |e|. For the reconstructed surface, 4 | e| are used to form 2 Ga-Ga dimers (only one of which is shown in Fig. 20c), 6 |e| go to form the 3 Ga adatom back-bonds and 4 |e| to give NBLP orbitals on the 2 N not bonded to the adatom. Under more Ga-rich conditions the Ga adlayer structure shown in Fig. 20d, with a Ga adatom back-bonded to each 3-fold N, becomes favorable. For very Ga-rich conditions, the Ga monolayer (Fig. 20e) is the most stable surface. Here a Ga adatom back-bonds to every under-coordinated surface Ga and N atom. Subsequently Ito et al. [380] extended this work to obtain the stability of different (112̄ 2) surface structures as a function of temperature and Ga BEP. At a sufficiently low temperature or high BEP a Ga bilayer forms as the most stable structure. 4.6.4.4. The (202̄1) surface. Experimental results for the (202̄1) surface (Fig. 4c,d) have been given by Bartoš et al. [189] and by Romanyuk et al. [238,240,242], and theoretical work has been reported by Mutombo and Romanyuk [415] and by Yamashita et al. [427]. As in the experimental work discussed above for other — semi-polar surfaces, (202̄1)- and (2021)-oriented samples were sliced from single-crystal boules grown by hydride VPE. In the most recent study [189], surfaces were cleaned in 1:1 HCl:H2O at 75 °C and in situ by cycles of 5 keV nitrogen-ion bombardment and

annealing in NH3 vapor (820 °C, 1.8x10-6 mbar). Following this process, XPS showed no C and only a trace amount of O, and a faceted (1x1) LEED pattern was observed. It was shown that PED — can be used to distinguish between the (202̄1) and (2021) surfaces. ̄ Yamashita et al. [427] investigated the (2021) surface theoretically using a 2DPS with 14 atomic layers (7 Ga-N bilayers) terminated on the bottom with PHs and with the lowermost 4 layers fixed in the ideal bulk configuration. The PW approach was used with a GGA functional (presumably the PBE). Summarizing briefly, a (2x1) SUC with desorbed N is found to be the most stable under N-rich conditions. With increasing Ga richness, first a Ga adatom and then a Ga adlayer structure becomes most favorable. Mutombo and Romanyuk [415] have commented that the SUC used in this work was incorrectly specified as rectangular rather than oblique, as shown in Fig. 4c,d. — Mutombo and Romanyuk [415] studied the (202̄1) and (2021) surfaces theoretically using a 2DPS with 6 Ga-N bilayers and the PW method with the PBE functional and the Ga 3d electrons treated as part of the PP. The bottom surface was terminated with PHs, and the lowermost 2 bilayers were fixed in the bulk configuration. The bare (202̄1) surface (labeled "B" for "bare") consists of 3- and 4-fold-coordinated Ga and 2- and 3-fold-coordinated N atoms (Fig. 4c,d). The 2-fold N atoms form N-N dimers, which leads to a (2x1) reconstruction that is the most-stable surface under very N-rich conditions. The bare surface can be viewed as ̄ nanobeing corrugated on a nano-scale, with (101̄0) and (1011) facets labeled "F1" and "F2" respectively. It is also possible to construct a corrugated surface model consisting of only one type of facet. Under conditions ranging from moderately N-rich to moderately Ga-rich, the bare (202̄1) surface with only (101̄0) nano-facets (F1) is the most stable structure. Under very Ga-rich ̄ nano-facets plus a layer of Ga conditions, a surface with (1011) adatoms back-bonded to surface N atoms (F2-Ga) becomes the most stable structure. This is only slightly more stable than a B-Ga model, which is the unreconstructed (1x1) surface with a Ga adlayer. Presumably the adatoms back-bond to both Ga and N in this case; although, this is not completely clear in the description and — diagrams provided. The bare (2021) surface comprises 2- and 3fold-coordinated Ga and 3-fold-coordinated N atoms and forms an unreconstructed (1x1) surface, with no dimerization, that is the most stable structure except under Ga-rich conditions, for which a B-Ga adlayer structure is most favorable. Again, to our knowledge none of these theoretically-predicted semi-polar surface reconstructions have been observed

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Fig. 20. Schematic top and side views of the (112̄ 2) surface. (a) the cleavage surface, the surfaces consisting of (b) a single Ga dimer, (c) a Ga adatom, (d) a Ga adlayer, (e) a Ga monolayer, and (f) a Ga monolayer built on Ga dimers. The (1x1) and c(2x2) unit cells are shown by dotted rectangles. Large and small circles represent Ga and N atoms, respectively. The Ga atoms forming Ga dimers and Ga adlayers are represented by aqua-colored circles. In (a), top-most Ga and N atoms on the cleavage surface are indicated by arrows. From Yamashita et al. [425] (Copyright 2009 The Japan Society of Applied Physics).

experimentally for GaN surfaces cleaned in situ. However, they might be formed via MBE homoepitaxy on well-oriented singlecrystal substrates. 4.7. Spectroscopy and surface electronic structure (UPS, ELS, STS) 4.7.1. Ultraviolet photoemission spectroscopy The most widely-used spectroscopic method for determining GaN surface electronic structure has been UPS (either angle-resolved or angle-integrated) supported by theoretical band-structure results. The present section will review this work together with STS results when such data are available. An introduction to ARUPS is given in the review by Damascelli [428]. As an historical note, the first photoemission experiment for GaN was reported by Pankove and Schade [429] in 1974. The surface of the MOCVD sample was prepared by heating in vacuo (o1x10-9 Torr) and the photoyield vs. hν observed, which gave ϕS = 4.1 eV and an electron affinity of 4.1 4 χ 4 2.1 eV. The lowering of ϕS by Cs adsorption was also demonstrated, which anticipated the extensive use of Cs/GaN for NEA applications (Section 5.10). As a footnote, it is common, particularly in the older engineering literature, to see the Pankove and Schade value for the work function used incorrectly for the electron affinity. The accepted

value for the latter, at least for the clean (0001) surface, is in the range of 3.2 to 3.4 eV; although, any sort of surface dipole layer will affect this result (Section 5.10). Before moving to a discussion of the individual surface orientations, some issues involving the Ga 3d shallow core level should be noted. The first concerns fine-structure in the photoemission spectrum. It is known from both theory and experiment (e.g., Refs. [430–433]) that there is a hybridization of the Ga 3d and N 2s orbitals in GaN, which are close in energy. Fig. 21 shows UPS data from above the VBM to below the Ga 3d together with a computed bulk DOS. The B3LYP hybrid functional, which generally gives better results for Eg than do pure-GGA functionals [199], was used in the calculation. Being surface-sensitive, the UPS data show surface states just above the bulk VBM that are not seen in the bulk DOS and which will be discussed shortly. The Ga 3d appears together with a lower-BE satellite that is typically identified as the N 2s level. However, the atom-resolved DOS shows that this feature comprises approximately equal Ga and N components and is better described as a band of anti-bonding states. The strong Ga 3d peak is derived almost entirely from Ga 3d orbitals and can be described as being due to non-bonding states. The calculation shows a small splitting of this peak due to band dispersion. At higher BE the DOS shows another peak with strong Ga and N

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Fig. 21. Upper: Comparison of (a) the calculated DOS for bulk wurtzite GaN and (b) the experimental (surface-sensitive) UPS. Binding energy is referenced to the bulk VBM. Structure in the DOS in the vicinity of the Ga 3d is shown on a compressed vertical scale. The ‘‘N 2s’’ peak is labeled as is conventional in experimental studies, and Eg is the computed bulk band gap. Lower: Total (a) and partial (b,c) DOS for the Ga 3d and N 2s levels. The bonding character of each band is indicated, and the anti-bonding band is repeated for each trace at 10-fold magnification. From Bermudez [433] (Copyright 2004, reproduced with permission from Elsevier).

components that represents bonding states. The discrepancy between the observed and calculated energies of the Ga 3d-N 2s hybridization states relative to the VBM has been discussed by Lambrecht et al. [430]. This structure has implications in the analysis of Ga 3d UPS and XPS data. Metallic Ga or Ga adatoms, which are frequently produced either intentionally or unintentionally on GaN surfaces, exhibit a 3d BE that is ~1–2 eV lower than that of GaN. This subject will be discussed in Section 5.18 in connection with Ga adsorption. While this BE difference is too small to confuse these features with the "N 2s", the presence of the "N 2s" satellite can sometimes complicate the least-squares lineshape fitting that is usually needed to extract a weak Ga adatom peak from the raw data. The dispersion-induced splitting of the main Ga 3d peak is generally not considered in lineshape fitting and is instead included in the

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Gaussian broadening, which is a fitting parameter. Structure on the high-BE side of the main Ga 3d peak can have three different sources, which can be difficult to distinguish. The first is the Ga 3dN 2s bonding band. The second is a GaOx satellite due to a small amount of O contamination, and the third, discussed below, is an intrinsic shift in the Ga 3d to higher BE (an SCLS) resulting from the under-coordination of surface atoms [434]. Typically, when fitting Ga 3d data of sufficiently-high resolution, it is necessary to include a weak satellite at ~1 eV to higher BE. This is generally ascribed to GaOx and is often accompanied by a small level of O contamination that is detectable in AES or XPS. However, the same assignment is sometimes made even when there is no detectable O, a practice that has been questioned by Barinov et al. [435] and by Plucinski et al. [436] who find evidence that it is instead an intrinsic feature, i.e., the Ga 3d-N 2s bonding band. A second issue, which is related to the first, concerns a possible surface core-level shift in BE in the Ga 3d and also the N 1s. A clear illustration of a Ga 3d SCLS is given in the results of Miller and Chiang [437] for GaAs (110) prepared by cleaving in UHV. For a cation (anion) the shift is to higher (lower) BE relative to the bulk [434] and varies in magnitude for different materials. The cation SCLS to higher BE arises from the reduced screening of the photoexcited core hole by nearest-neighbor anions at the surface vs. in the bulk due to the lower coordination number at the surface. Likewise the anion SCLS to lower BE results from the decrease in electrostatic repulsion between the photoexcited core hole and neighboring cations that occurs at the surface, a result again of the decreased coordination number at the surface. However, this simple description can be rendered inaccurate if reconstruction of the bare surface leads to a change in chemical bonding, such as the formation of dimer pairs between surface atoms. Some GaN studies assign a Ga 3d satellite at a lower BE than in the bulk to an SCLS. This would almost certainly be incorrect for a bare, ideally-terminated (0001) surface but is reasonable for Ga in the (0001) lattice-terminating layer in the presence of Ga adatoms or for the adatoms themselves. To our knowledge there has been no conclusive identification of a true Ga 3d SCLS (one that is not a result of adatoms or an adlayer) in GaN that is distinguishable from both a GaOx satellite and the Ga 3d-N 2s bonding band, and the effect may simply be too small to observe. Phonon broadening (including zero-point motion) makes a significant contribution to XPS linewidths [438] in partially-ionic materials such as GaN, which further complicates the task of identifying a small SCLS. For the N 1s, Widstrand et al. [129] observed a satellite shifted by 0.54 eV to lower BE relative to the bulk. While it might seem reasonable to ascribe this to a SCLS, Widstrand et al. noted that the feature was observed for a GaN (0001) surface, which should have no surface N. Such a low-BE satellite in this case might then be due instead to N adatoms remaining from the in-situ cleaning, the last step of which involved annealing in NH3. On the other hand, Barinov et al. [435] also found a satellite in the N 1s spectrum that was shifted about 0.5 eV to lower BE relative to the bulk. The surface in this case was shown to be N-polar; hence, this is may be an actual SCLS. However, if a Ga adlayer were present on this surface as is often the case for the (0001̄ ), that would also produce a shift of the N 1s to lower BE as a result of the metallic screening of the photoexcited core hole. The last point concerns the use of the Ga 3d BE to locate the VBM. This is an important issue in detecting the presence or absence of surface states in the gap but close to the VBM, which are sometimes difficult to identify in conventional (not angle-resolved) UPS experiments. The difference in BE between the Ga 3d peak (not resolved into 3d3/2 and 3d5/2 components) and the bulk VBM is a constant of the material, reported [439] to be 17.76 ±0.03 eV. Subtracting this from the BE of the Ga 3d relative to EF locates the VMB relative to EF at the surface. In addition to

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Fig. 22. UPS VB spectra of GaN (0001) for three different in-situ surface preparation methods including different occupied surface states as measured using He II radiation. Left: (2x2) structure formed after growth below 600 °C during cooling in the N plasma. The peaks at 2.05 eV (∼0.9 eV above the bulk VBM) and 3.5 eV (∼0.6 eV below the bulk VBM) are the ones labeled "S1" and "S2" respectively in earlier studies (Refs. [455–458]). Middle: surface structure formed after subsequent annealing in UHV at 600 °C. Right: (2x2) structure formed after Ga adsorption at 640 °C. The energy scale is given with respect to the Fermi level (EF ¼ 0 eV). From Himmerlich et al. [459] (Copyright 2013 by the American Physical Society).

providing essential information when determining BB and the SBH for a metal contact, this can be compared with EF-VBM as measured directly in surface-sensitive UPS. The latter quantity will be smaller than the value determined above if an unresolved band of surface states is present just above the VBM, as is frequently the case on clean semiconductor surfaces (e.g., Fig. 21). On the other hand, a surface state below the bulk VBM cannot be easily identified by this means. In this case it is necessary either to use ARUPS or to observe the response to adsorption. Another complication arises in situations where there is a large SPV effect (Section 4.7.3.2), in which case the BB seen in UPS can be significantly greater than that in XPS as a result of the much higher photon flux delivered by non-monochromatic laboratory xray vs. vacuum-UV radiation sources. For example, for an n-type GaN (0001) surface [440] near RT, the VBM at the surface lies ∼0.15 eV farther from EF (less upward BB) when the Ga 3d BE is measured with Mg Kα excitation (hν = 1253.6 eV, 3x1014 photons cm-2 sec-1) than with HeII (hν = 40.8 eV, 7x108 photons cm-2 sec-1 total HeI and HeII flux). Equivalently, SPV causes the Ga 3d BE relative to EF in n-GaN to be larger in XPS than in UPS. In this case the problem can be avoided by using HeII radiation to record both the Ga 3d BE and the apparent position of the VBM, since the two estimates of EF-VBM will then be unaffected by SPV. One further brief comment concerns the use of the N KLL AES lineshape for electronic-structure determination. This is potentially of significant value, as shown in a review by Ramaker [264]; although, little work of this nature has been reported for GaN. Endo et al. [441] have shown that small molecular models can be used to good effect in analyzing structure in the N KLL spectrum of GaN as a result of the localized nature of the Auger transition. The N KLL spectrum, with a KE in the 340–390 eV range, is more surface-sensitive than the Mg Kα-excited N 1s (KE ≈ 865 eV) and is free from interference from overlapping Ga LMM Auger features. 4.7.1.1. The Polar (0001) Surface. Experimental results for the electronic structure of the (0001) surface have been reported in Refs. [123,155,181,442–459]. Of these, Refs. [446,455–459] describe results for surfaces grown via MBE and studied in situ while the others address samples grown ex situ. Furthermore, the work of Valla et al. [450] reports an IPES study of CB structure; whereas, all others involve UPS results for the VB and/or shallow core levels

(Ga 3d and "N 2s"). Beginning with the studies of samples grown in situ, King et al. [446] formed n-type GaN (0001) on atomically-clean SiC (0001) substrates on which 250 Å of AlN had been grown in situ as a buffer layer. The growth method was gas-source MBE, in which NH3 is used as the source of N atoms. GaN grown at 650 °C exhibits a (1x1) LEED pattern; whereas, growth at 800 °C results in a (2x2) structure. For both surfaces, EF-VBM seen in HeI UPS agrees with that found in bulk-sensitive data obtained with Mg Kα excitation, which suggests the absence of surface states at or above the bulk VBM. However, any such surface states might have been eliminated by the adsorption of residual NH3 from the UHV background (Section 7.1). Gutt et al. [455] and Lorenz et al. [456–458] grew GaN (0001)(2x2) surfaces on atomically-clean SiC (0001) substrates using MBE. No evidence of C, O or a Ga adlayer is seen in XPS, and an upward BB of ∼0.4 eV is estimated. Two surface states are found in HeII UPS, one (S1) lying above the bulk VBM and another (S2) at or just below the VBM. Of the two, S1 is seen only for the (2x2) reconstruction and is more sensitive to adsorption, disappearing in the course of ∼2 hr while standing in UHV as a result of adsorption of reactive species (e.g., H2O) in the background. This state is seen clearly in HeII UPS but not in less surface-sensitive spectra obtained with HeI excitation [458]. The S2 state, on the other hand, is also seen for (1x1) surfaces and is less sensitive to contamination. Such (1x1) surfaces include those prepared in other studies by IBA as well as the surface that remains in the present work after H2O adsorption has eliminated the (2x2). Since the (2x2) is formed by cooling in the presence of the N plasma after growth, it was suggested [455,456] that N adatoms may be involved. Lorenz et al. [457] performed ARUPS studies of the (2x2) reconstruction using both HeI and HeII excitation. The S1 and S2 states are found to be non-dispersive across the BZ, and two other deeper-lying states, about 7 and 9-10 eV below EF, are also non-dispersive and thought to be surface-related. Qualitatively, the surface features are ascribed to either Ga or N adatom-induced reconstructions. Himmerlich et al. [459] compared the surfaces states in the vicinity of the VBM for three different surface preparations and obtained the results shown in Fig. 22, which were analyzed using ab-initio theory (described below). The first method was the same as that discussed above for producing the (0001)-(2x2) structure.

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In the second method, the (2x2) thus formed was annealed at 600 °C in UHV, which eliminated the half-order RHEED spots and gave a (1x1) that was somewhat more diffuse than that seen during growth. The third method involved deposition of a small amount of Ga at 640 °C, which yielded a weak (2x2) RHEED pattern. For all three, the same BEs and lineshapes are found for the Ga 2p, N 1s and Ga 3d levels, and EF-VBM indicates an upward BB of ∼0.4 eV. The VBM positions were obtained with Mg Kα excitation, rather than HeII, to avoid complications from surface states. The surface states change when the surface preparation is modified. Theoretical results, described below, were obtained for (2x2) structures with 0.25 ML of Ga (N) adatoms in T4 (H3) sites or 0.25 ML of Ga vacancies, all of which satisfy the ECR and give a semiconducting surface as observed in UPS. The DOS results in the vicinity of the VBM are similar for all three; however, detailed comparison with experiment indicates that the N adatom model best fits the data for the as-grown (2x2) surface. Here the S1 state observed by Gutt et al. and by Lorenz et al. is associated with the N doubly-occupied NBLP orbital and S2 with N-Ga back-bonds. For the surface annealed in UHV after growth, the VGa model best accounts for the data, while the Ga adatom structure provides good agreement for the surface with a small coverage of deposited Ga. In the latter case the surface state in the gap results from GaGa back-bonds. For all three models, theoretical results also exhibit empty surface states near the CBM that arise from DBs on adatom and/or surface Ga sites. Several groups have investigated the electronic structure of (0001) surfaces after in-situ cleaning. Lai et al. [155] and Ma et al. [442] observed changes in the shape of the VB, particularly in the upper edge, for surfaces that were depleted of N by Ar+-ion bombardment. These effects were attributed to the formation of metallic Ga clusters. Bermudez et al. [123] and Wu et al. [181] obtained UPS data for (0001) surfaces that were cleaned in situ by cycles of IBA. The former study employed 1 keV nitrogen ions with "brief" (3-min) anneals at 850–1000 °C, which resulted in a surface with no detectable contamination in AES and a (1x1) LEED pattern with good contrast and little or no evidence of faceting. Wu et al. [181] used 0.5 keV nitrogen ions with 10-min anneals at 900 °C. In the last few cycles the anneals were performed in a background of 10-7 Torr of N2. It was thought that ∼10% of the N2 was dissociated by the hot filament of the ionization gauge and/or by the hot Ta sample-holder parts and that atomic N thus produced was then able to repair the depletion of surface N atoms caused by preferential sputtering during ion bombardment. The resulting surface showed a Ga/N atomic ratio of 1.0 in AES, and the LEED was (1x1) with very sharp spots and a low background. In the work of Bermudez et al., HeII UPS data for the clean surface showed a shoulder near the VBM that was removed by exposure to H atoms, which indicates a surface state. In the work of Wu et al., incomplete removal of contamination from the as-received sample resulted in a similar VB feature; whereas, there was no obvious indication of a surface state on the clean surface. However, in subsequent work, Wu and Kahn [449] exposed the clean surface to O2 and observed the removal of surface states near the VBM as in Ref. [123]. Angle-resolved UPS studies of the (0001)-(1x1) surface have been reported by Dhesi, Smith et al. [443–445] who prepared clean surfaces of n-type MBE material by cycles of Ga deposition followed by annealing in UHV at 900 °C, which removed much of the O impurity. Subsequent IBA (1.5 keV nitrogen ions, 900 °C anneal) resulted in a surface with no contamination other than a small amount of O and a sharp (1x1) LEED pattern with a low background and no evidence of faceting. The surface polarity was not determined, but this work will be included in the Ga-polar section for the purpose of discussion. Recontamination of the clean surface, which was first detectable via changes in the ARUPS data, occurred

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quickly while standing in UHV and required that IBA be repeated every 2 hr. This effect is often noted for GaN (0001) surfaces after in-situ cleaning [387] or growth [455–459]; although, it is not known whether the highly-reactive site involves the lattice-terminating layer or Ga adatoms. The ARUPS data show a non-dispersive surface state just at the VBM that is eliminated by exposure to H atoms, but no surface states appear above the VBM. Exposure to H atoms decreases the upward BB by ∼1.0 eV as shown by the shift in Ga 3d BE. Based on polarization measurements, the surface state has spz character, which is consistent with a DB that is oriented essentially normal to the surface. It is noted here that this DB would have to be doubly-occupied, since it lies well below EF. Several other deeper-lying states are also found that disperse in the surface plane or along the surface normal. Xie et al. [453(abstract only)] appear to have done similar experiments and observed two surface states. Maruyama et al. [447,448] performed ARUPS experiments for (0001) surfaces cleaned by IBA (1.2-3 keV Ar+, 750 °C anneal), which gave a surface with little or no contamination detectable in AES and a (1x1) LEED pattern. The signal-to-noise ratio in the AES data was, however, rather poor, which suggests that a LEED-Auger retarding-field analyzer might have been used. The Ga 3d shows a very strong and broad high-BE satellite that was ascribed to the N 2s-Ga 3d bonding band, and there also appears to be a "tail" of states extending from the VBM almost up to EF. Chao et al. [451] obtained polarization-dependent ARUPS data, shown in Fig. 23, for a (0001)-(1x1) surface of n-type MOCVD material prepared by IBA (0.5 keV nitrogen ions, annealing at 850 ° C), which led to a very sharp LEED pattern and almost no detectable O contamination in AES. As before [443], the surface became contaminated while standing in UHV, to the point of affecting the ARUPS data, and had to be recleaned every 2 hr. In addition to the surface state identified earlier by Dhesi et al. [443], which is only weakly dispersive and very sensitive to H-atom adsorption, a second state was found that disperses throughout the (1x1) surface BZ and is believed to be associated with back-bonds involving surface atoms. This state, which also has pz character, is sensitive to the quality of the (1x1) ordering as reflected in the LEED pattern but somewhat less sensitive to contamination than the non-dispersive state. A third surface state, labeled "C" in Fig. 23, is observed in a small region of the surface BZ. The only known difference between these experiments and those of Dhesi et al. was the use of samples grown using MOCVD vs. MBE with the former, as used by Chao et al., exhibiting a higher degree of ordering. This is consistent with the absence of the order-dependent dispersive surface state in the earlier study by Dhesi et al. The surface polarity in this study was not conclusively determined; however, there is evidence that it was Ga-polar. Ahn et al. [387] and Sung et al. [398], using ISS, found that the N-polar surface of n-type MOCVD GaN after IBA cleaning is passivated by 3/4 ML of adsorbed H that diffuses out from the bulk. The presence of this passivating layer coincides with the appearance of a sharp (1x1) LEED pattern. Therefore, if the MOCVD surface studied by Chao et al., which exhibited a sharp LEED pattern, had been Npolar then no H-sensitive surface states would have been observed. There is the further point that, for the MOCVD material studied by Ahn et al. and Sung et al., the (0001) surface contaminates rapidly during standing UHV, as did the samples studied by Chao et al.; whereas, the (0001̄ ) does not. There has been some degree of controversy regarding the surface polarity in the work by Dhesi et al. [443] and by Chao et al. [451]. This stems from the experimental observation near the VBM of a surface state with little or no dispersion for a surface exhibiting a (1x1) LEED pattern. As will be seen latter in this and in the following section, for a bare and unreconstructed (1x1) surface such a state is consistent with the (0001̄ ) but not the (0001).

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Fig. 23. Left: ARUPS data recorded with different photon energies and azimuthal directions (45° angle of incidence). Spectra (a), (c), and (e) were recorded from the clean GaN (0001)-(1x1) surface. Spectrum (b) was recorded for a clean surface with streaky (1x1) LEED pattern, while spectra (d) and (f) were recorded after saturating the surface with hydrogen. Right: Measured two-dimensional band structure for a clean GaN (0001)-(1x1) surface in the (1x1) surface BZ. Surface-state features are labeled "A", "B" and "C". The recording geometry is indicated in the inset. From Chao et al. [451] (Copyright 1999 by the American Physical Society).

However, the experimental surfaces are demonstrably non-metallic since no emission is seen at EF, and therefore a direct comparison of the data with theoretical results for the ideal (non-defective) bare surface is difficult. Given what is known about the effects on surface stoichiometry of in-situ cleaning by IBA and bearing in mind the ECR, it is more likely that the experimental surface (whatever the polarity) is stabilized in a semiconducting state by Ga adatoms with a coverage of 0.25 ML in a (2x2) SUC. The T4 site is favored for a Ga adatom, but the H3 is only a little higher in energy [373]. Within the cell there are four T4 and four H3 sites, and if these were to be filled randomly then LEED would be expected to exhibit a (1x1) pattern with clear integral-order spots but blurred or missing fractional-order spots. Thus the atomistic structure of the experimental surfaces remains uncertain; although, as noted above, one can be fairly confident that the work of Chao et al, if perhaps not that of Dhesi et al., was performed on the Ga-polar surface. Plucinski et al. [452] reported ARUPS results for n-type (0001) −(1x1) surfaces prepared by outgassing at 450–500 °C followed by IBA (0.5 keV Ar+, prolonged annealing at 450–500 °C), after which a LEED pattern described as extremely sharp was observed. The samples were in the form of thin films grown on sapphire via MOVPE. Data were also obtained (see the following section) for (0001̄ ) surfaces of single-crystal wafers. For the (0001), surface states are found at 0.5 and at 1.5 eV above the bulk VBM. From the absence of a surface-state feature characteristic of Ga 4s orbitals in the (0001) terminating layer and from the high photocurrent above the VBM, it was concluded that the surface is terminated in a layer of metallic Ga, possibly the contracted Ga bilayer associated with a Ga-rich (0001) surface. However, no Ga 3d data, which might have exhibited a low-BE satellite, were given to verify this interpretation. Widstrand et al. [454] performed ARUPS on MOCVD samples that were cleaned first in 1:1 NH4OH:H2O at 65-85 °C and then in situ by outgassing at 500 °C followed by annealing in 1x10-6 mbar (7.5x10-7 Torr) NH3 at 750 °C. This was followed by annealing at 650 °C in a flux of Ga vapor (0.01-0.02 Å sec-1) and then another NH3 anneal, which resulted in a sharp, low-background LEED

pattern. A surface state is found just above the VBM that, with the aid of ab-initio theory, is assigned to Ga adatoms in T4 sites. Another surface-related structure associated with Ga adatoms is seen at higher BE together with two other surface states of uncertain origin. A structureless tail (described as a "slope") is seen to extend from the VBM up to EF and is ascribed to Ga-related defects. No dependence of this tail on photoemission angle is observed, unlike in the work of Plucinski et al. [452], and the strongly-dispersing surface state found by Chao et al. [451] was also not observed. Valla et al. [450] have reported IPES results for MBE GaN (0001)-(1x1) surfaces prepared in the manner described above in connection with the work of Dhesi et al. [443]. To our knowledge, this is the only IPES study that has been performed on wurtzite GaN. However, no unoccupied surface states were detected. Unfortunately, the surface polarity was not known with certainty, which complicates any comparison with theoretical results. As will be seen later in this and in the following subsection, most theoretical studies of the surface-state band structure for either the Gaor N-polar surface (e.g., Ref. [459]) find one or more empty states in the gap. Theoretical electronic-structure results are given in Refs. [373,459–470] for the (0001) surface. Other groups have conducted similar studies as part of an investigation of adsorption or interface formation, and these results will be described in later sections. Here we consider those studies that focus on the surfaces themselves. Wang et al. [460] performed calculations using the LDA for a 2DPS with four Ga-N bilayers the lower two of which were fixed in the bulk configuration and terminated with PHs. Soft PPs were used together with Gaussian orbitals to represent valence states, which included the Ga 3d levels. Structures with a full ML of adsorbed Ga in T1, T4 or H3 sites all have very similar energies (with T4 being slightly lower) and are favored under moderately- or very Ga-rich conditions; whereas, the bare surface is favored under N-rich conditions. These results differ from those described in Section 4.6.1, which indicate a (2x2) N-adatom structure, a (2x2) Ga-adatom structure and a laterally-contracted Ga bilayer on top of the Ga terminating layer as conditions change from very N- to very Ga-rich. Band structure calculations show

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both the bare and Ga adlayer structures to be metallic. The clean surface shows a dispersive and partially-filled surface-state band arising from Ga DBs. For the Ga adlayer occupying T4 sites, three surface state bands are found. One of these, which is derived from adatom DBs, is filled while the others, arising from Ga-Ga bonding between adatoms or between the adlayer and the lattice-terminating layer, are partially occupied. Tsai et al. [461] performed a band-structure calculation for the bare (0001)-(1x1) surface and also found it to be metallic, which results from the 3/4 |e| of electron density in each Ga DB. Rosa and Neugebauer [373] used the GGA with the PBE functional and NCPPs to study the most stable surface structures depicted in Fig. 13. The 2DPS consisted of nine GaN layers (presumably this means nine Ga-N bilayers) with the bottom terminated with PHs having an occupancy of 0.75 |e| to satisfy the ECR. (1x1) and (2x2) SUCs were used to model the clean and adatom surfaces respectively, while a (√3x√3)R30° SUC was employed for the laterally-contracted Ga adlayer and bilayer surfaces. The results for surface structure vs. μGa (or equivalently μN) essentially reproduce those in Fig. 13. As in all other studies, the bare surface is metallic, and the (2x2) Ga(T4) adatom structure is semiconducting. The latter exhibits four surface states in the gap, two of which are empty and derive from DBs on surface and adatom Ga sites, while the others are filled and arise from Ga adatom backbonds to terminating-layer Ga atoms. The two filled surface-state bands are very close in energy (perhaps too close to be resolved experimentally) and show essentially no dispersion, which agrees with ARUPS data [451]. As expected, the band structures for the contracted adlayer and bilayer surfaces show metallic behavior. An electron affinity of χ = 3.73 eV is computed for the (2x2) Ga(T4) adatom surface, which is in fair agreement with experimental values (3.2 ≤ χ ≤ 3.4 eV) for surfaces cleaned in situ using IBA. The ionization potential (I = Eg + χ) and work function (ϕS) for various surfaces were also obtained but are difficult to compare with experiment because they depend on accurate calculation of either Eg or BB (Fig. 24). Segev and Van de Walle [462] and Van de Walle and Segev [463] computed the band structure for the (2x2) Ga(T4) adatom surface and obtained results (Fig. 25) similar to those reported previously by Rosa and Neugebauer [373] and subsequently by Himmerlich et al. [459]. In this case, modified PPs [375] were employed that gave an accurate Eg and permitted the surface states to be located more precisely with respect to the band edges.

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Fig. 25. DOS for the GaN (0001)-(2x2) structure with 0.25 ML of Ga adatoms in T4 sites. From Van de Walle and Segev [463] (reproduced with the permission of AIP Publishing).

Filled- and empty-state bands are at 1.7 and 2.8 eV respectively above the bulk VBM. With regard to Fig. 25 it is noted that the theoretical results of Himmerlich et al. [459] reveal another surface state lying at or just below the bulk VBM. Li and Yan [464] showed that electron-phonon coupling leads to a reduction in GaN surface-state energies under hydrostatic pressure, which amounts to a shift of 55.48 meV at 20 GPa. The results appear to be generic in the sense that no particular surface structure was considered. Du et al. [465(abstract only)] reported theoretical results for the band structure, DOS, surface energy, work function and optical properties of the GaN (0001) surface. In agreement with earlier results, the surface has metallic character with a surface state near the CBM. The surface energy and work function are found to be 2.1 J m-2 (131 meV Å-2) and 4.2 eV respectively. The optical properties of the surface and bulk are also analyzed and found to differ significantly. Kempisty et al. [381,466,467] and Krukowski et al. [468–470] first reported what is termed the "surface states Stark effect" and its impact on adsorption energies obtained in 2DPS calculations for GaN (0001). Here either the effective charge on PHs used to terminate DBs on the bottom surface, or else the PH bond length, is varied to adjust the potential difference between the top and bottom surfaces. By this means the position of EF in the gap can be varied to simulate n- or p-type doping or to fill or empty surface states in the gap. For adsorption processes involving electron transfer, ΔEads is found to depend strongly on the position of EF; whereas, those that are electronically neutral show no such effect.

Fig. 24. (a) Schematic diagram (not to scale) defining energy-level quantities for the case of n-type material. Due to the electrostatic effect of band bending, all levels (including the vacuum level) shift identically with respect to EF. The BB is the difference in energy between the CBM (or VBM) at the surface and in the bulk. The CBM-EF difference in the bulk is typically small (∼0.06 eV for a doping density of ND ¼ 2x1017 cm-3) and is often neglected, in which case the BB is then taken as CBM-EF at the surface. (b) Schematic indication of how an adsorbed layer of dipoles with the positive end outward from the surface can reduce χ and ϕS relative to the bare surface. In (b), an effective-NEA condition is obtained if the vacuum level at the surface of the dipole layer lies below the bulk CBM. A dipole layer with the negative end outward has the opposite effect on χ and ϕS.

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Fig. 26. Surface band structures (left) and layer resolved DOS (right) of the GaN (0001) surfaces: (a) bare (2x2), (b) (2x2) Ga(T4), (c) (2x2) N(H3), and (d) (2x2) VGa. The gray shaded areas correspond to the projected bulk band structures. The bulk states have been shifted such that the bulk electrostatic potential is aligned to the value of the calculated slab electrostatic potentials at the fourth GaN double layer. The plots have been further shifted such that the bulk VBM is at 0 eV. The red points indicate the states with strong localization at the three topmost surface double layers. States below (above) the horizontal solid line are filled (empty). In the DOS plots the red solid, blue dashed, and magenta dot-dashed lines correspond to the first, second, and third double GaN layers from the surface, respectively. The DOS projected on the Ga and N adatoms in (b) and (c) are indicated by the dark green dotted lines. S’s indicate surface states in the gap and far from the band edges. From Himmerlich et al. [459] (Copyright 2013 by the American Physical Society).

The apparent band gap obtained in 2DPS calculations is also affected by the presence of an electric field across the slab. Himmerlich et al. [459] reported theoretical studies of the electronic structure of three different (2x2) reconstructions, in addition to that of the bare (1x1) surface, and compared these results (Fig. 26) with UPS data for samples grown in situ using MBE. The experimental data (Fig. 22) were described earlier in this subsection. The computational approach used the LDA with an on-site Coulomb correction ("LDA+U", Section 4.1.1), which improves the calculated Eg. The 2DPS consisted of 12 Ga-N bilayers with the bottom terminated with PHs. The theoretical results for the (2x2) Ga(T4), N(H3) and VGa models provide good descriptions of the data obtained for in-situ growth under conditions designed to produce Ga adatoms, N adatoms or Ga vacancies, respectively. Charge density plots are also given that clearly show the orbital composition of the uppermost filled surface state for each type of surface. On the other hand, none of the models agree in detail with ARUPS data for surfaces cleaned in situ, which suggests that such surfaces are structurally complex. Qualitatively, however, the non-dispersing state above the VBM for Ga(T4) corresponds to the adsorptionsensitive feature found in nearly all such data. An important finding of the theoretical part of this work is that all the (0001) surfaces studied have empty states at 2.6-2.8 eV above the VBM, which indicates that the commonly-observed upward BB of ∼0.5-0.8 eV on clean surfaces of n-type material is an intrinsic property. There are, to our knowledge, no theoretical studies that specifically address the electronic structure of surfaces grown ex situ and subsequently cleaned in situ. However, as discussed in Section

4.6.1, (0001) surfaces prepared in this way frequently exhibit "excess" Ga due to the preferential loss of N at the temperatures typically used for annealing. The Ga adatoms might actually be instrumental in stabilizing the surface in a semiconducting state since θGa = 0.25 ML of adsorbed Ga satisfies the ECR. As discussed above, UPS shows a surface state just above the VBM for these surfaces that is very sensitive to adsorption of, e.g., oxygen. Hence, theoretical studies of the electronic structure of the (0001) surface with Ga adatoms in a (2x2) structure are considered especially relevant here. Such investigations have been performed by Rosa and Neugebauer [373], Bermudez [433], Himmerlich et al. [459], Van de Walle and Segev [463], Segev and Van de Walle [462,471] and González-Hernández et al. [472]. Fig. 25 shows representative results [463] for 0.25 ML of Ga adatoms in T4 sites, which consist of a band of filled surface states at about 1.7 eV above the bulk VBM and a band of empty states lying about 0.6 eV below the bulk CBM. The former consists of GaGa bonding orbitals ("back-bonds") between the adatom and the lattice terminating layer, and the latter involves the empty DBs on the surface and adatom Ga. The exact energetic locations of the surface states with respect to the band edges differ somewhat among the various theoretical studies. However, these results are in qualitative agreement with UPS experiments, described above, for (0001) surfaces cleaned in situ by IBA or by Ga annealing, which show a surface state at about 0.5 eV above the VBM. They are also consistent with ELS results for such surfaces, discussed in Section 4.7.2, that show a surface-state feature at about 3.4 eV, which could be a transition out of filled or into empty surface

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states. It is noted again that the theoretical results of Himmerlich et al. [459] reveal another surface state lying at or just below the bulk VBM. The situation regarding surfaces cleaned in situ by annealing in NH3 is more difficult. In some cases, UPS data [137,140,473] show no clear evidence of surface states above the bulk VBM; whereas, other data definitely [454] or possibly [474] do show such states. Use of the Ga 3d BE, as described at the beginning of this section, can be of value here. In one study of a p-type GaN (0001) surface [137], EF-VBM = 1.24 eV can be deduced from the Ga 3d BE, which agrees well with the value obtained directly from UPS. In another such study [473], for a different sample, EF-VBM = 1.74 eV is found which again agrees with the UPS result. Both are consistent with an absence of surface states above the bulk VBM. In one case [473] a weak "tail" was seen to extend from the VBM almost up to EF and tentatively identified as surface-state emission, but this is almost certainly the result of higher-energy satellites of the HeI line (hν = 21.2 eV) that was used as the excitation source (see Ref. [446]). It is noteworthy that the electron affinity obtained in one of these studies [137], χ = 2.6 eV, is significantly less that the value of 3.2-3.5 eV typically found in UPS experiments not involving the use of NH3. Since NH3 is a good electron donor, this suggests the possibility of a surface dipole layer involving adsorbed [NH3]δ+ which would have the effect of lowering the measured χ as shown schematically in Fig. 24. It is known that NH3 has a long residence time in UHV chambers and readily adsorbs on the clean (0001) surface, which eliminates the surface-state features in UPS and ELS (see Ref. [123] and Section 7.1). This effect complicates the detection and analysis of possible surface-state features in UPS when NH3 is used for in-situ cleaning, even when this is done in an appendage chamber rather than in the main UHV chamber. When adsorption of residual NH3 is a factor, or indeed when any other effect contributes to a surface dipole layer, it is expected that the measured χ will vary between samples and between experiments on the same sample. Thus other studies in the same series gave χ = 2.6 eV [140], χ = 2.8 eV [140] and χ = 3.1 eV [473,474]. Measurement of χ can be regarded as an indirect method for the detection of residual NH3 when this reagent is used in in-situ surface cleaning. As discussed above, Widstrand et al. [454] performed ARUPS on GaN (0001) surfaces that were cleaned by annealing in NH3 as the last step. Here a narrow surface-state band was detected in the gap very close to the VBM, which suggests that adsorption of NH3 from the background was negligible in this case. Tracy et al. [474] observed a similar feature, in the form of a well-defined peak near the VBM. In this case, χ = 3.1 eV was also found, which suggests a surface that is essentially free of NH3. Thus it is not clear whether those experiments that show no obvious surface state emission are fundamentally different from those that do or if they might simply be affected by adsorption of NH3 from the UHV background. Given the high degree of sensitivity toward adsorbates exhibited by (0001) surface states in the gap, the NH3 coverage needed to eliminate such states might be too low to permit detection of the NH3 itself in UPS. In summary, the physical structure of the (0001) surface (Section 4.6.1) appears to be fairly complex. Under growth conditions the progression of structures with increasing μGa is well established on theoretical grounds (Fig. 13), but there are experimental complications. One is the effect of low levels of contaminants such as O and As on the observed reconstructions. Another is the apparent dependence of the structures on growth conditions, on the substrate and on post-growth processing as shown, for example, by Wang et al. [361]. Different models have been proposed for the (1x1) and (2x2) surfaces seen in various studies, and there may in fact be more that one structure that corresponds to either of these. Furthermore, some studies done under UHV conditions find a

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(1x1) surface with a single ML of adsorbed metallic Ga that may not to be stable under most MBE growth conditions. A further consideration of this issue is given in Section 5.18, which addresses the development of the first two MLs of adsorbed Ga. In cases where the physical structure of the (0001) is well characterized then so is the electronic structure. For certain (0001) surfaces grown in-situ using MBE, such properties appear to be fairly well understood as a result of the combined experimental and theoretical work of Himmerlich et al. [459] (Fig. 22 and Fig. 26). The contracted Ga bilayer formed under Ga-rich conditions does not appear to have been studied experimentally from this perspective. However, Plucinski et al. [452] suggest that their (0001) surface prepared by IBA might comprise such a Ga bilayer. For in-situ cleaning, the resulting surface states appear to be sensitive to the cleaning method. Some inconsistency among different experimental studies is noted, perhaps resulting in part from uncertainty as to the surface polarity in some of the earlier work, but there is general agreement that at least one surface state exists at or just above the VBM. Theoretical results, as well as a consideration of the effects on surface composition of preparation by IBA or by Ga-cleaning, suggest that filled surface states in this case are due to Ga adatom back-bonds to terminating-layer Ga atoms. It is worth noting that such Ga adatoms appear to be highly reactive. This is shown by the sensitivity of the surface-state features seen in UPS and ELS (Section 4.7.2) after IBA cleaning to either accidental or intentional exposure to reagents. The sensitivity to adsorption of background contaminants was noted above [443,451] and will be seen again in the following section. The discussions in Section 7 of the adsorption of NH3, O2, H2O and atomic H will also illustrate the highlyreactive nature of the species responsible for surface states as shown by the sensitivity to adsorption. The situation regarding surface states in the case of in-situ cleaning using NH3 is less clear, again because of uncertainty as to the surface structure and, especially, the possible role of residual NH3 adsorbed from the background. One final summary comment concerns the nature of the (0001)-(1x1) surface commonly seen after in-situ cleaning. One possibility, in addition to others described in the introduction to Section 4.6, is that it represents a single ML of adsorbed Ga. As discussed in Section 4.6.1, such a surface has been reported in several studies after MBE growth. While patches of adsorbed Ga (as distinct from individual adatoms) cannot be excluded, there appears to be no compelling evidence at this point to suggest that such a model provides a complete description of the (0001)-(1x1) surface formed by in-situ cleaning. It is also worth recalling that the ISS study of Ahn et al. [387] gave no indication of a Ga adlayer. However, as will be seen in the following section, the situation is somewhat different in the case of the corresponding (0001̄ )(1x1) surface. 4.7.1.2. The Polar (0001̄ ) Surface. The (0001̄ ) has been studied extensively using UPS [388,436,452,458,475–478]; although, all results except those in Refs. [388,458] are for samples grown ex situ and cleaned in situ. Beach et al. [388] reported XPS data, obtained using Al Kα excitation (hν = 1486.7 eV), for the (0001̄ )-(3x3) surface grown by MBE and studied in situ. A strong feature extending from the VBM to EF is seen as a result of the metallic Ga adlayer +adatom structure of this surface (Section 4.6.2). Lorenz et al. [458] reported angle-integrated UPS results for (0001̄ )-(1x1) surfaces grown and studied in situ. After growth, the sample was cooled in the nitrogen plasma, and a (1x1) structure was seen that exhibits a non-metallic surface (i.e., no emission at EF) with a surface state near the VBM. This is undoubtedly different from the (1x1) Ga adlayer structure seen (Section 4.6.2) after cooling in UHV followed by annealing, and the authors ascribe the surface

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state in this case to NBLP orbitals on surface N atoms. Since a bare and ideal (i.e., non-defective) (1x1) surface would be metallic as a result of partially-filled N DBs, the question of what stabilizes the present surface in a semiconducting state is unresolved. It is noted here that the fact that surface states are seen and that no N-H stretching mode is detected in HREELS argues against a significant coverage of adsorbed H. One possible model for this surface might be 0.25 ML of VN randomly distributed within a (2x2) cell, which would give a semiconducting surface according to the ECR and a (1x1) LEED pattern. Per (2x2) cell, there would be three surface N atoms with NBLP orbitals and three underlayer Ga atoms, with empty DBs, centered around the VN. This structure could result from incomplete nitridation, via exposure to the N plasma during cooling, of a Ga adlayer remaining from growth. It is known (Section 4.6.2) that the (0001̄ ) surface with 1 ML of Ga in T1 sites is very stable under either N-rich or Ga-rich growth conditions [391]. In the scenario suggested here, nitridation of the Ga adlayer ceases at θN = 0.75 ML to give what is essentially a bare (0001̄ ) surface with 1/4 ML of VN. Plucinski et al. [452], Ryan et al. [475] and Kowalski et al. [476– 478] reported ARUPS data for (0001̄ )-(1x1) surfaces grown ex situ and cleaned in situ. Ryan et al. [475] studied p-type MBE material with surfaces cleaned by IBA (0.5 keV nitrogen ions, 850 °C annealing), which resulted in a surface with no contamination seen in AES other than a small amount of O and a sharp (1x1) LEED pattern with a low background and no evidence of faceting. It was noted that the kinetic energies of features in the ARUPS data shift with sample temperature and with time. This was ascribed to SPV, which is known to have a large effect in photoemission for p-type GaN [440]. The time dependence might be related to the decay in the intensity of the synchrotron radiation source with elapsed time after injection or to drift in the sample temperature. Four different surface states are identified, all of which show no dispersion in the surface-normal direction and are removed by adsorption of H atoms. The polarization dependence shows that three states have pz character while the fourth, with the highest BE, exhibits s character. One of the pz states appears above the VBM in part of the surface BZ while the others remain below the VBM. It is also found, as in other work [443,451], that the surfacestate features are highly sensitive to adsorption of contaminants in the UHV background, which requires that the surface be recleaned every 2 hrs. However, if the surface states are removed by adsorption of H, the surface then becomes inert with respect to background contaminants, which indicates that the species or site responsible for the surface states is highly reactive when clean but is passivated by adsorbed H. This is consistent with the results of Sung et al. [398] concerning the passivating effect of H on the (0001̄ ) surface. However, Ryan et al. studied the (0001̄ ) surface of p-type MBE material and observed surface states that could be eliminated by exposure to H atoms. This indicates that the bare surface was not already saturated with H via out-diffusion from the bulk. On the other hand, Sung et al. [398] studied n-type MOCVD material and found that (0001̄ ) surfaces exhibiting a sharp (1x1) LEED pattern always involved 3/4 ML of adsorbed H. This difference is likely the result of a higher concentration of bulk H in MOCVD vs. MBE material. It may also be important that H+ (H−) is the dominant form of hydrogen in the bulk for p- (n-) type GaN [401], as shown in Fig. 17. Accumulation of mobile (at high temperature) H−, but not H+, on the (0001̄ ) could be promoted by the positive bound polarization charges on this surface (Section 4.2.2) or by the presence of electron-deficient N atoms (electronegative atoms with partially-filled DBs). Based on a comparison with theoretical results described below, Ryan et al. suggested that the surface states result from a Ga adlayer. However, since the surface is non-metallic and shows no

evidence of substantial Ga-Ga bonding in the Ga 3d spectrum, one might speculate that a model based on Ga adatoms would be more appropriate. One might also speculate that the same argument used to rationalize the appearance of a (1x1) LEED pattern for 0.25 ML of Ga adatoms that was discussed in connection with the work of Chao et al. [451] on the (0001) surface might also apply here. However, as will be seen later in this subsection, an interpretation that is closer to that of Ryan et al. has been supported by theoretical results. Plucinski et al. [452] performed ARUPS experiments for the (0001̄ ) surface of a single crystal that was doped highly n-type (ND ≈ 3-6x1019 cm-3). The surface was cleaned as described in the preceding section in connection with their (0001) results. The clean surface shows what is described as an extremely sharp (1x1) LEED pattern and is known (see below) to be N-polar but Ga-rich. One surface state is seen at 0.5 eV above the bulk VBM and another at 7.5 eV below the VBM. Based on theoretical results [479] described below, the latter is suggested to derive from adatom Ga 4s orbitals. The results are similar to those of Dhesi et al. [443] for a (1x1) surface of unknown polarity; although, in that case the deeper-lying state was ascribed to bulk emission. Kowalski et al. [476–478] performed an extensive series of ARUPS and other experiments on n-type (0001̄ )-(1x1) singlecrystal surfaces prepared as described by Plucinski et al. [452] except that chemical polishing or CMP was performed as a first step, which was not mentioned in the earlier report. In Ref. [476], some discussion of the proper in-situ cleaning approach is provided, which shows that prolonged (25.5 hrs.) annealing in UHV at 500 °C results in a Ga-rich, but still-contaminated, (1x1) surface. Subsequent IBA (0.5 keV Ar+) is then able to produce a clean and well-ordered Ga-rich surface. Four different surface states are seen [477], which agrees with the results of Ryan et al. [475], described above, except for differences in the relative intensities of various ARUPS features. The earlier study in this series by Plucinski et al. [452] observed only two surface states, but two of the present four states appear only in very restricted regions of the surface BZ and so might have been overlooked. As an aid in clarifying the nature of the surface states, Ga was deposited in situ at a sample temperature of 450–500 °C with monitoring via RHEED. The deposition was stopped when the (1x1) pattern began to weaken, and the structure was then restored by subsequent annealing. Thus the Ga-enriched surface, which showed evidence of metallic Ga in the Ga 3d spectrum, retained a (1x1) structure. This results in an attenuation of the surface-state feature near the VBM, which further demonstrates the association of this feature with the GaN surface itself. In the most extensive study in this series [478], the entire bulk and surface BZ was probed, and Fig. 27 summarizes the results obtained. Surface-related features, which are absent in the bulk band-structure calculations, are labeled as b, c, g, d and m. Of these, all but b can be attributed to an N-terminated surface covered with a Ga adlayer; whereas, b can be explained only by the existence of a bare but relaxed surface. This is supported by the observation that depositing Ga in situ attenuates the corresponding feature in ARUPS. The conclusion is that the best explanation of the data is in terms of a surface with a mixture of regions that are either bare or covered with a 1-ML Ga adlayer. As will be seen below, a similar model has been employed by Wang et al. [480] to interpret the ARUPS data of Ryan et al. [475]. In later work, Plucinski et al. [436] reported an ARUPS study of (0001̄ )-(1x1) surface states, and the effects of exposure to sulfur and/or O2, for n-type MBE material. The surface was cleaned in HCl solution and then in situ by outgassing at 850 °C followed by IBA (500 eV nitrogen ions, 850 °C anneal). This gave a very sharp LEED pattern with a low background, and XPS showed no detectable C and only a very small O coverage. One surface state, resulting from

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Fig. 27. Left: ARUPS taken under off-normal emission conditions from the GaN (0001̄ ) surface. Full and dotted lines are guides to the eye drawn through the revealed spectral features. Right: The experimental band structure diagram derived from the ARUPS data. All symbols mark the experimental points. Full lines show the calculated bulk band structure (Strasser et al. [479]) for a full adlayer of Ga in T1 sites, and dotted lines indicate positions of possibly surface-related features. From Kowalski et al. [478] (Copyright 2004, reproduced with permission from Elsevier).

Ga DBs, is seen at about 1.5 eV above the VBM, and another, ascribed to Ga s-orbitals, occurs at about 8 eV below the VBM. Both these features are associated with a metallic Ga adlayer on the basis of theoretical results described below. Theoretical electronic-structure results for the (0001̄ ) surface are presented in Refs. [340,399,460,461,463,471,479–481]. Smith et al. [340] obtained band-structure results for the (0001̄ )-(1x1) surface with a full ML of Ga adatoms in T1 sites above the N terminating layer. A metallic surface was found with three highlydispersive surface-state bands in the gap. The lowest in energy is completely filled, while, for the other two bands, one contains 0.25 |e| per cell and the other is empty. The origin of the different surface states was not described in detail but might be understandable in terms of the ECR. With 3 valence electrons, the Ga adatom uses 3/4 |e| to form a Ga-N back-bond to a surface N with 5/4 |e| in a DB. This would give one filled surface state and leave 9/ 4 |e| on the Ga. Bonding between Ga adatoms is thought to be important in stabilizing this surface structure. Two electrons would go to forming Ga-Ga bonds with two neighboring Ga adatoms to give filled bonding and empty anti-bonding orbitals, while the remaining 1/4 |e| occupies the last Ga DB (assuming sp3-hybridized Ga). This gives two filled, one empty and one partiallyfilled surface-state band. Only one filled surface state band is seen above the VBM; hence, the other might lie at a lower energy. The authors also present STS data confirming the metallic character of the (1x1) adlayer surface. Strasser et al. [479] reported theoretical results for what was termed the (0001)-(1x1):Ga surface, but the model was actually

the (0001̄ ) terminated in an adlayer of Ga in T1 sites as used by Smith et al. A parameterized method known as extended Hückel theory was employed, with parameters derived from a fully abinitio bulk band structure calculation, and only the Ga 4s and 4p orbitals were included as valence states. Two surface states are found in the gap, with a high degree of dispersion in the surface plane, that arise from Ga px and py orbitals involved in bonding between adatoms (where z is the surface normal). A third band, comprising Ga s and pz and N p orbitals, presumably represents bonding between the adlayer and the surface and disperses into the bulk VB over parts of the BZ. Several other deeper-lying and more-complex surface resonances are also identified. Normal- and off-normal-emission spectra were computed and compared with the ARUPS data of Dhesi et al. [443]. As noted in Section 4.7.1.1, the surface polarity in these experiments was uncertain. Nevertheless, the good agreement between theory and experiment leads one to believe that it might have been the (0001̄ ) surface. An important point is that, based on a comparison of observed and calculated results for normal emission, doubts are raised about the validity of the commonly-used experimental technique of locating the VBM by linear extrapolation of the VB edge to the baseline. Wang et al. [460,480] performed theoretical studies of the (0001̄ ) surface using methods described in the previous section in connection with their results for the (0001). In the earlier study of the two [460], it was found that an adlayer with a full ML of Ga in T1 sites is the most stable structure for the (0001̄ ) at any μGa. These results differ somewhat from those of Neugebauer [1] (Fig. 16), which find the adlayer to be favored only under conditions of

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moderate to high μGa. Band structure results were obtained for the Ga ML and also for the bare surface. For the bare surface a single surface-state band, derived from partially-filled N DBs, appears in the gap with only a small degree of dispersion. A highly-dispersive surface resonance is also seen, which was later [480] assigned to N-Ga back-bonds. The Ga adlayer shows three surface-state bands in the gap, all with a significant degree of dispersion. One is filled and is derived from Ga DBs in the adlayer and N DBs in the surface-terminating layer, while the others exhibit free-electron-like dispersion with one being weakly occupied and the other empty. These results are consistent with those of Smith et al. [340] and Strasser et al. [479] that were described above. The latter two bands suggest that the Ga adlayer behaves like a 2D metal. From this and the fact that DBs appear on both the Ga adlayer and the N terminating layer one infers that there is little chemical bonding between the two in these calculations. In the later study by Wang et al. [480], theoretical results were compared with the extensive set of ARUPS data reported by Ryan et al. [475] for a p-type sample that was known to be N-polar. It was proposed that the data can be explained in terms of a surface consisting of a mixture of some regions that are bare and others that are terminated in a full ML of Ga in T1 sites. Furthermore, the surface is proposed to consist of two domains separated by a 30° rotation such that the experimental ARUPS represents a superposition of the two. These considerations lead to an almostquantitative agreement between the observed and calculated surface-state band structures. However, an unresolved issue is that experiment shows little or no emission at EF; whereas, both the clean and Ga-adlayer surfaces are metallic. This cannot easily be explained in terms of, for example, adsorption of contaminants since the surface states are themselves sensitive to such effects. In the case of the Ga adlayer, however, the partially-filled band at EF is only weakly occupied (e.g., 1/4 |e| per SUC in the work of Smith et al. [340]) so that the DOS at EF might be too small to detect in a typical UPS experiment. Tsai et al. [461] performed theoretical studies for the (0001̄ ) surface, both bare and covered with 1 ML of adsorbed Ga, using the LDA with NCPPs. A (2x2) SUC was used in order to check for reconstruction, and the 2DPS consisted of 3 Ga-N bilayers with the bottom surface terminated with PHs. This work questions both the applicability of the ECR to GaN and the use of the thermodynamic approach, discussed in Section 4.1.2, to determine the stability of different surface structures. The criticism of the ECR centers on the use of this formalism to determine the occupancy of PHs that terminate the bottom surface of a 2DPS and the fact that surface atoms are not equivalent to those in the bulk. However, since the purpose of PH termination is specifically to make layers near the bottom of the slab appear electronically bulk-like, as illustrated by the results of Chen and Kuo [381], this criticism appears somewhat inappropriate. The criticism of the use of thermodynamics is essentially that, even under MBE conditions, the flux of Ga and N atoms at the surface is so low that μGa is independent of the Ga and N BEP (i.e., flux). It is estimated that typically a surface atom interacts with one N in 0.1 sec and one Ga in 3 sec and that surface relaxation or reconstruction occurs on a much faster time scale. Tsai et al. note that the bare (0001̄ )-(1x1) surface is stable against the displacement of a surface N atom away from its equilibrium position. However, this does not necessarily conflict with the thermodynamic analysis, which finds that other surface structures are more stable (lower in total energy) than the bare (1x1). In the present work, the bare (1x1) is found to be metallic, with bands near the VBM that cross EF, which represent the partially-filled N DBs. For a (2x2) structure with one VN per SUC, which satisfies the ECR, the remaining N atoms relax inward; although, the surface electronic structure was not described. Several 1-ML Ga adlayer models were considered for the (0001̄ ) surface including (1x1)

structures with atoms in T1, T4 or H3 sites and (2x2) models with trimers around T4 and H3 sites and a fourth Ga in a T1. The most stable structure is found to be the one with an H3-centered trimer, for which the energy per (2x2) cell is 0.98 eV lower than for the Ga adlayer structure (Fig. 15 and Fig. 16) proposed by Smith et al. The trimer exhibits Ga-Ga and Ga-N distances close to those in bulk Ga and GaN respectively, and the band structure for this surface shows metallic character. Values were also obtained for the work function of different polar and non-polar surfaces. This shows a strong dependence on orientation and termination as a result of the surface dipole layers associated with the different surface structures. To our knowledge, these alternative Ga-adlayer models have not been further investigated. Van de Walle and Segev [463] and Segev and Van de Walle [471] considered the (0001̄ )-(2x2) surface with θGa = 0.25 ML in H3 sites, which is found to be the most stable structure under very- or moderately N-rich conditions (Fig. 16, see also the correction in the caption). The band structure shows the surface to be semiconducting with a filled and non-dispersive surface- state band right at the VBM and an empty and non-dispersive surface state band lying 1.2 eV higher. The former is derived from doublyoccupied NBLP orbitals on surface N atoms and the latter from the DB on the Ga adatom. No mention is made of any surface states or resonances at higher BE, which makes it difficult to assess these results in relation to the ARUPS data of Ryan et al. [475] and Kowalski et al. [476–478]. However, the appearance of a non-dispersive surface state at the VBM in this model renders it an alternative to the relaxed bare surface [478,480] as a means of accounting for the appearance of such a feature in ARUPS, if one allows for the possibility that the factional-order spots in the (2x2) LEED pattern might be lost by the random occupation of H3 sites in the (2x2) cell. Romanyuk et al. [399] performed a theoretical study of the bare (0001̄ )-(1x1) surface, motivated by their quantitative LEED [400] and PED analyses of a single-crystal surface, the details of which are given in Section 4.6.2. The data showed the absence of a Ga adlayer but could not conclusively disallow the possibility of stabilization by adsorbed H [387,398]. The calculations employed the GGA with NCPPs and a 2DPS with eight Ga-N bilayers and the bottom surface terminated with PHs. The Ga 3d electrons were included in the core, not as valence states, and the functional was not specified but is assumed to be the PBE, which is the most widely used. The band structure shows a dispersionless surface state derived from N DBs lying right at the VBM, which appears similar to that in previous work [460,480]. Two other surface states, each with a lower DOS, are seen at about 1.5 and 5.3 eV below the VBM. Ptasinska et al. [481] obtained theoretical results for the (0001̄ ) surface using the GGA with the PBE functional and a 2DPS with eight Ga-N bilayers for which the bottom surface was terminated with PHs. The Ga 3d electrons were treated explicitly, and a dipole correction (Fig. 6) was included. In order to allow for the possibility of reconstruction, results were obtained for (1x1), (2x2) and (4x4) SUCs. The computational procedure was tested by comparing bulk band-structure results with those from previous calculations. The bare surface is unreconstructed with a dispersionless band of surface states at the VBM that arises from partially-filled DBs on surface N atoms as in previous work [399,460,480]. As in the work of Wang et al. [460], it was concluded from the agreement between these results and the experimental data of Chao et al. [451] that these authors had misidentified their sample as Gapolar. However, as noted in the discussion of the work by Chao et al. in the previous section, there is reason to believe that their sample was actually Ga-polar and to question any direct comparison of their results with band-structure calculations for a bare, ideally-terminated surface. Results were also obtained for 0.25,

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0.75 and 1.0 ML of Ga adatoms adsorbed on the N lattice-terminating layer; although, the adsorption site was not clearly specified. For θGa = 0.25 ML, a dispersionless band of surface states derived from N pz orbitals appears at the VBM, which also seems to coincide with EF, and an empty dispersionless band resulting from Ga DBs occurs above the bulk CBM. As expected, the band structures for higher θGa indicate surfaces that are more metallic. In summary, the situation regarding the structure of (0001̄ )(1x1) surfaces prepared in-situ by IBA appears to be somewhat more clear than that of the corresponding (0001)-(1x1) discussed in the previous section. The results of Ahn et al. [387] and Sung et al. [398] indicate that, in a case where H can accumulate at the surface, the structure is really the (2x2) stabilized by 3/4 ML of adsorbed H that appears to be (1x1) in LEED. This effect has been

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demonstrated for n-type MOCVD material, the most readilyavailable form of GaN, which has a high concentration of H− in the bulk. For other forms of material (n-type MBE [436], n-type singlecrystals grown by reaction of N2 and Ga at high pressure [452,476– 478] or p-type MOCVD [475]) the accumulation of a high θH on the (0001̄ ) surface via diffusion from the bulk appears not to occur. This is based on the detection in UPS of surface states in the gap that are sensitive to adsorption. In this case, deliberate adsorption of H removes these states [475] and renders the surface inert with respect to further chemisorption of background contaminants. Here ARUPS results and the theoretical analysis of Wang et al. [480] indicate that the appropriate clean-surface structure is a mixed phase consisting of bare regions and others with 1 ML of Ga as an adlayer. Still missing, however, is an understanding of the

Fig. 28. Structural and electronic properties of the (101̄0) (m-plane) GaN surface after growth (red) and O2 adsorption (blue). The UPS (He I) and XPS valence band spectra together with Ga 2p3/2, O 1s, N 1s and Ga 3d core level spectra are shown in (a) and (d), respectively, with the BE referenced to EF. The red-shaded area in (a) illustrates the contribution from the occupied surface state at 3.1 eV for the clean surface, while the black spectrum represents an intermediate stage after storage of the as-grown sample in the load lock chamber at 5x10-9 mbar (3.75x10-9 Torr) for 60 min (∼13.5 L), equivalent to the end of the RAS sequence shown in Fig. 29. (b) Energy diagram representing a schematic of the determined surface upward band bending at clean GaN (101̄0) surfaces together with a visualization of the density of occupied and unoccupied surface states and related transition energies to explain the detected signatures in UPS and RAS experiments. (c) RHEED pattern along the [0001] direction measured directly after MBE growth. From Himmerlich et al. [483] (reproduced with the permission of AIP Publishing).

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(0001̄ )-(1x1) formed by other in-situ methods, such as annealing in a flux of Ga or NH3. The high degree of stability, both in theory and experiment, of the (0001̄ )-(1x1) with 1 ML of adsorbed Ga appears to be an important factor in controlling the properties of the (0001̄ ) surface. As a final cautionary note, it should be mentioned that experimental studies of adsorption on the N-polar surface of n-type MOCVD GaN after cleaning by IBA should consider that the initial surface may be passivated by adsorbed H. 4.7.1.3. The Non-Polar (101̄0) and (112̄ 0) Surfaces. The electronic structure of the (101̄0), or m-plane, surface has been studied experimentally by Wichert et al. [482] using ARUPS, by Himmerlich et al. [483] using UPS and optical techniques (SE and RAS) and by Lymperakis et al. [206], Bertelli et al. [402], Eisele et al. [403] and Ivanova et al. [484] using STS. Kuo et al. [485] and Mishra et al. [486,487] studied the (112̄ 0), or a-plane, surface using UPS and/or XPS. Theoretical results for the (101̄0) surface electronic structure are given in Refs. [206,402,409,413,414,416,417,461– 463,471,482,488] and for the (112̄ 0) in Refs. [416,461,463,471]. A review of these topics has been given by Eisele and Ebert [6]. Beginning with experimental results for the (101̄0) surface, Wichert et al. [482] performed ARUPS experiments on surfaces prepared by cleaving single crystals in UHV. The data show a weakly-dispersive surface state near the VBM that is associated with N pz orbitals, the origin of which will be examined in the discussion of theoretical results given below. A strongly-dispersive surface resonance is also seen at higher BE that is derived from Ga s and N px orbitals, and these two features together are consistent with a theoretical model based on the surface structure proposed by Northrup and Neugebauer [409] (Section 4.6.3). Himmerlich et al. [483] studied surfaces prepared in situ by MBE homoepitaxy using HeI UPS, XPS and optical methods (RAS and SE in the 3.0 ≤ hν ≤ 4.0 eV range). The RHEED data after growth indicated a well-ordered surface with a low defect density, and the spectroscopic results are shown in Fig. 28 and Fig. 29. A surface state, which is highly sensitive to contamination, appears in UPS at 3.1 eV below EF. With the upward BB of 0.6 eV, this BE places the state at just below the VBM. Other deeper-lying states seen in UPS, which change at a higher coverage of adsorbed O, are ascribed to states in the bulk VB. The in-situ RAS data show a highly adsorption-sensitive transition at an energy of 3.3 eV, in addition to other structure at energies above Eg that corresponds to bulk interband transitions observed ex situ using SE. The lowenergy RAS feature is assigned to a transition between the surface state seen in UPS and an empty surface state lying just below the CBM. To our knowledge, this is the only instance of optical absorption spectroscopy having been employed to study surface states of this nature in situ on a clean GaN surface. It should be noted, however, that excitonic effects (i.e., an attractive interaction between the excited electron and the hole in the initial state) can lead to an underestimation of the energy difference between the occupied and empty states derived from optical or ELS data (Section 4.7.2). Such effects can be avoided using IPES, as done by Valla et al. [450] for GaN (0001), or STS to study empty surface states. Bertelli et al. [402] reported STS results for (101̄0) surfaces prepared by cleaving crystals in UHV. Surfaces with a low defect density (≤2x1012 cm-2) were obtained, and it is found that the empty surface state associated with Ga lies outside the gap and is instead resonant with the bottom of the CBM at the Γ-point. Eisele et al. [403] and Ivanova et al. [484] also performed STS studies for (101̄0) surfaces prepared by in-situ cleaving and found that both the filled and empty surfaces states lie outside the gap at the Γpoint. It was concluded that, therefore, Fermi-level pinning on this surface arises from defects and not from intrinsic surface states. Lymperakis et al. [206] also performed STS experiments on (101̄0) surfaces prepared by in-situ cleaving and initially saw no

Fig. 29. (a) RAS spectra measured at different surface preparation stages of GaN (101̄0) - red: as-grown GaN(101̄0), black: sequence of measurements during UHV storage at a pressure of 5x10-9 mbar (3.75x10-9 Torr) for up to 60 min (bold black) and blue: after O2 adsorption. (b) imaginary parts of the bulk anisotropic dielectric functions of m-plane GaN substrates obtained by ex-situ spectroscopic ellipsometry analysis, corresponding to the RAS signal after 0.5 ML oxygen adsorption. ε2⊥ and ε2|| refer to the absorption of light polarized perpendicular and parallel to the c-axis, i.e., along the [112̄ 0] and [0001] direction, respectively. "FXA/B" and "FXC" label exciton features, and "EPC" indicates an exciton-phonon complex. From Himmerlich et al. [483] (reproduced with the permission of AIP Publishing).

surface states in the gap. However, with the aid of ab-initio calculations (described below), it was shown that there is in fact an empty surface state lying about 1 eV below the CBM at Γ, which is the lowest-energy point in the BZ. This state is highly dispersive at Γ, which results in a very small DOS and a partial charge density that is localized close to the surface, all of which makes the state difficult to detect in STS. There is much less dispersion at higherenergy points in the BZ, which causes the DOS to peak at these higher energies and the surface state to appear in STS to be essentially degenerate with the CBM. With this information, the STS sensitivity was increased, and an empty surface state was detected with an onset at about 0.6 eV below the CBM in reasonable agreement with theory. Experimental studies of the (112̄ 0) surface electronic structure are relatively few in number. Kuo et al. [485] formed a heterojunction by growing first n-type then p-type GaN on a Si (111) substrate using MBE. The growth was in the [0001̄ ] direction, and — the sample was then cleaved in UHV to expose the (1120) (or ̄ equivalently the (1120)) surface after which soft-x-ray XPS data were recorded across the junction using synchrotron excitation (hν = 380 eV). The Ga 3d BE on either side of the junction was used to determine the location of EF in the gap on either side. This made use of the VBM-Ga 3d energy difference, which is independent of doping, and the value used (18.0 eV) differs slightly from that obtained earlier by Waldrop and Grant [439] (17.76 eV). The main

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Fig. 30. Layer-resolved total (gray shaded) as well as Ga (red) and N (green) projected contributions to the GaN 16-layer-slab DFT-PBE density of states for the (101̄0) surface. The insets show the atoms that have been considered in the projection of the density of states. Note the Ga-N dimer buckling illustrated in the firstlayer inset. The bulk-like contributions in the lowermost panel originate from the average of the eight central atomic layers of the slab. From Landmann et al. [417] (Copyright 2015 by the American Physical Society).

focus of this study was on BB and Fermi-level pinning, which are reviewed in Section 4.7.3. Mishra et al. [486,487] used XPS and UPS to study the (112̄ 0) surface; however, no in-situ surface cleaning (not even annealing) was done in this work. There have been several theoretical studies of the (101̄0) surface electronic structure, as noted above. There is general agreement that autocompensation occurs wherein (invoking the ECR) the 3/4 |e| of electron density in the Ga DB on the ideally-terminated Ga-N surface dimer transfers to the N DB where it adds to the 5/4 |e| in this bond to give a doubly-occupied NBLP orbital. The charge transfer is accompanied by a rehybridization that gives a higher-energy sp2 Ga and a lower-energy sp3 N and results in dimer buckling with Ga (N) down (up) relative to the ideal surface plane. The NBLP orbital on N then constitutes a surface state near the VBM, and the empty Ga DB forms a surface state near the CBM. The various theoretical descriptions then differ mainly as to the locations of these states relative to the bulk band edges, which has been the source of some controversy. This issue relates to the question of whether Fermi-level pinning on the non-polar surfaces results from intrinsic surface states or extrinsic effects such as defects. In the most recent theoretical study of the (101̄0) surface electronic structure, Landmann et al. [417] obtained the DOS shown in Fig. 30 using methods described in Section 4.6.3 in

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connection with the physical structure of this surface. An occupied surface state formed mainly from surface N 2p orbitals falls at the bulk VBM at the Γ-point, and an unoccupied surface state derived mainly from empty Ga orbitals occurs slightly below the bulk CBM at Γ where it is highly dispersive. The results for the identity and energetic positions of the filled and empty surface states concur with the qualitative expectation based on the ECR. The DOS shows that these states are not confined entirely to the surface but are detectable down to the fourth layer (third underlayer). Note that the orbital compositions of the contributions from the second and fourth layers (first and third underlayers) are opposite to those from the first and third layers (surface and second underlayer); namely, Ga near the VBM and N near the CBM. This is a consequence of an opposite charge transfer (N→Ga vs. Ga→N) that is associated with an opposite Ga-N dimer buckling (Ga up in the second and fourth layers vs. Ga down at the surface). To obtain an accurate estimate of the position of the empty surface state relative to the bulk CBM, calculations were done using different DFT methods and for a 2DPS with either 16 or 48 atomic layers. The effect of quantum confinement (Section 4.1.1) for 16 vs. 48 layers appears to be fairly small, but the thicker slab is necessary for obtaining an accurate description of states near the CBM. For the hybrid HSE functional in particular, Eg for 16 or 48 layers (3.55 or 3.58 eV respectively) is very close to experiment (3.50 eV at T = 0 K [24]). The result for the empty surface state is that it lies below the bulk CBM by 0.20 to 0.66 eV, depending on the method of calculation, which agrees with RAS [483] and STS [206] data. The bulk and surface optical properties were also computed, and features identified with surface-state excitation were found that concur with experiment [483]. The work of Landmann et al. [417], which was described first for convenience, was preceded by theoretical studies of the (101̄0) surface electronic structure by Lymperakis et al. [206] and by González-Hernández et al. [416], the latter having been done using methods described in Section 4.6.3 in connection with their work on the physical structure of this surface. Lymperakis et al. performed LDA+U calculations (Section 4.1.1), using the PAW approach, for a 2DPS with 48 atomic layers. As described above, an empty surface state was found that lies well below the CBM at the Γ-point but with a low DOS, as a result of a high degree of dispersion, that makes the contribution below the CBM difficult to detect in STS. González-Hernández et al. also obtained electronicstructure results similar to those of Lymperakis et al. The filled surface state derived from N NBLP orbitals lies at the VBM while the empty state associated with Ga DBs is highly dispersive at Γ but nearly flat at the X- and M-points. However, the empty state appears to lie very close to, an perhaps slightly above, the CBM. In summary, the issue of whether the empty Ga-derived surface state lies above or below the bulk CBM, which is of interest in determining whether EF on (101̄0) is pinned by intrinsic or extrinsic states, has been controversial both in experiment and theory. Some experiments [206,483] and several calculations find that it lies in the gap [206,413,414,417,462,463,482] while other experiments [402,403,484] and calculations [402,409] find the opposite. However recent experimental and theoretical work [206,417,483] has established that this state does in fact lie below the bulk CBM at Γ and provides an explanation for why the DOS near the Γ-point is difficult to detect in STS. Other work, by Ebert et al. [488], is also noteworthy although somewhat outside the scope of the present review. This study shows, in a theoretical analysis, that on a (101̄0) surface with an unpinned Fermi level only CB, and not VB, states can be imaged in STM due the existence of tip-induced BB. For the (112̄ 0), the most recent theoretical results pertaining to surface electronic structure are those of González-Hernández et al. [416]. Here there are two Ga and two N atoms per SUC (Fig. 2),

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which leads to two filled and two empty surface states lying very close to the bulk VBM and CBM respectively. However, in earlier work, Segev and Van de Walle [463,471] found that of the two empty Ga-derived surface states, one lies at ∼0.5 eV below the bulk CBM while the other falls slightly above the CBM. On the other hand, the filled surface states associated with N fall below the bulk VBM and make no contribution in the gap. 4.7.1.4. Semi-Polar Surfaces. Mishra et al. [487] studied the semipolar (101̄2), or r-plane, surface experimentally using XPS, UPS and AFM. Samples were grown by MBE on a (101̄2)-oriented sapphire substrate and then transported in air. The surface was cleaned ex situ in isopropanol and in 20% aqueous HCl solution, but no in-situ cleaning was performed, and XPS showed a substantial O contamination. Carbon may also have been present but was not discussed. The doping type was not mentioned, but it is assumed here to be unintentionally doped n-type as is commonly the case for GaN. The AFM data show the surface to be faceted, with an RMS roughness of 13.8 nm. The bulk-sensitive VB spectrum recorded using XPS shows EF-VBM = 2.0 eV, which for an n-type sample corresponds to an upward BB of ∼1.3 eV. An electron affinity of 4.5 eV was obtained using UPS data; however, this measurement is undoubtedly affected by the presence of surface oxide, which was not taken into account (Section 5.10). Skuridina et al. [260] reported XPS and AFM results for the (112̄ 2) surface. The sample was grown by MOCVD on a (112̄ 2)oriented single-crystal substrate that was grown via hydride VPE, and in-situ cleaning was done by annealing in UHV at 600 °C. No information was given regarding the resulting surface contamination, but AFM showed the surface to be smooth with an RMS roughness of 0.4 nm. Bulk-sensitive XPS data showed changes in the structure of the VB with photoelectron take-off angle. The origin of this effect is uncertain, but it is thought to be related to — the surface polarity, i.e., (112̄ 2) vs. (1122), and therefore of potential use in polarity determination for semi-polar surfaces. ̄ Lee and Kim [420] studied the electronic structure of the (1011) surface theoretically using methods described above in Section 4.6.4.1. The DOS was obtained for the (4x2)DV (dimer-vacancy) structure shown in Fig. 18d, which is the most stable surface under N-rich conditions, in addition to other surfaces that are less stable. The (4x2)DV, which satisfies the ECR, shows a gap between filled and empty surface states, but states appear above the bulk VBM and below the bulk CBM that are derived from the π orbitals of the N-N dimers. States derived from the NBLP orbitals on the 3-foldcoordinated N atoms also appear above the bulk VBM. — The electronic structure of the (101̄3) and (1013) surfaces (Fig. 19) has been studied theoretically by Kioseoglou et al. [424] using procedures described in Section 4.6.4.2. On the (101̄3), the Ga adlayer structure is the most stable for any μGa. Here the DOS shows filled states S1 and S2 below EF but above the bulk VBM and empty states S3 and S4 above EF but below the bulk CBM. S1 and S2 are derived from two different forms of Ga-Ga bonds, respectively (Gaad-Ga)D and (Gaad-Ga)T, where "ad" refers to "adatom" and "D" and "T" to "doubly (2-fold-)" and "triply (3-fold-)" coordinated (on the bare surface). In (Gaad-Ga)D the Ga adatom is bonded to one surface Ga site and to two N, which were 2-foldcoordinated (D) on the bare surface. In (Gaad-Ga)T, the adatom is bonded to one N atom, which was 3-fold-coordinated (T) on the bare surface, and interacts with two surface Ga sites (see Fig. 4a,b). S1 lies lower in energy, reflecting the greater stability of (GaadGa)D vs. (Gaad-Ga)T. S3 and S4 are derived from dangling orbitals on the (Gaad-Ga)T and (Gaad-Ga)D adatoms respectively, with S3 — lying lower in energy and just above EF. For the (1013) surface, the bare (2x1)-reconstructed surface, which is the most stable under N-rich conditions, is semiconducting. Several states derived from surface Ga atoms appear below the bulk CBM. These are empty

because they lie above EF, but the corresponding filled states were not identified. On the other hand, the Ga adlayer and bilayer structures that are favored under more Ga-rich conditions are metallic. 4.7.2. Electron Energy Loss Spectroscopy and related methods Here we are concerned with the use of ELS to study electronic transitions, which typically occur with an energy loss (ΔE) of a few eV or more. The investigation of vibrational modes and freeelectron excitations using HREELS, with ΔE o 0.5 eV, is discussed in Section 4.8. Several groups [123,322,423,489–495] have used surface-sensitive ELS to probe the electronic structure of GaN. Such studies are typically performed with a low-energy primary electron beam (Ep ≈ 100 eV) in order to minimize the escape depth of the inelastically-scattered electrons. Other groups have used ELS with much higher beam energies (∼100 keV or more), together with an electron microscope, to study spatially-resolved bulk electronic structure including measurement of the band gap and optical constants. These latter works are beyond the scope of the present review. The theoretical studies of surface electronic structure noted in the previous subsection are relevant to the present ELS data. In addition, theoretical work specifically addressing surface-sensitive ELS experiments has been reported [496–499]. In ELS, data are recorded as N(E), d[N(E)]/dE or −d2[N(E)]/dE2 where N(E) is the scattered intensity vs. KE. These expressions apply to a hypothetical electron energy analyzer for which the resolution, transmission, detector gain, etc. are all independent of KE. First-derivative spectra suppress the broad background that occurs for ΔE 4 Eg, making it easier to identify structure. Here the peak energy corresponds to the first-derivative inflection point, and, to make peak location easier, the second derivative is often used. Peak energies in the second derivative correspond to those in N(E), but this introduces two difficulties. First, peaks that are strong but broad in N(E) appear weak in −d2[N(E)]/dE2, which makes intensities difficult to interpret. Second, artifacts can occur when the wings of weak and strong peaks overlap in energy [500]. Berger et al. [489] and Troost et al. [490] obtained ELS data for GaN grown by in-situ nitridation of a GaAs (110) surface and for a GaN (0001) that was cleaned by bombardment with 250 eV Ar+ ions but not annealed. Various features associated with plasmon, interband and Ga 3d excitations were found, but specific assignments were difficult. Freundt et al. [322] studied GaN (0001) surfaces prepared by in-situ MBE, which exhibited a (1x1) LEED pattern (but see below). The ELS of the as-grown surface shows a transition, with an onset at ΔE = 2.53 eV and a peak at about 3.4 eV, superimposed on the bulk interband transition having an onset at 3.39 eV. The lower-energy transition is essentially eliminated by in-situ annealing at 600 °C and is ascribed to Ga vacancies resulting from growth in an N-rich MBE environment. Rizzi and Lüth [492] extended the work of Freundt et al. [322] using similar samples and methods; although, the data (Fig. 31) and interpretation are somewhat different from those given by Freundt et al. In addition to the low-energy transition with an onset at 2.53 eV, two additional loss peaks are found at ΔE = 888 and 974 meV, all of which show little or no change after an 800 °C anneal. It was concluded that the polarity of the sample was undetermined rather than being (0001), but it was suggested to be (0001̄ ) on the basis of the (1x1) LEED pattern appearing after MBE. However, it is noted here that it could also have been the (0001) with a single adlayer of Ga atoms [358,359] (Section 4.6.1). Together with a BB of about 1.0 eV, obtained using XPS, the energylevel diagram shown in Fig. 31 was constructed to account for the ELS data. This consists of a partially-filled band of states that pins EF at ∼1 eV below the CBM and two empty states lying just below the CBM. The microscopic origin of these states is difficult to

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Fig. 31. Left: ELS spectrum measured in situ after MBE growth of GaN (  250 nm thick). The energy range corresponds to electronic transitions across and within the gap. The dashed lines are the results of fits with an (hν-E)1/2 function. The energy scale is broken slightly below 2.5 eV. Right: Qualitative picture of the gap states at the GaN (0001) surface. The density of states (Ns) is plotted schematically together with the band scheme near the surface. The electronic transitions observed in HREELS are indicated by arrows. From Rizzi and Lüth [492] (with the permission of Springer).

determine, given that the surface composition is uncertain. However, one notes that theoretical results (Fig. 25) of Van de Walle and Segev [463] for the (0001) with 0.25 ML of Ga adatoms in T4 sites show a pair of empty surface state bands, derived from Ga DBs, lying just below the bulk CBM. This work will be revisited in Section 4.7.3.1, which addresses BB. Tsuruoka et al. [493] performed ELS experiments on (0001) surfaces that were prepared by annealing at 900 K in UHV, which resulted in a sharp (1x1) LEED pattern with no impurities detectable in HREELS vibrational spectra. The clean surface showed only the bulk inter-band transition with no indication of any surface-related features. Romanyuk et al. [423] performed ELS studies of well-ordered (0001̄ ) and (101̄3) surfaces prepared by immersion in hot HCl solution followed by outgassing in UHV via flashing to 1000 °C and then exposure to 2.6x10-6 mbar (2x10-6 Torr) of NH3 at 1000 °C. For comparison, surfaces disordered by 5 keV Ar+-ion bombardment were also studied, and XPS showed these to be depleted of N due to preferential sputtering. The (0001̄ ) surface showed a clear (1x1) LEED pattern while the (101̄3) exhibited evidence of (0001) facets. The ELS data as a function of Ep in the 200 to 1000 eV range and of scattering angle were analyzed to obtain the complex dielectric constants for the three types of surfaces ((0001̄ ), (101̄3) and disordered). However, no transitions that were clearly surface-localized were identified. A few groups have investigated surface states and their response to adsorption using ELS. These results will be revisited later, when studies of adsorption are reviewed. Here we are concerned with the electronic structure of the adsorbate-free surface. Bermudez et al. [123,491] observed a transition with ΔE = 3.4 eV that is strongly attenuated by exposure to H atoms, O2 or NH3 and is ascribed to an excitation involving surface states near the VBM and/or the CBM. This is close in energy to the peak discussed above [322,492], with an onset at 2.53 eV. Other transitions of uncertain origin, at ΔE ≈ 9 and 20 eV, are also sensitive to adsorption and undergo shifts and/or changes in intensity. In either study, clean surfaces were prepared by IBA (1 keV nitrogen ions, ∼850 °C anneal) and showed no impurities above the AES detection limit. A low-background (1x1) LEED pattern was obtained, which was strongly faceted for some samples [491] but less so for others [123], and there was no obvious dependence of the surfacesensitive ELS on the degree of faceting. Bellitto et al. [494] obtained similar results for the response of surface-sensitive ELS

transitions to H atoms and assigned the feature at ΔE ≈ 20 eV to a surface Ga 3d excitation. Grabowski et al. [495] reported ELS data for surfaces of undetermined polarity (designated "{0001}") that were cleaned ex situ in HF solution and then in situ by deposition of 200 Å of Ga followed by annealing at 800–850 °C. The resulting surface showed a trace of C as the only impurity detectable via AES and a faceted (1x1) LEED pattern. In agreement with the previous results, ELS data show a surface-state transition at ΔE = 3.4 eV, with a threshold at 2.7 eV, that vanishes after H adsorption. From a theoretical perspective, Noguez et al. [496–499] have computed ELS spectra in the range of 2 o ΔE o 6 eV for the nonpolar (101̄0) surface and compared these with similar results for the cubic (110) surface in order to gain insight into the effects of surface structure on optical properties. Results were obtained using a tight-binding approach (Section 4.1.1) for the ideally-terminated (101̄0) and for three different models [408–412] for the relaxed surface. A slab model was constructed for each of the surfaces and the imaginary part of the complex dielectric function ε(ω) = ε1(ω) + iε2(ω) computed using the optical dipole transition probability between filled and empty states. The real part, which is necessary for computing the ELS, was obtained by a KramersKronig transformation of the imaginary part. As an explanatory note, the overall shape of the bulk ELS spectrum is given by [501] −Im[1/ε(ω)] = ε2(ω)/[ε1(ω)2 + ε2(ω)2], where "Im" means "imaginary part". For the surface [496–499], ε2(ω) shows a strong dependence on structure and on polarization parallel or perpendicular to the Ga-N surface dimer bond direction. Structure is also found at energies above and below Eg that is associated with transitions involving dangling bonds and back-bonds at the surface. The ELS was computed for a fixed angle of incidence of the primary electron beam, relative to the surface normal, as a function of the angle of rotation of the sample around the surface normal. These results show anisotropies that are characteristic of the different surface structures and can be compared with the RAS data of Himmerlich et al. [483] and with calculations of the polarized bulk and surface ε2(ω) of Landmann et al. [417]. With the Y-axis defined as the [0001] direction (parallel to the Ga-N dimers) and the X-axis as the [112̄ 0] (perpendicular to the dimers), Himmerlich et al. plot RAS data as ΔR/R = (RY-RX)/(RY+RX) where R is reflectance. The data show that absorption related to surface states occurring at photon energies below or just above Eg is mainly X-polarized, which

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agrees with the results of Noguez [499] for transitions between bulk and surface states. However, transitions between surface states are predicted to be strongly Y-polarized. Also transitions between bulk states are computed to be mainly X-polarized; whereas, SE and RAS data [483] indicate a somewhat stronger Ypolarization. On the other hand, the theoretical results of Landmann et al. [417] appear to be in better agreement with the RAS data for both surface and bulk transitions. We close this section by briefly mentioning two non-linearoptical methods that have been demonstrated or proposed to be capable of giving information for GaN surfaces similar to that obtained in ELS. LoPresti et al. [502] used two-photon photoemission excited by intense hν = 4.35 and 5.67 eV laser pulses, having widths of 200 and 600 fsec respectively, to study surface states on MBE and MOVPE n-GaN surfaces cleaned by IBA. Onephoton excitation out of an occupied state or defect level at about 0.8 eV below the CBM was observed together with two-photon processes involving excitation from this state or from the VB into CB states followed by excitation into vacuum. These results are potentially significant because of the possible direct observation of a partially-filled surface state just below the CBM on the (0001) surface. To our knowledge this has not been achieved in conventional UPS experiments. Gavrilenko and Wu [503] developed the theory of second-harmonic generation on GaN polar surfaces and showed that differences between the surface-state structures on the (0001) and (0001̄ ) should be detectable by this means. 4.7.3. Band bending and surface photovoltage This section reviews mainly those results on band bending that are specific to clean GaN surfaces. The discussion will be divided into subsections addressing phenomena that occur "in the dark" and under illumination, the latter being termed "surface photovoltaic". By "in the dark" is meant "in the absence of irradiation capable of inducing SPV". Since most clean-surface BB measurements are done using UPS or XPS they are not truly "in the dark". The subject of BB and its effects on semiconductor surface properties, particularly adsorption and chemical reaction, has been extensively reviewed by Zhang and Yates [504]. The separate but related issue of metal-contact formation is discussed in Section 6. Likewise, the measurement and interpretation of SPV has been thoroughly reviewed by Kronik and Shapira [505]. These subjects will arise frequently in later discussions of adsorption and metal contacts, and further results of this nature will be described at the appropriate places. Some pertinent results have already been noted in previous sections focusing on electronic structure. 4.7.3.1. Band bending. Band bending is an electrostatic effect that results from a charge separation between the surface and bulk, which typically occurs when majority carriers are trapped at surface states or defects with energy levels in the gap. Here we are concerned mainly with BB on GaN surfaces that are atomicallyclean or nearly so; although, other results are also relevant. This is a complicated issue since it depends on surface preparation and stoichiometry. The discussion of BB can be divided naturally into structural and chemical effects, thermal effects, doping and material growth effects and "other" effects; although, there is overlap among the different topics. Almost all the studies reviewed here are experimental. The term "Fermi-level pinning" is often used interchangeably with BB but more properly refers to a situation in which the BB does not respond to external stimuli such as contact with a metal, which usually indicates a high density of partiallyfilled states at a particular energy in the gap. In discussing BB results, a common procedure is used wherever possible to determine the position of EF in the gap at the surface, (EF-VBM)surf. This is done in order to simplify comparison among different studies since it avoids difficulties in accurately locating

the VBM in surface-sensitive UPS that can result from either contaminants on an unclean surface [181] or surface states on a clean surface [449]. (EF-VBM)surf is obtained using the reported value of the Ga 3d BE (EF-Ga 3d) after subtracting (VBM-Ga 3d) = 17.76 eV±0.03 [439], which is a material constant. Where necessary, the Ga 3d BE is obtained from data plotted in figures. To obtain BB = (EF-VBM)bulk − (EF−VBM)surf, this quantity is subtracted from (EF-VBM)bulk = (CBM-VBM) − (CBM-EF)bulk where Eg = (CBM-VBM) = 3.39 eV at RT [24] and (CBM-EF)bulk for n-GaN is in the range of 0.08 to 0.04 eV for typical doping levels (ND = 15x1017 cm-3, Section 6). In some cases the results differ somewhat from those in the original references based on direct observation of the VBM in UPS. When this procedure cannot be applied, because the Ga 3d BE is not available, the results quoted in the original reference are used if the method employed is equally reliable. For example, (EF-VBM)surf can generally be obtained directly from XPS data recorded with an excitation energy sufficiently high that surface states near the VBM do not interfere. In the following, for brevity, the notation "EF-VBM" will be used when "(EFVBM)surf" is understood. It should be noted that the following discussion of BB, most of which is based on photoemission measurements, does not take into account the effect of SPV in reducing the magnitude of the observed BB. This "band-flattening" effect is small (∼0.15 eV) for nGaN (0001) at RT or above under illumination with conventional laboratory UPS and XPS excitation sources, which is the main focus of attention here, and is discussed in the following subsection. The effect is much larger for the p-GaN (0001) surface, which for that reason is not discussed in detail here. Structural and chemical effects on band bending [102,137,140,184,349,436,446,455,458,459,485,506–509] are in some cases closely related to the surface-cleaning issues discussed previously. Effects on BB resulting from strictly wet-chemical or other forms of ex-situ cleaning are less important in the present context and will generally be omitted. In the work of interest here, ex-situ treatment is always followed by in-situ cleaning, which involves high temperatures and is expected to alter the BB. However, in understanding thermal effects on BB, there is an interest in BB on "as-received" or "as-grown" surfaces, and it is furthermore useful in some cases to compare BB for clean and for air-exposed surfaces. King et al. [349,446] grew n-GaN (0001)–(1x1) and (2x2) surfaces using gas-source MBE, in which NH3 is used as the N-atom source. The (1x1) was grown at 650 °C and the (2x2) at 800 °C, and in either case the sample was cooled to 600 °C before turning off the NH3 flow. Growth at the higher temperature results in a smoother surface, and in either case the level of O contamination detected in AES or XPS, if any, was o1%. It was also noted that the (2x2) gradually converted to a (1x1) upon standing for a few hours in a vacuum of 10-9–10-8 Torr, which indicates a sensitivity to small amounts of contamination, but could be converted back to a (2x2) by annealing in NH3. The structure of the (1x1) and (2x2) surfaces was not determined, but the latter was tentatively ascribed to N adatoms since θN = 0.25 ML satisfies the ECR. The result for EFVBM was about 2.3 eV for the (1x1) and 2.5 eV for the (2x2). As discussed in the introduction to this section, these values were estimated here from the Ga 3d BEs in the plotted data and differ somewhat from those given in the original reference (2.7 and 2.4 eV respectively for (1x1) and (2x2)), which were obtained directly from the VBM. Hashizume et al. [184] grew an n-type (0001)-(2x2) surface using MBE and then exposed the sample to room air. This caused (EF-VBM) to decrease from 2.7 to 2.0 eV (i.e., an increase in upward BB from about 0.6 to 1.3 eV) as a result of oxidation. A (2x2) RHEED pattern was observed during growth, which according to Smith et al. [341] indicates the possibility of a trace of As contamination

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(Section 5.3). Hartlieb et al. [137] and Tracy et al. [140] observed the effects of cleaning by in-situ annealing in NH3 vapor on BB for nand p-GaN (0001)-(1x1) samples grown by MOVPE. For n-GaN, EFVBM = 2.8 eV and 3.2 eV (upward BB ≈ 0.5 and 0.1 eV) respectively for the clean and as-inserted surfaces. The small BB for the as-inserted sample is discussed below in connection with thermal effects. Typically UPS and XPS results for clean p-GaN surfaces are strongly affected by SPV, as discussed in the following subsection, so that BEs for such surfaces cannot be easily interpreted. Plucinski et al. [436] measured BB for the (0001̄ )-(1x1) surface of n-type MBE material that was cleaned in situ as described in Section 4.7.1.2 in connection with their ARUPS study. The result for EF-VBM is 2.0 eV on the clean surface and 2.7 eV after a large O2 exposure, indicating a large upward BB when clean that is significantly reduced by adsorbed O. Gutt et al. [455] and Lorenz et al. [458] grew n-type (0001)-(2x2) and (0001̄ )-(1x1) surfaces in situ using MBE and found EF-VBM = 2.8 and 2.3 eV respectively. These values were obtained here using the Ga 3d BE determined from the UPS feature excited by the HeIIβ line at hν = 48.4 eV that appears in the plotted HeII data. The N plasma was maintained during cooling after growth, as a result of which the (0001)-(2x2) probably represents 0.25 ML of N adatoms. The nature of the (0001̄ )-(1x1) surface formed under these conditions is uncertain but has been discussed in Section 4.7.1.2. The (0001)-(2x2) result is close to that of Hashizume et al. [184], EF-VBM = 2.7 eV. Himmerlich et al. [459] used MBE to grow three different types of (0001)-(2x2) surfaces on unintentionally-doped n-GaN with 0.25 ML of Ga adatoms, N adatoms or Ga vacancies, all of which satisfy the ECR and stabilize the surface in a semiconducting state. A Ga 3d BE of 20.5 eV (EF-VBM = 2.7 eV) is seen for all three, and it is significant that the BB appears to be independent of the stabilizing species. Garcia et al. [506] measured EF-VBM as a function of the O/Ga atomic ratio for a series of native oxides formed on MBE n-GaN (0001). The O/Ga ratio was determined using the O 1s and Ga 3d peak areas in Al Kα-excited XPS, and the latter apparently includes contributions from both GaN and GaOx. A linear relationship is found, with EF-VBM decreasing with increasing oxide content up to a thickness of ∼20 Å. This extrapolates to EF-VBM = 2.7 eV for an oxide-free surface; although, it is unknown if this is the same as EF-VBM before any O2 exposure. It is not clear why the BB should scale linearly with oxide thickness, but the implication is that defects at the interface increase in density and/or change in character as the oxide grows. These results are qualitatively consistent with those of Hashizume et al. [184] discussed above. Yang et al. [102] studied the (0001) and (0001̄ ) surfaces of bulk n-type single-crystals grown by hydride VPE. The samples were cleaned wet-chemically and then in situ in an NH3 plasma followed by heating to 650 °C in NH3 vapor. An O coverage of ∼1.1 ML was found on either face after cleaning, and it was suggested that the θO might have resulted from the use of a quartzglass tube as part of the plasma apparatus or perhaps from some other source. Values of EF-VBM = 2.5 and 2.7 eV (upward BB = 0.8 and 0.6 eV) respectively were found for the (0001) and (0001̄ ) surfaces. The (0001) result is similar to those obtained for clean surfaces, which suggests that the deposited oxide layer (which may be SiOx) has little effect on BB. The situation may be different when the GaN itself is oxidized (e.g., Refs. [184,506]), which can produce defects at the interface. Alternatively, species present in the NH3 plasma may reduce the density of defects in the oxide layer. Smaller BBs (o0.4 eV) were seen for as-inserted samples that were either not cleaned ex situ or only wet-chemically. Strictly in terms of internal compensation of the bound positive polarization charges (Section 4.2.2), the BB on the N-face would be downward [5]. However, the observed upward BB can be explained by a density of negatively-charged external species (e.g.,

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defects) that exceeds σb. This produces a net negative surface charge that then has to be compensated by the formation of a depletion layer (Fig. 9). Cho et al. [507] used surface-potential electron microscopy to measure BB on air-exposed MBE n-GaN (0001) samples that were cleaned in organic solvents and then in aqua regia or in KOH solution. With or without wet-chemical treatment, a BB in the range of 0.9-1.1 eV was found, which corresponds to EF-VBM ≈ 2.3 eV and is qualitatively consistent with the results of Garcia et al. [506] for similar air-exposed samples. Duan et al. [509] performed XPS measurements on MOCVD n-GaN (0001) with and without cleaning in HF solution but with no in-situ treatment. It was claimed that there is a small downward BB (0.055 eV) on the surface without HF treatment and a small upward BB (0.345 eV) for the treated surface. This was based on observation of small changes in the Ga 3d BE with photoelectron collection angle, which was intended as means of profiling through the SCL. This interpretation is, however, inconsistent with the observed Ga 3d BEs, which are in the range of 19.5 to 19.8 eV and indicate an upward BB of about 1.4 eV (EF-VBM ≈ 1.9 eV). On the other hand, Sumiya et al. [508] used hard-x-ray XPS (hν = 5.95 keV) to measure EF-VBM vs. depth for n-GaN by varying the photoelectron collection angle and found EF-VBM to change from 1.9 eV at the surface to 2.3 eV at the maximum escape depth (20 nm for VB photoelectrons). The samples were grown by MOCVD, but no cleaning procedure was described. Thermal effects on GaN BB have been widely reported [94,104,123,126,330,331,510] and can be significant. This was already noted in Section 4.5, which deals with thermal stability, and in the preceding paragraphs in connection with results for "asinserted" samples. Thermal effects are most clearly demonstrated in the results [123] shown in Fig. 32. The samples used in this study were initially suspected to be N-polar but were later found to be Ga-polar. An as-inserted n-type (0001) MOCVD sample, with no ex-situ or in-situ cleaning and no heating other than chamber bake-out (during which the sample temperature remained below 210 °C), was studied vs. annealing in UHV. This constitutes the first time that the sample was heated to high temperature except during growth. Here EF-VBM is ∼3.2 eV before treatment (i.e., a BB of ∼0.1 eV), decreases to 2.5–2.6 eV over the 300–600 °C range and

Fig. 32. (EF-VBM) vs. annealing temperature for as-inserted GaN samples (filled symbols) and for surfaces subjected to 1 keV nitrogen-ion bombardment (open symbols). The latter were obtained after first having completed the annealing series for the as-inserted samples. Different symbols indicate results for different samples, and the curves are intended only as visual aids. The sample was held for an arbitrarily-chosen period of 3 min at each of the indicated temperatures and data recorded after cooling to o 100 °C. The Fermi-level position ( 7 0.05 eV) was determined using the Ga 3d BE. The zero of energy is the VBM, with the CBM at 3.39 eV. The bulk Fermi-level position (dashed line) was estimated using the carrier concentration and electron effective mass (Section 6). The lines labeled "H-ads" show the position of EF for ion-bombarded surfaces, annealed at 900–1000 °C, after adsorption of H. From Bermudez et al. [123] (Copyright 1998, reproduced with permission from Elsevier).

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then remains stable up to the point of rapid decomposition (4 900 °C). The position of EF was determined in each case with the sample below 100 °C after a 3-min anneal at the indicated temperature, which had no significant effect on the levels of C and O contamination seen in AES. It was speculated that the cause of the BB change might be diffusion of Ga vacancies to the surface. The VGa defect is known [295] to be an acceptor, which could trap electrons and thus cause upward BB. Furthermore, MOCVD growth is inherently N-rich and so might be expected to lead to a relatively high VGa density. Subsequent nitrogen-ion bombardment further decreases EF-VBM to 2.2 eV, and annealing in stages increases this back to 2.6 eV with most of the change occurring in the 400–700 °C range. Implanted N remaining from ion bombardment of GaN is reported [155] to be eliminated at 350 °C, which suggests that the decrease in BB might be associated in some way with a partial restoration of crystalline order. The final EF-VBM of 2.65 eV after annealing the ion-bombarded (0001) surface is slightly larger than the value of 2.47 eV for the (0001̄ ) after IBA, based on the Ga 3d BE reported by Kowalski et al. [478]. It is also close to the result (EF-VBM ≈ 2.7 eV), discussed above, that is found for the (0001)-(1x1) or −(2x2) surfaces on n-GaN formed by MBE or by cleaning in-situ by annealing in NH3. As seen in Fig. 32, exposing the IBA surface to atomic H after the last anneal (1000 °C) causes a small decrease in BB, and similar effects are seen for O2 and NH3. Subsequent IBA cycles give the same results as the first, but the initial nearly "flatband" state of the as-inserted surface is never recovered by any of the surface-treatment methods used. The upward BB of ∼0.7 eV after IBA is typical for n-GaN (0001). In many studies, surfaces cleaned by IBA show a BB in the range of 0.6-0.9 eV. Qualitative evidence for a decrease in upward BB following exposure of a clean surface to reactive species (i.e., air) was also seen, using SE, by Choi et al. [511] for a (0001̄ )-(3x3) surface grown by MBE. However, as noted above, Hashizume et al. [184] observed a large increase in upward BB when an n-GaN (0001)-(2x2) surface grown by MBE was exposed to room air. Other studies [94,104,330,331] have reported basically the same thermal effect for n-GaN (0001) based on the Ga 3d BE. The upward BB, if any, is small for an as-inserted surface but increases by 0.35 to 0.8 eV after the first heating to ≥500 °C in UHV. This is seen for films grown by hydride VPE [94], MBE [104] and MOCVD [330,331] and also for bulk crystals grown by hydride VPE [102]. In the case of p-GaN (0001) [94,331,510], annealing for the first time in UHV causes an increase in downward BB, which suggests the accumulation of hole traps (i.e., donors). However, thermal effects for p-GaN are somewhat difficult to interpret because the usual dopant, Mg, bonds to H and is "poisoned" until the Mg-H complex is dissociated by annealing at high temperature (e.g., Ref. [25]). This is particularly the case for MOCVD growth, which is H-rich. Hence, some of the thermal effect on BB in this case might arise simply from dopant activation. A further complication in interpreting the p-GaN results is the possible effect of SPV, as discussed by Foussekis et al. [510] and in the following subsection. Thus it is possible that different mechanisms lead to annealing-induced BB changes for n- vs. p-GaN. Several other studies also present important BB results. Falta et al. [132] grew n-GaN (0001) by MOVPE and transferred the sample under dry N2 into a UHV surface-analysis chamber. The doping was not specified, but it is assumed here to be unintentionally ntype by impurity O as is typical for MOCVD GaN. The as-grown sample showed EF-VBM = 2.74 eV, which is about the same as that seen after nitrogen-ion IBA followed by in-situ exposure to a reactive gas but smaller than that for an air-exposed, as-grown MOCVD sample (Fig. 32). A substantial amount of impurity C and O was seen in XPS, at least some of which is likely to be a residue from growth. This is the only study, to our knowledge, in which

UHV surface analysis was performed on GaN after MOCVD growth without exposure to room air. For surfaces cleaned by Ga deposition and desorption at 900– 950 °C, Bermudez et al. [123] and Maffeis et al. [126] found EF-VBM = 2.6-2.7 eV for n-GaN (0001), and the latter authors also found a very small BB (EF-VBM = 3.1 eV) for the as-grown sample before any in-situ heating, in keeping with results discussed above. Eyckeler et al. [512] cleaned MBE samples ex situ in HF and then in situ by annealing at 800 °C in a flux of Ga equivalent to about 9 ML sec-1 followed by annealing in UHV at the same temperature. Raising the temperature was done slowly, at o1.5 °C s−1, which may be significant, and the resulting surface was described as clean and well ordered. EF-VBM = 2.94 eV was measured in the dark with a Kelvin probe to avoid SPV (Section 4.7.3.2). Widstrand et al. [127] found EF-VBM = 2.4 eV for n-GaN (0001) after cleaning by annealing at 650 °C in a flux of Ga followed by annealing at 750–800 °C in a flux of NH3. Schulz et al. found EF-VBM = 2.5 eV for an n-GaN (0001) surface cleaned by Ga deposition at RT followed by annealing at 650 °C [130]. The small differences among the BB results for the (0001) after Ga-cleaning may result in part from the different temperatures employed, from the varying degree of surface cleanliness and/or ordering and from differences in the outgassing procedures performed prior to cleaning. The effects of dopant concentration and/or material growth on BB have been examined in Refs. [513–517]. Kočan et al. [513] found that the BB after MBE depends on the Ga/N ratio during growth. For a (0001) surface grown under nearly-stoichiometric conditions, which leads to a rough and pitted surface (Section 4.3), EFVBM = 2.4 eV is found from the Ga 3d BE; although, a value of 2.89 eV was given in the original reference based on the VB edge observed in XPS. It is not obvious why the Ga 3d yields a smaller EF-VBM than direct measurement of the VBM. For Ga-rich growth, which gives a smooth surface, EF-VBM = 1.5 eV is derived from the Ga 3d BE, which is close to the value of 1.65 eV obtained from the XPS VBM. Although RHEED data were not given, one assumes that Ga-rich growth yields a (1x1) Ga adlayer or a "(1x1)" contracted Ga bilayer (Section 4.6.1), since XPS indicates the presence of metallic Ga; however, no information regarding doping was given. It is possible that the Ga-induced increase in upward BB is related in part to Schottky-barrier formation (Section 6), but it is unknown whether the Ga layer was sufficiently thick and continuous to define a Ga/GaN contact (Section 5.18). There have been numerous studies of BB on GaN surfaces that were subjected to little or no cleaning before measurement. These are generally outside the scope of the present review, but some results are noted here. Barbet et al. [514] and Köhler et al. [515] studied the dependence of BB on dopant concentrations for n- and p-GaN MOCVD samples in air or dry N2 using Kelvin force microscopy or sheet-resistance methods. The findings differ as to the extent of the dependence, and, to our knowledge, no similar study has been conducted for clean surfaces in UHV. Kudrawiec et al. [516,517] used contactless electroreflectance to characterize BB on nominally-undoped GaN (0001) grown by MOVPE vs. MBE and to compare BB on the (0001) and (0001̄ ) surfaces of MBE n-GaN. There is a small difference between MOVPE and MBE (0.3 and 0.4 eV respectively) but a larger difference between (0001) and (0001̄ ) (0.60 and 0.27 eV respectively). Interpretations were proposed based on theoretical results for the energies of states in the gap for clean surfaces (see below), but the data were obtained for air-exposed samples for which no surface cleaning was specified. Reddy et al. [518] observed an upward BB of 0.7 and 0 eV respectively in XPS experiments for homoepitaxial (0001) and (0001̄ ) surfaces of n-GaN. Again, all these results are for surfaces with little or no cleaning before measurement. From the limited amount of BB data [436,458,478] available for the clean n-type (0001̄ ) surface, it appears that the BB for this surface is larger than

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for the (0001) when both are atomically clean but smaller when both surfaces are contaminated. Other factors that are important in BB include polarity, polarization and defects. Jang et al. [258,519] performed synchrotron photoemission experiments on the (0001) and (0001̄ ) surfaces of MOCVD n-GaN that were cleaned in HF or HCl before measurement. Values for EF-VBM of about 1.6 and 3.0 eV respectively are obtained here, based on Ga 3d BEs in the plotted data, and the difference between the two faces was ascribed to differing modes of compensation of the bound polarization charges (Section 4.2.2). The (0001) BB is quite large (∼1.7 eV), and it is noted that others [126,330] have observed only a very small BB for similar (0001) samples after cleaning in HF but before heating. The non-polar surfaces are of interest because no bound polarization charges are present to affect the surface potential. Kuo et al. [485] formed a p-n junction on the (0001) surface by changing the dopant during MBE growth. The sample was then cleaved in — situ on the (1120) (a-plane), which is equivalent to the (112̄ 0). For the n-type component, EF-VBM = 2.7 eV, in agreement with previous studies of the (0001) surface. The p-type component gave EFVBM = 0.6 eV, which represents a small downward BB. However, these experiments were performed using focused synchrotron radiation, which is a high-brightness excitation source. Hence, the p-GaN results may have been affected by SPV as discussed in the following subsection. Chevtchenko et al. [520] grew (112̄ 0) GaN films on (101̄2) (rplane) sapphire substrates by low-pressure MOVPE. The samples were unintentionally doped lightly n-type, giving EF-VBM = 3.25 eV in the bulk. Surfaces were studied, using scanning Kelvinprobe microscopy, either as grown or after cleaning by solvent "degreasing" and etching in boiling HCl:HNO3. In either case, an upward BB of 1.1±0.1 eV was found, which corresponds to EF-VBM = 2.15 eV and could be accounted for by an acceptor level at 1.2 eV below the CBM with an areal density of 2x1012 cm-2. This is a larger BB than was found by Kuo et al. for a (112̄ 0) surface formed by cleaving in UHV (EF-VBM = 2.7 eV); however, Schulz et al. [131] found EF-VBM = 2.0 eV for n-GaN (112̄ 0) after cleaning by Ga deposition at RT followed by annealing at 750 °C. Schnedler et al. [521] studied EF-VBM on the non-polar (101̄0) (m-plane) surface prepared by cleaving in UHV. The sample was grown by MOCVD on a GaN (0001) substrate and was fairly heavily doped n-type (ND = 3x1018 cm-3). The cleaved surface was seen in STM to consist of large flat terraces separated by steps but with a low defect density. Upon initial examination, the STS data cannot be explained in terms of either a fully pinned or unpinned EF. The STS experiment was then simulated by solving the Poisson equation for the electrostatic potential including the effect of the dispersive band of empty surface state known to exist at ∼0.7 eV below the CBM (Section 4.7.1.3). This led to the conclusion that the pinning of EF depends on the tip voltage in STS and occurs only for a positive surface bias relative to the tip; whereas, EF is unpinned for a negative surface bias. The effect results from the low transition rate of electrons from the CB to the surface state, which impedes the filling of the surface state when shifted below EF by BB. Himmerlich et al. [483] studied the (101̄0) surface using samples and methods described in Section 4.7.1.3 and found EF-VBM = 2.7 eV, which was correlated with the presence of an occupied surface state lying just below the CBM. This state was identified, using optical spectroscopy, by observing a transition into it from a filled surface state at the VBM. The peak in the surface-state DOS occurs above the CBM, but the state is highly dispersive (Section 4.7.1.3). This gives rise to a tail of states with a lower DOS that extends into the gap, which provides a mechanism for the charge trapping that leads to BB. This work is exceptional in that it provides a clear interpretation of BB in terms of spectroscopically-

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identifiable surface states. Bartoš et al. [189] (note the Erratum) studied BB on polar, nonpolar and semi-polar surfaces using n-type samples prepared as described in Section 3.4 in connection with their results for surface cleaning. In general, annealing the as-received sample causes an increase in upward BB, but subsequent annealing in NH3 has little or no further effect on BB. On the other hand, nitrogen-ion bombardment causes a further increase in upward BB, which is reduced to approximately the value before sputtering by a subsequent anneal either in UHV or NH3. The annealing times and temperatures vary for the different surfaces, but the results are consistent with those shown in Fig. 32 for the (0001). All the surfaces studied, when cleaned, show small upward BBs of o0.5 eV. The (0001) for example shows a BB of 0.44 eV, somewhat smaller than previous results after in-situ cleaning, and EF-VBM = 3.26 eV for the (0001̄ ), which is almost no BB. The initial untreated (0001) surface shows only a small (o0.2 eV) upward (positive) BB, in agreement with previous work, but other surfaces show larger values that are downward (negative). The untreated (0001̄ ), for example, exhibits a downward BB of ∼0.75 eV (Fig. 4 of Ref. [189]), which would put EF above the CBM. No interpretation of the downward BB was given; although, the results for the clean surfaces were discussed qualitatively in terms of the compensation of bound polarization charges (Section 4.2.2). Since the samples were nominally undoped, and Hall measurements showed an ND of only ∼1x1016 cm-3, it is possible that the as-inserted samples might have charged positively during XPS, which would cause an apparent EF-VBM 4 Eg. There is also a discrepancy in some of the data presented. After — correction for the Erratum, the Ga 3d BE for the (1122) surface is close to 21.0 eV in the plotted data, which indicates a BB of nearly zero, but the tabulated value is 20.63 eV (0.43 eV upward BB). Rizzi and Lüth [492] grew an n-GaN surface using MBE and studied it in situ using XPS. The surface polarity was unknown but was suggested to be (0001̄ ) on the basis of the (1x1) LEED pattern appearing after MBE. However, it is noted here that it could also have been the (0001) with a single adlayer of Ga atoms [358,359] (Section 4.6.1). An EF-VBM of 2.4 eV was estimated from the position of the VBM in Al Kα-excited XPS and was found to be independent of annealing up to 800 °C. The BB was correlated with ELS data (Section 4.7.2) showing the presence of a partially filled surface state at ∼0.9 eV below the CBM (Fig. 31). This work is exceptional in that, like that of Himmerlich et al. on the (101̄0) [483], BB is analyzed in terms of a specific surface state that is observed, independently of the BB measurement, by spectroscopic means. Segev and Van de Walle [462,463,471] reported theoretical results that provide insight into the origins of BB on n-GaN surfaces. The methods employed were described in Section 4.7.1.1 in connection with their work on surface electronic structure. As shown in Fig. 25, the (0001)-(2x2) with 0.25 ML of Ga adatoms in T4 sites, which is thought to represent a Ga-polar surface cleaned by IBA (Section 4.7.1.1), exhibits an empty surface state at about 2.8 eV above the VBM. Partial filling of this state by CB electrons would then be consistent with the experimental result of EF-VBM ≈ 2.7 eV. For the (0001) with a "(1x1)" Ga bilayer, EF-VBM = 1.8 eV is found theoretically, which agrees well with the experimental value of 1.5 eV obtained by Kočan et al. [513] and discussed above. On the other hand, the (0001̄ )-(2x2) with 0.25 ML of Ga adatoms in H3 sites shows an empty surface state at 1.2 eV above the VBM. This does not agree well with the limited amount of BB data for clean (0001̄ ) surfaces, which give EF-VBM = 2.3 eV and 3.26 eV respectively for a (0001̄ )-(1x1) prepared by MBE [458] and by IBA [189]. Himmerlich et al. [459] have given theoretical results for Ga and N adatoms and for VGa on the (0001)-(2x2) surface, which are the most accessible means for forming this surface in a semiconducting state. The methods used were described in Section

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4.7.1.1 in connection with the electronic structure of the clean surface. All three surfaces show empty states, starting at 2.6-2.8 eV above the VBM, that arise from empty DBs on surface Ga atoms. Trapping of CB electrons in this state would be consistent with their experimental observation, described above, of EF-VBM ≈ 2.7 eV for all three types of surfaces. In summary, BB seems to be fairly well understood for the (0001) surface of n-GaN, which has been more heavily studied in this regard than other surfaces. For as-grown MOCVD material before any heating in vacuo, EF-VBM is typically ~3.1-3.2 eV, which indicates at most a slight upward BB. However, several studies [132,258,508,509,518] find a much larger BB for as-grown MOCVD surfaces. When the as-grown BB is small, annealing for the first time in UHV reduces EF-VBM, apparently irreversibly, to 2.6-2.7 eV, and subsequent ion bombardment causes a further decrease. The latter effect can, however, be reversed by annealing in UHV or NH3. As-grown n-type (0001) surfaces of MBE material exhibiting either a (1x1) or (2x2) LEED pattern generally give EF-VBM = 2.72.8 eV, which is close to that for MOCVD material after the first anneal in UHV or after IBA cleaning. Theoretical results [462,463,471] for a (0001)-(2x2) surface with θGa = 0.25 ML show an empty surface state that is consistent with an EF-VBM of about 2.8 eV if such states were to trap electrons on the n-GaN surface. Similar results are also found [459] for empty surface states on surfaces with 0.25 ML of N adatoms or VGa defects. The agreement between theory and experiment suggests that unfilled states in the gap arising from Ga DBs, which are common to all three (0001) surface terminations, are the source of BB on clean (0001) surfaces. On surfaces with θGa ≠ 0.25 ML, these DBs are occupied, which would pin EF at approximately the experimentally-observed energy. The role of Ga DBs in pinning EF is discussed in the theoretical work of Segev and Van de Walle [471]. Contributions to BB can also arise from compensation of σb (negative on the (0001) surface, Section 4.2.2) and from electron trapping at surface defects, both of which lead to a depletion layer

for n-GaN. On as-grown contaminated surfaces that have not been heated in UHV, there are presumably no Ga DBs and therefore no contribution to BB from this source. However, the existence of other types of charge traps is suggested by the upward BB that is seen in some studies for as-grown samples before in-situ cleaning. The thermally-induced decrease in EF-VBM for n-GaN could be related to the diffusion of acceptors to the surface, to the removal of positively-charged defects [12,13] that contribute to the external compensation of σb or to chemical changes in adsorbed contaminants. The relative importance of these different factors is not fully understood at present. The nearly-universal value of EF-VBM = 2.7 ±0.1 eV on the clean (0001) surface, for different methods of material growth and surface cleaning, suggests a single well-defined source of BB such as the unfilled Ga DBs. However, there is some variation in EF-VBM for such surfaces, which suggests that other factors may also be involved. One notes the limiting values of EFVBM = 2.94 eV, at the high end, obtained by Eyckeler et al. [512] after a careful in-situ cleaning procedure and, at the low end, EFVBM = 2.3 eV (based on the plotted Ga 3d BE) found by King et al. [349,446] for samples grown by gas-source MBE and studied in situ. Similarly on the (0001̄ )-(1x1) surface, for which 1 ML of adsorbed Ga is found to be very stable, BB could be associated with the partially-filled surface state identified in theoretical studies of this type of surface by Smith et al. [339] and Wang et al. [459]. This state lies fairly deep in the gap, which is consistent with results for MBE n-GaN obtained by Plucinski et al. [436] (cleaned by IBA) and by Lorenz et al. [457] (in-situ study after growth) that show a larger upward BB for the (0001̄ )-(1x1) than for (0001) surfaces. There is less information for BB on other surfaces and less consistency among the different results. For example, four different studies of clean non-polar (112̄ 0) surfaces prepared by different means report EF-VBM in the range of 2.0 eV [131] to 3.24 eV [189]. This is in spite of the fact that BB on the non-polar surfaces should, in principle, be simpler than on others as a result of the absence of bound polarization charges. A theoretical study [471] finds an empty surface state at about 2.9 eV above the VBM on this

Fig. 33. Schematic diagram showing SPV due to sub-band-gap excitation and its effects on XPS BE for (a) n-type and (b) p-type GaN. The upper panels show experimentallyobserved shifts of the Ga 2p3/2 level to higher (lower) BE for n- (p-) GaN under photoexcitation. In the lower panels, Rsb and Rbs are the surface-to-bulk and bulk-to-surface currents of majority carriers under photoexcitation, and Φ is the BB. From Sezen et al. [545] (Copyright 2014, reproduced with permission from Elsevier).

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surface, which can act as an electron trap. In this regard, the work of Himmerlich et al. [483] on the (101̄0) surface and of Rizzi and Lüth [492] on one of the polar surfaces is noteworthy in that the BB observed in photoemission is correlated with a spectroscopically-identifiable surface state near the CBM. This is achieved using the high energy resolution afforded by optical spectroscopy [483] or by HREELS [492], which is necessary to resolve the transitions between surface states from the lowestenergy interband transitions that are close in energy. Based on the experimental and theoretical results of Lymperakis et al. [206], Himmerlich et al. [483] and Schnedler et al. [521], BB on the (101̄0) surface can also be considered to be well understood in terms of a Ga DB surface state. Studies [184,506,507] of MBE n-GaN exposed to O2 or to room air find that either chemisorption of O (bonding of O to surface atoms) or oxidation (insertion of O into back-bonds) causes a decrease in EF-VBM (i.e., an increase in upward BB) vs. the clean surface. A similar result is found [440] for O2 chemisorption on MOCVD n-GaN after IBA with annealing at 800 °C. However, after IBA with annealing at 900 °C [491] a small decrease in BB is seen upon chemisorption of O2. This might indicate that adsorption of O can act to passivate defects caused by annealing at very high temperature in UHV but can also produce defects on initially lessdefective surfaces. However, this proposal has not been examined in detail. The effects of O2 on BB will be revisited in the following subsection that deals with SPV. 4.7.3.2. Surface photovoltage. It is well known that semiconductor BB decreases under illumination. This is the SPV effect, which has been reviewed thoroughly by Kronik and Shapira [505] and more briefly by Kronik and Shapira [522], by Schroder [523] and by Cavalcoli and Cavallini [524]. Here we are concerned mainly with the effects of SPV on GaN surface-science experiments rather than with SPV itself. Fig. 33 shows a schematic diagram for sub-Eg excitation of majority carriers captured in surface states. Taking n-GaN as an example, electrons excited out of surface traps and into the CB create a current (Rsb) that is swept into the bulk by the spacecharge field. The trapped positive charges remain at the surface, and the resulting charge separation produces a field that opposes the space-charge field, which leads to a decrease in BB that is detectable as a shift of core levels to higher BE. The reduction in BB permits a current of majority carriers (Rbs) to flow from the bulk to the surface, and steady-state equilibrium is established at a BB such that Rsb = Rbs. Similar considerations apply for above-Eg excitation of n-GaN, where electron-hole (e-h) pairs separate in the space-charge field and CB electrons (VB holes) are swept into the bulk (toward the surface) leading to a field that opposes the spacecharge field. This is sometimes referred to as a screening or a quenching of the space-charge field. Equilibrium is established at a BB such that the net flow of electrons to the surface, Rbs-Rsb, equals that of the photo-generated holes. The effect is largest at photon energies above Eg, where the creation of e-h pairs is efficient. Using SPV spectroscopy, in which the surface potential is measured vs. photon energy in the sub-Eg range, it is possible to study states in the gap associated with defects. However, as a result of the penetration depth of sub-Eg photons, it can be difficult to separate bulk and surface effects. The SPV effect decreases with increasing temperature, but for a widegap semiconductor like GaN it can be substantial at RT. The SPV "band-flattening" leads to an increase (decrease) in the BE of all photoemission features for n- (p-) type material that depends on temperature, excitation intensity and surface condition. Examples of the effects of SPV in UPS and XPS, particularly in reference to the measurement of SBHs, are given elsewhere [525,526], and work specific to SPV in GaN is described in Refs.

Fig. 34. Upper: ΦFV ¼ EF
VBM vs. increasing T for n- (open symbols) and p-GaN (solid symbols). The inset gives Jeh (the generation rate for e-h pairs), and the excitation source appropriate to each curve. "XPS" curves were obtained with different Mg-anode power levels, and "Hg arc" refers to XPS data recorded with simultaneous Hg-arc illumination. Smooth curves serve as visual aids. The dotted line at 2.55 eV gives the pinning position common to both types, and ΔVn,p indicates the respective directions for increased SPV (decreased BB). Lower: UPS data for n- and p-GaN before (squares) and after (circles) a saturation exposure (500 L) to O2 near RT. "Clean" and "dosed" refer to values obtained immediately before and after exposure, and the arrows show the direction of temperature change during data acquisition. The temperature-induced conversion of chemisorbed O to oxide at 4 300 °C affects the apparent SPV upon returning to lower temperature. From Long and Bermudez [440] (Copyright 2002 by the American Physical Society).

[82,222,223,230,440,484,507,510,527–551]. Here again, because of the nature of the present review, the main interest is in studies done in UHV on atomically-clean surfaces; although, many other relevant works will also be noted. Only a few SPV studies [440,542,545] have been reported for atomically-clean (or nearly so) GaN surfaces. Fig. 34 summarizes results [440] for MOCVD GaN (0001) prepared by IBA (1 keV nitrogen ions, ∼800 °C anneal) that illustrate a number of points. For the data shown, e-h pairs are created by the XPS or UPS excitation

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source with, in the case of the "Hg arc" data, additional excitation in the near-UV from a high-pressure Hg arc. The measured photon flux was used to estimate the resulting flux of e-h pairs (Jeh), and EF-VBM was found by observing shifts in core-level BEs. The XPS source intensity could also be reduced by an order of magnitude below the typically-used level (Jeh ≈ 3x1014 cm-2 s-1). The SPV effect decreases with increasing temperature and with decreasing light intensity (i.e., Jeh). The temperature effect results from an increased e-h recombination rate, and the dependence on Jeh is approximately logarithmic. At sufficiently high T and/or low Jeh, the position of EF in the gap becomes independent of T and Jeh and converges to a common position for both doping types. The result is EF-VBM = 2.55 eV for the samples and surface preparations used in this study, which can be taken to represent the BB in the dark (i.e., negligible Jeh). For n-GaN this is a slightly larger upward BB than that measured under typical XPS conditions (EF-VBM ≈ 2.7 eV). The difference of ∼0.15 eV is consistent with the small SPV effect in XPS that is measured for n-GaN at RT. Another contributing factor could be a small reduction in Eg for GaN between RT and 300 °C, at which temperature EF-VBM stabilizes for a low excitation intensity (Fig. 34). For p-GaN on the other hand, the position of EF in the dark represents a large downward BB as first reported by Eyckeler et al. [512] on the basis of Kelvin-probe data. For p-GaN one notes that the SPV is substantial at RT under typical UPS and XPS conditions, which in many cases makes it difficult to obtain a reliable photoemission result for the position of EF on p-GaN surfaces. In view of the discussion of BB on the (0001) surface in the previous section, a plausible explanation for the large p-GaN BB would be the capture of VB holes in partially-filled Ga DB surface states near the CBM. This would account for the essentially identical EF-VBM in the dark for n- and p-GaN since the same states are believed to be responsible for pinning EF on n-GaN. On a "perfect" (2x2) surface, with a well-ordered 0.25 ML of Ga adatoms (or VGa or VN), the Ga DB states near the CBM would be empty (e.g., Refs. [459,471]) and would be able to trap electrons on the n-GaN surface but not holes on p-GaN. On such a surface, which is difficult to achieve in practice, one would then expect EF on p-GaN to be pinned by filled surface states above the VBM [459,471], which should result in a much smaller downward BB. This suggests that the magnitude of the BB on p-GaN might be useful as a measure of surface quality. Eyckeler et al. [512] found even larger values of EF-VBM, using Kelvin-probe measurements in the dark at 150 K, than were obtained in Ref. [440], namely 2.94 eV for n-GaN and 3.22 eV for pGaN vs. 2.55 eV for either type. At 150 K, Eg is only slightly larger (by o 0.1 eV [24]) that at RT. The MBE samples were cleaned ex situ in HF and then in situ by annealing at 800 °C in a Ga flux of ∼9 ML sec-1 followed by annealing in UHV at the same temperature. As will be seen in the discussion of Ga adsorption (Section 5.18), this is a sufficiently high flux to maintain, on the surface at 800 °C, a Ga bilayer plus a dense array of droplets. Raising the temperature was done slowly, at o1.5 °C sec-1, which may be significant, and the resulting surface was described as clean and well ordered. The reason for the small differences in EF-VBM is not known at present. The surface condition also influences SPV via the effect on e-h recombination, as shown in Fig. 34. For n- (p-) GaN, chemisorption of O increases (decreases) the BB at RT, which is consistent with the formation of a negatively-charged surface species. To be more precise, capture of an electron by O to form an anion increases the electron depletion (reduces the hole depletion) for n- (p-) GaN. Upon subsequent annealing to 300 °C or above, chemisorbed O is converted to oxide, and the resulting surface then shows a different dependence of SPV on temperature during the cooling sequence. The magnitude and temperature dependence of the SPV

for the oxidized surfaces are similar to those obtained using UPS for the bare surfaces before O2, which show little or none of the hysteresis during temperature cycling that is seen in the first such cycle after O2 exposure at RT. Reliable measurement of the change in SPV due to O chemisorption was found to require the use of UPS, rather than XPS, since the much larger Jeh in the latter can overwhelm the small O effect. The reason for the different SPV behavior for surfaces with chemisorbed O vs. a thin oxide layer is uncertain. Sezen et al. [542,545] used XPS to study SPV transients for nand p-type MOCVD GaN (0001) surfaces that were cleaned by 200 eV Ar+-ion bombardment but not annealed. The transients were driven by laser radiation at λ = 405 nm (hν = 3.06 eV) that was blocked and unblocked with a 50% duty cycle and a period of 100 sec. Under static conditions (Fig. 33), a larger SPV is seen for p-GaN, as in the work described above, since the magnitude of the SPV generally scales with that of the BB in the dark. Shifts in the Ga 2p3/2 XPS peak position were used to follow SPV transients with a time resolution of about 0.1 sec, and these were found to be abrupt on this time scale. Such "fast" transients for sub-Eg excitation are taken to indicate rapid excitation out of surface traps in the ON state and rapid refilling in the OFF state. Different transient behavior is seen when a low-energy electron flood gun (FG) is in operation during the experiment. The FG induces a small negative charge on the n-GaN with a somewhat larger effect for the less-conductive p-GaN sample and, for p-GaN, also affects the transient behavior. This was explained by the accumulation of FG electrons near the bottom of the CB as a thin surface layer (in effect a 2DEG) as a result of the downward BB at the p-GaN surface. Many SPV studies have been conducted for air-exposed GaN (0001) surfaces with little or no cleaning prior to measurement (other than perhaps wet-chemical treatment) or surface characterization. However, these have generally been more extensive and detailed than the work done on atomically-clean surfaces in UHV and provide insights regarding the UHV work. Transient SPV has been analyzed for such samples [529–532,538], and, as noted in Section 4.2.1, SPV has been seen [222,223,230] to be potentially useful in distinguishing between (0001) and (0001̄ ) surfaces. The temperature dependence of SPV is discussed in detail in Refs. [510,544,546,548] for air-exposed (0001) surfaces mounted in a cryostat. A particularly significant finding of this work is that, at RT, the BB of p-GaN in the dark can take a long time to recover after exposure to light [510]. This can explain to some extent the variation in BB reported for p-GaN in different studies, but recovery can be accelerated by annealing in the dark prior to measurement at RT of properties related to BB. The effects on SPV of the method of material growth and of doping type and density have been reported in Refs. [539–541,547], and the use of SPV in characterizing surface defects, strain and processing damage has been described in Refs. [222,507,527,528]. Theoretical studies of GaN SPV have been reported by Miczek et al. [533] and by Matys et al. [543]. These are numerical simulations of SPV and PL as functions of the surface state density. All this work is important but lies outside the scope of this review. Somewhat more-closely related to the subject of the present review are several studies [82,222,230,534–539,549–551] of the dependence of SPV on the ambient (N2, O2 or vacuum) or on the presence of surface oxide for air-exposed GaN (0001). Shalish et al. [82] used SPV and other techniques to detect the presence of defects in the native oxide or at the oxide/GaN interface. Other SPV results [222,230,534–539] show that, for air-exposed n-GaN, UV irradiation in vacuo causes an increase in SPV (decrease on BB) and that upon subsequent exposure to room air in the presence of UV irradiation the SPV gradually decreases (BB increases). This is attributed to a photo-induced desorption of oxygen in vacuo and a

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photo-induced adsorption in air, which has been reported in other work [549–551] and is consistent with the effects of O2 shown for n-GaN in Fig. 34. It is speculated here that photodesorption of O may result from the capture by Oδ− anions of photogenerated holes that are swept to the surface of the SCL in n-GaN, thus enabling the formation and desorption of O2. It is further speculated that the photo-induced adsorption in air might arise in part from photochemically-generated ozone (O3). These results raise the interesting possibility of the use of photodesorption of O as a means for preparing clean GaN surfaces in UHV at low temperature, at least for n-GaN, which to our knowledge has not yet been investigated. However, it is not known if all O can be removed in this way. Also, to our knowledge, there are no reports of AES or XPS having been used to observe directly the effects of UV irradiation in vacuo on the surface composition of GaN with oxide or adsorbed O. However, one study [537] did observe the photo-induced oxidation of n-GaN in room air using XPS. This work used the unfiltered output from a Hg-arc (30 mW cm-2 incident power density) during oxidation, which might lead to oxidation via O3 (ozone) generation. 4.8. Vibrational properties and free-electron excitation There have been several studies of the vibrational spectra of adsorbates on GaN surfaces using HREELS, and these will be described in Section 7. In the present section the interest is in HREELS work that focuses on the GaN surface itself [322,458,552– 554]. To our knowledge, there have been no studies of adsorbates on GaN using other forms of vibrational spectroscopy such as IR or Raman, which probably results from a lack of sufficient surface sensitivity for readily-achievable sample configurations. The HREELS spectrum of GaN is dominated by strong FuchsKliewer (FK) loss peaks appearing at integer multiples of ωFK. In the bulk, propagating phonon modes occur at frequencies ω such that ε(ω), the complex bulk dielectric constant, equals zero. This occurs at the transverse-optic (TO) and longitudinal-optic (LO) frequencies, where, for a cubic crystal, ωLO = ωTO(ε0/ε∞)1/2 with ε0 and ε∞ being the low- and high-frequency dielectric constants. At the surface, propagating modes occur where ε(ω) = −1, and the

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corresponding expression [555] is ωFK = ωTO[(ε0+1)/(ε∞+1)]1/2, which gives ωFK close to ωLO. In wurtzite GaN, ωFK is typically reported at 700–704 cm-1 (∼87 meV), and for doped material HREELS also shows a broad continuum at the low-energy end, from the elastic peak up to ΔE ∼ 150 meV, due to free-carrier excitation. Doping densities can be estimated [552,553] by fitting this continuum (intensity relative to the elastic peak vs. loss energy) with an expression derived using ε(ω) for a free-electron gas. Freundt et al. [322] observed the effects of annealing on HREELS of polar GaN grown in situ using MBE and showed that pronounced decomposition occurs at 900 °C. Grabowski et al. [554] performed HREELS studies on GaN surfaces of undetermined polarity. Some samples were simply cleaned ex situ in aqueous HF solution with no additional in situ cleaning. Others were further annealed in situ in a Ga flux after which a 35 Å-thick Ga protective layer was deposited so that the sample could be transferred under moderate vacuum, via a mobile transport system, to the HREELS chamber. After thermal desorption of the Ga cap, no O but some C was detected in AES, and LEED showed a faceted (1x1) pattern. The FK losses, which occurred together with features due to adsorbed hydrocarbon impurities, were analyzed in detail. Lorenz et al. [458] performed HREELS studies of both the (0001)-(2x2) and (0001̄ )-(1x1) surfaces of n-type GaN prepared by in-situ MBE. The FWHM of the elastically-scattered peak was found to be larger for the (0001̄ ) surface and to decrease with Ep; whereas, that of the (0001) remained approximately constant. This was ascribed to a larger upward BB on the (0001̄ ) surface, which results in a thinner depletion layer, with a lower free-carrier density, for the (0001̄ ). The strong FK peaks in HREELS often obscure the weaker features due to adsorbates. Multiple-FK losses can be greatly reduced in intensity, or even eliminated, using numerical data-processing methods as described by, for example, Petrie and Vohs [556].

5. The chemical elements - adsorption and interfaces In this section we consider the experimental and theoretical aspects of the adsorption of various elements. Unless otherwise stated, this involves in-situ deposition and data acquisition for

Fig. 35. Summary of the elements that have been studied as adsorbates on wurtzite GaN surfaces as of mid-2015. The box coloration identifies the type of study reported, and the element color specifies whether or not, in the case of experimental work, the clean substrates were prepared using IBA. "No Results" or "Theory Only" means only that no experimental studies have been reported that fall within the scope of the present review. In many cases work has been reported that falls outside the range of topics discussed here. This figure was prepared using an editable periodic table [557].

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atomically-clean surfaces in UHV. More emphasis will be placed on these studies than on those for which the surface was cleaned only wet-chemically, or not at all, before adsorption. This is a consequence of the high reactivity of O2 and H2O with the clean surfaces of GaN (Sections 7.8 and 7.10) and of most of the elements of interest here. The discussion of atomic and molecular hydrogen, nitrogen and oxygen will be deferred to a later section, which concerns the adsorption of molecular species. Fig. 35 summarizes the available results for elemental adsorbates [557]. Here "No Results" or "Theory Only" means only that there have been no experimental studies reported that fall within the scope of the present review. In most cases there has been extensive work dealing with other topics lying outside the range covered here. A distinction is made between experiments according to how the clean surface was prepared. The label "IBA" in Fig. 35 refers to studies done on substrates that were first cleaned by IBA, which is the method used in the majority of adsorption and interface studies for which in-situ cleaning is employed. Typically this means that the sample was transported through ambient air from the growth apparatus to the UHV chamber. On the other hand, "not IBA" relates to those studies for which the clean substrate was either grown in situ by MBE, with no need for further cleaning, or else prepared by some other means not involving IBA. In principle, those elements for which both methods were employed (in different studies) afford an opportunity for a comparison of results in order to asses the effects of IBA. Unless otherwise noted, the theoretical work deals exclusively with idealized surfaces moreclosely related to non-IBA experiments. As a general comment, many of the interfaces reviewed here are seen to be reactive, at least in some if not all experiments. Interfacial reaction takes two generic forms. In the first, exemplified by Al, place exchange occurs between Ga and the metal atom in which Ga moves out into the metallic layer and some metal atoms move into the substrate to form a nitride. This is thermodynamically driven by the higher ΔHf of the metal nitride vs. GaN and is indicated in XPS by the appearance of a metal-like Ga 3d with a lower BE than for GaN and, for the deposited metal, a nitride-like core-level peak at higher BE than for the bulk metal. Usually these additional features appear as shoulders on the side of the main Ga and metal peaks. In the second type of reaction, exemplified by Ni, Ga moves into the metal layer to form an alloy and release N2. This is driven by the high thermodynamic stability of N2, which is detectable via a mass spectrometer, and is further indicated by the appearance in XPS of a metal-like Ga 3d feature. This type of behavior is observed for some metals that do not readily form stable nitrides under normal conditions. In either case, reaction may be accompanied by the appearance of an quasiordered phase in LEED or RHEED. The properties of this reacted layer at the interface are expected to affect the SBH of metal/GaN contacts. For many elements (see Fig. 35) both theoretical and experimental results are available; however, it is often difficult to establish a clear and direct connection between the two sets of results. This occurs most often when the experimental data were obtained for samples grown ex situ and then subjected to in-situ cleaning as discussed in Section 3. Potential problems arise because the structure of such surfaces is complex and not yet thoroughly understood. Theoretical work, quite understandably, needs to begin with a well-defined model and typically invokes either an ideally-terminated surface or one that is consistent with in-situ MBE growth. For example, it appears (see Sections 4.6 and 4.7) that high-temperature annealing in UHV, which is an integral part of most in-situ cleaning procedures, results in a GaN (0001) surface with excess Ga. One Ga adatom per (2x2) SUC yields a semiconducting surface, in agreement with UPS data, that satisfies the ECR; however, a clean-surface model of this description has not

often been used in calculations pertaining to the adsorption of either elements or molecules. Another difficulty in comparing theoretical and experimental results is that the former tend to focus primarily on structural and energetic considerations while omitting results that can be compared directly with spectroscopic experiments such as UPS, ELS or XPS core-level BE shifts. While the modeling of ELS or XPS data is non-trivial, a DOS is usually sufficient for comparison with an angle-integrated UPS experiment. Nevertheless, even when a direct and quantitative comparison might not be feasible, theoretical results for idealized surface can be very useful in providing insights when interpreting experimental data. Many of the theoretical studies reviewed here consider the incorporation of foreign atoms into the near-surface region of the GaN substrate. This can take the form of either substitution or site exchange. In the former, which is more relevant to material growth, the atom of interest simply replaces Ga or N. In site exchange, which is more relevant to adsorption at RT in UHV, the displaced lattice atom (usually Ga) remains as an adsorbate. In this case the total energy of the reaction can depend (sometimes strongly) on how the displaced atom is adsorbed. In the following, a notation will often be added to make clear what type of incorporation is being described. Another comment regards the measurement of adlayer thickness or coverage. For metals, this is typically done using a QCO thickness monitor, which gives the total deposited mass (M) expressed as a thickness (t). Here M = ρAt = NmA, where ρ is the bulk density of the deposited material, A the area covered and N the number of atoms per unit area. The atomic mass is m = W/Av where W is the atomic weight and Av is Avogadro's number. From this, N can be obtained from the measured t, bearing in mind that the result represents only the total amount of material deposited. Thus t or N corresponds to what the coverage would be for a uniform film. In the following, adatom coverages will usually be given as N expressed as a fraction of an ML, where 1 ML = 1.135x1015 atoms cm-2 for GaN (0001), which does not necessarily mean a uniform coverage. For adsorbates with a large "footprint", the saturation coverage will correspond to o 1 ML. Where the authors have reported layer thicknesses in Ångstroms, a conversion factor is given so that these can be expressed as fractions of an ML. The values used for the elemental densities and atomic weights are given in Ref. [558]. Of course, for coverages beyond a few MLs one expects the packing density to approach that of the bulk metal rather than that of the GaN surface. Nevertheless, expressing coverage in terms of MLs is useful as a measure of relative coverage that applies from low to high values. Also, coverages of different species can be compared directly, in the same units, which is difficult when using film thickness as a measure of coverage. Many of the elements discussed in this section are metals, for which measurements of the SBH are reported. Here only the specific results for each metal will be described, with no attempt to correlate results for different elements. The following section (Section 6) will briefly review various studies aimed at systematizing the metal/GaN SBH results for well-characterized interfaces prepared under atomically-clean conditions. 5.1. Aluminum The interaction of Al with GaN surfaces has been studied extensively with a view to contact formation and also to the formation of an AlN layer via reaction at the interface. Experimental results have been reported (all for the (0001) surface) by Bermudez et al. [559], Liu et al. [560], Wu and Kahn [561,562], Brown et al. [563], Orani et al. [564] and Tseng et al. [565]. Theoretical studies have been performed for Al on the (0001) surface by

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Fig. 36. AES data in the region of the Al L2,3VV transition for a clean (0001) surface (a) and after deposition of ∼3 MLs (b) and ∼24 (c) MLs of Al near RT. The relative intensities are quantitative. The inset shows a log-linear plot of the 380 eV N KLL and 1060 eV Ga LMM peak-to-peak heights, normalized to the respective cleansurface values, vs. Al coverage. The λ values give the effective attenuation lengths deduced from the initial slopes. The dashed line shows the alignment of the peak at 3 MLs with the shoulder at 24 MLs. From Bermudez et al. [559] (reproduced with the permission of AIP Publishing).

Timon et al. [566], Garcia-Diaz et al. [567] and Qin et al. [568] and on the (0001̄ ) by Picozzi et al. [569]. This system is an archetype of a reactive interface involving a nitride-forming metal, as will be seen later in discussions of other metal/GaN interfaces; although, the degree of reactivity appears to depend on the details of the clean-surface preparation. Bermudez et al. [559] studied the interaction of Al with MOCVD GaN (0001) using AES, ELS, UPS, XPS and LEED. Surface-sensitive Al 2p and Ga 3d XPS data were obtained using Zr Mζ excitation (hν = 151.65 eV [570]). Clean surfaces were prepared by depositing a thick layer of Ga metal in situ followed by annealing at ∼900 °C or below to desorb the metallic Ga, and the Ga 3d XPS was checked carefully to assure completion of the desorption. The resulting surface was atomically clean with a clear but faceted (1x1) LEED pattern. Since Al cannot be removed by this means, a new sample was used every time a clean surface was required. Fig. 36 shows the evolution of the AES data with increasing θAl at RT, which indicates a Stranskii-Krastanov growth process [571]. The first

Fig. 37. Surface-sensitive Ga 3d XPS for (a) clean GaN, (b) after depositing 3 MLs of Al near RT and (c) after annealing at 800 °C. Relative intensities are not quantitative, i.e., the data have been rescaled for display. The zero of energy is set at the kinetic energy of the clean-surface peak. The inset shows the coverage dependence of the integrated areas of the two peaks, obtained by least-squares fitting the data. Peak areas have been normalized to that of the clean surface. ‘‘GaN Ga 3d’’ (‘‘metallic Ga 3d’’) refers to the low- (high-) kinetic energy peak. Binding energy increases to the left. From Bermudez et al. [559] (reproduced with the permission of AIP Publishing).

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∼3 MLs grow uniformly, leading to exponential attenuation of the substrate Ga and N AES features. Beyond this, island formation occurs, which results in a slower attenuation. At low θAl the Al L2,3VV AES peak appears at a lower energy than, and with a shape different from, that of bulk Al metal, which indicates a chemical difference from metallic Al. At higher θAl this peak appears as a shoulder on the low-KE side of the metallic Al peak. Fig. 37 summarizes the Ga 3d XPS data. For a low θAl at RT, a satellite indicative of metallic Ga appears on the low-BE side of the GaN peak. With increasing θAl, this feature maintains approximately constant intensity while the GaN peak is continuously attenuated. This suggests an interfacial reaction that releases Ga that segregates to the surface of the reaction product layer, rather than remaining at the interface, since the corresponding peak is not attenuated. At RT, the reaction is complete at a low θAl since the free-Ga peak does not continuously gain intensity; however, annealing at 800 °C drives the reaction farther to release more Ga. The same thermal effect is seen in AES data, where annealing a thick Al layer (θAl = 24 ML) to 1000 °C converts essentially all of it to AlN. However, the reaction is much less extensive at ≤800 °C, which suggests that the higher-temperature process represents decomposition of GaN to release reactive atomic N rather than the spontaneous reaction between Al and GaN that takes place below ∼800 °C and is essentially confined to the Al/GaN interface. This is supported by the appearance of N2 pressure bursts, detectable via a mass spectrometer, during 1000 °C anneals. The high-temperature reaction product is identified as AlN (possibly alloyed with a small amount of Ga) on the basis of AES peak energies and lineshapes, Al 2p BE and ELS data and is consistent with the higher ΔHf for AlN vs. GaN (-74.8 vs. −26.4 kcal mol-1, Ref. [572]). Surfacesensitive ELS shows a peak at ΔE ≈ 1.7 eV (which is much less than the 6.2 eV band gap of AlN) that gains intensity with AlN thickness. This is ascribed to a VN defect in AlN resulting from the inability of the GaN substrate to supply N at a sufficient rate as the AlN thickness increases. Fig. 38 shows LEED data before and after AlN formation. The AlN is ∼30 Å thick and was formed by depositing a thick Al layer and then annealing at 1000 °C. The cleansurface pattern is complex, due to a high degree of faceting that depends on the sample. The satellite beams, the intensity of which depend strongly on Ep, all disappear after AlN growth, which gives a simple (1x1) pattern with somewhat diffuse spots and an increased background intensity. This suggests that the high-temperature reaction consumes the faceting features to give a relatively-smooth interface and an imperfectly-ordered AlN layer, possibly indicative of epitaxial growth strained by the 2.5% basalplane lattice mismatch between GaN and AlN. The Al/GaN SBH was also investigated in Ref. [559]. This phase of the work was marred by an incorrect location of the bulk GaN VBM relative to EF due to the undetected presence of a band of surface states, lying in the gap just above the bulk VBM, that caused the SBH to be overestimated (and the GaN electron affinity to be underestimated) by 0.5 eV. This was corrected in subsequent work [491,573], which gave a correct Ga 3d-VBM separation of 17.9 ±0.2 eV vs. the accepted standard value [439] of 17.76±0.03 eV. Liu et al. [560] used RHEED and AFM to study the epitaxy of Al on MOVPE GaN (0001). The samples were cleaned in organic solvents followed by boiling aqua regia (3:1 HCl:HNO3) and then loaded into an MBE system after which Al was deposited in situ at a sample temperature of either 15 or 150 °C. The streaked and sharp RHEED pattern for the bare GaN indicates that the surface is smooth and relatively free of contaminants even though no in-situ cleaning was performed. At either temperature, deposition of Al at a slow rate (0.26 Å sec-1) leads initially to a weaker and morediffuse RHEED pattern suggestive of surface roughening. After a few MLs the streaked and sharp RHEED pattern returns, which indicates an improvement in crystal quality. In this study,

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Fig. 38. LEED data for (a) clean GaN(0001)-(1x1) and (b) the AlN/GaN surface at primary beam energies of Ep ¼ 94 and 51 eV respectively. The AlN is ∼30 Å thick and was formed by annealing a thick Al layer at 1000 ºC. The GaN pattern, for the samples used in this study, is strongly dependent on Ep and shows evidence of extensive faceting. In (a), Ep was chosen to emphasize the intensity of the facet beams. From Bermudez et al. [559] (reproduced with the permission of AIP Publishing).

1 ML is defined as a thickness equal to the Al (111) lattice-plane spacing of 2.338 Å. For an Al density of 2.70 gm cm-3, 1 Å = 6.027x1014 Al cm-2 = 0.684 ML where 1 ML is defined instead as 1 Al per surface lattice site. The behavior of the RHEED pattern with increasing θAl further indicates 2D (layer-by-layer) growth with a flat surface. For a higher deposition rate (0.89 Å sec-1) at 15 °C, RHEED shows that the ordering of the Al layer is not as good as at the slower growth rate, but it can be improved by a subsequent 300 °C anneal. Further evidence for Al epitaxy was obtained using XRD and ion-channeling analysis, and the latter shows that the crystalline quality of the film is better at the higher growth temperature. The AFM data indicate that, at 150 °C and a 0.26 Å sec-1 growth rate, Al forms large flat islands separated by crevices that are smaller in depth than the thickness of the film, so that the Al layer is essentially continuous. The apparent absence of an interfacial reaction was explained in terms of a residual contamination layer on the acid-etched surfaces that does not, however, prevent epitaxial growth. Wu and Kahn [561] used UPS, XPS, AES and LEED to study Al on MOCVD GaN of uncertain polarity, which was nominally (0001) Ga-polar. Surface-sensitive Al 2p and Ga 3d XPS data were obtained using Zr Mζ excitation. Clean surfaces were prepared by cycles of IBA (0.5 keV nitrogen ions, 900 °C anneal) after which a sharp (1x1) LEED pattern with a low background intensity was seen. A surface-state band appears in UPS at a few tenths of an eV above the bulk VBM for a surface with excess Ga as well as a small level of impurity C and O, and an upward (downward) BB of 0.75 eV is found for clean n- (p-) type GaN surfaces. The BB is ascribed to defects created by the IBA cleaning process. The interface is found to be reactive, and the Al 2p for 6 Å of Al appears at a high BE indicative of AlN formation. With increasing θAl a second Al 2p peak grows in at the BE of bulk Al metal, and a 900 °C anneal converts all of the metallic Al to AlN, which indicates a more-extensive reaction. For up to 20 Å of Al, EF for both n- and ptype GaN moves by o 0.15 eV from the clean-surface position and is unaffected by annealing, which is explained by the fact that the interfacial AlN reaction layer is an insulator with Eg = 6.2 eV. An SBH of 0.8 eV is found from these results. An extension of this work was reported by Wu et al. [562] in which Al/n-GaN (0001) contacts were prepared in situ on atomically-clean substrates and studied using I-V measurements. The surface cleaning procedure was the same as that employed in Ref. [561], and the I–V experiments were performed for both as-deposited Al (100 nm thick) and after annealing either in UHV or in forming gas (5.7% H2 in N2). The contacts are rectifying for anneals up to 400 °C (either in UHV or in forming gas) and Ohmic for a

≥500 °C treatment. These results show that the rectifying characteristic is intrinsic to the as-deposited contact and not the result of an oxide, which might have been formed had the contact been prepared under conditions that were not atomically clean. Since the UPS data given previously [561] show that a 500 °C anneal has little or no effect on the position of EF in the gap, the change from rectifying to Ohmic behavior is not associated with any large alteration in the SBH. It is instead attributed to the doping effect of the high density of VN defects (which are donors) that is created by reaction with Al to form AlN. This in turn causes a reduction in the depth of the depletion region, which allows electron tunneling through the barrier. It is noted here that another contributing factor might be a polarization effect (Section 4.2.2) resulting from strain at the AlN/GaN interface [574]. The SBH deduced from I–V data (before annealing) is 0.6 eV, and various factors affecting the SBH and the small difference in SBH between I–V and XPS results are discussed in detail in the original reference. Brown et al. [563] used RHEED, medium-energy electron diffraction (MEED), AFM, SEM and TEM to study the epitaxy of Al on GaN (0001). The samples were grown by MBE and the Al deposited in situ. The streaky MEED pattern of the bare substrate, which indicates a small degree of local misorientation and disorder, transformed to a (1x1) at the start of Al deposition. The spacing of this pattern is found to represent the GaN substrate, and AFM shows the surface to be very flat, with an RMS roughness of 0.2 to 0.7 nm. Application of SEM, TEM and RHEED shows that the Al layer consists of ∼500 nm grains, having a (111) growth surface and some degree of polycrystallinity, that constitute twin islands. Orani et al. [564] employed XPS to measure the SBH using samples for which the GaN (0001) substrates were grown by MBE and Al deposited in situ. The GaN RHEED pattern was (2x2) during growth and changed to (1x1) when the sample was cooled to below 350 °C while maintaining the nitrogen plasma flux used during growth. The composition of a (1x1) surface prepared in this manner was not described. A sharp (1x1) RHEED pattern was also observed after Al deposition, indicating good epitaxy. For Al thicknesses in the range of 1 to 4 nm, no evidence of interfacial reaction was seen in the form of changes in the Ga 3d or Al 2p XPS lineshapes using monochromatic Al Kα excitation (hν = 1486.7 eV). The SBH was found to depend somewhat on the thickness of the GaN MBE layer, being 0.41 eV for a 20 nm layer and 0.61 eV for ≥100 nm. This dependence was explained in terms of defects formed in an Al/GaN interfacial reaction that was not detectable in the XPS data. Tseng et al. [565] observed epitaxial growth for in-situ deposition of a 130-nm-thick Al layer at RT on GaN (0001) grown by MBE.

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The RHEED pattern shows that up to 10 Å a (111)-oriented Al layer develops with a lattice spacing equal to that of GaN. Between 10 and 15 Å the pattern changes to that of bulk Al, and greater thicknesses show only crystalline Al. Results obtained using XRD and HRTEM show that the Al layer is oriented with the [24̄ 2] axis of the ̄ axis of the GaN, which gives a FCC lattice aligned with the [1010] 12% lattice mismatch in agreement with the RHEED data. These results show that Al at the interface is under tensile stress and further suggest that the Al-GaN interaction is sufficiently strong to overcome this stress to achieve epitaxy. The stress is relieved within the 10–15 Å thickness range via the formation of defects and dislocations. The tensile stress in the interfacial Al, which also produces a compressive stress in the GaN, was shown to influence the SBH through piezoelectric polarization (Section 4.2.2). Timon et al. [566] performed calculations for Al on GaN (0001) using NCPPs and the PW91 functional with the Ga 3d electrons treated as valence states. A (2x2) SUC was used, and the 2DPS comprised 6 Ga-N bilayers, of which the upper 2 (as well as any adatoms) were allowed to relax while the remainder were fixed in the optimized bulk-lattice configuration. The N DBs on the bottom surface were terminated with real (not pseudo) H atoms. This leads to a metallic surface, since the ECR is not satisfied, but it reduces the potential difference between two surfaces of the 2DPS, which in turn reduces the need for a dipole correction (Fig. 6). The calculations addressed a situation in which the (0001) surface is covered with a full ML of N adatoms in T1 sites and then each of the 4 adatoms in a (2x2) SUC is sequentially replaced with Al. The goal was to investigate the structure and stability of various adlayer (2x2) surfaces involving impurity species. With 2 Al and 2 N per SUC the adsorbed N atoms form a dimer with a bond length of 1.21 Å (vs. 1.09 Å for free N2). With 1 Al and 3 N, the adsorbed N atoms form a triangular trimer structure with bond lengths of 1.51 Å. However, all the Al-containing structures formed in this way, except for 4 Al per SUC, are less stable than the bare surface. The 4 Al structure is slightly more stable than the bare surface, by 0.07 eV per SUC, for any value of μN. Garcia-Diaz et al. [567] performed calculations using the PBE functional and USPPs for a 2DPS with 4 Ga-N bilayers and a (2x2) SUC. The bottom layer was terminated in PHs and the upper 3 bilayers and the adatoms were free to relax during optimization. The starting surface was the bare (0001), and the most favorable site for an Al adatom on this surface is the T4, where it can interact with an underlayer N atom. This is more stable by 0.31, 0.66 and 1.76 eV than H3, Br and T1 sites respectively, where H3 is above an underlayer hollow site, Br bridges two surface Ga sites and T1 lies directly above a Ga. Site exchange with a surface Ga is energetically favorable to the greatest degree when the displaced Ga

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occupies a T4 site in which it bonds only to other surface Ga atoms as opposed to forming a Ga-Al bond with the incorporated Al. Since Al has three valence electrons, θAl = 0.25 ML in the form of adatoms satisfies the ECR. For a full Al ML, the most stable configuration is shown in Fig. 39. Here all surface Ga atoms have exchanged with Al, and each displaced Ga is bonded to one Al and two Ga atoms to form the chain-like structure shown in Fig. 39. Relative formation energies for different surface terminations show that, for the full range of Ga chemical potential, this structure is more stable than either the bare surface or the single Al adatom per (2x2) SUC. These results are consistent with the experimental observations of a reactive interface noted above. Qin et al. [568] studied Al adsorption and substitution on GaN (0001) using the PAW method with the PBE functional and a 2DPS with four Ga-N bilayers. A (2x2) SUC was used for the bare surface and a (√3x√3) for a surface terminated in a laterally-contracted Ga metal bilayer. The adlayers and the upper two Ga-N bilayers were allowed to relax, and the bottom surface was terminated in PHs. Adsorption of Al on the bare surface was studied in steps of 0.25 ML up to a full ML. For θAl = 0.25 (i.e., one Al per (2x2) SUC) the relative energies for the T4, H3, Br and T1 sites are consistent with those of Garcia-Diaz et al. [567], but the differences decrease with increasing coverage. At θAl = 1 ML the energies are nearly identical at about ΔEads = −3.5 eV per Al with the T1 site being slightly more favorable. The distance of the Al above the surface plane increases with θAl, suggesting that a repulsive Al-Ga or Al-Al interaction overcomes the attractive Al-N interaction for Al in a T4 site. At θAl = 1 ML the Al layer assumes an hexagonal structure, which is consistent with the experimental observations of epitaxy noted above. In keeping with the ECR, the DOS indicates that the bare surface is metallic but becomes semiconducting for θAl = 0.25 ML and then metallic again at higher coverages. The bare surface has a total unpaired electron density of 3 |e| in four Ga DBs, three of which form Al-Ga two-electron bonds using the three Al valence electrons, leaving the Al DB and the remaining Ga DB empty for θAl = 0.25 ML. Adding more Al to this passivated surface reintroduces partially-filled orbitals and metallic character. Substituting Al for Ga is found to be energetically favorable; whereas, substituting for N or forming an interstitial is not. It is also found that substitution for subsurface Ga sites (i.e., in the second and third Ga-N bilayer) is more favorable than for surface sites. The stabilizing effect of substituting Al for Ga is attributed to the higher ΔHf for AlN vs. GaN. (One assumes that either a thicker 2DPS or a more-extensive relaxation was used when treating Al incorporation into the third bilayer.) The process discussed in Ref. [568] is substitution and not site

Fig. 39. Schematic structure for the GaN bilayer-terminated GaN(0001) surface with an Al monolayer. "Bilayer-terminated" here means no Ga or N adatoms or adlayer. The first Ga layer is replaced by the Al layer, and the Ga atoms form a chain on top. (a) Top view and (b) side view. From Garcia-Diaz et al. [567] (Copyright 2010, reproduced with permission from Elsevier).

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exchange since no mention is made of the fate of any displaced Ga. The former is relevant to, e.g., MBE growth in the presence of an Al flux; whereas, site exchange relates more to Al deposition on a stable substrate at nominal RT. Incorporation into a surface with an adsorbed Ga bilayer was also considered in order to simulate growth under very Ga-rich conditions, and here again substitution for Ga sites in or below the first Ga-N bilayer, which permits Al-N bonding, is more favorable than for Ga in the metallic bilayer. Finally, a phase diagram was constructed by computing the relative energies of different structures as functions of μAl and μGa. It is found that under Al-poor conditions only the bare-surface structures occur, which change from N adsorbed in an H3 site to Ga adsorbed in a T4 site to a Ga bilayer with increasing μGa. For more Al-rich conditions, incorporation of an ML of Al into the third Ga-N bilayer is most favorable except under very Ga-rich conditions for which the metallic Ga bilayer is present. Here the structure formed has one Al in the second Ga-N bilayer and three in the third. Although such incorporation processes are thermodynamically favorable, the activation barriers are presently unknown. Picozzi et al. have reported extensive theoretical studies of Al/ GaN, all but one of which deal exclusively with the zinc-blende GaN (001) surface. The one giving results for GaN (0001̄ ) as well as — for the related zinc-blende (111̄ ) surface, Ref. [569], is discussed here. These were all-electron calculations employing the FLAPW method and the LDA using a 2DPS with 6 layers of Ga, 7 of N and 6 Al. The use of an all-electron method enabled shifts in core-level BEs to be obtained. Having either side terminated in a layer of N allows the study of two types of surfaces, termed "A" and "B", for which the N is back-bonded to three or to one Ga atom respectively. The former corresponds to a bare (0001̄ ) surface and is of more interest in the present discussion. The surface was described as (0001) but, given the construction, is more properly labeled (0001̄ ). The 2DPS is thick enough for the middle to appear bulklike, and all atoms were allowed to relax during optimization. One of the objectives of this study was the computation of the SBH, which is very sensitive to interfacial structure. The Ga-N bond length at the relaxed interface is found to be only about 1% larger than in the bulk; whereas, the Al-Al distance deviates by as much as 10% from the calculated Al (111) interplanar distance. The relaxation process itself was also investigated but will not be described here. On the A surface, the partial DOS of Ga and N at the Al/GaN interface are similar to those in bulk GaN, which indicates that such atoms exhibit a bulk-like electronic structure. The partial DOS for Al at the interface resembles that of bulk Al and exhibits metallic characteristics. The electric field across the slab was found using the shift in N 1s BE, which varies linearly with distance. The origin of this field, which arises from the inequivalence of the A and B surfaces, was discussed in detail. For the relaxed Al interface at the A surface, an SBH of 2.07 eV was obtained from these results. Good agreement was claimed with the experimental results in Ref. [559] for Al on the (0001) surface; however, as noted above, these were subsequently corrected in Ref. [491]. To summarize, it appears from the available experimental data that reaction at the Al/GaN interface depends on whether the substrate was annealed at high temperature before deposition of Al. In the two studies in which a reaction was clearly observed, the sample was heated as high as ∼900 °C following either Ga metal deposition and desorption [559] or nitrogen-ion bombardment [561,562]. On the other hand, in studies where this was not done [560,563–565], the reaction (if it occurred at all) did not appear to be as pronounced, and epitaxial growth was observed. Theoretical work appears to support the possibility of both epitaxial growth and interfacial reaction on defect-free GaN (0001) surfaces. If in fact high-temperature annealing of the bare surface is required for reaction, then either VN defects or excess Ga may be implicated since the desorption rate in vacuo of N exceeds that of Ga above

780 °C (Section 4.5). It also appears that the SBH depends on the details of how the bare surface and/or the contact is formed. It is unlikely that this merely represents measurement error since all photoemission studies are based on the correct Ga 3d-VBM energy difference and on the Al-induced shift in the Ga 3d BE relative to EF. In Section 5.20, which deals with Au, a study will be discussed that focuses specifically on the dependence of the Au/GaN SBH on the method of clean-substrate preparation. 5.2. Antimony The interaction of Sb with the GaN (0001) surface has been studied experimentally using UPS, XPS and LEED by Grodzicki et al. [575], and theoretical results for the (0001) and (112̄ 0) surfaces have been reported by Gokhale et al. [576,577]. The motivation for this work lies in the potential use of Sb as a surfactant in GaN MBE growth and also as a means of modifying surface electronic properties. The experiments [575] were performed on p-type GaN (0001) samples that were cleaned in solvents followed by annealing at 800 °C in UHV, after which Sb was deposited in situ. The clean surface showed no C but a small amount of O in AES, and the Ga 3d XPS (not shown) indicated small amounts of metallic Ga and Ga-O bonding. The LEED pattern was a sharp, low-background (1x1) with additional features suggesting faceting (Section 3.3.1). Depositing Sb leads to a disordered layer and an increase in downward BB by 1.0 eV to give an SBH of about 2.50 eV. This neglects any SPV "band flattening" (Section 4.7.3.2), which would reduce the apparent SBH. A brief anneal at 400 °C of a 5 nm-thick Sb layer leads to desorption of the metal with ∼0.2 nm remaining in or on the GaN surface. For an Sb density of 6.685 gm cm-3, 1 Å = 3.307x1014 Sb cm-2 = 0.291 ML where 1 ML is defined as 1 Sb per surface lattice site. Hence the residual Sb amounts to ∼0.6 ML. The LEED and VB UPS return approximately to the respective cleansurface appearances, but the electron affinity is χ = 1.9 eV vs. 3.0 eV for the initial clean surface. Also, the downward BB is only partially reversed, being ∼0.4 eV greater than on the clean surface. The effect on χ suggests that the remaining Sb forms a dipole layer with the positive side outward, which would lower the resulting value (Section 5.10). However, the Sb 4d for the residue shows no apparent BE shift relative to that in metallic Sb, which suggests the absence of a chemical interaction with the surface. Theoretical work by Gokhale et al. [576,577] employed the PW91 GGA functional with USPPs and an 8-layer 2DPS with a dipole correction. The top 4 layers were allowed to relax while the bottom 4 were fixed in the ideal bulk-lattice configuration. Several different (0001) SUCs were employed ((√3x√3)R30°, (2x2), (2√3x√3)R30°, (1x1) and (1x2)), which determines what reconstructions are possible as well as the minimum value of θSb that can be addressed. Nitrogen is found to adsorb preferentially at FCC (H3) sites and Ga at HCP (T4) sites, as in other studies (Section 4.6.1), while Sb adsorbs at both with the same energy. For the (2x2) surface, diffusion barriers of 0.54, 0.55 and 0.99 eV are found for Ga, Sb and N, and, furthermore, incorporation of Sb into the lattice is found to be unfavorable. A phase diagram was computed which, for a low μSb, shows the reconstructions characteristic of a clean (0001) surface. At intermediate μSb, reconstructions are seen that comprise 0.75 ML or 0.25 ML of Sb or 0.125 ML of Sb + 0.125 ML of N, all of which are described as satisfying the ECR. The 0.75 ML structure was not discussed in detail, but one can speculate as to what it might be. In order to satisfy the ECR, there would be an Sb-Ga back-bond to 3 of the 4 Ga atoms in a (2x2) cell with a NBLP orbital on each Sb and the fourth Ga with an empty DB. The remaining 2 unpaired electrons on each Sb could be used to bond to 2 neighbors to form a triangular Sb trimer. This would account for a total

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of 18 |e|, 3 |e| from the Ga DBs and 15 |e| from the 3 Sb adatoms. Such a structure would be under tensile stress since the Sb covalent radius is 1.38 Å (optimum Sb-Sb distance ≈ 2.76 Å); whereas, the Ga-Ga distance is 3.2 Å in GaN. The other structures obviously satisfy the ECR for species such as N or Sb that typically form 3 two-electron bonds. The experimental observation [575] of a stable coverage of θSb ≈ 0.6 ML is then consistent with a mixture of regions with θSb = 0.75 and 0.25 ML. Under conditions of high N and/or Sb richness, surfaces with 0.5 ML of N + 0.5 ML of Sb or with 1 ML of Sb can also form. The surfactant effect of Sb was examined, and it was found that on the (2√3x√3)R30° surface SbN forms with an energy barrier of 0.67 eV and adsorbs strongly (ΔEads = −4.31 eV). The diffusion barrier for SbN is 0.70 eV, and the overall energy surface strongly favors N mobility via SbN diffusion. Computational results were also obtained for the (112̄ 0) surface, which is non-polar and does not reconstruct. A (1x1) SUC was used, and ΔEads for Sb on this surface is much smaller (−2.50 eV) than for the (0001) (−4.96 eV). This suggests a weaker surfactant effect for the (112̄ 0), since the steady-state coverage of adsorbed Sb will be lower. Due to the presence of Ga-N dimer rows (Fig. 2d), diffusion on this surface is anisotropic. Thus the barrier for Sb diffusion is 0.30 (1.34) eV parallel (perpendicular) to the dimers, where the dimers are aligned in the [0001] direction; whereas, the barriers for N diffusion are very high (2.63 and 2.85 eV respectively). The implications of these results for the use of Sb as a surfactant in GaN growth are discussed in detail in Refs. [576,577]. 5.3. Arsenic Arsenic on GaN (0001) has been studied experimentally in Refs. [117,347,357,578,579], motivated by its use as a surfactant during MBE growth to reduce the GaN surface roughness. Timon et al. [566], Ramachandran et al. [579] and Zywietz et al. [580] have studied As on GaN (0001) theoretically. Arsenic on the N-polar surface has also been studied theoretically by Zywietz et al. [580]. Zhao et al. [578] used RHEED, AFM, RBS and EDAX on samples grown homoepitaxially by MBE with AsH3 as the As source. The homoepitaxial layer initially shows a streaked (2x2) RHEED pattern that changes to (1x1) as As is deposited, which was ascribed to the passivation of surface dangling bonds by adsorbed As. The surface layer is stable since, once formed, the (1x1) pattern persists even after the As source is turned off. The decrease in surface roughness due to As, which is more significant at higher growth temperature, was verified using AFM. The RBS data show very little incorporation of As, which indicates that it remains on the surface as the GaN grows. At higher growth temperatures (4 740 °C), where As evaporation becomes significant, a continuous flux of As during growth is needed in order to maintain the surfactant effect. At lower growth temperature, a continuous flux can lead to a small amount (∼1%) of incorporation as seen in RBS and EDAX. Ramachandran et al. [579] investigated the effects of As on GaN (0001) for the purpose of determining whether the (2x2) structure sometimes observed in RHEED during MBE growth of GaN (e.g., Ref. [345]) might be a consequence of unintentional As contamination [341] resulting from prior MBE growth of GaAs. The As flux was obtained from a resistively-heated GaAs wafer and was much lower than that used by Zhao et al. [578]. The surfactant effect noted above (i.e., a reduced surface roughness) was also observed under mildly N-rich growth conditions and attributed to an increased mobility of surface Ga in the presence of As. One might speculate that this results from the As-induced surface passivation noted by Zhao et al., which would eliminate sites for the strong adsorption of Ga. By varying the Ga flux and the As BEP, a phase diagram describing the (1x1) and (2x2) regions of stability was constructed. (The BEP is the pressure of As vapor for which the random flux arriving at the surface would equal the directed

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flux from the MBE source.) The conclusion of this work is that the (2x2) reconstruction of the (0001) surface during growth is in fact a result of As adsorption at θAs ≈ 0.25 ML (determined using AES), with one adatom per SUC. It should be noted that this structure is different from the (2x2) that is observed for the clean, As-free surface. It was furthermore concluded that the (4x4) and (5x5) structures also reported by Xue et al. [345] result from Ga adsorption on the As-induced (2x2). Vézian et al. [357] also investigated the effects of As on GaN (0001) surface reconstructions using RHEED and STM. The results agree with those of Ramachandran et al. [579] for the As-induced (2x2) and (4x4) structures; although, the (5x5) was not reported in this study. In earlier work, Foxon et al. [117] and Hughes et al. [347] also observed a (4x4) reconstruction on the (0001̄ ) surface, which was suggested to result from As contamination at a level too low to be detected in AES. A (4x4) was also found to result from a low level of O contamination, and the point was made that attention must be paid to the effects of adsorbed impurities when assigning a particular RHEED or LEED pattern to a specific substrate polarity. Zywietz et al. [580] have studied As on GaN theoretically using the LDA with soft (Troullier-Martins) PPs and the Ceperley-Alder and Perdew-Zunger exchange and correlation functionals. The 2DPS models were either symmetric, with 9 atomic layers, or asymmetric with 4 atomic layers (i.e., 2 Ga-N bilayers) and the bottom surface terminated in PHs. Both (0001) and (0001̄ ) were considered, with the former being ideally-terminated and the later being covered by a monolayer of Ga adatoms in a (1x1) structure. The structure used for the (0001̄ ) is the most stable under Ga-rich MBE growth conditions. Minima in the surface energy are found at an As coverage of 0.25 ML for either surface, but the decrease relative to clean surface is larger for (0001̄ ) than for (0001) (0.8 vs. 0.2 eV) due to the higher dangling-bond density on the former. It was inferred from this that the (0001̄ ) terminated in a Ga adlayer is more reactive than the ideally-terminated (0001) and therefore more susceptible to impurity incorporation during growth. Ramachandran et al. [579] performed theoretical studies of As adsorption on the ideally-terminated (0001) surface for three different structures, all based on a (2x2) SUC. These were 1 As adatom per SUC (i.e., θAs = 0.25 ML) in T4 or H3 sites and an As trimer in a T4 site. The As-free, Ga-terminated surface (modeled as the (2x2) Ga adatom structure) is the most stable only under Aspoor conditions, and an adsorbed As trimer is the most stable surface species only for a very As-rich environment. Otherwise the single-adatom structure gives the lowest energy with As in the H3 site being slightly lower (by 0.1 eV per (2x2) cell). Both the T4 and H3 structures result in extensive surface relaxation. It was further established that at the typical MBE substrate temperature of 700 ° C, the As-adatom-stabilized (2x2) is the lowest-energy structure of those considered for an As2 (As gas-phase dimer) pressure in the range of 10-12 to 10-2 Torr. Timon et al. [566] performed calculations for As on GaN (0001) using methods described in Section 5.1 in connection with their work involving Al. The calculations addressed a situation in which the (0001) surface is covered with a full ML of N adatoms in T1 sites and then each of the 4 adatoms in a (2x2) SUC is sequentially replaced with As. The goal was to investigate the structure and stability of various adlayer (2x2) surfaces involving impurity species. With 2 As and 2 N per SUC the adsorbed N atoms form a dimer with a bond length of 1.17 Å (vs. 1.09 Å for free N2). With 1 As and 3 N, the adsorbed N atoms form a triangular trimer structure with bond lengths of 1.48 Å. For 3 As and 1 N (or for a full ML of As), three As atoms form a trimer with a bond length of 2.49 (or 2.61) Å. The former result is similar to that of Ramachandran et al. [579], who computed a trimer bond length of 2.48 Å. At a high value of μAs a full ML of As is found to be the most stable surface for any value of μGa, which is consistent with the (1x1) As-induced

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structure seen by Zhao et al. [578]. 5.4. Barium The adsorption of Ba on GaN (0001) has been studied experimentally by Benemanskaya et al. [581–586]. This work was motivated in part by a desire to understand better the Cs/GaN interface, which is important as an effective-NEA system, by comparison with results for Ba. Much of the Ba work relates to the subsequent discussion of Cs/GaN (Section 5.10), which should be regarded as a continuation of the present section. In the first studies [581,582], the photoemission threshold for s- and p-polarized light was investigated as a function of θBa. Here s- (p-) refers to polarization perpendicular (parallel) to the plane of reflection. For a non-zero angle of incidence (45° in this case), the photoelectron spectrum excited by s- (p-) polarized light is relatively more bulk- (surface-) sensitive. The n-type sample was grown by MOCVD and the surface prepared by annealing at ∼750 ° C in vacuo followed by in-situ deposition of Ba up to θBa = 2 ML. Up to θBa = 0.4 ML there is a sharp decrease in the threshold photon energy for photoemission, which is equal for both polarizations. At higher coverage, up to θBa = 1.2 ML, the threshold remains approximately constant at about 1.90 eV. The dependence of the threshold energy on θBa follows that of the sample work function ϕS. Above the threshold energy (hνs) the s-polarized photoemission intensity, Is(hν), follows the Fowler relationship Is(hν) = (hν −hνs)2, which is characteristic of a bulk metal. This indicates the presence of an accumulation layer (or 2DEG) at the interface shown schematically in Fig. 40. However in later work [585] (hν −hνs)3, which is characteristic of a semiconductor, was found to give a better fit to the data. In effect, adsorbed Ba acts as a donor. Electrons are transferred into the CB, and the layer of trapped Baδ+ charges leads to downward BB and the formation of an accumulation layer as diagrammed in Fig. 40. The ratio Ip(hν)/Is(hν) can be used as a measure of the surface photoemission spectrum (Fig. 40), and this quantity reveals two states (S1 and S2) that are unique to the Ba/GaN interface and are

ascribed to adatom bond formation. These lie at about 0.15 and 0.30 eV below EF, and the corresponding photoemission features gain intensity up to θBa ≈ 0.6 ML and then remain essentially constant at higher θBa. The authors further suggest that the hybridization of the Ba bonding orbitals changes from mainly s-d at lower θBa to mainly p-d at higher θBa based on the θBa dependence of the width and intensity of the S1 and S2 photoemission features. With the Ba-induced reduction in hνs, photoemission occurs at energies well below Eg, for which the bulk material is transparent. Thin-film interference effects are then detected in Is(hν) with a fringe spacing corresponding to the thickness of the GaN MOCVD layer. Subsequently [583] a model was developed to describe photoemission from the Ba-induced 2DEG based on the Urbakh-Brodsky theory for threshold photoemission. The experimental phase of this work employed s-polarized excitation, for which the Is(hν) spectrum is bulk-sensitive with an effective sampling depth of ~30 nm. The 2DEG was modeled as a Lorentzian distribution of states, peaked at EF, with all states below (above) EF filled (empty). The resulting theoretical expression for Is(hν) gave a good fit to the data and was used to characterize the energy distribution of the 2DEG electrons. It was later found [584] that co-adsorption of Ba and Cs multilayers followed by annealing at ∼600 °C leads to formation of regular surface structures, which were studied using AFM, electron microscopy and photoelectron spectroscopy. The features are described as combs, about 60–70 nm in diameter and 7 nm high, that consist of a BaGaN solid solution with a minor content of Cs. The photoelectron quantum yield of this surface is an order of magnitude higher than that of a Cs/GaAs (100) standard photocathode. The self-organization effect was explained in terms of an initial strongly-adsorbed incommensurate layer followed by a mobile phase comprising Cs+ and Ba2+ ions coupled to polarons. (A polaron is a quasi-particle consisting of a charge carrier and the surrounding lattice distortion that results from the charge-induced polarization of the ionic lattice.) The foregoing results were reviewed and further extended in Ref. [585], which examined the origin of the Ba-induced surface states in more detail and showed

Fig. 40. Left: Schematic band diagram for Ba/n-GaN (0001) showing the accumulation layer and the occupied surface states (S1 and S2). Ec and Evac are the CBM and the vacuum level respectively. hνs and φ are the photoemission threshold and work function respectively. Right: Surface photoemission spectrum, Ip/Is, for θBa ¼ 0.5 ML. From Benemanskaya and Frank-Kamenetskaya [581] (with the permission of Springer).

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that they involve Ga DBs. These are believed to be empty on the bare surface, based on the computed DOS for the (0001)-(2x2) Gaadatom surface [462] (Section 4.7.1.1). It is noted here that this assumes a Ga adatom coverage of 0.25 ML and that for θGa ≠ 0.25 ML the DBs are partially filled. It was further shown that the interfacial layer, which consists of covalent Ga-Ba bonds and terminates the 2DEG, is insulating and ∼0.5 nm thick. In the most recent study [586], synchrotron photoemission experiments were performed with excitation energies in the range of 20 o hν o 400 eV to probe the VB and the Ga 3d, Ba 4d and Ba 5p core levels. The n-GaN (0001) samples and surface preparation methods were similar to those used previously, and residual carbon was detected via XPS after cleaning by annealing at 900 K in UHV. With a maximum available hν of 400 eV it was not possible to access the O 1s level. In common with other studies, the clean surface shows a surface state at about 0.4 eV above the bulk VBM, which is removed by Ba adsorption. At low θBa the Ba 4d5/2 appears at a BE of 90.3 eV, which is interpreted as an indication of Ba-Ga interaction. Above θBa ≈ 0.9 ML the Ba 4d peaks appear at slightly lower BE, indicating Ba-Ba interaction, and a broad feature is seen at BE ≈ 95 eV, which may be a loss- or shake-up satellite also related to Ba-Ba interaction. An emission peak extending from EF down to about 1.5 eV below EF is seen in UPS and is assigned to the 2DEG. For the clean surface, the GaN bulk VBM falls at about 2.9 eV below EF, corresponding to a small (∼0.5 eV) upward BB on n-type GaN. For θBa ≈ 1.0 ML, on the other hand, the VBM appears at about 3.9 eV below EF, which is greater than the GaN Eg of 3.4 eV and indicates a downward BB of about 0.5 eV, consistent with the presence of the 2DEG. However the corresponding Ga 3d BE, which would further corroborate the position of EF relative to the band edges via subtraction of VBM-Ga 3d = 17.76 eV [439], was not reported. 5.5. Beryllium Beryllium adsorption and incorporation on the GaN (0001) surface have been studied theoretically by Northrup [587], motivated by its possible use as an alternative to Mg for p-type doping. In this application it is necessary that Be substitutes for Ga rather than forming electrically-inactive clusters or extended defects. (Researchers planning experiments involving Be should be aware that the oxide, in the form of dust or a powder, is highly toxic.) The calculations made use of the LDA and a model with a bilayer of Ga on top of the Ga terminating layer, which is relevant to MBE growth under Ga-rich conditions. A (2x2) SUC was used with a 2DPS consisting of 8 GaN layers (presumably 8 bilayers) in addition to the Ga bilayer. Three Be sites were considered: (a) replacing a Ga in the adlayer adjacent to the terminating layer, (b) replacing Ga in the terminating layer and (c) in an interstitial site within the terminating Ga-N bilayer. Site (a) is found to be highly unfavorable relative to Site (b), due to the tendency of Be to bond to N. Under very Ga-rich conditions appropriate to MBE growth, Site (b) is 1.02 eV lower in energy than Site (c), which suppresses the formation of undesirable interstitials in favor of substitutional Be. It was also shown in this work that substitutional incorporation of Be can be enhanced by using a layer of adsorbed In to create compressive stress in the GaN surface, which is then effectively relieved by Be substitution.

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The substrate was not specifically identified as (0001) but one assumes this to be the case based on the appearance of a (2x2) RHEED pattern. A very small amount of Bi incorporation into the GaN surface was noted, which is barely above the AES detection limit. The interaction of Bi with the GaN (0001) and (112̄ 0) surfaces has been studied theoretically by Gokhale at al. [577]. This works parallels that done by the same group for Sb, which was discussed in Section 5.2. Like Sb, Bi does not incorporate into the lattice and adsorbs at FCC (H3) and HCP (T4) sites on the (0001) surface with the same ΔEads; although, ΔEads is smaller for Bi than for Sb (−4.70 vs. −4.96 eV) as is the diffusion barrier (0.47 vs. 0.54 eV). The energies for the formation and diffusion of BiN were computed using a (2√3x√3)R30° SUC, and it was found that Bi is also effective as a surfactant in promoting N diffusion (via BiN) although less so than Sb. 5.7. Boron Farivar et al. [589] have studied the deposition of B in an MBE environment with a view toward the possible growth of BN/GaN heterostructures. The B coverage, as determined via AES, was in the range of 0.1 to 0.5 ML. In RHEED, an hexagonal layer structure, believed to be metallic B, was seen at low coverage. This transformed into an island structure and/or a rough surface at higher coverage. The deposition was performed in the presence of an N2 radio-frequency plasma to suppress B clustering; although, RHEED gave no indication of BN formation. The mechanism whereby the plasma prevents B clustering was not determined. Palomino-Rojas et al. [590] reported theoretical studies of B on GaN (0001) and (0001̄ ) surfaces using a 2DPS with USPPs and the PBE functional. Both (2x2) and (√3x√3) SUCs were considered. The 2DPS was 3 or 4 Ga-N bilayers in thickness with DBs on the bottom surface terminated with PHs. For the ideally-terminated (0001) surface the lowest-energy B adatom site is the T4, in which B back-bonds to 3 surface Ga atoms and lies above an underlayer N. Site exchange between B and a surface Ga is highly favorable, as expected on the basis of the reported ΔHf of BN and GaN (−2.6 and −1.1 eV respectively). In the most stable such configuration the displaced Ga occupies an H3 site in which it back-bonds to 3 surface Ga atoms. Another (0001) surface is the pseudo-(1x1) structure terminated in an incommensurate and laterally-contracted Ga bilayer, which is applicable to MBE growth under highly Ga-rich conditions. Several configurations for adsorbed B were considered, the most stable being the HD-1, in which the B lies between the two Ga layers and is 6-fold coordinated with 3 bonds each to top- and second-layer Ga atoms. For the (0001̄ ) under Garich conditions the surface is terminated in a (1x1) Ga adlayer with Ga atoms directly above the outermost N atoms. Here there is little difference in energy between B in T4 and H3 adatom sites, the latter involving B back-bonds to 3 surface Ga atoms and lying above a 3-fold-hollow site in the N layer. Site exchange between B and surface Ga is also very favorable on the Ga-terminated (0001̄ ) but is accompanied by an extensive rearrangement of the surface. Calculations of the DOS for the various structures were reported, which show the effects (or lack thereof) of B adsorption on the surface metallic character. 5.8. Carbon

5.6. Bismuth The formation of Bi layers on GaN has been studied experimentally by Foxon et al. [588], motivated by its potential use as a surfactant during MBE growth. Epitaxial formation of a continuous, crystalline Bi layer was achieved at a substrate temperature of 250 °C on GaN (0001) grown in situ using MBE.

There have been several studies dealing with the growth of graphene on GaN (or vice versa) and with the interface between the two materials, mainly from the perspective of fabricating heterostructural electronic devices. These are beyond the scope of the present review, and this section will focus instead on those works that consider the adsorption of C in various forms on GaN.

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Experimentally, Nienhaus et al. [591] and Takashima et al. [592] have studied the adsorption of C60. Diale et al. [593] have investigated adventitious impurity carbon, Kimura and Hashizume [594] have examined the effects of deliberate C incorporation and Tsai et al. [595] have studied the electrical properties of graphene/ GaN interfaces. In theoretical work, Akiyama et al. [596] have ̄ and (0001) surfaces and studied C incorporation into the (1011) Espitia-Rico et al. [597] have discussed the formation of a graphene ML on the (0001) surface. Nienhaus et al. [591] used AES and LEED to study the growth of C60 layers on MOCVD GaN surfaces of unknown polarity (termed "{0001}"). The substrates were cleaned in aqueous HF then in situ using 3 keV nitrogen-ion bombardment. As a final in-situ step, 200 Å of Ga was deposited and then desorbed at 1175 K. The resulting surface showed a sharp but faceted (1x1) LEED pattern, no detectable O and residual C at a level of o0.03 ML. The N (KLL)/Ga (LMM) AES intensity ratio indicated a surface covered with almost 2 ML of adsorbed Ga. The C60 layer was grown in situ by evaporation onto the substrate at nominal RT and exhibited uniform growth up to 1 ML, at which point island formation commenced. This indicates that the interaction of C60 with the GaN surface (or the Ga adlayer) is stronger than that between C60 molecules. Upon annealing, C60 above 1 ML desorbs at 650 K; whereas, C60 in contact with GaN is not completely removed until 1275 K, which is well above the temperature (~1100 K, Section 4.5) at which GaN surface decomposition begins (but see below). Desorption of 1 ML occurs gradually over a range of temperatures, rather than at one well-defined value, which suggests a range of different adsorption sites and/or bond energies. A sequential annealing process was developed that shows that a C60 ML impedes the thermal decomposition of GaN (0001). It was suggested that decomposition occurs preferentially at step sites and that C60 bonds most strongly to such sites, which then suppresses decomposition. Evidence for strong Ga-C60 interaction was seen in UPS data (described but not shown). It is noted that, in this study, decomposition of the bare surface (without C60) is detected as an increase in the N/Ga AES ratio relative to the value measured for the clean unannealed surface. However, as discussed in Section 4.5, thermal decomposition is known to yield a Ga-rich surface when applied to the bare (0001), which should lead to a decreased N/Ga AES ratio. This can be understood if the decomposition described in these experiments involves mainly the Ga adlayer and not the GaN substrate itself. Takashima et al. [592] used RHEED and AFM to study the growth of C60 layers on GaN (0001) via MBE. The substrate was grown, presumably ex situ, by MOCVD, but no details regarding surface preparation were provided. The GaN surface appeared rough in AFM, which influences the structure of the C60 layer. Growth of C60 does not occur at 150 °C due to re-evaporation, which indicates that the interaction of C60 with GaN is weak in comparison to that with an H-terminated Si surface (of unspecified orientation). However, for growth at 100 °C, RHEED shows formation of an ordered FCC layer with the [111] axis parallel to the GaN [0001] axis, and AFM shows a continuous coverage of densely-packed C60 islands. On a rough GaN surface, the C60 layer is polycrystalline. With increasing growth temperature the density of the islands decreases quickly and the size increases only slowly. This is ascribed to the competition between surface diffusion and re-evaporation, which effectively limits the diffusion length. Formation of an epitaxial layer could be promoted by first growing at 30 °C, then annealing at 100 °C for 10 min. The two studies described here give different results for the interaction between C60 and the GaN surface, which is quite likely the result of differences in surface preparation. Diale et al. [593] used AES and XPS to observe the effects of temperature on adventitious impurity carbon (and oxygen), which

are relevant to cleaning by in-situ annealing (Section 3.3.2). The sample was cleaned in organic solvents and in H2O before mounting in the analysis chamber. Heating in situ up to about 1000 °C reduces, but does not completely eliminate, the coverages of impurity C and O, and sputter profiling shows that the impurities are localized near the surface. The N KLL and Ga LMM AES intensities approach constant values as the temperature is raised. This suggests the absence of significant decomposition up to 1000 °C, which may be impeded by the surface contamination. The C KLL AES lineshape shows no significant change in structure over this temperature range; however, C 1s XPS data (not shown) indicate three chemically-distinct forms of C. These are graphitic C, C substituting for N and C substituting for Ga with BEs of 283, 285 and 287 eV respectively. The substitutional C species are proposed to be thermally removable and to account for the net loss of C during annealing. Kimura and Hashizume [594] intentionally incorporated C into GaN of unspecified polarity and concluded that C substitutes for Ga to form a shallow donor (i.e., an n-type dopant). Tsai et al. [595] prepared graphene/GaN interfaces by wet-chemical methods and used XPS to measure SBHs of 0.85 and 2.50 eV respectively for nand p-type GaN. Evidence for C-O bonding (i.e., impurity O) was seen in XPS, and Raman data showed considerable disorder in the graphene layer. However, the dependence of the SBH on dopant type suggests that the Fermi level is unpinned at the interface in that the sum of the n- and p-type SBHs essentially equals Eg. Akiyama et al. [596] performed theoretical studies of C in̄ and polar (0001) surfaces corporation into the semi-polar (1011) under MOVPE conditions. The interest was in determining under what conditions C can be made to occupy an N lattice site, in which case it functions as a p-type dopant. The 2DPS models consisted of eight Ga and N atomic layers (four bilayers) with a (2x2) SUC and the bottom surface terminated with PHs. The PW method was used with C and N treated using USPPs and Ga using an NCPP with the 3d electrons included via NLCC. The illustration ̄ cell used in the calculation provided for the rectangular (1011) indicates that it is (2x1) with respect to the non-primitive SUC in Fig. 3d and thus contains the same number of atoms as a (2x2) structure based on the primitive SUC. At a high H2 pressure (i.e., high μH), which corresponds to MOVPE growth, C-free surfaces are stable over a wide range of μC and μGa. At a sufficiently-high μC, however, C is present on either surface. On the (0001), adsorbed CH3 and NH occur but only under conditions that are not Ga rich. The CH3 is back-bonded to one Ga site in the (2x2) SUC and the NH to the remaining three sites. This structure satisfies the ECR since CH3 and NH contribute one and four electrons respectively, which, together with the three Ga DB electrons per (2x2) SUC, gives four doubly-occupied bonding or̄ C incorporation occurs at any μGa as bitals. In the case of the (1011), long as μC is high enough. The resulting surface is some combination of CH2, NH, NH2 and GaH depending on μGa and μC. The CH2 can either replace a two-fold-coordinated N as a bridge between two first-underlayer Ga sites or it can form a bridge between twofold N atoms (thus occupying a Ga site), depending again on μGa and μC. The former process (CH2 replacing two-fold N) is favorable for the use of C as a p-type dopant. The incorporation of C is promoted by the stability of Ga-C and N-C bonds, and it is suḡ than the gested that the process is more favorable on the (1011) (0001) because two Ga-C or N-C bonds per C can form on the ̄ vs. only one Ga-C bond on the (0001). It is also found that C (1011) ̄ is stable to higher temperatures than in incorporated on the (1011) the case of the (0001). Espitia-Rico et al. [597] investigated a graphene layer on GaN (0001) under both Ga- and N-rich conditions. The PBE functional was used with, presumably, USPPs since a low PW cut-off energy (30 Ry) was employed, and long-range (i.e., non-covalent)

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interactions were treated semi-empirically. The 2DPS consisted of four Ga-N bilayers with the bottom surface terminated with PHs. The bare Ga-polar surface was used to represent N-rich conditions, while Ga-rich conditions were modeled using a double adlayer of Ga on the Ga termination layer. For the former, the most stable structure consists of a (4x4) GaN SUC interfaced with a (3√3x3√3) graphene unit cell, for which the lattice mismatch is 0.72%. The energy is nearly independent of the registry between the two materials but is slightly lower for a configuration in which C occupies an H3 site. The structure of the Ga-N bilayer at the interface is nearly bulk-like, but the graphene layer shows a slight degree of distortion with C-C distances in the range of 1.41 to 1.46 Å (vs. the computed ideal value of 1.42 Å) and a vertical buckling of 0.54 Å. For Ga-rich conditions, the most stable structure has a (2√3x2√3) GaN SUC interfaced with a (√(21)x√(21)) graphene unit cell, for which the lattice mismatch is 1.1%. The C is in a T1 site (i.e., directly above a Ga in the outermost adlayer). The Ga adlayer is disordered by the presence of graphene, but the graphene itself is nearly ideal in comparison to the case for N-rich conditions. Band-structure results show that the electronic structure of the graphene π-bonded network remains intact in either case and that a slight magnetic moment is introduced under Ga-rich conditions. 5.9. Cerium The deposition of Ce on GaN (0001) was studied by Xiao et al. [598] using LEED, UPS and XPS, for samples grown by MOCVD, with a view toward exploring the contact characteristics. Clean surfaces were prepared by IBA (0.6 keV nitrogen ions, 1100 K anneal) and were well characterized. Deposition of Ce on a RT substrate leads to layer-by-layer (Frank-van der Merwe, Ref. [571]) growth. Evidence of interfacial reaction is seen in the appearance of a high-BE satellite in the Ce 3d spin-orbit doublet and a low-BE satellite in the Ga 3d. The former is associated with the Ce+3 oxidation state and the latter with metallic Ga, indicating that Ce reacts to form a nitride phase (possibly comprising a mixture of Ce and Ga nitrides) and release free Ga. This is thermodynamically favorable according to the reported ΔHf of CeN and GaN (−78.3 and −25 kcal mol-1 respectively). With increasing coverage, the Ce 3d spectrum gradually becomes that of the elemental metal, which indicates that the layer of reaction products formed during the initial deposition acts as a diffusion barrier to inhibit further reaction. Simultaneously, the n-type GaN upward BB increases from 0.5 eV on the clean surface to 1.3 eV with a "thick" Ce film. The SBH of 1.3 eV cannot be explained by either the MIGS or the Cowley-Sze model, which is attributed to the fact that neither considers the effects of the interfacial reaction layer. Annealing up to 800 K after deposition of a high coverage of Ce overcomes the effect of the interfacial diffusion barrier and leads to further reaction at the interface. 5.10. Cesium The interaction of Cs with GaN has been studied extensively both experimentally [449,512,582–585,599–603] and theoretically [604–612] due to its importance in effective-NEA devices. In keeping with the spirit and scope of the present view, the many papers that deal primarily with the fabrication, operating characteristics or material properties of Cs/GaN NEA photocathodes will not be discussed here. An illustration of the various energylevel terms employed in this section is given in Fig. 24. It is appropriate to begin with a brief discussion, aided by reference to Fig. 24, of the electron affinity (χ) for the clean GaN (0001) surface, for which scattered results are found in the literature. This is often measured using the total width (W) of the UV photoemission spectrum, which is the difference in KE between

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the VBM and the slow-secondary threshold. This assumes that the apparent VBM is unaffected by the presence of surface states and that a small negative bias is applied to the sample so that the vacuum level lies above that of the electron energy analyzer. Referenced to EF, the maximum photoelectron kinetic energy is (KE)max = hν− (EF−EVBM), and the minimum energy for escaping slow-secondary electrons is (KE)min = Evac − EF = ϕS, where Evac is the energy of the vacuum level and ϕS is the sample work function. This gives W = (KE)max − (KE)min = hν − I where I = (Evac-EVBM) = (Eg+χ) = (ϕS + (EF−EVBM)) is the GaN ionization energy. The final result is then W = hν-Eg-χ. Alternatively one can measure (EFEVBM) using the Ga 3d BE, as described in Section 4.7.3.1, and add this to ϕS to obtain I. This avoids the direct measurement of the VBM energy and the possible complication of structure near the VBM arising from surface states or contamination. It is noted, however, that when SPV effects are important it is necessary to measure (EF-EVBM) and ϕS under the same conditions of sample temperature and excitation source intensity [573]. For the clean (0001) surface, values reported for χ are 3.2 eV [491], 3.3 eV [449,600,613] and 3.35 eV [512]. In contrast, significantly larger values of 3.8 eV [486,614] and 3.9 eV [104] are obtained for O-contaminated surfaces. This is the result of a dipole layer, with the negative side outward, that is formed by adsorption of electronegative O atoms. It is seen [491] that an O2 exposure of ∼103 L, which saturates the initial chemisorption phase on GaN (0001) at a coverage of 0.40 ML (measured using AES), increases χ by 0.58 eV. The result, χ ≈ 3.8 eV, is essentially the same as that obtained for O-contaminated surfaces. It is likewise possible to cause a large decrease in χ by adsorbing an electropositve species such as Cs to form a dipole layer with the positive side outward. Another type of electropositive adsorbate is NH3 or certain Ncontaining organic molecules (Section 8.4). As noted by Yang et al. [102], the value of χ can vary among the different GaN surfaces as a result of bound polarization charges. These are compensated in part by external effects (i.e., charged surface states, defects or adsorbates), and the resulting surface dipole layer can modify χ as diagrammed in Fig. 24. Thus positively-charged species compensating the negative σb on the (0001) surface can reduce the observed χ; whereas, the opposite can occur on the (0001̄ ). For a layer of N dipoles/cm2 with a surfacenormal moment of μ⊥ Debyes, the potential difference in eV across the layer is given by 3x10-16(4πNμ⊥). This neglects any dipole-dipole interaction (i.e., adsorbate polarizability), which should be valid for a small coverage of adsorbates. Given the magnitude of σb (1.37x1013 cm-2 ≈ 0.012 ML, Section 4.2.2), any effect of compensating external charges is expected to be fairly small (e.g., δχ = 0.052 eV for μ⊥ = 1 D). To our knowledge, the difference in χ between the (0001) and (0001̄ ) surfaces has not been precisely measured, and Yang et al. [102] argue that it should be small (∼0.16 eV) for ideally-terminated surfaces. In the case of real surfaces, for which the (0001) and (0001̄ ) can have different terminations (e.g., Ga adatoms or an adlayer), the difference may be larger for reasons unrelated to σb. Eyckeler et al. [512] and Kampen at al. [599] used UPS, XPS and contact potential difference measurement to study Cs on n- and ptype (0001) surfaces. The MBE samples were first cleaned in HF solution and then in situ by heating at 800 °C in a flux of Ga vapor and then at the same temperature in UHV. The resulting surface showed a (1x1) LEED pattern with residual impurities at levels below 0.1 ML. Vapor deposition of Cs in situ at 150 K yields a layerby-layer (Frank-van der Merwe, Ref. [571]) growth with a greater sticking coefficient for the first layer than for the second, indicating that Cs-GaN interaction is stronger than for Cs-Cs. With increasing θCs, the upward BB on n-GaN first increases by ∼0.3 eV and then decreases by ∼0.5 eV, and HeI UPS (Fig. 41) shows the attenuation of a surface state just below the VBM and an increase

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Fig. 41. Upper: HeI UPS data vs. Cs coverage for n- and p-type GaN (0001) at 150 K. The sample is biased at Us ¼
10 V relative to ground to shift the vacuum level above that of the electron energy analyzer. From Eyckeler et al., Ref. [512] (reproduced with the permission of the American Vacuum Society). Lower: Schematic energy level diagrams for true and effective NEA materials. A lowering of the vacuum level at the surface can be effected by the presence of a layer of adsorbed dipoles (not shown) with the positive end directed away from the surface. The diagram also indicates how, in the case of effective NEA, a photo-excited electron at the CBM is swept to the surface and out into vacuum by the downward BB at the ptype surface. From Wu and Kahn [600] (Copyright 2000, reproduced with permission from Elsevier).

in emission at KE values lower than the onset observed for the clean surface. This constitutes an increase in W, as discussed above. Using the relationship W = hν − I, which is independent of BB and therefore of SPV (Fig. 24), I is seen to decrease from 6.8 eV for the clean surface to 4.5 eV after Cs deposition. The change in I is independent of doping type and (with Eg = 3.45 eV at 150 K) indicates a decrease in χ from 3.35 to 1.05 eV. A δχ of −2.3 eV is very close to what is estimated for an ML of Gaδ−-Csδ+ dipoles formed by electron transfer from Cs to the terminating Ga layer. The position of EF in the gap can be found using EF-EVBM = I − ϕS; however, the fact of a significant SPV effect for p-GaN prevents the measurement of ϕS using UPS (Section 4.7.3.2). Instead ϕS is measured in the dark with a calibrated Kelvin probe and is seen to decrease with increasing θCs up to ∼1 ML and then to increase slightly, finally stabilizing at the value for bulk Cs. The net change in ϕS upon completion of the first ML is δϕS ≈ −2.7 and −3.5 eV respectively for n- and p-GaN, which represents the combined effects of δχ and the change in BB [δϕS = δχ + δ(ECBM-EF)]. In other work, on p-type GaN (0001) [512], changes in BB were measured by observing shifts in the BEs of various n-GaN core levels with increasing θCs, and Kelvin-probe measurements in the dark at 150 K were used to observe δϕS. Since δχ is the same for nand p-GaN at the same θCs, δ(ECBM-EF) for a sub-ML of Cs on p-GaN can be obtained from the n-GaN data, which are much less sensitive to SPV. The VBM for the bare p-GaN surface is found to lie at 3.22 eV below EF, which constitutes a large downward BB with EF only ∼0.28 eV below the CBM at the surface at 150 K. Together

with the Cs-induced δχ of −2.3 eV this leads to a vacuum level lying ∼2.1 eV below the bulk CBM, which exemplifies effectiveNEA behavior (Fig. 41). The strong downward BB on p-GaN (0001) in the dark, which has been noted elsewhere [440,510], is essential to effective-NEA behavior but also results in a large SPV effect in photoemission experiments (Section 4.7.3.2). Wu and Kahn [449,600] prepared clean p-type MOCVD GaN (0001) surfaces by cycles of IBA (0.5 keV nitrogen ions, annealing at 900 °C) after which a sharp (1x1) LEED pattern was observed with o 0.01 ML of oxygen impurity. Surface-sensitive UPS data were obtained for the VB using HeII excitation and for the VB and Ga 3d using the Zr Mζ line (hν = 151.65 eV, Ref. [570]). Exposing the clean surface to O2 removes surface states above the VBM. The existence of such states can also be deduced by noting that the energy difference between the Ga 3d and the VBM in bulk-sensitive Al Kα-excited XPS data is about 0.6 eV less than the difference between the Ga 3d and the apparent VBM in surface-sensitive data for Zr Mζ excitation. A value of χ = 3.3 eV is obtained for the bare surface by adding ϕS to (EF-EVBM) to get I = (Evac-EVBM) and then subtracting Eg. A downward BB of 1.2 eV is found for the bare surface, substantially less than the value of 3.2 eV measured in the dark by Eyckeler et al. [512]. The smaller BB seen in UPS quite probably results from the large SPV effect [440] that occurs for pGaN (0001). After deposition of θCs = 1 ML at RT, the downward BB increases by 0.2 eV, which might arise in part from a suppression of the SPV, and χ decreases by 2.2 eV. The δχ result, which is independent of BB (and therefore of SPV), agrees with that found by Eyckeler et al. The net result is an effective-NEA system (Fig. 41) with the vacuum level at the surface lying lower (by ∼0.3 eV in this case) than the bulk CBM as a consequence of the dipole layer formed by adsorption of electropositive Cs. In contrast, a true NEA material would have the vacuum level at the surface lower than the CBM at the surface. The χeff of about −0.3 eV seen in this study is significantly smaller than the value of −2.1 eV found by Eyckeler et al. [512], which reflects the smaller downward BB that results from SPV. Unlike χ, χeff depends on BB. Exposure to O2 prior to Cs deposition results in a more-negative effective NEA (χeff = −0.7 eV) due to the production of an Oδ−-Csδ+ dipole layer with the Csδ+ end outward. Hence, differences in χeff among various studies could also be affected by differences in the level of O contamination on the starting surface. Afanas'ev et al. [601] deposited Cs in situ on n-type MOCVD GaN (0001) surfaces prepared by heating at 800 °C in UHV and measured photoemission thresholds and photoelectron yields for photon energies in the visible/near-UV range. These experiments are similar to those described in more detail in Section 5.4 in connection with their studies of Ba adsorption. With increasing θCs the threshold photon energy (hνs) in s-polarization drops abruptly from 42.8 to 1.4 eV at 0.5 ML, and the dependence of photoemission intensity on hν follows the Fowler-Nordheim relationship I(hν) ∼ (hν − hνs)2 characteristic of a metal. However in later work [585] (hν − hνs)3, which is characteristic of a semiconductor, was found to give a better fit to the data. As in the case of Ba/n-GaN (Fig. 40), the results are ascribed to a Cs-induced downward BB leading to the formation of a 2DEG at the GaN surface. In this experiment, p-polarized radiation yields a higher surface sensitivity than for s-polarization. The threshold shift is seen to be independent of photon polarization, which is taken to indicate the absence of surface states near the CBM that would have led to a lower threshold in the more surface-sensitive data. No specific account is taken in this study of the possible effect of a Gaδ−-Csδ+ dipole layer, if any. Benemanskaya et al. [582–585,602,603] performed extensive studies of Cs and Ba on GaN (0001). The work involving Ba as well as Cs [582–585] was discussed above in Section 5.4. In the most recent Cs study in this series [585], Cs-

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induced interface states similar to S1 and S2 shown for Ba in Fig. 40 were found at about 0.32 and 0.50 eV below EF. There appears to be a conflict between this model and the results of Eyckeler et al. [512]. In that study, the CBM remains above EF for θCs up to 1 ML or more on n-GaN (0001), and Cs forms a Gaδ − -Csδ+ dipole layer with no net charge and only a small effect (≤0.3 eV) on BB. On the other hand, Afanas'ev et al. find that Cs adsorbed on n-GaN acts as a donor. Electrons are injected into the CB, and the layer of trapped Csδ+ charges leads to downward BB and the formation of an accumulation layer as shown in Fig. 40 for the similar case of Ba adsorption. Both studies provide convincing evidence to support their interpretations. The reason for this disagreement is difficult to discern, and one can only point to real or possible differences between the two studies. The work of Afanas'ev et al. was done at RT using MOCVD GaN, while Eyckeler et al. used MBE samples and worked at 150 K. Another difference is that a more-extensive surface cleaning was done in the work of Eyckeler et al. Theoretical results described below suggest different behavior for Cs on the (0001) vs. (0001̄ ) surface; hence, one study or the other might actually have used N-polar samples. Several theoretical studies have also been reported. Du et al., in Refs. [604,605] and [606(abstract only)], investigated Cs on the (0001) and (0001̄ ) surfaces using a 2DPS with a (2x2) SUC and six Ga-N bilayers for which the bottom surface was terminated in PHs and the uppermost three bilayers and the adsorbed Cs allowed to relax. For (0001), the lowest-energy adsorption site for θCs = 0.25 ML is an H3 with ΔEads = −2.02 eV; although, a very slight lowering in energy (by 0.02 eV) can be achieved by displacing the Cs so that it bridges two underlayer N atoms. Other sites are only a little higher in energy, the highest being a T1 with ΔEads = −1.89 eV. With increasing θCs, ΔEads becomes less exothermic and turns endothermic for θCs 4 0.75 ML, which indicates that this is the saturation coverage for chemisorption. It is noted here that a saturation coverage of 0.75 ML is consistent with the ECR if each Cs donates one electron. Also the ordering of the different adsorption sites with respect to ΔEads changes with θads which, together with the decreasing magnitude of ΔEads, is ascribed to a repulsive interaction between Cs atoms. For three of the five adsorption sites considered (T1, T4 and bridging two underlayer N atoms), the computed ϕS goes through a distinct minimum at θCs = 0.5 ML; whereas, for H3 or for bridging between two surface Ga atoms very broad minima occur at about 0.75 ML. At the bridge-site minimum, δϕS is reduced by 2.4 eV relative to the bare surface, which agrees well with the experimental [512,599] result of δϕs ≈ −2.75 eV for Cs/n-GaN. It was shown that the magnitude of the Gaδ−-Csδ+ dipole moment decreases monotonically with coverage in the 0.25-1.0 ML range; hence, the minimum in ϕS arises from the opposing effects of the increase in the areal density of dipoles and the decrease in the moment per dipole. The latter effect is ascribed to an interaction between Cs atoms that reduces the partial positive charge and thus the dipole moment. The atom-resolved DOS was obtained for the bare ideally-terminated surface and for the same surface with θCs = 0.25 ML. Both are metallic, but the latter less so (with a smaller DOS at EF) as a consequence of the net reduction in unpaired electron density in Ga DBs that results from electron transfer from Cs to the surface. Optical properties were evaluated via computation of the imaginary part of dielectric function (Ref. [606(abstract only)]), and the absorption and reflectance spectra are seen to shift to lower energy after Cs adsorption. Somewhat different results are found [605] for Cs on the (0001̄ ) surface. Here H3 is the most stable site for θCs = 0.25 ML, with ΔEads = −3.88 eV, but the others are close in energy, the highest being T1 with ΔEads = −3.59 eV. With increasing θCs, ΔEads decreases monotonically in magnitude but remains exothermic at 1.0 ML, which is attributed to a strong Cs-N interaction, and ϕS also

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decreases monotonically. The difference in the behavior of ϕS vs. θCs shown by (0001) and (0001̄ ) is found to result from the larger electronegativity of N vs. Ga, which causes the Nδ−-Csδ+ dipole moment to increase in magnitude up to 1 ML. Ji et al. [607] considered the effect of VGa and VN (one per (2x2) SUC) on the properties of Cs on the (0001) surface. The computational methods were essentially the same as those used by Du et al. [604,605] as described above. Before introduction of Cs, the distance between the Ga terminating layer and the N first-underlayer is found to be 0.272 Å for VGa and 0.436 Å for VN vs. 0.653 Å with no defect and 0.647 Å in the bulk. In the case of VGa the effect is shown to result from an increase in the covalent interaction between the Ga and N layers and in the partial ionic charges on some of the Ga and N. However, for VN the covalent interaction and the partial charges are decreased relative to the non-defective surface, which does not account for the reduced interplanar spacing. Here the smaller reduction in interplanar spacing, relative to the pristine surface, is ascribed to unspecified dipolar effects. For VGa the most stable site for Cs is directly above the vacancy; whereas, for VN it is in a bridge site between two Ga atoms. However, with VN the difference in ΔEads among the various sites (excluding H3) is small (at most 0.09 eV). The most stable Cs site with VGa (ΔEads = −1.89 eV) is lower in energy than the most stable site with VN (ΔEads = −1.57 eV), and in either case ΔEads is exothermic for all adsorption sites but less so than on the nondefective surface (ΔEads = −2.04 eV). Shen et al. [608–610] and Su et al. [611] performed extensive theoretical studies of the adsorption of Cs on GaN (0001) and on Al0.25Ga0.75N (0001) and also of Cs+O co-adsorption on GaN (0001) with an interest in understanding photocathode activation. Only the results for O-free Cs/GaN are within the scope of the present review. These repeat those of Du et al. [604,605] in that ΔEads = −2.02 eV (−2.04 eV) is found for Cs in an H3 site (bridge between two N atoms), and the computed behavior of ϕS vs. θCs is the same as in previous work. Strak et al. [612] reported theoretical studies of the (0001) and (0001̄ ) surfaces both bare and with various coverages of Cs. The 2DPS consisted of 24 Ga-N bilayers (termed "double atomic layers") and a (4x4) SUC. The Ga 3d orbitals were included as valence states, and the PBE functional was used. In order to improve the accuracy of Eg relative to pure LDA or GGA results, a "half-occupation" method was employed to correct for self-interaction. This gives values of Eg for AlN, GaN and InN that agree very well with experiment. On the (0001) surface, Cs adsorbs in T1 sites up to θCs = 0.5 ML followed at higher coverage (up to 1 ML) by the formation of a second layer of Cs. At lower θCs, up to about 3/8 ML, the adsorbed Cs is ionized, and the resulting Gaδ−-Csδ+ dipole lowers ϕS by about 3.5 eV relative to the bare surface. At higher θCs, ϕS increases and above 0.5 ML becomes that of bulk polycrystalline Cs (2.14 eV [615]), which indicates a metallic layer. The results are qualitatively consistent with the dependence of ϕS on θCs observed by Eyckeler et al. [512] and by Benemanskaya et al. [602,603] for nGaN. Somewhat different results are obtained for the (0001̄ ) surface, which is ascribed to the higher electronegativity of N vs. Ga and its effect on Cs ionization. Here the H3 is the favored site for Cs adsorption up to 0.25 ML; whereas, at higher θCs the repulsion between Cs ions leads to a complex structure with Cs in a single layer but displaced from H3 sites. Up to θCs = 3/4 ML, Cs ions form with the released electron transferring to partially-filled N DBs, which decreases ϕS by as much as ∼3.5 eV. According to the ECR, the N DBs are all doubly occupied at θCs = 3/4 ML at which point ϕS increases with further addition of Cs. 5.11. Chlorine The interaction of Cl with the GaN (0001) surface has been

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studied experimentally by Lai et al. [155] and by Kuwano et al. [616], motivated by the importance of Cl and chlorinated reagents in etching. Lai et al. [155] used XPS and LEED to investigate the adsorption of Cl2. Clean surfaces were prepared by IBA (1 keV Ar+, 823 K anneal) and were described above (Section 3.3.4) in connection with their systematic IBA studies. Briefly, the clean surface shows a substantial coverage of metallic Ga and a high-background, but unfaceted, (1x1) LEED pattern. The XPS data were obtained with high surface sensitivity using appropriately-chosen values of hν provided by a synchrotron radiation source, and the Cl2 exposures were done using a pinhole molecular-beam doser [617] with the sample at 100 K. Exposure to Cl2 removes the metallic-Ga feature from the Ga 3d spectrum and leaves a complex structure suggesting several overlapping components. However, the N 1s is relatively unaffected, except for a loss in intensity, which implies that only Ga-Cl bonds are formed. The Cl 2p3/2 spectrum shows two peaks, with BEs of 199.4 and 200.6 eV, which are assigned to GaClx and adsorbed Cl2 respectively. Annealing at 133 K leads to a loss of Cl2 due to the combined effects of desorption and reaction with the surface, the latter being seen as an increase in the GaClx component in the Ga 3d spectrum. At successively higher temperatures (up to 873 K) the GaClx desorbs, and, ultimately, a Cl-free surface with a residue of metallic Ga is obtained. This residue, which is much less than what is present on the initial IBA surface, can be further diminished by additional cycles of Cl2 adsorption and annealing. For comparison, results were also obtained for surfaces prepared with IBA using nitrogen, rather than Ar+, ions. In this case much less metallic Ga is seen in the clean-surface Ga 3d spectrum, which is dominated by bulk GaN with an additional satellite at lower BE that is ascribed to surface atoms (presumably Ga adatoms). Reaction with Cl2 leads to a shift to higher BE due to the presence of unresolved GaClx components, which are gradually desorbed with increasing annealing temperature. The N 1s XPS shows a weak satellite at higher BE, that is assigned to NClx species formed by the chlorination of surface N atoms. Presumably these are more accessible on a surface without a metallic-Ga overlayer. The Cl 2p XPS, after adsorption at 100 K on the nitrogen-IBA surface, is dominated by molecular Cl2, which indicates that this surface is less reactive than the Ar+-IBA surface possibly as a result of the lower metallic-Ga coverage. There appears to be a fundamental difference between the two types of surfaces (i.e., Ar+ vs. nitrogen-ion IBA) as to the GaClx species formed in that those on the Ar+ surface are more volatile and desorb at lower temperatures. It is suggested that predominantly GaCl is formed for nitrogen-ion IBA; whereas, GaCl2 and GaCl3 are produced for surfaces cleaned by Ar+ IBA. Kuwano et al. [616] used STM and RHEED to study the adsorption of Cl atoms. The surface was cleaned in situ by heating at 670±30 °C in a radio-frequency N2 plasma, followed by deposition of Ga at 360 °C, which gave a pseudo-(1x1) RHEED pattern identified with a Ga bilayer similar to that seen in MBE under Ga-rich conditions. Exposure to Cl was done in situ using a CdCl2 electrochemical cell, and etching reactions were promoted by heating either during or after exposure. It should be noted that this study involves exposure to Cl atoms; whereas, that of Lai et al., discussed above, employed Cl2. Under the conditions used in the present study, a 10-min Cl exposure at 645 °C removes the metallic Ga bilayer, which had an estimated initial coverage of 1.8 ML, and leaves a surface with alternating smooth and jagged bilayer steps. Up to 670 °C, etching occurs via reaction at the step edges, which is more rapid at the jagged edges where N atoms have 2 DBs and are thus very reactive. A (1x1) RHEED pattern is seen for a surface that has undergone etching at step edges. When the sample is heated at ≥680 °C

during Cl exposure, triangular etch pits (with a depth of 1 bilayer) and also triangular islands are seen. This indicates that reaction is occurring on the terraces by incomplete removal of Ga-N bilayers, which leads to increasing surface roughness. For comparison, a surface described only as "N-rich" was also studied. In this case no steps or pits are observed after heating at 680 °C in a Cl flux. This was explained in terms of preferential adsorption of Cl at Ga surface sites, which means that the "N-rich" surface does not support a sufficiently-high coverage of adsorbed Cl to maintain the steadystate formation of volatile GaClx species and the release of N2. The proposed model suggests that it is necessary to remove one or more Ga ligands from each of a pair of nearest-neighbor N atoms in order for N2 to be formed. 5.12. Chromium The adsorption and diffusion of Cr on GaN (0001) has been investigated theoretically by González-Hernández et al. [618], motivated by the possible use of transition-metal-doped GaN as a dilute magnetic semiconductor. The calculations were spin-unrestricted and used the PBE functional together with USPPs, and the Cr 3d and Ga 3d electrons were treated as valence electrons. The 2DPS comprised 4 Ga-N bilayers with the bottom layer terminated with PHs and a (2x2) SUC having one adatom per cell. During geometry optimization the lower two bilayers were fixed in the bulk-lattice configuration while the upper two and the adsorbed Cr were allowed to relax. Adsorption at the T4 site is somewhat more favorable than at H3 (ΔEads = -3.003 eV for T4 vs. -2.948 eV for H3) but much more favorable than at T1 (ΔEads = -1.743 eV). The small preference for T4 over H3 is attributed to a weakly-attractive interaction with the first-underlayer N atom. The magnetic moment per SUC with adsorbed Cr is 2.98 μB vs. 6 μB for the free atom, which is attributed to the charge transfer of 0.178 |e| from GaN to Cr that reduces the unpaired spin density. Recalling that, on the bare surface, there are three unpaired electrons per (2x2) cell in Ga DBs, one can suggest a simple qualitative interpretation in which three spin-up electrons on Cr pair with three spin-down Ga electrons to form three Cr-Ga back-bonds leaving a net magnetic moment of 3 μB per SUC. The diffusion barrier from H3 to T4 is about 0.40 eV (which is very close to the barrier computed for a Ga adatom) and slightly less than the barrier from T4 to H3, which reflects the greater stability of T4 vs. H3. The transition state in the diffusion process has Cr occupying a Br site (Fig. 1b). It is suggested that the finite diffusion barrier means that it will be possible to prepare a surface with a stable Cr adlayer. The clean but unreconstructed (0001) surface shows a band of metallic states at EF due to the partially-filled Ga DBs. Adsorption of Cr saturates these DBs and introduces additional states in the gap but below EF, which indicates a semiconducting surface. Within the gap, the majority-spin states are due to Cr orbitals and the minority states to Ga DBs. 5.13. Cobalt The interaction of Co with GaN (0001) has been studied experimentally by Li et al. [619–621] using LEED, STM, XRD, TEM and EDAX and theoretically by González-Hernández et al. [618], Li at al. [620] and Qin et al. [622]. The interest is in the possible use of ordered layers of magnetic metals in spintronic applications. Li et al. [619] used samples grown in situ by MBE, for which two starting surfaces were obtained. These are the "(1x1)" (or pseudo(1x1)), which involves a Ga bilayer on the Ga terminating layer of the GaN lattice, and a (1x1) consisting of only a single Ga adlayer that is obtained by annealing the "(1x1)" in UHV [358,359]. Depositing Co on the "(1x1)" at RT leads initially to a disordered layer that, with increasing thickness, develops into two sets of

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hexagonal patterns both of which are consistent with bulk Co. One corresponds to Co (111) aligned with the GaN substrate and the other, for which the LEED beams are more intense, to a 30° rotation of the Co lattice. The rotation has the effect of reducing the lattice mismatch between Co and GaN. On the other hand, deposition on the (1x1) surface at RT leads initially only to a Co (111) lattice aligned with the GaN for which the LEED pattern becomes better defined with increasing thickness. The STM data for the two samples show, for Co on "(1x1)", a rough surface consisting of rotated and non-rotated islands and, for Co on (1x1), a relatively smooth and compact surface. Both types of samples were further investigated after in-situ annealing at 600 °C. For "(1x1)" the as-deposited film is mostly HCP with some evidence of an FCC component; whereas, after annealing, the FCC structure dominates. For (1x1) on the other hand, the HCP structure remains dominant, which indicates the absence of the Martensitic HCP→FCC phase transition that occurs for bulk Co at ∼400 °C. It was suggested that this results from a stronger interfacial bonding in the case of (1x1). Although XRD gives no indication of interfacial reaction leading to new crystalline phases, TEM shows a more disordered interface after annealing, and EDAX reveals the presence of Ga and N in the Co layer. The magnetic properties of the various samples were also described. In another study, Li et al. [620] performed further STM and LEED experiments for Co on the "(1x1)" surface. For 0.14 ML of Co, STM reveals 2D islands with a height of ~1.6 Å, which is slightly less than the c-axis lattice constant of HCP Co (~2 Å). The coverage of these islands is 0.42 ML, i.e., 3X higher than that of the Co deposition, which is ascribed to formation of a CoGax alloy via reaction with the substrate. Increasing the coverage to 0.2-0.4 ML leads to a two-domain rotational superstructure described as (√7x√7)R±19.1°. The structure is complex, and a further theoretical analysis (described below), shows that it results from Co3 trimers located slightly below the uppermost Ga adlayer. Subsequently Li et al. [621] studied macroscopic defects in the Co layer and their dependence on the initial GaN surface structure using SIMS in addition to the methods employed in earlier work. For the "(1x1)" GaN surface, the Co film is seen in STM to have a step-and-terrace morphology consistent with the growth of 2D islands, which also exhibit stacking faults and screw dislocations. Additionally, some FCC islands are found among the majority HCP islands. Annealing to 1000 K, to promote the Martensitic phase transition, leads to FCC islands with a high density of stacking faults. For (1x1) the step-and-terrace structure is not seen, which may indicate a lower Co mobility than for the "(1x1)", and annealing to 1000 K leads to a smoother surface with few stacking faults. A lower mobility would be consistent with a stronger interfacial bonding in the case of the (1x1). However, triangular pits are found, which are attributed to desorption of Co from highenergy sites, and a (√3x√3) reconstruction of uncertain origin appears in LEED. For both "(1x1)" and (1x1), TEM shows a disordered interface beneath a well-ordered FCC Co film, which indicates that the Martensitic transition is not reversed when the sample is cooled rapidly after annealing. Here the (1x1) result differs somewhat from that given earlier [619], where the phase transition was not seen after annealing at a lower temperature (600 °C). Small amounts of Ga and N are seen in the Co using SIMS and EDAX. These are probably present as dilute solutions since no evidence of CoGax or CoNx compounds is seen. Li at al. [620] performed theoretical studies of Co3 trimers in order to understand their experimentally-observed (√7x√7)R ±19.1° superstructures. The PAW method was used with the PBE functional and a 2DPS with 6 Ga-N bilayers. The bottom-surface DBs were saturated with PHs, and the top surface was covered with a laterally-contracted Ga bilayer to model the "(1x1)" structure. A (√7x√7) SUC was used with either Co or Co3 in various

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high-symmetry sites, and the upper three Ga-N bilayers were relaxed along with the Ga adlayers and the adsorbed Co. Two Co3 structures, in which the Co atoms lie in either T4 or H3 sites and slightly below the outermost Ga adlayer, are found to be the most stable at any allowed value of μCo. The choice of μGa (or equivalently μN) was unspecified; although, the conditions were presumably Ga-rich in order to maintain the metallic-Ga bilayer. These Co3 structures are essentially degenerate in energy and are more stable than any isolated-Co configuration. The theoretical methods used by González-Hernández et al. [618] have been described previously in the discussion of their Cr results. Cobalt is slightly more stable in the H3 site than in the T4 but much more so than in the T1, with ΔEads values of -4.000, -3.906 and -2.286 eV respectively. The preference for H3 over T4 is ascribed to Co-Ga bonding being more energetically favorable than Co-N bonding, so that Co tends to avoid the T4 site where it lies above a first-underlayer N atom. The magnetic moment per (2x2) cell with one Co in an H3 site is 1.41 μB vs. 3 μB for the free atom, where the reduction is attributed to a transfer of electron density (0.097 |e|) from the Co to the surface Ga. (The value of 1.41 μB for the H3 site is taken from Fig. 2b of Ref. [618]. There is a typographical error for the corresponding entry in Table I of this reference.) Presumably a large contribution to the decrease in magnetic moment derives from the pairing of Co and Ga DB orbitals to form bonds. The T4→H3 diffusion barrier is about 0.40 eV, which is close to that for a Ga adatom, and about 0.5 eV for H3→T4, which reflects the greater stability of H3 vs. T4. The DOS shows that a single Co adsorbed in a (2x2) SUC essentially saturates DBs on the surface Ga. Empty majority-spin (filled minorityspin) states derived from Ga (Co) orbitals appear at EF but with only a small DOS. Qin et al. [622] carried out theoretical studies for Co substitution on a bare (0001) surface with a (2x2) SUC and on a surface with a Ga bilayer and a (√3x√3) SUC. The PAW approach was used with the PBE functional and a 2DPS having four Ga-N bilayers with DBs on the bottom layer saturated with PHs. The upper three bilayers and the Ga and Co adlayers were allowed to relax. For the bare (0001), substituting Co for a single surface Ga is endothermic by 2.94 eV but less so than substituting for N (5.84 eV) or forming an interstitial (4.52 eV). With increasing θCo up to 1 ML, ΔEf for substitution continues to be less endothermic for surface vs. subsurface Ga sites. For the structure terminated in a Ga bilayer, Co substitution up to 1.33 ML favors Ga sites in the outermost adlayer. Hence, for either structure, Co substituting for Ga is least unfavorable for Ga in the outermost layer. However, these results apply to the total energies for substitution and not site exchange since no mention is made of the fate of any displaced Ga. For the bare (0001) under growth conditions that are very N- and Co-rich, substitution of 2, 3 or 4 Co per (2x2) SUC is exothermic with 4 Co per cell leading to the most stable structure. On the other hand, for the same surface under less N-rich conditions, substitution is endothermic for any θCo. For a surface with a Ga bilayer, Co incorporation is exothermic when substituting for 1, 2 or 3 Ga per SUC in the outermost layer but only under very Ga- and Co-rich conditions. The structure with 3 substitutions is barely stable while the others are nearly degenerate and lower in energy. The magnetic characteristics of the Co-doped surfaces were further discussed and analyzed with the aid of DOS calculations and spinand charge-density plots. In summary, the interaction between Co and GaN (0001) depends on the composition of the initial surface and is controlled by the nature of the Ga adlayer, being stronger for a (1x1) with only a single adlayer. There appears to be an interfacial reaction at elevated temperature, since both Ga and N are seen in the Co layer. However, for Co deposited in situ on MBE samples, the reaction is limited since only a dilute concentration of Ga and N is found. This

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is supported by theoretical results showing that Co substituting for Ga is favorable only under certain conditions and then only in the Ga adlayer or in the terminating bilayer of the substrate. 5.14. Copper Copper on the GaN (0001) surface has been studied experimentally by Dumont et al. [623] using XPS and AES, and theoretical results have been reported by Nieto et al. [624] for the (0001) and by González-Hernández et al. [625] for the (0001), (112̄ 0) and (101̄0) surfaces. The main interest was in the properties of the metal/GaN contact and also in the magnetic characteristics of the Cu-doped surface. In the experimental work, n-type MOVPE samples were prepared by wet-chemical cleaning followed by different procedures in UHV, which included annealing and exposure to atomic H (generated by a plasma source) or to a Ga flux. Wet-chemical cleaning, by either immersion in first KOH then aqua regia or immersion in boiling HNO3, did not eliminate all impurity C and O even when followed by annealing at 900 °C in UHV. The optimum procedure was found to be a combination of atomic H to remove C and a Ga flux (with the sample at 950 °C) to remove O. The final surface showed little or no C or O and an upward BB of about 0.9 eV. During Cu deposition no changes are seen in any of the GaN or Cu XPS lineshapes, which indicates a non-reactive interface. The film growth is described in terms of a modified Stranskii-Krastanov process involving growth of hemispherical islands on top of an incomplete 2D layer having an abrupt interface with the substrate. The attenuation of the GaN XPS peak intensities vs. Cu coverage indicates that the density of the Cu layer is less than that of bulk Cu. This suggests that the structure, and therefore the density, is probably determined by interaction with the substrate, which implies some form of bonding at the interface. The SBH is found to be 0.84 eV in agreement with the prediction of MIGS theory (Section 6). Nieto et al. [624] studied Cu on GaN (0001) using the PBE functional and a 2DPS with four Ga-N bilayers and a bottom surface terminated with PHs. A (2x2) SUC was used, and the upper two bilayers and the adsorbate were allowed to relax. The H3 site is the most favorable for adsorption of one Cu atom per cell (ΔEads = -3.45 eV) but only slightly more so than the T4 and the Br (ΔEads = -3.32 and -3.38 eV respectively). The T1 site, on the other hand, is much less stable (ΔEads = -2.7 eV). With θCu up to 1 ML, the ordering of energies generally remains the same (except for the relative Br energy); however, the differences depend on θCu, and ΔEads for the most stable sites decreases in magnitude somewhat with increasing θCu. For up to 1 ML, incorporation into the substrate is found to be least unfavorable (endothermic) when Cu substitutes for Ga in the surface layer vs. in the second Ga-N bilayer, which suggests that Cu will tend to accumulate at the surface rather than diffusing into the bulk. However, the results apply to substitution rather than site exchange since there was no mention of the fate of any displaced Ga. Results are also given for Cu adsorption on a surface with a laterally-contracted Ga bilayer on top of the (0001) Ga terminating layer, for which a (√3x√3) SUC was used. Here again, Cu substitution is least unfavorable in the outermost layer of the Ga bilayer. The substitution energies were also calculated as functions of μGa, and the results show that the process is favorable only under N-rich or moderately Ga-deficient conditions and only for one Cu substitution per (2x2) SUC. For moderately Ga-rich conditions, adsorption of Ga at a T4 site is more favorable, while for more Ga-rich conditions formation of a pristine Ga bilayer is slightly more favorable than substituting a Cu for Ga in the outermost Ga adlayer. The DOS shows that partially-filled Ga DBs on the bare surface are saturated by the adsorption of one Cu per

(2x2) SUC; however, new states appear at or very near to EF that are composed of overlapping Cu and Ga orbitals. González-Hernández et al. [625] studied Cu on the (0001), (112̄ 0) and (101̄0) surfaces under conditions that are both Ga- and Cu-rich using the PAW method with the PBE functional. For (0001) the 2DPS consisted of four Ga-N bilayers of which the lower two were fixed in the ideal bulk-lattice configuration with DBs on the bottom surface terminated with PHs. For the non-polar (112̄ 0) and (101̄0) surfaces the 2DPS comprised 11 and 16 Ga and N layers respectively, and in this case the central layers were fixed while the others were allowed to relax in order to facilitate the computation of surface energies. For (0001) and (101̄0), Cu substituting for Ga is much less endothermic than substituting for N or forming an interstitial; whereas, for (112̄ 0) under the same conditions, Cu replacing N is somewhat less endothermic than replacing Ga. This description is based on the results in Table 1 of the original reference, which in the case of the (112̄ 0) surface differ from the text. In all cases, ΔEf for Cu substitution is less endothermic in the surface layer than at subsurface sites. It is also found that ΔEf is much less endothermic on the (0001) than on the other surfaces and that the magnetic moment of a Cu substituting for Ga is 0.00 and 0.95 μB per SUC respectively on the (0001) and (101̄0) surfaces, while Cu replacing N on the (112̄ 0) has a moment of 0.00 μB per SUC. The surface magnetic characteristics were analyzed in detail using partial-DOS results. There appears to be general agreement between theory and experiment that Cu adsorption occurs easily but that reaction at the interface leading to incorporation in the surface layer is unfavorable other than under certain growth conditions. Mention is also made here of the theoretical work of Kang and Lee [626] on the magnetic moment of Cu on the surface and in the bulk of GaN, which is outside the scope of the present review. 5.15. Europium Europium on GaN (0001) has been studied experimentally by Maruyama et al. [627] using PL, XPS and RPES with an interest in understanding the effects of surfaces on the luminescent properties of rare-earth-doped GaN. Samples were grown by MBE and Eu-doped in the bulk at concentrations from 0.1 to 16.6 atomic-%. Sample preparation consisted of nitrogen-ion bombardment until no C or O was detectable in XPS. The PL data, which are bulksensitive, show only Eu+3 emission, which peaks in intensity at 2.2 at.-%. However, surface-sensitive XPS shows Eu 3d5/2 peaks, with approximately equal intensity, for Eu+3 and Eu+2. The RPES experiment was performed by recording the VB for different hν using a synchrotron radiation source. These data show a peak at BE = 3.3 eV that exhibits a strong enhancement at hν = 140 eV, which is assigned to excitation of the 4f7 level of Eu+2 undergoing a 4d→4f resonant enhancement. For Eu+2, this process can be described as 4d104f7 + hν(140 eV) → [4d94f8]* → 4d104f6 + e− where [...]* represents a transient excited state. It is concluded that essentially all the Eu in the outermost two layers of GaN is in the +2 state, which is ascribed to a reduced coordination number at the surface. With fewer anion nearest-neighbors than in the bulk, Eu near the surface is less stable in the higher oxidation state. 5.16. Fluorine The adsorption of F on GaN (0001) has been studied experimentally by Bermudez [628] using UPS, XPS and XAES. The interest was in understanding the role of F in etching, particularly in chemically-assisted ion-beam etching. Surfaces of MOCVD GaN were cleaned by IBA (nitrogen ions, with annealing at ∼900 °C), and no impurity C or O was detected after annealing; although, before annealing, impurities at a level of

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Fig. 42. Ga 3d XPS data (a) F-saturated GaN (0001)-(1x1) and (b) ion-bombarded GaN dosed with XeF2. In either panel, the upper trace shows data (points) after deconvolution of the instrument response function. The lines show the results of least-squares fitting a sum of Gaussian-broadened Lorentzians and a polynomial background. For display, the resulting background has been subtracted from both the data and the fit, which have been displaced vertically for clarity. The resolution in the processed data is about 0.6 eV. The lower trace in either panel shows the spectrum of residuals (fit minus data, not statistically weighted) multiplied by a factor of 5 relative to the data. The zero-level for the residuals is indicated. For the ordered surface the BE of the main peak is 21.107 0.05 eV, relative EF, after F adsorption. The arrow labeled "clean" marks the Ga 3d peak position on the clean surface. In (b), "GaAs" marks the approximate Ga 3d position in that material and "GaF" and "GaF3" the positions for those species, based on F/GaAs data. Note that these are not peak assignments for the GaN data. From Bermudez [628] (Copyright 1997, reproduced with permission from Elsevier).

o0.03 ML were sometimes observed via electron-excited AES. Surface-sensitive Ga 3d XPS data were obtained using Zr Mζ excitation (hν = 151.65 eV [570]). Fluorine was adsorbed by exposure to XeF2 vapor using a pinhole molecular-beam doser [617], and care was taken to assure that no significant desorption of F occurs as a result of irradiation by the ultraviolet or x-ray excitation source. Saturation, at a coverage of θF ≈ 0.67 ML, occurs for a dose of about 2 XeF2 per surface atom at RT, indicating a high reaction probability. The coverage obtained for a damaged surface, i.e., one that was not annealed after ion bombardment, is significantly higher. This was attributed to the presence of highly reactive broken Ga-N bonds, rather than to a difference in stoichiometry, since little or no such difference is seen in electron-excited AES. The F 1s XPS shows two peaks, separated by 3.4±0.15 eV. Based on the modified Auger parameter and on the structure of the F KLL spectrum in XAES, the lower-BE peak (which is also the more intense) is assigned to F bonded to Ga in an ionic "GaF3-like" species. The assignment of the second peak is uncertain, and it was speculated that the doublet structure might arise from a BE difference for F on the edges vs. on the inside of fluorinated islands. A lower F 1s BE would be expected for F surrounded by other F, as on the inside of a GaFx island, since the core hole would be screened more effectively than at the periphery of the island. In the surfacesensitive Ga 3d XPS, an F-induced satellite appears at ∼0.9 eV higher BE than the GaN peak, as shown in Fig. 42. Based on a comparison with results for F/GaAs, this is assigned to a GaFx

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species having an average composition of (2≤x≤3). As can be seen in Fig. 42, the BE shift for GaF1 would be too small for it to be separated from the GaN Ga 3d peak. The appearance of such GaFx (x 42) species for θF o 1 ML suggests that fluorinated patches are formed, which implies that a GaF1 site is more reactive than a bare Ga site. In XPS, both the N 1s and bulk Ga 3d component (Fig. 42) show a rigid shift of 0.60 eV to higher BE, relative to the clean surface, after F saturation that indicates a reduction in upward BB for the n-type sample. The final position of EF is 3.34±0.06 eV above the VBM, which indicates that the bands are essentially flat. This is attributed to an emptying of occupied surface electron traps by the F atom. More precisely, adsorption of F passivates electron traps on the clean surface and allows the trapped electrons to return to the depleted SCL, thus eliminating the BB. The electron trap in this case is a Ga DB, which is passivated by the formation of a Ga-F bonding orbital that appears in UPS at ∼5 eV below the VBM. A state derived from F 2p orbitals has also been found at about 5 eV below the VBM in a theoretical study of an interstitial F impurity in bulk GaN by Janotti et al. [629]. Thermal desorption of F begins at about 550 °C and is essentially complete at 750 °C, at which point the BB returns to the initial clean-surface value. Similar results were obtained by Rickert et al. [84] for n-GaN surfaces after immersion in aqueous HCl solution. With adsorbed Cl, EF is 3.34 eV above the VBM (based on a Ga 3d BE of 21.1 eV) but shifts to ∼2.5 eV above the VBM after thermal desorption of the Cl. The untreated sample shows EF-VBM = 2.9 eV, based on a Ga 3d BE of 20.7 eV. 5.17. Gadolinium The adsorption of Gd on the MOCVD GaN (0001) surface was studied by Xiao et al. [613] using UPS, XPS and LEED. The interest was in contact formation and in the luminescent properties of rare-earth-doped GaN. Clean surfaces were prepared by IBA (0.6 keV nitrogen ions, 1100 K anneal), after several cycles of which a clear (1x1) LEED pattern was observed. The clean n-type surface exhibited an upward BB of 0.9 eV with χ = 3.3 eV. Deposition of Gd on the RT substrate leads to layer-by-layer (Frank-van der Merwe) film growth. Initially the Gd 4d5/2 appears at a BE of 143.0 eV and then gradually shifts to 141.6 eV with increasing θGd. Of this 1.4 eV difference, 0.6 eV arises from an increase in upward BB with θGd (since it is also seen in the bulk-GaN Ga 3d) and 0.8 eV from the growth of metallic Gd. The higher BE seen for the initial deposit indicates cationic Gd formed by an interfacial reaction. Concurrent with this, the Ga 3d develops a low-BE shoulder, characteristic of metallic Ga, which indicates that Ga is present in the Gd matrix. The interfacial reaction appears to be thermodynamically driven since the estimated ΔHf for GdN is -78.3 kcal mol-1 vs. -25 kcal mol-1 for GaN. The reaction leads to an interface consisting of GdN, Ga and some form of GaxGdyN alloy, which acts a diffusion barrier that prevents further reaction at RT. The SBH is found to be 1.5 eV, which is larger than the predictions of MIGS or Cowley-Sze theories, both of which assume an ideal interface with no reaction. Annealing at temperatures up to 1000 K is seen to increase the extent of the reaction, yielding a thicker mixed layer with less metallic Gd and a smaller SBH. 5.18. Gallium There is an extensive literature on the interaction of Ga with various GaN surfaces due to its importance in growth. The present section involves mainly those studies that focus on the interaction and bonding between Ga adatoms and the GaN surface, including some that address adsorption, desorption and adatom mobility. References dealing largely with Ga desorption in relation to

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surface stability and decomposition were discussed in Section 4.5. Work addressing Ga adsorption mainly in the context of surface reconstruction was described in Sections 4.6 and 4.7. However, there is necessarily some overlap between this discussion and those in earlier sections. Given the focus of the present review, results pertaining mainly to GaN growth will be excluded. For a Ga density of 5.91 gm cm-3, 1 Å = 5.105x1014 Ga cm-2 = 0.450 ML. Within the stated context, experimental studies of the (0001) and (0001̄ ) surfaces are described in Refs. [630–650] and [478,511,639,640,651] respectively. Results for (101̄0), (112̄ 0) and (112̄ 2) surfaces are reported in Refs. [404,405,647,648], [648,652] and [653] respectively. Theoretical results are given for the (0001), (0001̄ ) and (112̄ 2) surfaces in, respectively, Refs. [372,566,576,577,654–661], [654-657,662] and [426], and theoretical results for the non-polar (101̄0) and/or (112̄ 0) surfaces have been reported in Refs. [576,577,656,663,664]. It is also noted in passing that superconductivity, with a transition temperature as high as 5.4 K, has been observed [650] for a Ga bilayer on GaN (0001). Beginning with experimental results for Ga/GaN (0001), Guha et al. [630] measured the lifetime of Ga adatoms vs. T (685-750 °C) on a (0001) surface grown in situ using MBE and found ΔEa = 2.2 ±0.2 eV for desorption. Care was taken to avoid θGa 4 1 ML so that the result reflects the interaction between Ga and the substrate rather than evaporation from Ga droplets or from a bilayer. A rate of loss of Ga due to substrate decomposition of 3-4 ML min-1 was found at 830 °C, which is much lower than that shown in Fig. 10. This might result in part from a difference in temperature measurement. Klauser et al. [631] performed UPS studies of Ga adsorption on GaN substrates prepared by solvent "degreasing" followed by immersion in 30% NaOH solution and annealing in UHV at 500 °C. The resulting surface showed no O but some C, and the Ga 3d XPS for θGa = 1.5 ML showed evidence for metallic Ga, possibly in the form of clusters. The Ga 3d spin-orbit splitting (∼0.45 eV [437]) can be partially resolved for metallic Ga because the phonon broadening is less than for partially-ionic GaN [438]. Pavlovska and Bauer [632] used LEED and LEEM to study Ga wetting layers on the (0001) surface of samples grown by MBE on either SiC or MOCVD GaN substrates. The latter substrates were cleaned in situ by exposure at 675 °C to nitrogen from the plasma source, which resulted in a (√3x√3) LEED pattern. As noted in Sections 4.6 and 4.6.1, this structure has sometimes been observed in other work on the (0001) surface. In the present study, deposition of Ga at o200 °C on such homoepitaxial GaN layers, followed by annealing at up to 700 °C, leads to (2x2), (6x1), (1+1/6) and (1+1/12) structures with increasing θGa in the 0.3 to 2.0 ML range. These were reported previously by Smith et al. [339,340]; however, others (namely the (2x1), (5x5) and (6x4)) were not found, which is attributed to differences in the clean-surface structure. The thermal stability of the different structures, and particularly the (1+1/6) ↔ (1+1/12) interconversion, were studied in detail. The LEED data also indicate that wetting by Ga, which leads to the higher-coverage (1+1/12) structure, is more complete on smooth areas of the surface, and it was further suggested that strain in the heteroepitaxial GaN/SiC samples has an effect on the structure of Ga adlayers. The LEEM data indicate that the (1+1/6) ↔ (1+1/12) interconversion results from a structural change in the Ga adlayer with no change in θGa; although, this interpretation appears to conflict with the conclusion that the (1+1/12) corresponds to a higher θGa. During growth, LEEM indicates that a double-layer of excess Ga is needed to avoid surface roughening, in agreement with numerous other MBE results showing a Ga surfactant effect. A specific model was proposed for this effect. The surface energy on the bare surface is determined by ionic interactions, which favor the non-polar surfaces and lead to roughening via the

formation of pyramidal structures with non-polar faces. The metallic Ga bilayer, on the other hand, stabilizes the (0001) by reducing the importance of such ionic interactions, thus allowing the 2D growth of a smooth surface. Such an effect could act in concert with the surfactant effect exhibited by a metallic Ga bilayer, wherein the mobility of N atoms is increased. Mula et al. [633] and Adelmann et al. [634–637] used primarily RHEED to conduct extensive studies of the growth of Ga layers on GaN (0001) as a function of temperature and Ga flux. This work relates mainly to MBE growth of GaN, which is outside the scope of the present review, but such information could be very useful in understanding and optimizing surface cleaning by annealing in a flux of Ga vapor (Section 3.2.1). At a typical MBE temperature of 740 °C, a Ga flux of ≤0.2 ML sec-1 yields θGa ≤1 ML. At 0.2 ML sec-1 (BEP ≈ 1x10-6 Torr [144]) there is an abrupt and discontinuous transition from θGa = 1.0 to 2.5 ML that is consistent with a laterally-contracted Ga bilayer (Section 4.6.1). This persists up to a flux of 0.72 ML sec-1 above which Ga droplets form [637]. Quantitative interpretation of the results required the use a temperature-dependent activation energy in the kinetic analysis. Later work by Bruno et al. [649], discussed below, showed that the Wolkenstein theory of adsorption can fit the data with a constant ΔEa. Barinov et al. [638] used photoelectron microscopy to observe the effect of an electric field on the mobility ("electromigration") of Ga adsorbed on GaN (0001) cleaned by IBA (500 eV nitrogen ions, 800 °C anneal). The results demonstrate the importance of vacancies and trapping centers in Ga diffusion. The high spatial and energy resolution also allows accurate observation of the different Ga 3d BEs for metallic Ga (18.8 eV) vs. Ga adatoms (19.2 eV) and bulk GaN (20.5 eV) as well as the lesser degree of broadening for the metallic Ga 3d as noted above. Several groups have studied Ga adsorption and desorption on GaN (0001) under MBE conditions. Koblmüller et al. [639–642] and Brown et al. [643] used mass spectroscopy and RHEED to observe the morphology and coverage of Ga adlayers vs. temperature and Ga flux. At a sufficiently low temperature, θGa increases continuously with Ga flux to 2.4 ML, characteristic of the laterally-contracted bilayer, followed by droplet formation at higher flux (Fig. 43). The bilayer consists of 1.0 ML of Ga in the bottom layer and 1.4 ML in the top layer in agreement with theoretical results. This differs somewhat from earlier work [637], based on RHEED alone, that showed a discontinuous increase in θGa from 1.0 to 2.5 ML at a certain critical flux. In Ref. [643], there is a rapid but continuous increase in θGa to 2.4 ML as the Ga flux increases to ∼1.2 nm min-1 at 681 °C, above which θGa remains nearly constant until droplet formation begins at ∼2.4 nm min-1. Here 1 ML is defined as 0.259 nm (the Ga-N bilayer thickness); hence, 1.2 nm min-1 = 0.077 ML sec-1 for this definition of an ML or 0.090 ML sec-1 with 1 ML defined as 1 Ga per surface lattice site. The fluxes used appear to be reasonably consistent with those employed by Adelmann et al. at a somewhat higher temperature. Different desorption kinetics are also found for the first and second layers of the Ga bilayer and for Ga droplets [639]. Özcan et al. [644] used grazing-incidence small-angle x-ray scattering (GISAXS) to study the growth of Ga layers on GaN (0001) and on sapphire in real time under MBE conditions above and below the flux at which droplets form. The kinetic results are very different for the two substrates. He et al. [645] used RHEED to study the desorption of Ga adsorbed on GaN (0001) and found ΔEa = 2.76±0.02 eV in the absence of an N-atom flux, which is larger than an earlier result (ΔEa = 2.2±0.2 eV, Ref. [630]). Choi et al. [646,647], Misra et al. [648] and Bruno et al. [649] used SE to study the growth of Ga layers, and in related work Cobet et al. [665,666] also used SE to show the presence of a Ga bilayer during growth by MBE but not by MOVPE. Here the

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Fig. 43. (a) Ga/GaN (0001) adsorption diagram correlating the exponential Ga flux dependence of Ga coverage and droplet formation on substrate temperature. The activation energy for θGa ¼ 1 ML was determined from in-situ temperature-dependence measurements, as shown in (b). The Ga fluxes and substrate temperatures used for 90 sec adsorption intervals are indicated as open circles. (b) Arrhenius plot for the determination of single-exponential activation energies and atomic attempt frequencies for critical fluxes to realize θGa ¼ 1.0 and 2.4 ML. For the critical flux to form 1.0 ML Ga on GaN after a 90 s Ga adsorption, an activation energy of 2.43 7 0.11 eV and a prefactor of 6.77x1012 nm min-1 were obtained. From Brown et al. [643] (reproduced with the permission of AIP Publishing).

ellipsometric angles Ψ and Δ are measured vs. hν in the 1.5 to 6.5 eV range and used to compute the complex pseudo-dielectric constant (PDC), o ε4 = oε1 4 + ioε2 4 . The PDC is obtained by applying the Fresnel relations describing reflection from the bare substrate to data recorded with the Ga layer present, and trends in the PDC vs. temperature, Ga flux, etc. then provide information about the Ga layer. Choi et al. [646,647] used samples grown by hydride VPE and cleaned in situ by adsorption and desorption of Ga and found that oε2 4 increases with θGa. For a given temperature, with increasing Ga BEP (i.e., flux), oε2 4 reaches saturation at a level corresponding to θGa = 2.5 ML (termed the "critical thickness" in this work). When the BEP exceeds a certain level, which increases with temperature as a result of the competition between adsorption and desorption, droplet formation begins and is detectable by the onset of light scattering. These results are consistent with those of earlier studies. It is also found that, when droplets are present, desorption occurs from the surface of the Ga bilayer, and the lost

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Ga is then replaced by diffusion from the droplets. The bilayer thus remains intact until the droplets have been depleted. This phenomenon, whereby Ga droplets "feed" a bilayer during desorption from the bilayer, is seen in several different studies. Activation energies of ΔEa = 2.86±0.07 and 2.81±0.12 eV respectively are found for evaporation from the first layer and from the bilayer with the latter being close to that for bulk Ga. The slightly higher value for the first layer suggests a bonding interaction between the adatom and the substrate. Subsequent work by Bruno et al. [649] et al. analyzed SE results in terms of the Wolkenstein theory of adsorption on semiconductors, which takes into account charge transfer between adsorbate and substrate. It is found that Ga adsorbed on n-GaN (0001) exists in both neutral (weakly-bound) and anionic (strongly-bound) states. The former dominates at low θGa, for which Langmuir theory adequately describes the adsorption and desorption kinetics; whereas, at higher θGa the equilibrium between charged and neutral Ga must be included in the analysis. For desorption, which involves only neutral Ga, an apparent ΔEa of 2.85±0.02 eV is found, which is independent of temperature unlike in earlier kinetic studies [637] based on Langmuir theory. Misra et al. [648] performed SE and RHEED experiments on samples grown in situ using MBE on a GaN template grown by hydride VPE. The results are similar to those obtained in other studies of Ga/GaN (0001) described above including a critical thickness corresponding to θGa = 2.5 ML. This work also reports data, discussed below, for the (101̄0) and (112̄ 0) surfaces. Experimental work for Ga/GaN (0001̄ ) has been described in several studies. Kowalski et al. [478] performed ARUPS for a (0001̄ )-(1x1) surface formed by a Ga adlayer. These results were described above in Section 4.7.1.2. Koblmüller et al. [639,640] conducted studies similar to those discussed above for the (0001). The stable Ga adlayer coverage in this case is 1.1 ML, which is consistent with what is predicted theoretically and measured experimentally for the (0001̄ )-(3x3) MBE surface (Section 4.6.2). In the present work [640], this structure was observed in RHEED below 300 °C. Choi et al. [511] reported SE data for Ga adsorption and desorption on surfaces prepared as described above. The (0001̄ ) surface is found here to consist of bare, N-terminated regions and areas that are covered with a Ga ML, which is consistent with other results (Section 4.7.1.2) for (0001̄ ) surfaces cleaned in situ. Adsorption occurs in two stages. The first, which is complete at θGa = 0.5 ML of additional adatoms, represents the formation of a Ga ML on the initially-bare areas. The ΔEa for desorption at this stage, 3.19±0.11 eV, is close to that for GaN decomposition (3.1±0.1 eV, Ref. [328]), which suggests a strong bonding interaction. The second stage ends with a total of 1.5 ML of added Ga and shows a ΔEa of 2.78 eV, which is close to that for bulk-Ga evaporation and suggests that Ga-Ga bonding characterizes this stage. It is also found that the sticking coefficient for Ga on the (0001̄ ) with a Ga adlayer is 1/3 that for a bare (0001) surface even though a surface Ga atom on the former has three DBs (with the Ga in a T1 site) and one DB on the latter. This is attributed to the effect of the DB orientation on adatom bonding. Alam et al. [651] used low-temperature STM to study Ga adatoms on the (0001̄ )-c(6x12) surface (Section 4.6.2) prepared in situ using MBE. It was found that Ga adatoms, in addition to those that define the c(6x12) structure, remain from growth and are highly mobile at RT and therefore not easily detected. At liquid-He temperature (4.2 K) the adatoms "freeze out" to form a high-density array of L-shaped clusters. The structures are chiral, as is the c (6x12) surface, and exist in left- and right-handed forms and also in two different orientations separated by a 180° rotation. The rotation is associated with the rotation of N-Ga back-bonds that occurs when crossing over a one-bilayer-high step edge on the

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(0001̄ ) surface. The structure and bonding of these adatom features are analyzed in detail in the original reference. For Ga on GaN (101̄0) (the m-plane), RHEED studies were done by Brandt et al. [404,405]. Two stable phases are seen following MBE growth on γ-LiAlO2 (100), chosen because of the good lattice match with GaN (101̄0). These are a bilayer of adsorbed Ga showing superimposed (1x2) and (4x2) structures and a trilayer with a (4x4) structure. The structural results were discussed in Section 4.6.3. Desorption studies of the bilayer with droplets show the same "feeding" effect noted above, in which Ga desorbed from the bilayer is replaced by diffusion from the droplets. The dependence of θGa on temperature, Ga flux and the additional presence of an N-atom flux is analyzed at length in the original references. Choi et al. [647] performed SE, as described above, for GaN (101̄0) grown by MBE on γ-LiAlO2 (100). The results are similar to those for the (0001) with, however, some differences. The critical thickness defining the boundary between layer growth and droplet formation is greater for the (101̄0) surface (6.66 vs. 4.76 Å). There is also a second, metastable phase above the critical thickness that appears under certain conditions of flux and temperature but immediately disappears, leaving only the critical-thickness layer, when the Ga supply is terminated. For the same flux and temperature, such that θGa is below the (0001) critical thickness, θGa is the same for either surface, but adsorption is slower and desorption faster on the (101̄0). Misra et al. [648] used SE and RHEED to study Ga/GaN (101̄0) grown by MBE on γ-LiAlO2 (100). A critical thickness of 0.48 nm (i.e., the same as for the (0001)) was obtained using RHEED since the presence of Ga droplets made SE thickness measurements beyond ∼0.5 nm unreliable in this study. The effects of an N-atom plasma on Ga adsorption and desorption were also studied. There appears to be some disagreement among the three Ga/ GaN (101̄0) studies. It is noted here that the (101̄0) surface is inherently anisotropic [417,483,499], with different optical constants for light polarized parallel and perpendicular to the [0001] axis (Fig. 2), and it is possible that the same applies to an ML or bilayer of adsorbed Ga. This does not appear to have been considered in either SE study when quantifying the data (e.g., in obtaining the layer thickness). For Ga/GaN (112̄ 0) (the a-plane), experimental work has been done by McLaurin et al. [652] using RHEED for samples grown by MBE on (101̄2) sapphire (r-plane). It is found that the critical thickness (or critical θGa) is o1 ML, above which droplets form, and the RHEED intensity vs. flux and temperature is analyzed in terms of shadowing of the surface by the droplets. As in other studies, the droplets act as a sink for excess Ga above the critical θGa during deposition and as a source to maintain the critical θGa during evaporation. Misra et al. [648] used SE and RHEED for samples grown via MBE on a GaN template grown by hydride VPE. The critical-layer thickness, 0.50 nm, was obtained using RHEED and is essentially the same as that found in this study for the (0001) and (101̄0) surfaces. As in the case of the (101̄0), there are inconsistencies between the two studies. Finally, Ga/GaN (112̄ 2) has been studied by Lahourcade et al. [653] using RHEED with samples grown by MBE on an AlN (112̄ 2) buffer layer on a sapphire (101̄0) substrate. The surface was identified as Ga-polar (as in Fig. 3a,b) by comparing the effect of immersion in molten KOH with that for an MOVPE sample of known polarity. The critical thickness is found to be 1.05±0.10 ML, and, as a check, a value of 2.5 ML is obtained using the same methods for the (0001). As usual, droplets form at higher θGa. The critical thickness for the (112̄ 2) surface is based on the atom density on the (0001). When corrected for the (112̄ 2) density, 1.19x1015 cm-2, the critical thickness becomes 1.0 ML. This is consistent with theoretical results (Section 4.6.4.3) of Yamashita et al.

[425,426], which show that an ML of Ga is the most stable structure for this surface under very Ga-rich conditions. The growth and structure of (112̄ 2)-oriented GaN was also discussed in detail but is beyond the scope of the present review. As noted above, there have been numerous theoretical studies of Ga on GaN. Here we briefly discuss those that focus mainly on adsorption and interface formation rather than on growth aspects. Theoretical work addressing Ga adsorption in relation to surface reconstruction and electronic structure was described in Sections 4.6 and 4.7. For Ga/GaN (0001), Zywietz et al. [654] studied adsorption and diffusion on the ideally-terminated surface using a 2DPS with nine Ga-N bilayers and a (2x2) SUC. The FCC (H3) and HCP (T4) sites are essentially degenerate for Ga adsorption, and ΔEa for diffusion between sites is 0.4 eV via a bridge-site transition state. Adelmann et al. [637] reported a theoretical analysis of their experimental results described above. The focus was on the interaction of Ga adatoms with the surface of the metallic-Ga bilayer as a means of understanding droplet formation. The PBE functional was used with soft PPs for which Ga 3d electrons were treated via NLCC (Section 4.1.1). A 2DPS with a (√3x√3) or (2√3x2√3) SUC and a Ga bilayer on top of two Ga-N bilayers was employed, and increasing the thickness to four Ga-N bilayers had no significant effect. The bottom surface was terminated with PHs, which together with the lower bilayer, were fixed during relaxation. For a single Ga adatom in a three-fold hollow site, ΔEads = -2.52 or -2.41 eV respectively for a (√3x√3) or (2√3x2√3) SUC, which indicates a small decrease in ΔEads as the adatom θGa decreases from 1/3 to 1/12 ML. For two, three or four adatoms in an island in a (2√3x2√3) SUC, the ΔEads per Ga is -0.15, -0.30 and -0.34 eV relative to an isolated adatom, which suggests a tendency toward clustering. The cohesive energy of an island is less than that of bulk Ga, and islands then serve to nucleate the growth of droplets. Takeuchi et al. [657] studied the effects of Ga coverage and electronic excitation of the GaN (0001) on adsorption and diffusion of Ga. The calculations used PWs and USPPs with a 2DPS having four Ga-N bilayers and SUCs of various dimensions with the bottom two bilayers and the terminating PHs fixed during geometry optimization. Electronic excitation was addressed by promoting one electron from the highest doubly-occupied to the lowest unoccupied level. For the ideally-terminated surface and a (2x2) SUC, T4 is the lowest-energy site with ΔEa = 0.72 eV for diffusion via a bridge-site transition state. The barrier decreases somewhat, to 0.63 eV, for a (2√3x2) SUC, and electronic excitation leads to a further decrease to 0.29 eV as a result of a weakening of the adatom back-bonds. For the "(1x1)" laterally-contracted Ga bilayer, a Ga adatom adsorbs in a three-fold site (either H3 or T4) with ΔEa = 0.39 eV for diffusion via a bridge transition state. Gokhale et al. [576,577] studied Ga adsorption on the bare (0001) using methods described in Section 5.2 in connection with their work on Sb. For θGa = 0.25 ML, ΔEads = -3.55 eV for adsorption in an HCP (T4) site, which is the most favorable, and ΔEa = 0.55 eV for diffusion. In the studies noted thus far, the ΔEa results for Ga diffusion on the bare (0001) surface are qualitatively consistent. Witczak et al. [660] reported a theoretical study of the physical and electronic structure of a Ga layer on GaN (0001) beginning with an adatom and progressing to a fully-developed metal/ semiconductor contact. A 2DPS with eight Ga-N bilayers, a (2x2) or (4x4) SUC and the bottom surface terminated with PHs was used together with NCPPs and the Wu-Cohen GGA functional. Doping was simulated by substituting a Si (n-type) or a Mg (p-type) for a bulk Ga, and free carriers were simulated, when needed, with an electronic temperature of 1000 K in the Fermi-Dirac distribution. For a (4x4) SUC the previously-reported [381–383] (2x1) reconstruction of the clean surface is seen, and adsorption of a single Ga adatom is most favorable in a T4 site, with ΔEads = -4.237 eV. As

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θGa increases to 41 ML the preferred Ga site changes from T4 to T1, consistent with other results (Section 4.6.1) for the laterallycontracted bilayer. At θGa = 2 ML the epitaxial relationship is lost, and beyond that the structure quickly converges to that of bulk Ga, which is consistent with the experimental results described above. With increasing θGa, ΔEads decreases nearly monotonically to -3.224 eV per adatom for adsorption on top of 5 MLs of Ga. This can be compared with the cohesive energy of bulk Ga, 2.8 eV [637]. For the bare n- and p-type surfaces, EF is pinned near the CBM by the partially-filled Ga DBs, as discussed in Sections 4.7.3.1 and 4.7.3.2. On p-GaN this leads to a large downward BB as seen experimentally [440,512]. For θGa = 5 ML, corresponding to a fullydeveloped contact, the n-type (p-type) SBH is about 0.9 (0.6) eV. In addition a dipole layer with a potential difference of 1.5 eV is seen to result from bonding at the Ga-GaN interface. This arises from electron transfer from GaN to the Ga metal and is independent of doping type, which is consistent with its origin being in the polarization of the Gaδ−-Gaδ+N bond at the interface. Chugh and Ranganathan [661] performed a theoretical study of the adsorption of Ga on GaN (0001) and its dependence on coverage in the range of 0.04 to 0.25 ML. The calculations used the PBE functional with USPPs and SUCs ranging in size from (2x2) to (5x5) with one Ga adatom per SUC. The 2DPS consisted of six Ga-N bilayers with the bottom surface terminated in PHs and the upper three bilayers and the adatom free to relax. A dipole correction (Section 4.1.1) was considered but found not to be needed. The bare surface, with a SUC as large as (5x5), remains flat during relaxation. Thus no (2x1) reconstruction is observed, which differs from some other theoretical results [381–383,660] (Section 4.6.1) for large SUCs. However, adsorption of Ga, which is most favorable in an HCP (T4) site, leads to a distorted surface with the Ga atoms to which the adatom back-bonds displaced outward by 0.45 Å. When the adatom is removed and the surface relaxed again, most of the distortion remains, and the surface energy is slightly lower than for the flat surface (by about 6x10-4 Ry Å-2 = 0.07 eV per surface site for a (5x5) SUC). The authors point out that this suggests the possibility of some form of reconstruction of the clean surface. It is noted here that the process of adding and removing the Ga adatom to create a distortion may serve to overcome a barrier to complete relaxation of the flat surface at T = 0 K. Decreasing θGa from 1/4 to 1/9 ML (i.e., increasing the SUC from (2x2) to (3x3)) leads to a slightly more exothermic ΔEads, but further reduction to 1/16 and 1/25 ML causes a more substantial increase in ΔEads. For a (2x2) vs. (5x5) SUC, ΔEads for one Ga is -3.83 vs. -5.47 eV. This results from an increasing relaxation of the lattice, which is partially suppressed for a smaller SUC by the interaction between translational images, since little or no variation in ΔEads with θGa is seen when the slab is fixed in the configuration of the flat clean surface and only the adatom is allowed to relax. It is shown that dipolar interactions make little contribution to the variation in ΔEads. Charge density difference plots show that the adatom-induced lattice distortions, which extend over the whole SUC, are associated with charge redistribution that leads to an overall stabilization of the larger SUCs. A similar effect accounts for the stabilization of the distorted clean surface relative to the flat clean surface mentioned above. The charge redistribution shown in the difference plots suggests a reduction in the charge density in DBs on the distorted surface. Theoretical results for Ga on the (0001̄ ) have been given by Zywietz et al. [654] for a surface terminated in one ML of Ga in T1 sites. The HCP (T4) site is slightly favored (based on results plotted in Fig. 3 of the original reference), and ΔEa is very low (0.2 eV) for diffusion via a bridge-site transition state. The barrier is much higher (1.0 eV) for the bare (0001̄ ) surface, which indicates the surfactant effect of the Ga adlayer. Tsai [662] did ab-initio MD studies of a Ga atom impinging on a bare (0001̄ ) surface. The

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trajectory is complex and depends on both the point of impact and the method used to approximate heat dissipation. The results suggest that the Ga does not always come to rest in the lowestenergy adsorption site. Takeuchi et al. [657] obtained results, similar to those described above, for Ga on the (0001̄ ) with one ML of Ga in T1 sites and a (2x2) SUC. The T4 and H3 sites are essentially degenerate, and ΔEa for diffusion via a bridging site is only 0.08 eV. For Ga on the (112̄ 0) surface, theoretical results were obtained by Gokhale et al. [576,577] using methods described in Section 5.2 in connection with their work on Sb. For a (1x1) SUC, ΔEads = -2.10 eV for adsorption, and ΔEa = 0.28 eV for diffusion parallel to the [0001] direction. A much higher, but unspecified, ΔEa is found for the orthogonal direction. Lymperakis and Neugebauer [663] studied the anisotropic diffusion of Ga on the (101̄0) and (112̄ 0) surfaces using 2DPS models with six Ga-N bilayers and the bottom surface terminated in PHs. For the m-plane surface (the (101̄0)) the barrier is much smaller for diffusion perpendicular to the [0001] axis; whereas, the reverse is true for the a-plane surface (the (112̄ 0)) in agreement with the results of Gokhale et al. For the mplane, Ga adsorbs with a bond to a single N atom, with ΔEads = -2.17. The lowest-energy diffusion path is perpendicular to the [0001] axis with a transition state midway between two N atoms and ΔEa = 0.21 eV. In contrast, for diffusion in the [0001] direction, the transition state is midway between two Ga atoms with ΔEa = 0.93 eV. These are farther apart than two surface N atoms, and the Ga-Ga bond is weaker than the Ga-N bond, which accounts for the higher barrier in the [0001] direction. For the a-plane surface, Ga bonds to one N and two Ga atoms, with ΔEads = -2.30 eV. Diffusion in the [0001] direction, which is diagrammed in the original reference, occurs with ΔEa = 0.32 eV, while diffusion in the orthogonal direction exhibits a ΔEa of 0.63 eV. Jindal and Shahedipour-Sandvik [664] studied Ga diffusion on the (101̄0) and (112̄ 0) surfaces theoretically using the LDA with a (2x2) SUC and a 2DPS with four Ga-N bilayers. Apparently the slab was symmetric since no mention was made of terminating DBs on the bottom surface. Results were also obtained for Ga diffusion on the ideally-terminated (0001) and (0001̄ ) surfaces. For the former, the HCP (T4) adsorption site (termed "H2 hcp" in this study) is found to be the most favorable, with ΔEa = 0.32 eV for hopping between sites via an FCC (H3) transition state. For the latter, the FCC (H3) site is the most stable, with ΔEa = 0.85 eV for diffusion via a bridging transition state. These results are qualitatively consistent with those described above for the bare (0001) and (0001̄ ) surfaces. For the (101̄0) surface, the minimum-energy adsorption site places the Ga near a surface N atom, and diffusion is highly anisotropic, with ΔEa = 0.13 and 1.6 eV respectively for diffusion perpendicular and parallel to [0001]. (The latter value was given as 1.6 eV in the text and 1.49 eV in the conclusions section of the original reference.) The predicted diffusion anisotropy was verified experimentally by homoepitaxial MOCVD growth on a polished m-plane substrate. The initial surface was smooth; whereas, after growth AFM showed a striated surface consistent with rapid growth in a direction perpendicular to [0001]. For the (112̄ 0) surface, the minimum-energy Ga site is again near a surface N atom, and ΔEa = 0.68 and 1.6 eV respectively for diffusion parallel and perpendicular to [0001]. This was also verified in a homoepitaxial MOCVD experiment. The theoretical results are consistent with those obtained previously [576,577,663]; although, the ΔEa values are generally higher, which might result from the use of the LDA rather than the GGA. Akiyama et al. [426] studied Ga adsorption on the (112̄ 2) surface theoretically using a 2DPS with 14 atomic layers (i.e., 7 Ga-N bilayers) with the bottom surface terminated with PHs and the lowermost two bilayers fixed in the bulk configuration. Two

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surfaces were considered; namely, the c(2x2) with one Ga adatom per SUC (Fig. 20c) and the (1x1) with a full ML of Ga adatoms (Fig. 20e), both of which were described previously in Section 4.6.4.3. For the c(2x2) the most favorable site for an additional Ga is above a surface N that is not bonded to the first Ga adatom, where a Ga-N bond forms to give ΔEads = -2.98 eV. The ΔEa for diffusion is quite high (1.2 eV), and the adsorption energy in the transition state is sufficiently low (-1.76 eV) that desorption is considered to be more likely than diffusion under MBE conditions. For a Ga adsorbing on the (1x1), the most stable site (ΔEads = -2.73 eV) is above the Ga adlayer where it appears to be positioned so as to back-bond to three Ga atoms. The ΔEa for diffusion is only 0.19 eV in this case, which reflects the weakness of Ga-Ga vs. Ga-N bonds. In summary, the experimental studies of Ga on the (0001) and (0001̄ ) surfaces provide information that is consistent with what is known from other sources (Sections 4.6 and 4.7) about the structure and composition under Ga-rich conditions. For the (0001), the laterally-contracted bilayer of metallic Ga forms with the first layer interacting weakly with the substrate and the second exhibiting the properties of bulk Ga. Beyond this point only droplet formation occurs. Likewise for the (0001̄ ) the stronglybound Ga ML, with a small additional coverage associated with the (3x3) structure, is identified. Experimental phase diagrams have been constructed that show how the surface composition depends on the balance between temperature (i.e., Ga desorption) and Ga BEP. A general observation is that the Ga layer or bilayer remains intact, at the expense of the droplets, during desorption. On a practical note, these results may be of value in understanding and in optimizing the Ga-cleaning process (Section 3.2.1). It has also been shown [638] that the Ga 3d BE can be distinguished for Ga metal, Ga adatoms and GaN, which is helpful in analyzing XPS data. Regarding theory, it should be noted that one study [661] indicates the importance of large distortions in the terminating Ga layer of the substrate when Ga adsorbs on the (0001) surface. 5.19. Germanium Germanium adsorption on GaN (0001) has been studied both experimentally, using STM, and computationally by Qi et al. [667]. The interest was in the mechanism of incorporation and the possible use of Ge as a dopant. The samples, which were grown by MBE and studied in situ, exhibited the "(1x1)" (or pseudo-(1x1)) structure formed by a laterally-contracted bilayer of Ga on top of the Ga lattice terminating layer. Deposition of 0.2 ML of Ge converts the "(1x1)" structure to a (2x2) in the form of domains separated by rows of missing atoms. The theoretical calculations were performed using the FLAPW method, but no further details were given. For θGe = 1/6 ML (the lowest θGe considered), the (2x2) structure results from site exchange between Ge and Ga in the outermost layer of the Ga bilayer. Metallic Ga-Ga bonds in the outer layer are replaced with covalent Ge-Ga bonds, which eliminates the fluid-like character of this layer and imparts a tetrahedral geometry to the local structure like that in GaN. The Ga bilayer (with a low concentration of substituted Ge) then converts from the "(1x1)" to a true (1x1). The Ga atoms displaced in this process, including the "extra" Ga present in the initial fluid-like outer layer, then occupy T4 adatom sites to give the observed (2x2) structure. The domains, which comprise regions of different stacking (HCP or FCC), form as a means of relieving the strain that results from the covalent size mismatch between Ge and Ga. For a higher θGe, the additional Ge is found to adsorb as a T4 adatom rather than undergoing site exchange. 5.20. Gold There is an extensive literature on the interaction of Au with

GaN, motivated mainly by an interest in contact formation, particularly since Au is a component in various alloys designed for thermally-stable Schottky contacts. This work [125,126,330,435,474,561,562,564,623,668–677] has all been experimental and all on the (0001) surface except for that of Walker et al. [676] on the non-polar surfaces and of Barinov et al. [435,669,670] on what was probably the (0001̄ ). There has been one theoretical study of Au/GaN [678], but that was for the (001) surface of the cubic form and will not be discussed here. Sporken et al. [668] performed XPS studies of Au/n-type MOVPE GaN (0001). Three different approaches were used for sample cleaning: (a) organic solvents only; (b) hot KOH solution followed by aqua regia; (c) like (b) but also heating in UHV to 900 ° C. Method (c) gives the cleanest surface, with only a small amount of C. It is noted here that a small O 1s feature would have been difficult to detect in the Al Kα-excited XPS due to interference from structure in the Ga LMM Auger spectrum. (For a Au density of 19.282 gm cm-3, 1 Å = 5.896x1014 Au cm-2 = 0.519 ML where 1 ML is defined as 1 Au per surface lattice site.) In the Au 4f XPS, in-situ deposition of 5x1014 Au cm-2 (0.44 ML) leads to a satellite at ~0.7 eV higher BE than the bulk-Au peak, which is ascribed to AuGa bond formation involving excess Ga at the surface. This satellite is attenuated by further Au deposition, which leads to layer-bylayer film growth. For a low θAu, the Ga 3d and N 1s peaks shift by about 1 eV to higher BE relative to the bare surface. This indicates a decrease in upward BB, which is about 2.2 eV before Au deposition, and with further Au deposition the SBH stabilizes at 1.15±0.15 eV. A very large BB on the clean surface that decreases with contact formation is unusual for n-type GaN. It is speculated here that the clean surface is highly defective and that Au deposition removes these defects and leads in the end to an SBH similar to what is found for a less-defective initial surface. The work of Rickert et al. [84] suggests that the use of KOH in wet-chemical cleaning might have led to the large upward BB on the bare surface as a result of the formation of VGa acceptors. The effect of annealing a thicker Au film at 600 and 710 °C was also investigated. (The film was described in a figure caption as having 5.6x1015 Au cm-2 and in the text as being 10 nm thick, which corresponds to 5.9x1016 Au cm-2.) This leads to a loss of Au 4f intensity, the formation of Au islands (~25 nm high, as seen in AFM) and the appearance of two Au 4f doublets. It is proposed that the islands acquire a negative charge, leading to a shift to lower BE; whereas, the area between islands retains only a thin Au coverage and is uncharged. It was also concluded that there is little, if any, interdiffusion at the interface. In a later study, Dumont et al. [623] prepared a clean surface using a combination of Hatom exposure and Ga deposition and desorption as described above (Section 5.14) in connection with their Cu results. An SBH of 1.15 eV was found, which is identical to that in Ref. [668], but no value was given for the BB on the clean surface. Wu and Kahn [561] used UPS, XPS, AES and LEED to study Au on GaN of uncertain polarity, which was nominally (0001) Gapolar. The experimental details were given above in connection with their work on Al (Section 5.1). The interface appears to be essentially non-reactive, even for a 900 °C anneal. The SBH is about 1.3 eV for n-GaN and 1.2 eV of p-GaN and exhibits little or no change with annealing. An extension of this work was reported by Wu et al. [562] in which Au/n-GaN (0001) contacts were prepared in situ on atomically-clean substrates and studied using I-V measurements. The experimental details were summarized previously in the discussion of their work with Al. An SBH of 1.2 (0.89) eV was found using photoemission (I-V measurement). The ideality parameter is nearly unity since the interface is non-reactive. Maffeis et al. [330] used XPS and I-V measurements to investigate Au/n-GaN (0001) contacts prepared in situ in UHV. The

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MOCVD GaN surface was cleaned by immersion in HF solution followed by heating in UHV to 600 °C. The existence of an oxiderelated feature on the high-BE side of the N 1s was mentioned, but no further information regarding residual surface contamination was given. The mean value of the SBH for several samples after insitu deposition of a thick Au layer is found to be 1.24 eV from I-V data. Shifts in the Ga 3d BE were used to follow changes in BB during Au deposition, and it is seen that the upward BB increases by 0.35 eV due to the in-situ anneal and by another 0.25 eV after deposition of 1 Å of Au, with no further shift up to 55 Å. The annealing-induced BB increase of 0.35 eV is consistent with other results (Section 4.7.3.1) for n-GaN (0001). The 0.60 eV net increase in BB is less than the SBH determined from I-V data (1.24 eV), from which it is inferred that there is an initial BB of about 0.6-0.7 eV for the unannealed surface that, when added to the net BB shift, gives the I-V SBH. It is noted here that data plotted in this paper show a Ga 3d BE of 20.8 eV before annealing. Subtracting the reference value of VBM-Ga 3d = 17.76 eV [439] then gives only ∼0.3 eV for the initial upward BB. Adding this initial BB to the net change in BB seen after annealing in UHV followed by Au deposition gives a photoemission SBH of about 0.90 eV, which is in fair agreement with earlier results obtained for what were probably cleaner initial surfaces (1.15 eV [668], 1.2 eV [562]). Barinov et al. [435,669,670] used photoemission microscopy at hν ≈ 495 eV, aided by synchrotron excitation, to investigate Au/nGaN interfaces. Of these, Ref. [670] deals mainly with Ti-Au alloys but also discusses Au. Clean surfaces of MOCVD GaN were prepared by IBA (0.6 keV nitrogen ions, 900 °C anneal), which gave a faceted (1x1) LEED pattern with very faint additional (3x3) spots. The appearance of the (3x3) was taken to indicate that the surface was the (0001̄ ), with the (3x3) being due to Ga adatoms remaining from cleaning (Section 4.6.2). The clean-surface upward BB was 0.5 eV, which was somewhat reduced from the "in the dark" value by SPV. The SPV "band flattening" was estimated to be 0.2±0.1 eV,

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based on temperature-dependent shifts in BE (Section 4.7.3.2)), which then gives ~0.7 eV for the true BB. The Ga 3d (Fig. 44) shows satellite features to higher and lower BE, as are often observed, and the N 1s shows a low-BE satellite. With a BE of ∼398 eV, the N 1s was observed with a high degree of surface sensitivity using hν ≈ 495 eV, and an SCLS to lower BE in the N 1s is consistent with an N-terminated surface in contact with a Ga adlayer as suggested by the faint (3x3) LEED pattern. Fine-structure in the Ga 3d and N 1s spectra was discussed in more detail above in Section 4.7.1. A patch of Au that was ∼4 ML thick at the center and 10–15 μm wide was deposited on the clean surface. The edges of the patch were graded in thickness; hence, acquiring data at various positions allowed measurements to be made as a function of θAu. Deposition of Au causes both the Ga 3d and the N 1s to shift to lower BE, indicating an increased upward BB that arises from the combined effects of Schottky barrier formation and the reduction in SPV-induced "band flattening". At a thickness of about 3-4 ML the SBH has stabilized at 1.4±0.1 eV, and SPV effects have become negligible. A deviation from layer-by-layer growth is seen in the attenuation vs. coverage for θAu 4 1.5 ML. The Au 4f spectrum exhibits three components that vary in intensity with θAu. One of these, which is shifted by 0.9 eV to higher BE relative to bulk Au, gains intensity up to 1 ML and then becomes negligible at higher θAu. This is assigned to Au interacting with surface defects. A second feature, shifted by 0.3 eV to higher BE relative to bulk Au, grows continuously up to 3.5 ML, and both components exhibit the same BE shift vs. θAu as do the Ga 3d and N 1s. Beginning at 1 ML the bulk-Au 4f emerges, but the growth in intensity with coverage is slower than expected for layer-by-layer growth, which indicates island formation. It should be noted here that surface-sensitive data for the Au 4f level must be interpreted with some caution since there is a substantial SCLS to lower BE for surface atoms [679]. Annealing in stages up to 870 °C increases the Ga 3d and N 1s intensities, decreases that of the Au 4f and also results in changes

Fig. 44. Valence band (VB), Ga 3d and N 1s spectra measured vs. Au thickness, illustrating the coverage effect after deposition of Au at RT. The surface is believed to be the (0001̄ ). From Barinov et al. [435] (© IOP Publishing. Reproduced with permission. All rights reserved.).

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in lineshape and in BE. Up to 300 °C only changes in intensity and BE are seen, with the latter effect being ascribed to a return of SPV. These changes indicate a structural rearrangement of the Au layer leading to a clustering of the deposited Au into larger island, which uncovers part of the surface and renders the film discontinuous. There is, however, little or no evidence of a chemical reaction at this stage. Above 500 °C, a low-BE Ga 3d satellite appears that signals Ga in a metallic environment, and simultaneously the Au 4f shifts to a higher BE. Both effects indicate the formation of a Au-Ga ("gold gallide") alloy. At this temperature, the vapor pressure of Au is too low for evaporation to be a significant factor. Above 750 °C a second Ga 3d component appears at even lower BE, coinciding with that of bulk Ga metal. The thermally-induced degradation of the interface results in a continuous but inhomogeneous layer of Au-Ga alloy and/or free Ga, which eliminates any SPV. At 870 °C, the interface completely degrades to form Au-Ga islands; however, a Au-free area shows no degradation up to 900 °C, which indicates that Au is actively involved in the process. This differs from the finding of Wu and Kahn [561] that the interface is non-reactive even at 900 °C. Wu and Kahn also prepared clean surfaces by IBA but studied what may have been the (0001) surface and not the (0001̄ ), which might account for the difference in reactivity. Throughout the annealing stages the SBH monotonically decreases, ending at 0.75 eV after an 820 °C anneal, which is attributed to the replacement of the initial Au/ GaN contact with a (Au-Ga)/GaN alloyed contact. Although the alloy layer is structurally inhomogeneous, the stoichiometry is uniform, which is consistent with the observation that the SBH is also uniform across the contacted surface. Peiró et al. [125] and Maffeis et al. [126] used XPS and I-V data, with MOVPE GaN (0001), to study the effects of surface cleaning methods on the Au/n-GaN SBH. The procedures employed were (a) immersion in acetone, then HF solution, then DI H2O with no further treatment in UHV; (b) like (a) but with a 600 °C anneal in UHV; (c) like (a) but with cleaning in UHV by Ga adsorption at RT and desorption at 900 °C (Section 3.2.1). Gold was deposited in situ on each type of surface and studied over a range of thicknesses using XPS, after which a thick film was deposited and the sample removed for I-V experiments. As expected, the O 1s/Ga 3d XPS intensity ratio decreases and the N 1s/Ga 3d ratio increases with each succeeding cleaning step, indicating the removal of a GaOx surface layer. There was, however, no mention of the C impurity level. The attenuation of the Ga and N core-level XPS peaks vs. θAu indicates a Stranskii-Krastanov growth process [571], which is consistent with the results of Barinov et al. [435,669,670] for the (0001̄ ) surface. Data obtained for normal vs. off-normal emission in XPS suggest that the interface is relatively abrupt (i.e., non-reactive) for Surfaces (a) and (b) but not for (c). When Au is deposited on Surface (a) or (b), there is an immediate increase in upward BB, which stabilizes after ∼30 Å to give an SBH of about 0.86 eV (based on the Ga 3d BE of 20.25 eV, VBM-Ga 3d = 17.76 eV [439] and CBM-EF ≈ 0.04 eV in the bulk). It may be significant that stabilization of the SBH required about 30 Å (15.6 ML) of Au; whereas, in the work of Barinov et al. on the (0001̄ ) surface described above, only ∼4 ML was needed. For Surface (c), the dependence of BB on θAu is more complicated, and the resulting SBH is 0.70 eV, which is about the same value found above by Barinov et al. for a Au-Ga alloy contact on the (0001̄ ) surface. The Au 4f on Surfaces (a) and (b) stabilizes at the BE of bulk Au at about the same θAu where the SBH stabilizes. On Surface (c), on the other hand, the Au 4f is still changing slightly for ~60 Å of Au and exhibits a BE slightly higher than that of bulk Au. All of these observations are consistent with a reactive interface in the case of Surface (c), which is confirmed by TEM data showing extensive intermixing. This differs from results for (0001) surfaces prepared either by simply heating to 900 °C in UHV [668] or by IBA

with annealing at 900 °C [561], which show the interface to be non-reactive. The I-V results for many different samples gave a mean SBH of 1.24 eV with good ideality factors for Surface (b); whereas, Surface (c) gave a mean SBH of 0.84 eV with poor ideality. Possible reasons for these differences were discussed in detail, and this subject will be revisited later in Section 6. Preble et al. [671] used XPS, HRTEM, SEM, XRD and I-V measurements to study the Au/n-GaN (0001) interface. The MOVPE sample was cleaned in a series of organic solvents then in HCl solution after which it was cleaned in situ by heating in a flux of NH3 vapor (Section 3.2.2). The resulting surface showed no detectable impurities in AES. The XPS core-level attenuation data indicate that the Au layer grows in a layer-by-layer (Frank-van der Merwe) mode, and SEM shows a crystalline, epitaxial interface. As noted previously, some studies observe Frank-van der Merwe growth for Au/GaN while others find a Stranskii-Krastanov process. This may depend on the Au deposition rate since it reflects a difference in how Au grows on Au, which may result from the effect of a finite diffusion rate. For a 770 Å-thick layer, the contact is initially rectifying but becomes Ohmic after a 600–800 °C anneal; however, SEM shows that the interface remains smooth and intact. This result differs from that of Barinov et al. [435,669,670], who found that an 800 °C anneal completely degrades the interface for a much thinner Au layer on a (0001̄ ) surface prepared by IBA. However, it is consistent with the report by Wu and Kahn [561] that the interface is non-reactive, even at 900 °C, for a nominal (0001) surface cleaned by IBA. Tracy et al. [474] performed XPS, UPS, I-V and C-V measurements on n-type MOVPE samples cleaned by annealing in situ at 860±25 °C in a flux of NH3 vapor, followed by Au deposition via electron-beam evaporation onto the substrate at RT. For I-V and CV experiments the samples were removed from UHV after the final Au deposition. The clean surfaces were well characterized with no C or O contamination above the detection limit, and the upward BB was given as 0.3±0.1 eV based on the apparent EF-VBM in UPS. No evidence of an interfacial reaction was seen in XPS in the form of satellites or changes in linewidth for the Ga 3d, N 1s or Au 4f core levels or in HRTEM or electron diffraction data. In this work EF-VBM was obtained directly from UPS measurement of the VB edge. However, the Ga 3d BE on the clean surface was 20.4 eV. Subtracting 17.76 eV for VBM-Ga 3d [439] and assuming CBM-EF ≈ 0.04 eV in the bulk gives an upward BB of 0.66 eV. It is not clear why a smaller BB was obtained in UPS since unresolved surface states just above the VBM (the usual source of error in this measurement) would have resulted in a larger apparent upward BB (i. e., a smaller apparent EF-VBM). The discrepancy could be the result of SPV if the photon flux was much higher in UPS than in XPS, which would lead to a greater "band flattening" in UPS. A SBH of 0.9±0.1 eV was found by adding the XPS shift in Ga 3d BE due to Au contact formation to EF-VBM observed in UPS. If instead one uses the Ga 3d BE of 19.9 eV to obtain EF-VBM after Au deposition, the SBH increases somewhat to 1.16 eV. This value will be used later, in Section 6, in the discussion of SBHs. Maslova et al. [672] and Oreshkin et al. [673(abstract only)] used RHEED, STM and STS to study reconstructions induced by Au adsorbed on GaN (0001). The starting surface was a pseudo-(1x1), grown by MBE with a bilayer of metallic Ga, and the Au film was deposited and studied in situ. Depositing a sub-ML of Au produced a commensurate c(2x12) phase (termed "α") and another, incommensurate phase (termed "β"). The two form simultaneously and, at 1 ML, cover the whole surface. The α-phase consists of atom rows running in the [112̄ 0] direction, while the β-phase is proposed to result from 2D Au islands on top of an intact but immobile Ga bilayer. There is the further suggestion that Ga may penetrate into the Au islands. The STS data reveal a quasi-1D electronic structure for the α-phase that derives from the presence

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of atomic rows in this reconstruction. Orani et al. [564] used XPS to measure the SBH for Au/n-GaN using procedures described above in connection with their work on Al (Section 5.1). Interfaces were formed by depositing Au on GaN grown in situ using MBE; hence, no surface cleaning was necessary. An SBH of 0.98±0.06 eV was found, and there was no obvious indication of an interfacial reaction. A (2x1) RHEED pattern was observed after depositing Au on the (1x1) bare surface, which indicates epitaxial growth of the metal layer. Zou et al. [674,675(abstract only)] used RHEED, XPS and UPS to investigate the growth of Au films on MBE GaN (0001) that was not intentionally doped. The photoemission experiments were done with a high degree of surface sensitivity using appropriate photon energies provided by a synchrotron radiation source. The samples were cleaned by IBA (Ar+-ions, 600 °C anneal) after which no impurities were seen in XPS and a hexagonal RHEED pattern was observed. For a small thickness (≤4 Å) the Au appears to form islands, as evidenced by the appearance of both cubic and hexagonal RHEED patterns, with reaction at the interface. The authors inferred a reaction based on the sharp decrease in Ga 3d intensity, which is attributed to formation of a Au-Ga alloy in which the electron attenuation length is much shorter than in pure Au. The island formation persists to higher θAu. Deposition of Au causes a 0.8 eV increase in upward BB, as shown by shifts in the Ga 3d and N 1s BEs, which leads to a SBH of 1.4 eV [675(abstract only)]. However, it is not clear from the information available how the SBH was obtained, and the Ga 3d BE after Au deposition (19.0 eV [674]) indicates a much larger SBH (assuming n-type material). Lineshape changes occur in the Au 4f that suggest reaction at the interface to form a Au-Ga alloy. Note is again taken of the substantial SCLS [679] to lower BE associated with the Au 4f. Two Au 4f components appear with BEs that are 0.8 and 0.3 eV higher than for bulk Au (which dominates for thicknesses 4 4 Å), in agreement with the results of Barinov et al. [435,669,670] for the (0001̄ ) surface. Little or no lineshape change is seen for the Ga 3d, which is attributed to a small chemical shift for Au-Ga alloy vs. GaN. Changes are also observed in the VB that are interpreted in terms of a Au-Ga bonding interaction. McHale et al. [677] used XPS to study the interface between Au and the (0001) surface of MBE GaN doped with rare-earth (RE) elements (Yb, Er and Gd). High surface sensitivity was achieved using synchrotron radiation as the excitation source. The Yb and Gd concentrations near the surface, as seen in XPS, were about 12%, while that of Er was about 5%. Clean surfaces were prepared using IBA (Ar+ ions), but no further details were given. There is evidence that the REs influence the GaN surface properties and that, therefore, the results might not be characteristic of pure GaN. The Ga 3d and VB photoemission data vs. θAu depend on the RE, and the SBHs (1.33, 1.64 and 1.68 eV, respectively, for Gd, Er and Yb doping) are somewhat larger than those reported above for Au on pure GaN. The Au films grow in the form of 3D islands (a VolmerWeber process [571]). Structure in the Ga 3d and in the Er 5p, which are close in energy but well resolved, indicates reaction at the interface that results in both Au-Ga and Au-RE alloys. Walker et al. [676] studied Au on (101̄0) and (112̄ 0) surfaces prepared by cleaving in situ. The actual surfaces were designated as (011̄0) and (1̄21̄0), but these should be equivalent to the (101̄0) and (112̄ 0) respectively. As noted elsewhere [406], cleaving on the (112̄ 0) plane is more difficult, but this was found here to give more useable regions than did the (101̄0). The dependence of the Ga LMM and N KLL AES intensities on Au coverage indicates a uniform layer growth. For good cleaves, which show no visible features in SEM after Au deposition, a Au-induced increase in upward BB by 1.7 eV is seen relative to the clean surface. These results were obtained by careful measurement of changes in KEs of Auger peaks. For bad cleaves, which lead to a rough surface, EF before Au

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deposition is already pinned at the same position in the gap as for the good cleaves after Au and shows only a slight change when Au is deposited. The 1.7 eV increase in BB seen for Au after a good cleave is close to the SBH computed for an ideal Schottky contact, which implies that the bare-surface BB is essentially zero and in turn suggests a low, if any, density of electrically-active surface states in the gap. This is consistent with results for the electronic structure of the (101̄0) surface, discussed in Section 4.7.1.3, that indicate a low density of Ga DB surface states below the bulk CBM. In summary, there appears to be little or no reaction at the Au/ GaN (0001) interface, even at elevated temperature, except when excess Ga is present. The same may be true for the (101̄0) and (112̄ 0) surfaces prepared by cleaving in situ since no evidence for Au-induced defects is seen for these surfaces; however, the Au/ GaN (0001̄ ) interface may be more reactive. This might be a consequence of the fact that the (0001̄ ) surface often entails a substantial coverage of adsorbed Ga (Section 4.7.1.2). There are insufficient data at present to permit a more definitive statement about the relative importance of surface preparation and orientation. However, cleaning the (0001) surface by Ga deposition followed by desorption appears to have an adverse effect on subsequent Au contact formation. Also, the process whereby the Au film grows (Frank-Van der Merwe, Volmer-Weber or StranskiiKrastanov) differs among the various studies, which may be related to differences in the deposition rate. This may influence growth because of a finite rate of diffusion for Au atoms on a Au surface. 5.21. Hafnium Parkhomovsky et al. [680] deposited Hf in situ on GaN (0001̄ ) grown by MBE and studied the resulting films using AFM and RHEED. For a thick (100 nm) film the as-deposited RHEED pattern shows epitaxial growth. The pattern is rotated by 30° relative to that of the GaN, which is ascribed to reaction at the interface to form (111)-oriented cubic HfN. Furthermore, the RHEED beam separations suggest a (√2x√2)R30° surface reconstruction of the Hf surface, which may result from the adsorption of residual hydrogen in the UHV background. The AFM data show a rough Hf surface with hillocks and terraces. There have also been several studies of the growth and electrical characterization of Hf nitride contacts on GaN, but these are beyond the scope of the present review. 5.22. Indium The interaction of In with GaN surfaces has been studied due to its potential use as a surfactant during growth. Although there have been many reports on the effects of In on GaN growth and surface morphology, only a few studies have focused on the In/ GaN interface itself at an atomistic level. In the experimental arena these include the work of Choi et al. [681] for the (0001) surface and of Moon et al. [682] for the (0001̄ ), while theoretical work for the (0001) has been performed by Timon et al. [566], Northrup and Neugebauer [683], Neugebauer et al. [684], Northrup and Van de Walle [685] and Salinero et al. [686]. Northrup et al. [418] and Northrup and Neugebauer [683] have also studied theoretically ̄ and the effects of In on surface morphology for the (0001̄ ), (1011) — (1011) surfaces, and Neugebauer [687] has presented a review of the theory of In surfactant effects on GaN. Choi et al. [681] used SE to observe the growth of In layers in situ on the (0001) surface under MBE conditions by following the development of the complex pseudo-dielectric constant oε 4 = oε1 4 + i oε2 4 . Here one records the ellipsometric angles Ψ and Δ vs. hν in the 2.5-5.5 eV range as a film grows and from these computes the dielectric constant using the Fresnel relations for

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polarized reflection from the bare substrate (ignoring the presence of the film). The quantity thus determined is referred to as a pseudo-dielectric constant. A high In BEP (2.41x10-7 Torr) was used in order to maintain steady-state growth at the substrate temperature of 630 °C. The BEP is the pressure of a hypothetical In gas for which the random flux arriving at the surface would equal that from the In evaporation source. For the first two In layers, oε2 4 is seen to increase linearly with coverage in the photon energy range of 2.5-5.5 eV and to return to the initial value when the In source is shut off, allowing the surface In to desorb. Thus the interface appears to be non-reactive, and observation of the imaginary component, o ε2 4 , as a function of both temperature and In BEP shows that the first layer grows more rapidly than the second. In the proposed model, the first layer forms in registry with the GaN surface with In occupying T1 sites, where it bonds to one Ga and forms In-In bonds to its neighbors. Due to the greater size of In vs. Ga, the first layer is complete at θIn = 0.7 ML (where 1 ML means one In per surface Ga). The second layer, which is not necessarily in registry with the substrate, begins to resemble bulk In. After completion of the second layer, subsequent growth occurs in the form of droplets, or 3D islands, rather than as a uniform wetting layer. An indicator of this 3D growth is the onset of light scattering, resulting in depolarization and a loss of specularly-reflected intensity, which suggests that the dimensions of the islands are comparable to the wavelength of the light. The time dependence of oε2 4 after the In supply is turned off suggests that desorption occurs by a mechanism in which In leaves the second layer and the vacancies thus created are filled by In diffusing from the 3D islands. This continues until the islands are depleted, at which point the second layer undergoes permanent loss of In. The kinetics of In adsorption and desorption were studied by observing o ε2 4 vs. time as a function of BEP at different temperatures. An activation energy of ΔEa = 2.64 eV is found for desorption from the first ML, which is only slightly greater than that for bulk In (2.52 eV), suggesting that the first ML is stabilized mainly by In-In bonds. For desorption from the second layer, ΔEa = 2.53 eV, and the difference between ΔEa for the first and second ML represents the small effect of In-Ga interaction. These results are similar in some respects to those obtained for Ga adsorption (Section 5.18) by the same group. Moon et al. [682] reported XPS data for In deposited on GaN (0001̄ ). The samples were not prepared under well-controlled (i.e., atomically-clean) conditions but rather involved electron-beam evaporation of In at a base pressure of 5x10-7 Torr onto substrates that had been subjected to dry (presumably plasma) etching. For both the as-deposited In layer and after a 300 °C anneal, the In 3d5/2 showed evidence of both In-In and In-N bonding, which indicates an interfacial reaction. Although no assessment of contamination was provided, the data show only a small contribution from In-O bonds. These results are significant in light of those of Choi et al. [681] since they suggest a possible difference in reactivity between In and the (0001) and (0001̄ ) surfaces. Neugebauer et al. [684] studied the surfactant effect of In on GaN (0001) theoretically using the LDA with soft (Troullier-Martins) PPs and a 2DPS consisting of four Ga-N bilayers with the DBs on the bottom surface saturated with PHs. A phase diagram was computed which, under In-poor conditions, reproduces the reconstructions of a clean GaN surface; namely, a (2x2) N adatom structure, followed by a (2x2) Ga adatom phase, then a Ga bilayer and finally Ga droplets as one progresses from N-rich to Ga-rich conditions. Under extremely N-rich conditions, In incorporates into the first and second bilayers where it forms an InGaN alloy. In a less N-rich or a moderately Ga-rich environment and under Inrich conditions a (1x1) In adlayer forms, and the diffusion barrier for a Ga adatom on this surface is only 0.12 eV vs. 0.7 eV on the

bare surface, which constitutes surfactant behavior on the part of In. For the same In adlayer, an N adatom is found to adsorb between this layer and the underlying Ga layer. The diffusion barrier is 0.5 eV for a path in which N remains below the In layer vs. 1.3 eV on the bare surface and 41.5 eV for a path in which the N moves above the In layer. The mechanism identified for the increased N mobility, termed adlayer-enhanced lateral diffusion (AELD), is based on the formation of a relatively strong In-N bond in the diffusion transition state, which reduces the height of the energy barrier. In N diffusion, the initial stable state has N back-bonded to three Ga atoms and weakly interacting with one In adatom. In the transition state, two of the back-bonds are broken, and N is positioned between one Ga and the In. The same study presented experimental verification by comparing STM data for MBE growth on (0001) and (0001̄ ) surfaces under N-rich conditions with and without an In adlayer. In the case of the (0001̄ ), In is found to substitute for surface Ga in addition to forming an adlayer via In-N bonding; whereas, little or no substitution is found on the (0001) except under extremely N-rich conditions. Thus In appears to be more reactive with the (0001̄ ) surface, in agreement with the experimental results described above. In accord with the proposed AELD mechanism, growth on the (0001) gives a smoother surface, suggesting higher N mobility, with the In adlayer than without; whereas, In has no similar surfactant effect on the (0001̄ ). Northrup and Van de Walle [685] performed LDA calculations comparing the stabilizing effects of an H vs. an In adlayer on the (0001) surface. A 2DPS with four Ga-N bilayers and the bottom DBs saturated with PHs was used, and all atoms in the slab were allowed to relax during optimization. The energy needed to incorporate In at a Ga site in the surface is found to be large (2.0 eV) since an In-N bond is weaker than a Ga-N bond. The relative stabilities of different surface phases at 1100 K were calculated vs. μGa for a high (1 atm) pressure of H2 and for very In-rich conditions just below the point of droplet formation. These are considered to be typical of the conditions achievable during MOCVD growth on GaN. The most stable phase for any degree of Ga richness is found to be an In bilayer in which the first layer is adsorbed at T1 sites and the second at T4. The AELD diffusion barrier for N in the presence of the In bilayer is found to be 0.4 eV, slightly less that the value of 0.5 eV found by Neugebauer et al. [684] for just the single In adlayer. Thus In can function as a surfactant in both MBE and MOCVD even though the latter process typically involves a high ambient H2 pressure. Timon et al. [566] and Salinero et al. [686] performed calculations for In on GaN (0001) using methods described above (Section 5.1) in connection with their Al work. The calculations addressed a situation in which the (0001) surface is covered with a full ML of N adatoms in T1 sites and then each of the 4 adatoms in a (2x2) SUC is sequentially replaced with In. The goal was to investigate the structure and stability of various adlayer (2x2) surfaces involving impurity species. With 2 In and 2 N per SUC the adsorbed N atoms form a dimer with a bond length of 1.21 Å (vs. 1.09 Å for free N2). With 1 In and 3 N, the adsorbed N atoms form a triangular trimer structure with bond lengths of 1.51 Å. Under In-rich conditions, a surface with 4 In per SUC is the most stable for all conditions from N- to Ga-rich; whereas, for In-poor conditions the In-free surface, with a reconstruction that depends on μGa, is the most stable [686]. ̄ Northrup et al. [418] studied In incorporation on the (1011) surface theoretically together with an investigation of the In-free surface as discussed in Section 4.6.4.1. In the Ga adlayer that forms on this surface under Ga-rich conditions there are two different Ga sites. These are T1, with Ga back-bonded to a single three-foldcoordinated N atom, and B2, with Ga in a bridge between two-fold N sites. Substitution of In for either a T1 or a B2 Ga is very

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exothermic, giving an energy lowering of 2.0 (1.5) eV for T1 (B2) in a situation where the In out-diffuses from the bulk, which simulates surface segregation. Northrup and Neugebauer [683] studied theoretically the effects of In on surface morphology for the — ̄ and (1011 (0001), (0001̄ ), (1011) ) surfaces. The calculations used the LDA with soft PPs for which the Ga 3d and In 4d orbitals were treated as valence states. The 2DPS supercells contained from 20 to 50 atoms depending on the system. It is found that In acts as a differential surfactant, i.e., one that changes the relative surface energies of different surface orientations. Under the N-rich conditions required for incorporation, In lowers the surface energy of ̄ much more than that of (0001). This alters the growth the (1011) morphology of the (0001) surface by promoting the formation of ̄ facets. On the other hand, the (0001̄ ) hexagonal pits with (1011) — surface does not exhibit an analogous formation of (1011) facets. 5.23. Iron The interaction of Fe with GaN (0001) and (0001̄ ) surfaces has been studied experimentally in Refs. [688–698] and Refs. [695,699] respectively, not all of which involve atomically-clean surfaces. Theoretical work for the (0001) surface has been reported by González-Hernández et al. [618,700,701] and by Lin et al. [697] and for the (0001) and (0001̄ ) surfaces by Gao et al. [695]. The main point of interest is in possible spintronic applications. Meijers et al. [688] and Calarco et al. [689] used LEED, XRD, AFM and RBS to study the epitaxial growth of Fe on MOCVD GaN (0001). Clean surfaces were prepared by heating to 800 °C in UHV, which reduced the level of C and O contamination as seen in AES and also gave a sharp (1x1) LEED pattern. Iron was deposited in situ, to a thickness of between 5 and 70 nm, with the substrate at either RT or 250 °C and then annealed at 500 °C. (For an Fe density of 7.874 gm cm-3, 1 Å = 8.492x1014 Fe cm-2 = 0.748 ML where 1 ML is defined as 1 Fe per surface lattice site.) The LEED and XRD data show that the Fe film is epitaxial with the (110) plane parallel to the surface, and AFM shows that the large lattice mismatch results in island formation. The RBS results show the presence of a small (~1% at the surface) concentration of Ga in a 70-nm Fe layer, which suggests reaction at the interface. The magnetic and structural properties of the thick Fe films were discussed in detail but are beyond the scope of the present review. Ryan et al. [690] used XPS and x-ray magnetic circular dichroism (XMCD) to study the growth of Fe layers on MOCVD GaN (0001). Clean surfaces were prepared by IBA (nitrogen ions, ~850 °C anneal) and showed no C and only a trace of O with a clear (1x1) LEED pattern, after which Fe was deposited in situ. On a wellordered surface, the decay of the Ga 3d XPS intensity with θFe indicates a uniform layer-by-layer growth with little intermixing. However, the decay of the N 1s intensity is much faster, which suggests that N (or N2) desorbs during Fe deposition, and a small N 1s signal remains for a thick Fe layer indicating that diffusion of N into the Fe also occurs. A strong low-BE satellite appears in the N 1s spectrum, which is consistent with diffusion of N into a metallic (Fe) environment. A weak low-BE satellite also appears in the Ga 3d, which is ascribed to free Ga produced by the interfacial reaction and which remains at the interface where it then prevents further reaction. On a disordered surface, for which no annealing was done after ion bombardment, the dependence of the Ga 3d and N 1s intensities on θFe indicates 3D island growth followed by coalescence of the islands to form a more uniform film. It is suggested that ion bombardment leaves a Ga-rich surface that blocks reaction with the Fe, thus preventing the release of N (or N2) seen for the ordered surface. This is consistent with the absence in this case of any significant Ga 3d or N 1s lineshape changes due to Fe deposition. The magnetic ordering of the Fe was also discussed on the basis XMCD data.

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He et al. [691] used STM to observe the growth of Fe layers on both bare and pseudo-(1x1) GaN (0001) surfaces. The samples were prepared by outgassing MOCVD GaN at 300 °C in UHV followed by deposition of ∼3 ML of Ga. No assessment of surface contamination was provided. A brief anneal at 700 °C gave the pseudo-(1x1) surface, which consists of a laterally-contracted Ga bilayer on top of the Ga termination layer of the bulk lattice, and a longer anneal yielded the bare (1x1). Deposition of 0.16 ML of Fe on the pseudo-(1x1) surface leads to the appearance of ordered regions with a (√7x√7) reconstruction. At 0.48 ML, islands appear on top of the (√7x√7) regions, and further increasing θFe up to 7 ML leads to an essentially layer-by-layer growth of a smooth Fe layer. The layer growth is different on the bare surface. Here 3D island formation occurs at the first deposition of Fe and continues with increasing coverage. The magnetic properties of the films were studied using the surface magneto-optic Kerr effect. Gao et al. [692] investigated the thermal stability of epitaxial Fe/GaN (0001) using AFM, RHEED, EDAX, SIMS and XRD. Samples were grown by MBE and Fe deposited in situ at 50 °C followed by anneals at a series of temperatures up to 900 °C. The bare surface was formed by desorbing the Ga bilayer following growth but was not further described. The anneals were performed ex situ, in an N2 ambient, using a rapid-thermal-anneal (RTA) apparatus. The RHEED data indicate growth in the form of 3D islands (i.e., a Volmer-Weber process [571]) as well as multi-domain epitaxy. The morphology of a ∼37 nm-thick Fe layer is independent of annealing temperature up to 650 °C, but at 850 °C large grains appear that contain substantial amounts of Ga and O. The O is found to have entered during the RTA process. The XRD data show that the Fe (110) plane lies parallel to the GaN surface, and SIMS shows that there is no interdiffusion up to 650 °C. The crystalline quality of the Fe film improves with increasing annealing temperature up to 650 °C; however, for an anneal at 4850 °C, an FexGa1-x phase appears in EDAX. which indicates decomposition of the GaN substrate. The effects of annealing on the Fe magnetic properties were also examined. Honda et al. [693] used RHEED and STM to observe the growth of Fe nanostructures on GaN (0001). The samples were MOCVD substrates that were cleaned in a piranha solution (Section 3.1) to remove oxide before mounting in the UHV system. The as-inserted samples showed a (1x1) RHEED pattern, after which Fe was deposited in situ. Initially, a ring-like RHEED pattern appears, which indicates a polycrystalline Fe layer. After about 0.5 nm of Fe, RHEED indicates the presence of epitaxial α-Fe (i.e., the bodycentered-cubic structure). The STM data show the presence of Fe nanodots that grow in size with increasing Fe coverage. The shape and epitaxial orientation of the nanodots, and the Fe magnetic properties, were discussed briefly. Gao et al. [694] performed RHEED ϕ scans during deposition of Fe on GaN (0001) at 50, 350 and 500 °C. The samples were grown by MBE, and the Ga bilayer remaining from growth was desorbed prior to in situ Fe deposition. Here the RHEED pattern is recorded while the sample is rotated about the surface normal as the Fe layer grows. The data show that growth occurs with the Fe (110) plane parallel to the GaN surface and the Fe [001] axis parallel to the GaN [112̄ 0] axis. This is the so-called Pitsch-Schrader orientational relationship (Fig. 45a), and this epitaxial ordering takes place within the first 2 MLs of deposition. It is also found, using XRD, that 350 °C is the optimum growth temperature in terms of the crystallinity of the Fe film. Gao et al. [695] used RHEED, high-resolution XRD and electron back-scatter diffraction (EBSD), as well as ab-initio theory, to study the deposition of Fe on GaN (0001) and (0001̄ ) surfaces. The samples were grown by MBE and Fe deposited in situ at a substrate temperature of 350 or 500 °C. For the (0001) surface, RHEED shows that the Fe layer forms with the Pitsch-Schrader

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Fig. 45. Upper: Schematic ball-and-stick models for Fe (red) in the (a) PitschSchrader, (b) Burgers, and (c) cube-on-hexagon orientational relationships on the top Ga layer (yellow) of GaN (0001). The models show a superposition of all symmetry-equivalent orientations (which in reality do not coexist in one unit cell) and the dashed rectangle highlights one of these orientations. Lower: Theoretical surface energies for Fe films of different thickness in MLs grown on Ga- and N-polar surfaces of GaN, in three different orientational relationships. The dotted lines represent linear extrapolations arising from the small residual strain in the bulk. From Gao et al. [695] (Copyright 2010 by the American Physical Society).

orientational relationship described above. On the other hand, for (0001̄ ), two distinct diffraction patterns are seen. The orientational descriptions given here are those provided in the original reference.In the first, the Fe (101) plane lies parallel to the GaN — (0001) and the Fe [111] or Fe [111̄ ] axis lies parallel to the GaN ̄ [1120], which is termed the Burgers orientational relationship (Fig. 45b). In the second, the Fe (001) plane lies parallel to the GaN (0001) and the Fe [010] axis lies parallel to the GaN [112̄ 0], which is described as a "cube-on-hexagon" orientational relationship (Fig. 45c). The interpretation of the RHEED data was confirmed using high-resolution XRD experiments, and ab-initio computation (discussed below) provided consistent results for the relative stability of the different orientational relationships. Wong et al. [696] used RHEED to observe the growth of Fe films (2.5 to 150 MLs thick) on GaN (0001). Samples grown by MOCVD were cleaned in 1:1 HCl:H2O and 1:99 HF:H2O followed by annealing in UHV at 600 °C. No information regarding surface contamination was provided. The Fe layer is found to grow in the form of 3D islands, and the films are not continuous below 2.5 ML but instead form clusters. Data from XRD show that the Fe (110) plane is parallel to the surface in agreement with other results noted above. The magnetic properties of the films were also measured and discussed. Lin et al. [697] used RHEED, STM and ab-initio theory to study the initial adsorption of Fe deposited in situ on GaN (0001) grown by MBE. The theoretical aspect will be discussed later in this section. The starting surface was the pseudo-(1x1), with a Ga bilayer on top of the Ga lattice termination layer. Two different forms of this pseudo-(1x1) were considered; namely, the socalled "(1+1/12)" and "(1+1/6)" structures, which were discussed in Section 4.6.1 (Ref. [340]). Deposition at 360 °C on the (1+1/12), which is the more Ga-rich of the two structures, yields a smooth

and well-ordered surface with (√3x√3)R30° phase at growth temperature that develops into (6x6)-reconstructed patches at RT. The metallic Ga bilayer is liquid-like at the Fe deposition temperature, and it is suggested that Fe induces (√3x√3)R30° ordering in this fluid phase which then becomes the precursor for the (6x6) structure upon cooling to RT. It is further demonstrated, on the basis of STM line profile height measurements, that the (6x6) structure involves adsorption of the Ga that is displaced by Fe incorporation into the liquid-like layer. Kim et al. [698] observed the effects of Fe film thickness on the magnetic properties of Fe/GaN (0001). Although somewhat beyond the scope of the present review, this work reports results that pertain to the current discussion. It is shown that GaN films grown on c-plane sapphire by hydride VPE are significantly strained, which can affect the magnetic properties of a thin Fe film via magnetostriction. Nearly strain-free interfaces were formed by MBE deposition of Fe on MOCVD GaN that was first "degreased" in organic solvents, then immersed in HCl solution followed by buffered HF solution and finally outgassed at 200 °C in UHV. No surface-analysis results were reported. It was found that the roughness of the interface increases with Fe thickness, which might then result in interdiffusion. Orlowski et al. [699] studied the growth of Fe layers on the GaN (0001̄ ) surface using UPS. The sample was a bulk single crystal that was mechanically and chemo-mechanically polished and then cleaned by IBA, after which up to 4 MLs of Fe were deposited in situ. No further sample characterization was provided. The Fe contribution in the VB region was resonantly enhanced using an excitation energy of hν = 56 eV, which corresponds to the Fe 3p→3d transition. The resonant enhancement can be described as Fe(3p63d6) + hν → Fe[3p53d7]* → Fe(3p63d5) + e− where [...]* is a transient excited state. This process occurs in addition to the normal non-resonant excitation. After deposition of 2 or 3 ML at RT, VB features attributed to FeN appear, which suggests a reactive interface. A clear Fermi edge is observed, indicating the presence of metallic Fe islands. Annealing at 500 °C causes a loss in intensity for all Fe-derived features, including the Fermi edge, which is attributed to Fe diffusion into the substrate with the formation of an FexGa1-xN intermixed layer. The existence of Fe-N bonding is demonstrated by comparison of the UPS data with a calculated DOS for FeN. In summary, the experimental results cited above for Fe provide another example of the apparent dependence of metal/GaN interfacial reactivity on the details of the clean-surface preparation; although, not all studies are equally sensitive to such processes. Surfaces prepared by IBA or simply by heating in vacuo show more obvious evidence of reactivity with Fe at or near RT than do other substrates. In some studies the initial surface may not have been atomically clean; hence, another factor is the possible presence of impurity C and/or O, which may inhibit metal/GaN reaction. There is also evidence that excess Ga at the surface can inhibit reaction with Fe. This might account for the lack of obvious reaction when Fe is deposited in situ on MBE samples since such surfaces typically involve one or more adlayers of metallic Ga. Beyond considerations of interfacial reactivity, Fe appears to grow epitaxially on GaN (0001); although, the morphology and crystallinity depend on the details of the growth process. González-Hernández et al. [618] performed theoretical studies of Fe interacting with the GaN (0001) surface using methods described previously in the discussion of their Cr results. Adsorption at the H3 site is slightly more favorable than at T4 (ΔEads = -3.698 eV for H3 vs. -3.651 eV for T4) but much more favorable than at T1 (ΔEads = -2.286 eV). The small preference for H3 over T4 is attributed to a weakly-repulsive interaction with the first-underlayer N atom. The magnetic moment per (2x2) SUC with one Fe at an H3 site is 3.22 μB vs. 4 μB for the free atom, which is

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attributed to the charge transfer of 0.411 |e| from Fe to GaN that reduces the unpaired spin density. The diffusion barrier from H3 to T4 is about 0.39 eV (which is very close to the barrier computed for a Ga adatom) and slightly higher than the barrier from T4 to H3, which reflects the greater stability of H3 vs. T4. The clean but unreconstructed (0001) surface shows a band of metallic states at EF due to the partially-filled Ga DBs. Adsorption of Fe reduces the DB DOS and introduces additional states in the gap. Only the majority-spin DOS crosses EF, which indicates a semi-metallic character. González-Hernández et al. [700] carried out further theoretical studies of Fe/GaN (0001) that were aimed at understanding the structure and stability at higher Fe coverages. The 2DPS comprised a (2x2) SUC with 8 Ga-N bilayers and the bottom surface terminated in PHs with the adlayer and the uppermost 2 Ga-N bilayers free to relax. For θFe = 0.25 (i.e., one Fe per (2x2) cell), the results are essentially the same as those obtained previously [618]. The H3 site is slightly more stable than the T4, and the large ΔEads (-3.700 eV per Fe in H3) suggests a high degree of stability. With increasing θFe up to 1 ML, the T4 site becomes more stable than the H3, and at 1 ML the respective values for ΔEads are about -3.65 and -3.37 eV per Fe. The large magnetic moment of 3.19 μB per Fe at 1 ML indicates ferromagnetic ordering. Diffusion between H3 and T4 occurs via the bridge (Br) site, which is the transition state. Here Fe forms a bridge between two nearestneighbor surface Ga sites, and the H3→T4 diffusion barrier is 0.37 eV and 0.34 eV in the reverse direction. For θFe = 0.25 in H3, the DOS shows ferromagnetic, semi-metallic character as before [618]. The semi-metallic description is based on the appearance of a small band gap for the minority-spin states. The majority-spin states near EF arise mainly from Ga DBs that remain partially filled after Fe adsorption, while the minority states near EF originate mainly from Fe 3d orbitals. In the case of the T4 site, both spin states exhibit metallic behavior; however, the minority-spin state near EF, which is localized on the Fe, is below EF for H3 and above EF for T4. Charge density difference plots were given, which show a covalent Fe-Ga interaction with a transfer of electron density of 0.23 (0.36) |e| from Fe to Ga for H3 (T4). González-Hernández et al. [701] also studied the incorporation of Fe into the GaN (0001) surface, either bare or covered with a pseudo-(1x1) laterally-contracted Ga bilayer. The methodology was essentially the same as that described above in the discussion of their Cr results [618], with a (2x2) SUC for the bare (1x1) and a (√3x√3) cell for the pseudo-(1x1). For the bare surface, substitution of one Fe per (2x2) cell is least unstable in a surface Ga site (ΔEf = 0.41 eV, an endothermic value). Substitution in an N site or as an interstitial or in a subsurface Ga site, is much more endothermic. At a high Fe concentration, N-rich conditions favor the incorporation of 4 Fe atoms per (2x2) cell, all in the surface Ga sites, which is stabilized by Fe-N bond formation. This surface is ferromagnetic with an average total magnetization of 3.60 μB per Fe. Upon progressing to more Ga-rich conditions, incorporation of 3 Fe atoms becomes most favorable, followed by an Fe-free surface with Ga adsorbed in a T4 site and finally an Fe-free Ga bilayer. Lin et al. [697] performed theoretical studies of Fe incorporation into the GaN (0001) pseudo-(1x1) surface in connection with their STM experiments, described above. The calculations used PWs with USPPs and an unspecified GGA functional, most likely the PBE. The 2DPS comprised 4 Ga-N bilayers with the bottom surface terminated in PHs and the lowermost bilayer fixed in the bulk-lattice geometry. A double layer of metallic Ga was added to represent the pseudo-(1x1) surface, and both (√3x√3)R30° and (3x3) SUCs were considered. Under Ga-rich conditions, for which Fe incorporation into the Ga bilayer is found to be slightly favorable, three competing structures are found to have very similar energies. These are all based on a (3x3) SUC. The most favorable

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involves 2/9 ML of Fe + 21/9 ML of Ga with an additional two Ga atoms (2/9 ML) adsorbed as a dimer. Other, nearly-degenerate structures consist of 1/9 ML of Fe + 22/9 ML of Ga with or without the additional 2/9 ML of adsorbed Ga. The Fe/Ga atomic concentration ratio was determined using AES for the surface with (6x6) patches, as described above. Using the areal density of these patches, the observed ratio is in good agreement with 2/9 ML of Fe in the patches, but not with 1/9 ML, which is consistent with the calculated lowest-energy model. It is noted that all of these Ferelated structures are only slightly more stable than the Fe-free pseudo-(1x1), which means that Fe incorporation is difficult, at best, on a (0001) surface with a metallic Ga bilayer. Gao et al. [695] performed ab-initio studies for 1 to 4 MLs of Fe on the (0001) and (0001̄ ) surfaces using a 2DPS with 4 Ga-N bilayers and the bottom surface passivated with PHs. The PAW method was used together with the GGA, and all atoms except those in the lowermost bilayer were free to relax. The results (Fig. 45) are consistent with the experimental interpretation given in this reference. For the (0001), the Pitsch-Schrader orientational relationship, described above, is energetically favored for all Fe thicknesses. On the other hand, the behavior for (0001̄ ) is more complex, with each of the three structures being thermodynamically favored at different coverages. It is suggested that the Burgers and cube-on-hexagon structures are "locked in" during the early stages of growth and then persist at higher coverage, due to a kinetic limitation, even though the Pitsch-Schrader phase can be energetically more stable. 5.24. Lead Kampen and Mönch [702] deposited Pb on GaN (0001) and obtained the SBH using ex-situ I-V measurements in the dark to avoid SPV effects. Surfaces were prepared by immersion in buffered HF solution followed by in-situ cleaning via exposure at ∼800 °C to 1x1016 Ga cm-2 sec-1 (∼8.8 ML sec-1). No contamination was detected in XPS after cleaning, and a sharp (1x1) LEED pattern was observed. Lead was deposited in situ on the clean surface, and an SBH of 0.73 eV was found in the I-V experiments, but the interface was not further characterized. 5.25. Magnesium The interaction of Mg with GaN surfaces has been extensively studied due its wide-spread use as a p-type dopant in GaN. The (0001) and (0001̄ ) surfaces have been investigated experimentally in Refs. [561,562,703–717] and Refs. [706–708,718] respectively. ̄ has been studied experimentally by Tomita et al. [719] The (1011) and the (112̄ 2) by Lahourcade et al. [720] and by Das et al. [721]. Theoretical results are given for the (0001) in Refs. [367,380,419,722–727], for the (0001̄ ) by Sun et al. [725], for the ̄ by Ito et al. [380] and (101̄0) by Northrup [726] and for the (1011) by Akiyama et al. [419]. There are several points of interest regarding Mg/GaN. These include (a) the adsorption of Mg and its effects on surface electronic structure, (b) the surfactant effect of Mg during GaN growth, (c) the incorporation of Mg under growth conditions, (d) the phenomenon of polarity inversion caused by surface Mg during growth and (e) the surface segregation of Mg incorporated as a dopant. Given the nature of the present review, the focus here will be mainly, but not entirely, on Topics (a) and (e) while omitting most other work that pertains largely to material growth. Wu and Kahn [561] used UPS, XPS, AES and LEED to study Mg on n- and p-GaN of uncertain polarity, which was nominally (0001) Ga-polar. The experimental details were summarized previously in the discussion of their work with Al (Section 5.1). Deposition of up to 25 Å of Mg leads to the appearance of a low-BE Ga

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3d satellite, due to reaction at the interface that releases free Ga into the Mg layer, and an attenuation of the Ga 3d intensity. (For a Mg density of 1.74 gm cm-3, 1 Å = 4.312x1014 Mg cm-2 = 0.380 ML, where 1 ML is defined as 1 Mg per surface lattice site.) For the first Mg deposition (3 Å) a Mg 2p peak appears that is assigned to MgN bonding, and, for thicker films, a metallic Mg 2p XPS emerges. A thin Mg film has little or no effect on EF-VBM for n-type GaN but increases this quantity (i.e., the downward BB) by 0.95 eV on ptype GaN, which is ascribed to the formation of a Schottky barrier with a low-work-function metal (ϕ = 3.66 eV for polycrystalline Mg [615]). It should be noted that EF-VBM measured for p-type GaN in UPS and XPS can be affected by the large SPV effect (Section 4.7.3.2). Thus, some of the increase in downward BB seen after Mg deposition could result from a decrease in SPV-induced "band

flattening". Annealing at 900 °C desorbs all metallic Mg but leaves a small residual coverage, which is attributed to Mg that has diffused into the GaN, and also decreases EF-VBM by 0.25 (0.35) eV on n-type (p-type) GaN, relative to the bare surface, which is ascribed to an increased density of acceptors due to in-diffused Mg. Bermudez [703] used AES, XPS, ELS and LEED to study the interaction of Mg with n-type MOCVD GaN (0001). Surface-sensitive Ga 3d and Mg 2p XPS data were obtained using Zr Mζ excitation (hν = 151.65 eV [570]). Clean surfaces were prepared by IBA (nitrogen ions, 1170 K anneal) after which no impurities were detected in AES. The sample polarity was unknown at the time but was later determined to be (0001). For a Mg thickness of 10 Å, measured using a QCO thickness monitor, a thickness of 13.0±1.8 Å was estimated from the attenuation of the N KLL Auger spectrum.

Fig. 46. (Left) Zr Mζ-excited Ga 3d for (a) clean GaN and (b) after deposition of 10 Å of Mg. The points are the data after numerical processing to enhance resolution, and the lines show least-squares fits with Gaussian-broadened Lorentzians. The residuals (fit minus data, not statistically weighted) are also shown on a vertically-expanded scale. The polynomial background obtained as part of the fit has been subtracted from the data for display purposes. The relative intensities are approximately quantitative, EF is at 146.41 70.1 eV and "0" on the vertical scale refers to the residuals. The data show the attenuation of the Ga 3d intensity by the Mg layer, the ∼0.6 eV increase in upward BB (in the form of the shift to lower BE) and the appearance of a shoulder due to Ga in a metallic environment. (Right) Similar data obtained before and after annealing. The data show the increase in intensity when the metallic Mg desorbs, the slight (∼0.1 eV) decrease in upward BB and the persistent free-Ga satellite that is shifted closer to the GaN component. The same data are shown in the Left (b) and Right (a) panels. The schematic diagram below (not to scale) shows the proposed model for the interface (a) before and (b) after annealing. The "adatoms" could also be small non-metallic clusters. From Bermudez [703] (Copyright 1998, reproduced with permission from Elsevier).

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From the similarity of these results it was inferred that the layer grows essentially uniformly with little or no N incorporation into the metal layer, since either island formation or intermixing of N would lead to an apparent AES thickness smaller than the QCO value. A 20 Å Mg layer gives a low-background (1x1) LEED pattern characteristic of the hexagonal metal as seen by the dependence of the spot intensity on beam energy, which agrees with results for the (0001) face of a Mg bulk single crystal. This indicates epitaxial growth as expected from the similarity of the Mg (3.209 Å) and GaN (3.190 Å) basal-plane lattice constants. A 4 Å-thick Mg film shows surface and volume plasmon losses in ELS like those seen for thicker films; whereas, such features are not clearly seen for a 2 Å film, which suggests that the onset of metallic behavior occurs after completion of the first ML (∼2.6 Å). A series of Mg depositions, up to a total of 20 Å, leads to the appearance of a low-BE satellite in the Ga 3d XPS (Fig. 46) and a high-BE feature in the Mg 2p. In the Ga 3d, the satellite intensity relative to that of the bulk-GaN peak saturates after ~10 Å, above which the intensity ratio is nearly constant. Simultaneously, the VBM shifts from 2.60 eV below EF on the clean surface (upward BB of ∼0.80 eV) to 2.02 eV below EF (upward BB of ~1.38 eV) after about 10 Å of Mg. Almost all of the change in EF-VBM occurs during deposition of the first ML, i.e., before the Mg layer becomes metallic. These results are interpreted in terms of reaction at the interface in which Mg displaces Ga to form Mg-N bonds and release free Ga, which remains near the interface. This is believed to be driven thermodynamically by the higher ΔHf of Mg3N2 vs. GaN. Due to the volatility of Mg, a 10 Å-thick metal film is entirely desorbed by a brief anneal at about 520 K, after which AES shows about ~0.5 ML of residual Mg, ELS shows no Mg plasmon losses and LEED indicates a disordered surface. A subsequent anneal at 620 K does not further reduce the Mg coverage. The low-BE Ga 3d satellite remains after the 520 K treatment (Fig. 46) but is shifted to slightly higher BE relative to that seen when metallic Mg is present. The Mg 2p after annealing can be resolved into two overlapping peaks, both of which are at higher BE than for metallic Mg, and EF-VBM increases very slightly, by o0.1 eV. This is interpreted as follows. After desorption of Mg metal, some Mg remains in the form of adatoms and as atoms incorporated into the GaN surface and bonded to N. This gives the two Mg 2p features, with the adatoms appearing at the lower BE of the two. Likewise, the Ga displaced by the reaction remains as adatoms with a BE that is closer to that in GaN due to the loss of metallic screening. The progression in BEs for element X (X in GaN 4 X adatom 4 X in metal) has been seen elsewhere for the Ga 3d in GaN [638]. The conclusion is that the shift in EF-VBM seen during deposition is not directly related to an SBH since it takes place mainly before the Mg layer becomes metallic and is largely unaffected by desorption of the metallic Mg. It is instead ascribed to the presence of Mg acceptors, which increases the density of electron traps at the surface. There are points of agreement and disagreement between Refs. [561] and [703]. Both agree that the interface is reactive, releasing free Ga that remains at the interface and producing Mg-N bonds, and that some Mg remains after desorbing the unreacted metal. Both also agree that Mg incorporated into GaN increases the concentration of acceptors, which decreases EF-VBM in n-type material by 0.25 eV [561] or ~0.50 eV [703], relative to the clean surface, after desorption of the metallic Mg. The major disagreement concerns whether acceptor activation requires annealing [561] or occurs spontaneously when Mg is deposited at RT [703]. The annealing temperature after Mg deposition was much higher in Ref. [561] (900 °C) than in Ref. [703] (520 K ≈ 250 °C), the latter being just high enough to desorb metallic Mg without significantly affecting the GaN. A possible explanation for the different behavior might be a higher content of residual, near-surface H in the

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samples used in Ref. [561]. In this scenario, Mg incorporation occurs spontaneously, as in Ref. [703], but acceptor activation does not occur until Mg-H complexes are decomposed during hightemperature annealing. The "poisoning" of the Mg dopant by MgH bonding is a well-known effect in p-GaN (e.g., Ref. [25]). In this case, the BB change seen for the initial deposition of Mg on p-GaN is then the result of SB formation as originally suggested by Wu and Kahn. Here the activation of the Mg dopant in the bulk of the as-grown material (as opposed to the deposited Mg) occurs during the annealing that is done during IBA. Yang et al. [704] used synchrotron-based photoemission microscopy to study Mg on MOVPE GaN (0001). The samples were cleaned by heating in UHV, but no further details or diagnostic results were presented. Mg layers were found to grow in a Stranskii-Krastanov mode [571], i.e., uniformly for the initial wetting layer followed by island formation at higher thicknesses. The Ga 3d shows a low-BE satellite, as seen in the studies discussed above, indicating a reactive interface. Also, the Ga 3d BE for bulk GaN varies by as much as ∼0.5 eV between different locations on the surface, which correlates with variations in the Mg thickness and is attributed to BB differences. Ramachandran et al. [706] used RHEED, AFM and STM to study the interaction between Mg and GaN (0001) under MBE conditions. Under N-rich conditions, a rough surface forms under normal conditions due to 3D growth, but a smooth surface results when growth occurs in the presence of Mg. Under very N-rich conditions a (2x2) RHEED pattern is observed. The effect of Mg on surface morphology indicates that it acts as a surfactant to facilitate 2D layer growth. Only a small Mg coverage (∼0.2 ML) is sufficient to achieve an effect, and the Mg tends to segregate to the surface under growth conditions. The surfactant effect is explained in terms of the ECR and the appearance of the (2x2) reconstruction. It is proposed that replacing 3/4 ML of Ga with Mg, i.e., 3 Mg per (2x2) SUC, yields a passivated surface with no partially-filled DBs over which Ga can diffuse readily to give 2D growth. There are four Ga atoms per (2x2) SUC, which contribute a total of 3 |e| in DBs on the ideally-terminated surface. Removing three Ga per cell, each with 3 |e|, and replacing them with three Mg, each with 2 |e|, eliminates the three excess electrons to give a surface with all DBs empty that satisfies the ECR. Li et al. [707] and Ptak et al. [708] found that Mg incorporation during MBE growth depends on the GaN polarity, being much higher for the (0001) than for the (0001̄ ) surface. This topic, although important, is mentioned here only in passing since the same effect might be expected to apply to the case of Mg adsorption under UHV conditions. It is suggested here that the difference might be explicable in terms of stronger Mg-N vs. Mg-Ga bonding (which would make it easier for Mg to replace Ga than N) and/or in terms of the ECR, which indicates that replacing N with Mg does not easily yield a passivated surface. In an extension of the work described in Ref. [561], C.I. Wu et al. [562] prepared Mg/n-GaN (0001) contacts in situ on atomicallyclean substrates and studied them using ex-situ I-V measurements. The experimental procedures were described in Section 5.1 in connection with their work on Al/n-GaN (0001); however, the source of the GaN used in these studies was different from that in Ref. [561] but the same as that used by Bermudez [703]. The SBH found from I-V data (0.62 eV) agrees fairly well with the photoemission result (0.8 eV). However, the I-V results show the effect of the reaction product layer at the interface. This takes the form of a voltage-dependent barrier height and an increased carrier recombination rate due to defects associated with the reaction layer. It is also noted in passing that L.L. Wu et al. [728] have found that a heavily Mg-doped layer on a p-type GaN surface (of unspecified orientation) can improve the Ohmic properties of contacts prepared under non-UHV conditions.

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Hashizume [709] used AES and XPS to study the effects of Mg accumulation on the (0001) surface of Mg-doped p-type GaN after exposure to room air. The bulk Mg density for different samples was in the range of 3-9x1019 cm-3. The samples were cleaned by immersion in aqueous KOH or NH4OH at 50 °C to remove contaminants remaining from growth and handling but were not otherwise treated other than, in some cases, by exposure to an N2 plasma at 300 °C. The concentration of Mg within the AES and XPS sampling depths is found to be more than an order of magnitude higher than in the bulk (measured using SIMS), which is evidence for surface segregation. The O 1s XPS shows the surface oxide to be a mixture of MgO and Ga2O3, and the Ga2O3 component is not greatly reduced in intensity by the aqueous KOH treatment, unlike in the case of a Mg-free sample. It is suggested here that the MgO might form an outer protective layer on top of the Ga2O3 or that the mixed oxide might constitute an etch-resistant compound. The Ga 3d and N 1s XPS data also provide evidence for a thick (3 to 4 nm), disordered and chemically-resistant oxide layer for heavily Mg-doped GaN. The Fermi level falls only a little below mid-gap, indicating a large downward BB, which is ascribed to hole trapping by defects at the oxide/GaN interface. Ramachandran et al. [705] first reported that GaN polarity can be inverted (i.e., switched from Ga- to N-polar) during MBE growth through Mg exposure, and this phenomenon has been further studied by Grandjean et al. [710], Green et al. [711] and Pezzagna et al. [713] among others. This topic, although important, is mentioned here only in passing since it is primarily a growthrelated issue. Schmidt et al. [714] used XPS microscopy to study the segregation of Mg from the bulk to the (0001) surface. The surface preparation, if any, was not described, but the bulk Mg density was 1x1020 cm-3. Even at this high a density, Mg should not be detectable in XPS since the Mg/Ga concentration ratio is only ∼1x10-3; nevertheless, a Mg 2p XPS peak is clearly seen. This feature is only partly removed by Ar+-ion bombardment, which suggests that the Mg enrichment extends at least a few tens of nanometers into the bulk. As a result of this segregation, the nearsurface p-type doping can be significantly higher than that in the bulk. The possible contribution of MgO, resulting from the oxidation of surface-segregated Mg dopant, to persistent low levels of O impurity on GaN surfaces was noted in Section 3.5. Pezzagna et al. [715] used RHEED and STM to study the layerby-layer growth of Mg on GaN (0001) under MBE conditions. An immediate onset of epitaxial growth occurs when the substrate at RT is exposed to Mg, and the deposited layer is continuous beginning at a coverage of about 2 ML. The evolution of the surface morphology with θMg, which is somewhat complex, was studied in detail for values below 2 ML. Xing et al. [712] and Tomita et al. [716] used SIMS to study Mg segregation on the (0001) surface. This was done by using MOCVD to grow a nominally-undoped GaN layer on a heavily Mg-doped GaN template and observing the resulting Mg concentration profile in the undoped overlayer. Schmidt et al. [717], in an extension of the work described in Ref. [714], used XPS microscopy and x-ray standing waves (XSW) to study Mg segregation and incorporation on GaN (0001). As in the previous study, the bulk Mg density was as high as 1x1020 cm-3, which corresponds to a Mg/Ga concentration ratio of ∼1x10-3, and it was found that the zone of Mg surface segregation extends more than 50 nm into the bulk. The dependence of XSW data on the bulk Mg concentration, in the range of 1x1019 ≤ [Mg] ≤ 1x1020 cm-3, indicates that Mg substitutes for Ga at lower values of [Mg] but also incorporates in non-substitutional sites at higher [Mg]. These sites are thought to involve defects that were either present before Mg doping or else were produced as a result of the doping. A model involving inversion domain boundaries was developed to account for Mg

incorporation at non-substitutional sites. Proceeding now to other surfaces, Ramachandran et al. [706] used RHEED and STM to observe several Mg-induced reconstructions on (0001̄ ) surfaces that were formed on the (0001) by the Mg-induced polarity inversion [705] occurring during growth, as mentioned briefly above. Deposition of 0.04 to 0.08 ML of Mg on the Ga-adlayer-terminated (0001̄ )-(1x1) surface leads to a (5x5) reconstruction, which transforms to (4x4), (3x3) and (6x6) with increasing θMg. This progression can be reversed by desorption of the Mg at 400 °C. The structures were not analyzed in detail but are thought to arise from weakly-bound Mg substituting for Ga in the various (0001̄ ) adlayer+adatom structures (Section 4.6.2). Tanikawa et al. [718] used AFM and optical microscopy to investigate the effects of Mg on the (0001̄ ) surface morphology of GaN grown by MOVPE. It is found that Mg enhances the surface diffusion of Ga during growth, which reduces the size of hillocks but increases step bunching. Tomita et al. [719] studied Mg seḡ surface using methods described regation on the semi-polar (1011) above in connection with similar work [716] for the (0001). Less ̄ than for (0001), which sugout-diffusion of Mg occurs for (1011) ̄ surface occurs more gests that incorporation of Mg into the (1011) easily than into the (0001). A high density of bulk H was also seen ̄ sample, which was suggested to be a contributing in the (1011) factor in Mg incorporation. Lahourcade et al. [720] and Das et al. [721] used SIMS, AFM and other techniques to investigate Mg incorporation and segregation on the semi-polar (112̄ 2) surface. Mg doping is seen in AFM to increase surface roughness. For samples that are either not intentionally doped or else doped n-type with Si, a uniform Ga adlayer is present on the (112̄ 2) surface during MBE if the incident Ga flux falls within a specified range. This adlayer, which was discussed in Section 5.18 in connection with Ga adsorption [653], is important as a surfactant to promote 2D growth. With Mg doping this adlayer does not form, from which it is inferred that Mg segregates to the surface. It was also noted that no Mg-induced polarity inversion was observed in this case. The first theoretical work for Mg on GaN was that of Rapcewicz et al. [367] and Bungaro et al. [722], which addressed the difference in incorporation between the (0001) and (0001̄ ) surfaces [707,708] mentioned above. These calculations used the LDA approach with PWs and NCPPs. The Ga 3d electrons were included in the core, but a NLCC [197] was employed that avoided the need to include these as valence electrons. The model consisted of a (2x2) SUC with 4 Ga-N bilayers for which the bottom surface was terminated with PHs and the lowermost bilayer fixed in the bulk geometry. On the (0001) surface, the most stable structure (except under very Ga-rich conditions) has 1 Mg per (2x2) cell (i.e., 1/ 4 ML) substituting for a surface Ga. (This description is based on the results in Ref. [722], which differ in detail from those in Ref. [367].) It is noted here that this structure does not satisfy the ECR since removing one Ga per (2x2) cell creates a passive surface, but adding an Mg puts 2 |e| into Mg and/or Ga surface DBs. For the (0001̄ ) surface, which is terminated in an ML of adsorbed Ga under Ga-rich conditions, Mg is most stable when adsorbed on top of the Ga adlayer. Under less Ga-rich conditions, Mg and Ga adatoms remain coadsorbed on the (0001̄ ) surface. Incorporation into the Ga layer of the outermost GaN bilayer of the (0001̄ ) is highly unfavorable, unlike in the case of the (0001), which is consistent with the experimentally-observed higher Mg incorporation rate during growth on Ga- vs. N-polar substrates. Northrup [723,724] reported theoretical studies of the effects of Mg on the growth and structure of GaN (0001). Of these, Ref. [723] focuses on Mg at inversion domain boundaries, which is primarily a bulk phenomenon; whereas, Ref. [724] deals with surface effects that are the main interest here. The PW-PP approach was used with, presumably, the LDA since no GGA functional was mentioned. The 2DPS consisted of 4 Ga-N bilayers with the bottom

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surface terminated in PHs, and the Ga 3d electrons were included as valence states. Determining the relative stability of different structures involves the use of μGa, μN and μMg. For Mg, μMg = (1/3)[E (Mg3N2) - 2μN], where E(Mg3N2) is the total energy of the bulk material under the assumption of Mg-rich conditions that pertain due to the strong tendency of Mg to segregate to the surface. For N, μN is defined as described in Section 4.1.2, which leaves μGa as the only independent variable. All the most-stable structures are based on Mg substituting for Ga in the surface layer; hence, the interest is in how the energy varies with Mg concentration. Northrup noted that θMg = 1/4 ML, as proposed by Bungaro et al. [722], violates the ECR since replacing one Ga per (2x2) SUC with Mg leaves two DB electrons on an electro-positive atom (Mg or Ga). The 1/4 ML structure, and also a full ML of substitutional Mg, are found to be unstable. The θMg = 3/ 4 ML model does satisfy the ECR, as discussed above in connection with the work of Ramachandran et al. [706], and under Mg-rich conditions is found to be the most stable structure except under very Ga-rich conditions. Interesting structural changes also occur in the surface layer due to Mg incorporation. The removal of electron density from the Ga DBs causes a shift from sp3 to sp2 hybridization, resulting in a more planar surface in which both Mg and Ga are displaced inward. The ∼9% larger Mg-N vs. Ga-N bond length also leads to a compressive stress in the surface layer. With θMg = 3/4 ML, the range of μGa over which the Ga bilayer is stable is significantly reduced, which restricts the surfactant effect associated with this bilayer (Section 5.18). One assumes, though, that the θMg = 3/4 phase should aid the growth of a smooth (0001) surface, as observed experimentally by Ramachandran et al. [706]. This surface is passivated and therefore should be less able to adsorb Ga and N strongly, thereby enhancing 2D growth. Under less Mg-rich conditions, a θMg = 1/2 ML structure becomes slightly more stable than θMg = 3/4 ML over an intermediate range of μGa. The extent to which θMg = 1/2 ML can be reconciled with the ECR was not discussed (but see Ref. [726], discussed below). Sun et al. [725] performed theoretical studies of Mg adsorption and incorporation on the (0001) surface using the PW approach with USPPs and the PBE functional. The 2DPS consisted of six Ga-N bilayers with the bottom surface terminated in PHs and the uppermost three bilayers allowed to relax. A (2x2) SUC was used except in modeling the surface terminated in a metallic Ga bilayer, for which a (√3x√3) SUC was employed. For 1/4 ML of Mg on the ideally-terminated surface, displacement of a surface Ga (which then occupies a T4 adatom site) is more favorable by 1.45 eV than Mg adsorbing as a T4 adatom. The H3 and bridge sites are even less favorable since a Mg adatom placed here spontaneously moves to a T4 site during relaxation, which indicates only a small barrier for diffusion out of either site. There is a repulsive interaction between the substituted Mg and the adsorbed Ga, as a result of which the Ga occupies the T4 that is farthest from the Mg. The ΔEads at this site is ∼0.8 eV less than for Ga on the Mg-free surface, which is consistent with a surfactant effect wherein Mg weakens Ga adatom bonding and thereby enhances surface diffusion. For an N adatom, Mg incorporation increases ΔEads but greatly reduces the barrier to surface diffusion. For θMg ≤ 0.5 ML, Mg incorporates most favorably into the surface Ga layer; whereas, at higher θMg up to 1 ML, incorporation of one or two Mg per SUC into second-bilayer Ga sites becomes more stable. In these calculations for substitution (rather than site exchange), the fate of any displaced Ga atoms was not described. Structural changes are also noted. These include a flattening of layers containing Mg (as found by Northrup [724]) and, in the case of subsurface incorporation, a decoupling from upper bilayers since Mg replacing Ga within a layer does not form a bond to the next layer above it. For the "(1x1)" structure, which is formed by a metallic Ga bilayer on top of the (0001) terminating Ga layer, Sun et al. found

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that a Mg adatom is unstable and spontaneously displaces a Ga in the metallic bilayer, which remains as an adatom. For Mg incorporation at θMg = 1/3 ML (one Mg per (√3x√3) SUC), the lowest-energy Mg site is in the Ga terminating layer of the substrate, which causes an outward expansion of the metallic bilayer. With increasing θMg up to 1.33 ML, the most stable configurations have Mg substituting for Ga in the metal bilayer and in the uppermost two GaN bilayers, and the onset of a phenomenon resembling polarity inversion [705] is observed. The results are consistent with the observed accumulation of Mg near the surface during MBE growth under Ga-deficient or moderately Ga-rich conditions. A detailed series of phase diagrams was also presented to show the relative stabilities of different structures for a range of μGa under moderately- and very Mg-rich conditions. The effects of electronic excitation of the GaN on Mg incorporation into the ideally-terminated (0001) surface was also investigated, using methods described by Takeuchi et al. [657]. It is found that excitation reduces the tendency of Mg to surface-segregate, relative to what is observed in the electronic ground state. Incorporation of high concentrations of Mg into Ga sites in the second and third bilayer is still unfavorable but less so in the presence of excitation. Northrup [726], in an extension of the work described above, considered the effect of H coadsorption on the stability of Mgincorporated surfaces. The computational methods were similar to those described above, and the results are summarized in Fig. 47. A θMg = 1/2 ML structure stabilized by the adsorption of one H per SUC (termed "2Mg+H") forms and satisfies the ECR. Removing two Ga atoms from the (2x2) SUC removes the 3 |e| in DBs on the ideally-terminated surface and also introduces a deficiency of 3 |e|. This is compensated by adding two Mg atoms, with a total of 4|e|, and the "extra" |e| is then paired with the electron on H to form a Ga-H bond and give a closed-shell system. A lower-coverage (θMg = 1/4 ML) phase, with one Mg replacing a Ga to give an Mg+2H structure, is also stable. Here the 2 |e| from the Mg and the 2 |e| from the H atoms are used to form two Ga-H bonds. The one remaining Ga DB per (2x2) cell is empty, thus satisfying the ECR. Under MBE conditions that are rich in Ga but poor in H, the Mgfree (2x2) surface with one T4 Ga adatom per SUC forms at low to moderate μMg, and the θMg = 0.75 ML ("3Mg") structure described previously [723,724] occurs at higher μMg. If H2 is added so that MBE occurs under conditions that are both Ga- and H-rich, Mg incorporation into the surface layer (in the form of Mg+2H) begins at a much lower μMg than in the absence of H, for which only the 3Mg structure is stable. With increasing μMg under Ga- and H-rich conditions, first the 2Mg+H and then the 3Mg structure becomes the most stable. Growth under MOCVD conditions, which are both N- and H-rich, was also considered. At low μMg the most stable structure is the Mg-free Nads+2H with a Ga-H and an NH in an H3 site back-bonded to three Ga atoms. At higher μMg this transitions to a Nads+Mg+H structure in which Mg replaces one Ga and NH then back-bonds to the Mg and to two Ga atoms. The total of 8 |e| in N, Mg and H goes to form the four two-electron bonds, which leaves the remaining Ga DB empty. At still higher μMg the 3Mg phase is favored. Yan et al. [727] reported theoretical results for the adsorption of Mg on the ideally-terminated (0001) and (0001̄ ) surfaces, which were obtained using ab-initio MD based on the Car-Parrinello method. The BLYP (Becke-Lee-Yang-Parr) GGA functional was used together with PWs and NCPPs. The 2DPS consisted of only two GaN bilayers with a (2x2) SUC. No mention was made of how DBs on the bottom surface were terminated nor of which atomic layers were fixed or allowed to relax. On the (0001), there appears to be no strongly-preferred adatom site, in contrast to previous results [725] indicating a strong preference for T4. On the (0001̄ ), the H3 site appears to be strongly preferred. Akiyama et al. [419] and later Ito et al. [380] obtained

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Fig. 47. Various structures formed in the coadsorption of Mg, N and H on GaN (0001). (Left): (a) Nads þ2H, with 0.25 ML of N adatoms in H3 sites and 0.5 ML of H saturating the dangling bonds on the N adatoms and the Ga rest atoms. (b) Nads þ Mg þ H, with 0.25 ML of Mg bonded to four N atoms and the Nads dangling bond saturated by H. (c) 3Mg, consisting of 0.75 ML of Mg, with 0.5 ML in the top layer and 0.25 ML in the third layer. (Right): (a) 2Mg þ H, with 0.5 ML of Mg replacing Ga at the surface. (b) Mg þ 2H surface, with 0.25 ML of Mg replacing Ga at the surface. All structures have all Ga and Mg dangling bonds empty, thus satisfying the ECR. From Northrup [726] (Copyright 2008 by the American Physical Society).

theoretical results for Mg on the (0001) surface using the PW approach with NCPPs for Ga and H, a USPP for N and the PBE functional. The 2DPS consisted of four Ga-N layers and a (2x2) SUC with the bottom terminated with PHs and the lowermost two bilayers fixed in the bulk configuration. For the ideally-terminated surface under moderately to highly Mg-rich conditions, incorporation of one Mg per (2x2) cell at a surface Ga site is the most-favorable process over almost the entire range of μGa even though the ECR is not satisfied. It is suggested that Mg-Ga bond formation, which would use the two excess electrons per SUC, might contribute to the stabilization. Calculations were also done for a high pressure of H2, i.e., μH = -1.05 eV, which corresponds to ∼7.6 Torr at 1050 K or ∼760 Torr at 1300 K (Fig. 8). In this case, Mg incorporation occurs only for Mg-rich conditions and forms the Mg+2H structure shown in Fig. 47. Under conditions that are less Mg-rich, the Nads+2H (also termed Nads-H+Ga-H) structure (Fig. 47), which is free of Mg and which satisfies the ECR, is the most stable over a fairly wide range of μGa. Thus it appears from these results that a high μH impedes Mg incorporation on the ideallyterminated (0001) surface since it necessitates a higher pressure of Mg vapor. This conclusion seems contradictory to that of Northrup [726], described above; however, the calculations of Akiyama et al. considered only one Mg per (2x2) SUC under the assumption that μMg will always be much less than the Mg-rich limit under practical growth conditions. Sun et al. [725] performed theoretical studies of Mg adsorption and incorporation on the (0001̄ ) surface using methods described above in connection with their work on the (0001). For θMg = 0.25 ML on the ideally-terminated surface, Mg adsorbs strongly (ΔEads = -4.76 eV) in a T4 site; whereas, replacing a Ga in the uppermost N-Ga bilayer is unfavorable. Under moderately Ga-rich

conditions, the (0001̄ ) surface forms a (2x2) structure with one Ga adatom per cell in an H3 site. Here again, 1/4 ML of Mg adsorbs (in an H3 site) rather than displacing a Ga in the terminating N-Ga bilayer, which indicates that Mg will accumulate at the (0001̄ ) surface under N-rich or moderately Ga-rich conditions. Under very Ga-rich conditions, the (0001̄ ) is covered with a single adlayer of Ga in T1 sites, giving a (1x1) structure (Section 4.6.2). Here Mg replacing a Ga adatom is more favorable than adsorbing on top of the adlayer, which differs from the LDA result of Bungaro et al. [722] discussed above. With increasing θMg, substitution for adlayer Ga is the most favorable process for θMg ≤ 0.5 ML; whereas, at higher θMg up to 1 ML, substitution for Ga in the terminating NGa bilayer becomes favorable. A detailed series of phase diagrams was presented to show the relative stabilities of different structures for a range of μGa under moderately and very Mg-rich conditions. Northrup [726] presented theoretical results for Mg on the (101̄0) surface using either (1x2) or c(2x6) SUCs and methods described above in connection with the (0001). For a very low H2 pressure (10-10 atm) and T = 900 K, which simulates MBE growth, a (1x2) Mg+H structure is the most stable under N-rich or moderately Ga-rich conditions. Here Mg replaces half the surface Ga, and H bonds to the corresponding dimer N site (Fig. 2) to satisfy the ECR. In the (1x2) cell there is a total of 4 |e| in DBs. Replacing one Ga with Mg leaves 3 |e|, which is used to form an N-H bond on one N and a NBLP orbital on the other while leaving the cation DBs empty. At such a low H2 pressure, no adsorption occurs without the presence of Mg, which leads to the highly-stable Mg+H structure, the removal of H from which is endothermic by ∼1.5 eV. Under very Ga-rich conditions, a laterally-contracted bilayer of metallic Ga with a c(2x6) structure is used to model the Mg-free

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segregation of bulk Mg to the surface, and the accumulation of Mg near the surface is manifested by the effects on EF-VBM of the increased density of acceptors. However, as noted above, there are some discrepancies between the results [561,703] for the two studies involving IBA, and it is not clear from the available experimental data how reactive is the interface for a substrate that has been grown in situ by MBE, i.e., one that has not been subjected to high temperature in UHV during cleaning after ex-situ growth. On the other hand, theoretical studies predict the Mg-Ga site exchange that is seen experimentally [706–708] under MBE conditions. Other GaN surfaces are also relatively well understood in the context of Mg adsorption, at least theoretically. Fig. 48. Ball-and-stick model of the proposed structure for the domain wall and (√3x√3) structure for 0.33 ML of Mn on the GaN (0001) pseudo-(1x1) surface. "1st Layer Ga" refers to the lower of the two Ga adatom layers that defines the pseudo(1x1) and "2nd layer Ga" to the top Ga layer. The 1st layer Ga atoms are in T1 sites relative to the terminating layer of the lattice. In Domain I (Domain II) the 2nd layer Ga atoms are in T4 (H3) sites, and the thick domain wall represents a transition between the two. The zigzag line labeled "domain wall" marks the mid-point, where the deviation from T4 and H3 is maximal. Within the domains, Mn occupies T4 sites, which gives the (√3x√3) reconstruction. At the domain walls, Mn adatoms are displaced from one domain to another by about half the (1x1) lattice constant, as indicated by the two solid lines. From Cui and Li [729] (Copyright 2003, reproduced with permission from Elsevier).

surface. This is more stable than the Mg+H phase and will inhibit Mg incorporation under very Ga-rich conditions, but replacing one Ga in the lower of the two metallic layers (the one in contact with the substrate) with Mg is only moderately endothermic, by 0.35 eV per c(2x6) SUC. For conditions simulating MOCVD growth (T = 1170 K and H2 and NH3 pressures of 0.1 atm and 0.9 atm respectively), the Mg+H structure is the most stable under moderately Mg-rich conditions. Under very Mg-rich conditions, a 2Mg+2H structure with one Mg+H unit per (1x1) SUC is the most favorable. Akiyama et al. [419] and later Ito et al. [380] obtained theorē surface using the tical results for Mg on the semi-polar (1011) approach described above and in Section 4.6.4.1 in connection with their work on the clean surface. These authors find that for low-to-moderate μGa the two-fold-coordinated N atoms on the ideally-terminated surface (Fig. 3c,d) are unstable and desorb leading to Ga-Ga dimers across the N vacancies. With reference to the non-primitive SUC shown in Fig. 3d, low μH, a moderate-tohigh μMg and a low-to-moderate μGa favor a structure with one of the dimer Ga atoms in the clean-surface SUC replaced with Mg. This is termed the "Ga-Ga dimers+MgGa" structure. At higher μGa, an ML of Ga adatoms stabilizes the two-fold N atoms on the ideally-terminated surface to give a structure ("Ga monolayer + MgGa") with one Mg per SUC replacing a Ga adatom. For a high μH the only stable structure across almost the full range of μGa is the "4N-H+MgGa", which is described in terms of a (2x1) supercell based on the non-primitive (1x1) SUC (i.e., four primitive cells). The Mg-free surface at high μH (Section 7.3) forms a structure ("4N-H+Ga-H") with an N-H bond at all four three-fold N atoms per supercell and all two-fold N removed and replaced with Ga-Ga dimers except that one Ga-Ga dimer forms a single Ga-H bond. Under sufficiently Mg-rich conditions the other Ga of this pair is replaced by Mg and the H at the Ga-H site is eliminated. At low μMg only the Mg-free surface structures are stable, and the implications of these results for growth and Mg incorporation are discussed in detail in the original references. In summary, Mg on the GaN (0001) surface is fairly well understood at both the experimental and theoretical levels. The interface is reactive, at least for substrates prepared by IBA [561,703] or by heating in UHV [704], which results in site exchange between Mg and Ga. The Mg layer becomes metallic for very small thicknesses and grows epitaxially [703,715]. Incorporation occurs easily on the (0001), which is consistent with the pronounced

5.26. Manganese The interaction of Mn with GaN surfaces has been studied with an interest in possible applications as a dilute magnetic semiconductor. Experimental results have been reported for the (0001) surface by Cui and Li [729], Qi et al. [730] and K. Wang et al. [731] and for the (0001̄ ) in Refs. [732–737]. Theoretical results have been given for the (0001) surface by González-Hernández et al. [618], Qi et al. [730], K. Wang et al. [731] and Hao and Zhang [738] and for the (0001̄ ) and (101̄0) surfaces by Chinchore et al. [737] and by J. Wang and G. Huang [739] respectively. There have also been studies [740–744] of the MBE growth of thin magnetic Mn:Ga alloy layers on polar GaN surfaces, which are important but beyond the scope of the present review. Cui and Li [729] used STM and RHEED to study Mn on the GaN (0001)-"(1x1)" surface using samples grown by MBE, after which Mn was deposited in situ at 500 °C. Deposition at 600 °C does not lead to an ordered structure, and adsorbed Mn begins to desorb at 550 °C. For θMn = 0.33 ML, (10x10) domains form with a (√3x√3) R30° reconstruction within the domain, where "10" refers to the average domain size relative to the GaN basal-plane lattice constant. (For a Mn density of 7.3 gm cm-3, 1 Å = 8.003x1014 Mn cm-2 = 0.706 ML where 1 ML is defined as 1 Mn per lattice site.) The proposed surface structure, which is closely connected with that of the "(1x1)" Ga bilayer, is shown schematically in Fig. 48. For the Mn-free surface, the uppermost Ga layer is liquid-like and exhibits rapid fluctuation of the atomic positions that ceases when Mn is deposited due to the strong Mn-Ga bonding. The domain structure then occurs as a mechanism for releasing the tensile strain resulting from the Ga-Ga and Ga-Mn distances (2.7 and 2.3 Å respectively) both being smaller than the GaN in-plane lattice constant (3.2 Å). However, it is unknown whether the Mn incorporates into the Ga bilayer or remains as an adatom. Qi et al. [730] used STM to study the adsorption of Mn on the GaN (0001)-"(1x1)" surface using samples grown by MBE, after which Mn was deposited in situ at RT or at 300 °C. For a low θMn (well below 0.5 ML) at RT, disordering of the "(1x1)" occurs. As θMn increases, this disordered phase grows and (3x3) structure begins to appear, which then becomes dominant at 0.5 ML. Depositing the same coverage at 300 °C yields a mixed (3x3) and (5x5) phase. These results were analyzed theoretically, as will be described later in this section. K. Wang et al. [731] used RHEED and STM to study Mn on GaN (0001)-"(1x1)" surfaces using samples prepared by MBE followed by Mn deposition at ∼250 °C. For up to θMn = 0.5 ML, RHEED shows no fractional-order streaks in the [112̄ 0] direction but pronounced changes in the [11̄00]. These consist of 1/3- and 2/3-order streaks that vary with θMn and indicate an ordered superstructure. At low θMn (∼0.2 ML), the Mn appears to be highly mobile and to aggregate into many small reconstructed areas. These form two phases, termed "α" and "β", that appear as striped regions of different width oriented along the [11̄00] direction. At θMn = 0.5 ML, the α and β phases merge into a wider γ phase, which forms wide

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stripes along the three equivalent [11̄00] directions and exhibits (√3x√3)R30° ordering within the stripes. The analysis was supported by ab-initio theoretical results, which are discussed below. The interface appears to be non-reactive since no evidence for such an effect was reported. The (√3x√3)R30°-ordered stripes might be related to those observed by Cui and Li [729] and discussed above. Kowalik et al. [732] used UPS to study Mn layers on the GaN (0001̄ ) surface. The samples were bulk single crystals with surfaces cleaned by IBA (Ar+ ions, 500 °C anneal) after which Mn was deposited in situ. The UPS experiments were done both on and off resonance, where resonance occurs at hν = 51 eV and corresponds to Mn 3p63d5 + hν → [Mn 3p53d6]* → Mn 3p63d4 + e−. Here [...]* indicates a transient excited state and off-resonance means the direct excitation Mn 3p63d5 + hν → Mn 3p63d4 + e−. The difference between UPS data recorded on and off resonance emphasizes regions of the VB that involve large Mn 3d contributions. For θMn ≤ 2 ML, features appear in the VB that are not characteristic of pure Mn, and a low-BE satellite is seen in the Ga 3d, from which it is concluded that the interface is reactive and that a Ga-Mn compound is formed. Annealing a 2 ML deposit of Mn at 400 °C causes a more extensive reaction. Based on the appearance of the Mn 3d contribution to the VB, Mn is tetrahedrally coordinated in the reacted region which suggests incorporation into the GaN lattice at Ga sites. Further evidence for a strong Mn-GaN interaction stems from the fact that the 3p → 3d transition energy for Mn/GaN is significantly different from that of pure Mn. Dumont et al. [733] used STM and SIMS to study the incorporation of Mn into GaN (0001̄ ). The sample was a bulk single crystal in the form of a thin wafer that was etched in KOH and NaOH solutions to determine polarity (Section 4.2.1) and then mechanically and chemically polished. In-situ cleaning consisted of cycles of IBA (1 keV Ar+, 600 °C anneal) after which a sharp (1x1) LEED pattern was obtained. For the clean surface, STM shows (3x3), (6x6) and (6x12) regions, which are characteristic of the (0001̄ ) surface with excess Ga resulting from preferential removal of N during IBA. As discussed in Section 4.6.2, a similar series of (0001̄ ) structures ((3x3), (6x6) and c(6x12)) is seen for surfaces grown via MBE with various Ga adatom coverages on top of a full Ga adlayer. The appearance of these structures after IBA is a clear indication of the presence of excess Ga and suggests that under some circumstances it may be possible to prepare clean surfaces by IBA that are similar to those grown by MBE. Depositing 0.3 ML of Mn at RT (meaning a quantity of Mn equivalent to a uniform coverage of 0.3 ML) leads to islands that are 2-3 ML high and 5 nm in diameter. Annealing to 575 °C causes coalescence into larger islands with (3x3)-ordered bare areas between the islands, and a 675 °C anneal restores the clean-surface STM. Diffusion of Mn into the substrate after the 675 °C anneal is demonstrated using SIMS, which is consistent with the results of Kowalik et al. [732] discussed above. However, no clear indication of actual Mn-N or MnGa bonding was reported. Chinchore et al. [734] used RHEED to study Mn on the GaN (0001̄ )-(1x1) surface, which was formed via MBE with a layer of Ga adatoms in T1 sites on the N terminating layer of the substrate. During in-situ deposition of Mn at 150 °C, RHEED shows the onset of 1/3- and 2/3-order streaks at θMn = 0.15 ML, which reach maximum intensity at 0.90 ML. Concurrently, the first-order streaks lose intensity, eventually becoming weaker than the fractional-order streaks, for which the 2/3:1/3 intensity ratio is 2.9:1 at the point where the fractional-order streaks reach maximum intensity. The intensity ratio excludes a simple (√3x√3)R30° reconstruction, with θMn = 0.33 ML, for which the ratio would be unity. The proposed model, which is developed in more detail in subsequent work, consists of a modified (√3x√3)R30° structure with two Mn per unit cell (i.e., θMn = 0.66 ML) that leads to the

Fig. 49. (a) Large-scale (80 nm x 87 nm) STM image in 3D perspective view of MnGa islands on N-polar GaN surface (VS ¼ 0.87 V; IT ¼ 56 pA); (b) zoom-in STM image of island A surface (VS ¼ 0.67 V; IT ¼ 154 pA); (c) similar zoom-in of adatom wetting layer (VS ¼ 0.87 V; IT ¼ 156 pA); region devoid of adatom stripes is labeled "Dev"; adatom protrusions are marked with white circles. From Chinchore et al. [736] (reproduced with the permission of AIP Publishing).

formation Mn chains running in the [101̄0] direction. The Mn-Mn distance is √3a/2 along the chain and 3a/2 between chains, where a = 3.190 Å is the GaN in-plane lattice constant. The chains exist in three domains, separated by 120° rotations, and the predicted RHEED pattern for this structure is in good agreement with experiment. In an extension of the above work, Shi et al. [735] demonstrated the formation of a Mn δ-doping layer on the (0001̄ ) surface. A δdoping layer is an ML of foreign atoms (e.g., dopants or metal atoms) that is present in a stable state below the surface of a bulk semiconductor. First, MBE is used to grow a (1x1) surface, which is characteristic of the (0001̄ ) with a Ga adlayer (Section 4.6.2). Any excess Ga beyond 1 ML is then desorbed at 700–750 °C, which also introduces N vacancies into the terminating layer of the lattice. Then the sample is exposed at 200 °C to about 2/3 ML of Mn (not all of which adsorbs) to form a (√3x√3)R30° structure consisting of Mn and Ga adatoms. Finally the surface is exposed to a nitrogen plasma, which forms a stable Ga:Mn mixed-nitride layer (with 1/3 ML of Mn) terminated in N and refills any N vacancies in the lattice terminating layer. GaN is then grown by MBE on top of this Mn-containing layer, which remains buried at the interface. The structure and composition of the δ-doping layer are discussed in detail in the original reference. Chinchore et al. [736] used STM, together with RHEED and AES, to study structures formed when Mn is deposited on GaN (0001̄ ). The samples were grown by MBE in such a way that there was ~0.4 ML of Ga adatoms on the surface in addition to a finite coverage of Ga droplets. It was not stated explicitly, but one assumes that this excess Ga was in addition to the 1-ML Ga adlayer that stabilizes the (0001̄ ) surface. Mn was then deposited at 250 °C to a coverage of ~0.4 ML. This results in an array of islands (Fig. 49)

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with perfectly flat tops, steep sides and heights of either 0.93 or 1.13 nm (both ±0.01 nm). The island edges lie along the GaN [112̄ 0] direction, and the area between islands exhibits a (3x3) adatom (Ga or Mn) reconstruction. This (3x3) is considered to be similar to that found for a low coverage of Ga adatoms on the (0001̄ ) Ga adlayer surface (Section 4.6.2). The average Mn/Ga atomic ratio seen in AES is ∼0.20, and STM line profile analysis indicates an average island height of six layers with a spacing of 1.89 Å. Sixlayer-thick islands are the only structures observed to be stable; whereas, five- and seven-layer structures are not, which is explained in terms of a quantum size effect. Chinchore et al. [737] reported experimental and theoretical results focused on understanding the (3x3) and (√3x√3)R30° Mn-induced structures. Beginning with a (0001̄ )-(1x1) Ga-adlayer surface, Mn is deposited at 80–100 °C to a coverage of 0.1 to 0.5 ML, which leads to the (3x3) structure. Subsequent annealing at 500 °C then gives the (√3x√3)R30° surface. The authors note that forming a (3x3) by Ga adsorption on the (1x1) adlayer requires only 1/9 ML (i.e., one Ga per SUC); whereas, the Mn-induced (3x3) needs a higher θMn, which suggests that there is more than one Mn per SUC. Another difference is that the Ga (3x3) is stable up to ∼300 °C and reappears when the temperature is lowered, but the Mn (3x3) exists only up to ∼115 °C whereupon it begins to change irreversibly to the more-stable (√3x√3)R30°. The metastable Mn-(3x3) structure is found to arise from an Mn3 trimer adsorbed on the Ga adlayer. The (√3x√3)R30° phase, which is stable up to the point of decomposition at ∼750 °C, appears to have a structure like that of the GaN surface itself, with one Mn per SUC, and to exhibit Mn-N bonding. The theoretical component of this study is discussed later in this section. Hao and Zhang [738] performed theoretical studies of the adsorption, diffusion and clustering of Mn on the GaN (0001)-(2x2) surface with one Ga per SUC in a T4 site. This is the most stable (0001) surface under moderately Ga-rich conditions and satisfies the ECR with no occupied Ga DBs (Section 4.6.1). The 2DPS consisted of 8 atomic layers (i.e., 4 Ga-N bilayers) with a (4x4) SUC and the bottom surface terminated with H atoms (presumably 3/4 ML, which satisfies the ECR). The PAW method was used together with the GGA; although, the functional was not specified. The Ga 3d and Mn 3p were treated as valence states, and the NEB method was used to compute activation barriers. In the most stable structure for one Mn per SUC, the Mn is in a so-called "Sp" site where it displaces one of the three terminating-layer Ga atoms to which the Ga adatom is back-bonded to give a Mn-Gaadatom bond. The displaced Ga then remains as another adatom (termed a "dangling Ga" in the original reference). All other surface and subsurface substitutional and interstitial sites, as well as adatom sites, are less stable by 0.59 eV or more. For Mn adsorption rather than incorporation, T4 is the least unfavorable site; however, there is a large barrier (1.1 eV) for moving into the more-stable Sp site but a smaller barrier (0.7 eV) for moving between T4 sites. If a layer of GaN is grown on top of a surface with a T4 Mn adatom, it then becomes kinetically easier for this buried atom to move to an Sp site. Hence, a T4 Mn adatom is an intermediate to doping at Sp during growth. There is an attractive interaction of 0.94 eV between two Mn adatoms in T4 sites, which, in view of the relatively low barrier for hopping between T4 sites, means that clustering is favorable. In the most stable configuration for a second Mn per SUC, this Mn occupies a T4 site close to the Sp Mn where it can interact with both the first Mn and the original Ga adatom. The magnetic properties with two T4 Mn or with one Sp and one T4 Mn per SUC were also discussed. Qi et al. [730] investigated Mn incorporation on the (0001) surface theoretically in conjunction with their STM experiments described earlier. The FLAPW method was used with a 2DPS consisting of nine Ga-N bilayers and a (√3x√3)R30° SUC with a

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Ga bilayer to model the (0001)-"(1x1)" surface. The bottom four Ga-N bilayers were fixed in the bulk-lattice positions, but the method of terminating DBs on the bottom surface was not mentioned. Larger SUCs, with fewer Ga-N bilayers, were also used to check the effects of Mn-Mn distance. The (3x3) structure forms via incorporation of two Mn per SUC into the upper layer of the Ga bilayer with the displaced Ga then becoming an adatom that is bonded to the Mn. This imparts a tetrahedral structure to the "(1x1)" metallic Ga bilayer. These results are qualitatively consistent with those of Hao et al. [738] for Mn on the (0001)-(2x2) Ga-adatom surface. The two Mn per SUC are next-nearest neighbors and are anti-ferromagnetically coupled. The contours of the DOS, integrated over energy ranges corresponding to different tip biases, are in good agreement with STM data and also reveal a small difference in the surface-normal positions of spin-up and spin-down Mn. One notes, however, that the (3x3) model involves 2/9 ML of Mn; whereas, this structure appears most prominently in STM after deposition of ∼1/2 ML. This might indicate that the sticking coefficient of Mn is less than unity, as suggested by Shi et al. [735]. The (5x5) phase that was also seen in STM after depositing Mn at 300 °C is ascribed to Ga adatom trimers that form together with Mn-rich domains with some of the Mn possibly incorporated beneath the outer-most metallic-Ga layer. González-Hernández et al. [618] reported theoretical results for Mn on GaN (0001) obtained using methods described previously in the discussion of their Cr results. Adsorption of one Mn per (2x2) SUC at a T4 site on the ideally-terminated surface is somewhat more favorable than at H3 (ΔEads = -3.168 eV for T4 vs. -3.091 eV for H3) but much more favorable than at T1 (ΔEads = -1.762 eV). The small preference for T4 over H3 is attributed to a weakly-attractive interaction with the first-underlayer N atom. The magnetic moment per SUC with adsorbed Mn is 4.00 μB vs. 5 μB for the free atom, which is attributed to the charge transfer of 0.041 |e| from GaN to Mn that reduces the unpaired spin density. Presumably a large contribution to the decrease in magnetic moment derives from the pairing of Mn and Ga DB orbitals to form bonds. The large magnetic moment for Mn suggests that it is potentially useful for constructing magnetic layers on GaN. The diffusion barrier from H3 to T4 is about 0.46 eV (which is close to the barrier computed for a Ga adatom) and slightly lower than the barrier from T4 to H3 (0.53 eV), which reflects the greater stability of T4 vs. H3. The clean but unreconstructed (0001) surface shows a band of metallic states at EF due to the partially-filled Ga DBs. The DOS shows a reduction in the density of states near EF, relative to the bare surface, as a result of Mn adsorption, and only the majority-spin DOS crosses EF, which indicates semi-metallic behavior. Within the gap, Mn makes only a small, minority-spin contribution with the rest of the gap states being due to Ga orbitals. K. Wang et al. [731] studied Mn on GaN (0001) theoretically in conjunction with their STM work described above. The calculations used the PW method with USPPs and a GGA functional (not specified), and the DFT+U approach (Section 4.1.1) was employed to analyze the most stable structures. The 2DPS consisted of four Ga-N bilayers, plus a Ga bilayer, with the bottom surface terminated with PHs. The lowermost bilayer and the PHs were fixed during optimization, and (√3x√3)R30° and (4x√3) SUCs were used. The most stable (√3x√3)R30° structure for any μGa is the HD-1, in which Mn embeds into the laterally-contracted uppermost adlayer to give one Mn and three Ga per SUC in this layer. The RHEED and STM patterns computed for HD-1 are in very good agreement with experiment, as are the spin-resolved DOS and the STS data. A mechanism for the production of the striped domains seen in STM, which involves a magnetically-ordered arrangement of Mn atoms, was also proposed and analyzed in terms of the (4x√3) SUC. Chinchore et al. [737] reported theoretical results for Mn on the (0001̄ ) surface in conjunction with their STM studies described

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above. The calculations used the LDA with NCPPs, which included NLCC and relativistic effects. It is not stated explicitly but presumably this refers to scalar-relativistic effects, i.e., not including spin-orbit coupling. The valence states were expressed in terms of localized basis sets rather than PWs. The 2DPS consisted of nine NGa bilayers with a Ga ML on top of the N lattice-terminating layer to model the bare (0001̄ )-(1x1) surface and with the bottom surface terminated with PHs. The lowermost four bilayers were fixed in the bulk-lattice geometry. The lowest-energy (3x3) structure, except under Mn-deficient conditions, is the "H3 trimer hollow" with three Mn per SUC occupying a trimer of H3 sites on the surface of the Ga adlayer with the center of the trimer empty (i.e., not occupied by a Ga). In an H3 site, the Mn is above a three-fold hollow in the uppermost N-Ga bilayer. Relaxation causes adlayer Ga atoms close to the trimer to displace laterally away, which allows the Mn to move downward and closer to the adlayer plane. The trimer structure involves only Mn-Ga, not Mn-N, bonding and is energetically favored over an isolated adatom, in agreement with previous theoretical results for Mn on GaN (0001) that indicate a tendency to form clusters. On the other hand, for very low μMn, a single Mn adatom in a T4 site, where it lies above the Ga adlayer and above a Ga in the uppermost N-Ga bilayer, defines the most stable (3x3) structure. The lowest-energy (√3x√3)R30° structure, except for low μGa, is the "substitutional+T4" in which Mn displaces one Ga per SUC from the adlayer, which then becomes an adatom at a T4 site on the adlayer. Relaxation of this structure leads to substantial displacements of surface atoms. On the other hand, for very low μGa, simple substitution with no adsorption of the displaced Ga is energetically favored. Both sets of results give very good agreement between observed and calculated STM images. The experimentally-observed irreversible conversion from (3x3) to (√3x√3)R30° beginning at 105 °C is then explained in terms of the dissociation of Mn3 trimers, which allows the Ga-Mn site exchange and lowers the total energy by 100 meV per (1x1) SUC. It is noted that both structures involve the same coverage, θMn = 1/3 ML, and so the structural conversion is simply a rearrangement of Mn and adlayer Ga atoms. J. Wang and G. Huang [739] performed theoretical studies of Mn adsorption on the non-polar (101̄0) surface with an interest in δ-doping (as defined earlier in this section). The PW approach was used with USPPs and the PBE functional. The 2DPS comprised eight GaN layers (presumably this means bilayers) and a (2x1) SUC (presumably this means 2x in the direction perpendicular to [0001], Fig. 2). No information was given regarding the termination of DBs on the bottom surface or about which layers were fixed during relaxation. For each (101̄0) plane in succession, starting at the surface, half the Ga was replaced with Mn (i.e., one Mn per (2x1) cell) and the energy computed. The formation of the doped layer is endothermic in all cases but less so at the surface than in a deeper-lying layer and less so under N-rich than Ga-rich conditions. The DOS with Mn in the surface layer shows the highestenergy occupied majority-spin band crossing EF but a band gap for the minority spin, which indicates semi-metallic behavior, and the total magnetic moment is 4.0 μB per cell. In summary, the behavior of Mn deposited in situ on polar GaN surfaces after MBE growth is complex but appears to be well understood for the (0001) [731] and (0001̄ ) [737] surfaces. In general the morphology and structure depend sensitively on θMn and on the temperature either during or after deposition. Such interfaces appear to be non-reactive; although, to our knowledge, no XPS data have been reported for these systems. On the other hand, here again, there is evidence for reaction when the GaN (0001̄ ) surface is cleaned by IBA. A common aspect of nearly all studies is a tendency of Mn adatoms to form small clusters and to undergo site exchange with nearby Ga atoms whether in a Ga adlayer or in

the lattice-terminating layer. Another general observation, for both polar surfaces, is the formation of (3x3) and/or (√3x√3)R30° structures; although, the Mn coverages and the proposed structural models differ among the various studies. 5.27. Nickel The interaction of Ni with GaN (0001) has been studied experimentally in Refs. [331,745–753] and theoretically by GonzálezHernández et al. [472,618,754]. Nickel is of interest in metal contacts and as a catalyst in the activation of Mg-doped p-type GaN, where Ni films have been found to aid in the removal of hydrogen that bonds to Mg and "poisons" the dopant. Further information on this particular application can be found in Refs. [755–759], and it is noted that Co and Pt films have also been used for the same purpose [760]. In Section 7.3 it will be seen that recombinative desorption is the rate-limiting process in the removal of H from Mg-doped GaN, and this appears to be catalyzed by certain metal adlayers. Bermudez et al. [745] used AES, ELS, LEED and XPS to investigate the interaction between Ni and n-type MOCVD GaN. Historically, this was the first study of this type on a metal/GaN interface. The sample polarity was not known, but it was probably (0001). Clean surfaces were prepared by depositing Ga metal in situ at nominal RT and then heating in UHV to 900–950 °C. After several cycles, no contamination was detected in AES, and the LEED showed a sharp, low-background pattern with no evidence of faceting (which, for these samples, did not appear until heating above 950 °C). The coverage dependence of the Ni and Ga LMM peak intensities in AES indicates 2D layer-by-layer (Frank-van der Merwe [571]) growth. The Ga result further indicates a lack of significant intermixing, which would have led to a slower attenuation. After deposition of a thick Ni layer (∼90 ML) at nominal RT, AES shows a small N KLL feature but no Ga LMM. (For a Ni density of 8.912 gm cm-3, 1 Å = 9.145x1014 Ni cm-2 = 0.806 ML where 1 ML is defined as 1 Ni per surface lattice site.) The N KLL lineshape is different from that in GaN but very similar to what is seen for nitrogen ion-implanted into Ni (110), which suggests that the detected N is on or near the Ni surface. The spectrum remains unchanged for anneals up to about 600 °C, above which the Ga LMM intensity increases abruptly, the N KLL spectrum vanishes and a rise in chamber pressure due to N2 evolution (identified via mass spectroscopy) is observed. Evaporation of Ni is negligible at the temperatures of interest here. The interpretation is that an interfacial reaction occurs even at RT that releases N, which diffuses to the Ni surface while the "free" Ga remains near the interface. Heating above 600 °C causes a more extensive reaction that releases larger amounts of N2 and leads to intermixing of Ga and Ni. The phase diagram shows that Ga is soluble in Ni up to a Ga concentration of 28 atomic-%, and N is known to desorb as N2 at 650 °C when chemisorbed on Ni (111). From thermochemical data it was estimated that the reaction GaN + Ni → Ni[Ga] + Ni[Nads] is exothermic by 117 Kcal mol-1 (5.07 eV), where Ni[Ga] is a dilute solution of Ga in Ni and Ni[Nads] is N adsorbed on Ni (111). It was also shown that N could be "recaptured" before N2 desorption by depositing a thick layer of Ga on the Ni surface that, upon annealing at 800 °C or above, combined with N to form GaN. This was recognizable by the lineshapes of the N KLL and low-energy Ga Auger spectra and by the LEED and low-energy ELS data, which indicated a poorly-ordered GaN layer. It is possible that this GaN layer could be used as a substrate for the MBE growth of a thicker, higher-quality GaN layer on top of the buried Ni-Ga thin-film alloy. The LEED results are summarized in Fig. 50. Depositing a thin (∼6 ML) Ni layer at RT and annealing at 900 °C leads to a nested

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Fig. 50. Upper: LEED results for different Ni/GaN (0001) surface treatments (Ep is the primary-beam energy). (a) and (c) were obtained for one sample and (b) for another; hence, (b) appears rotated by 30°. (a) Clean GaN (0001) (Ep ¼ 98 eV); (b) 6 ML of Ni at RT followed by 900 °C anneal (Ep ¼ 117 eV); (c) another 85 ML of Ni at RT (Ep ¼ 121 eV). Lower: (a) (√3x√3)R30° for thick Ni layer deposited at RT followed by 800 °C anneal (Ep ¼ 97 eV); (b) (2x2) after 900 °C anneal (Ep ¼ 107 eV), overexposed to show weak fractional-order spots. From Bermudez et al. [745] (Copyright 1993 by the American Physical Society).

hexagonal pattern for which dinner/douter = aNi/aGaN = 0.78, where dinner is the distance between two spots of the inner set that are 180° apart (and likewise for douter), aNi is the (111) lattice constant of Ni and aGaN the basal-plane lattice constant of GaN. This shows that annealing a thin, initially-uniform Ni layer causes it to coalesce into (111)-ordered crystallites. Further deposition of Ni at RT causes the inner (GaN) spots to disappear, giving a somewhat diffuse Ni (111) LEED pattern. This indicates that the Ni crystallites serve to nucleate the growth of a thicker crystalline layer, which may also contain dissolved Ga. Annealing this thick, ordered Ni layer (which causes Ga to segregate to the surface as described above) leads to the appearance (Fig. 50) of adsorbate-induced reconstructions showing first a (√3x√3)R30° and then a weaker (2x2) LEED pattern. Both structures have been observed elsewhere for other adsorbates (Si and Ge) on Ni (111). Surface-sensitive Ga 3d XPS data were also obtained, using Zr Mζ excitation (hν = 151.65 eV [570]). These show a low-BE satellite indicating Ga in a metallic environment (i.e., dissolved in or adsorbed on Ni) and a shift of the bulk-GaN component to lower BE. Kim et al. [331] reported UPS and XPS data for Ni on n- and ptype MOCVD GaN (0001) obtained with high surface sensitivity using synchrotron radiation. This was part of a study of binary Au/ Ni contacts. Surfaces were cleaned ex situ in HF solution at 50 °C followed by a DI H2O rinse and in situ by annealing in UHV at 500 ° C. No further details regarding procedure or contamination levels were provided. For an n-type sample, the Ga 3d BE before annealing in UHV shows essentially no BB (i.e., a flat-band condition); whereas, after annealing an upward BB of about 0.7 eV appears, in agreement with previous results [123]. For a p-type sample, the downward BB is ~1.7 eV before annealing and 2.3 eV after. However, in either case the effect of SPV on the apparent BEs is unknown (Section 4.7.3.2). The results indicate that annealing

causes the n-type (p-type) surface to become more negatively (positively) charged relative to the bulk, which in turn suggests an enhanced accumulation of majority carriers at the surface. Deposition of 3.6 ML of Ni leads to a uniform film with a metallic Fermi level. The N 1s XPS shows a satellite at ∼4 eV higher BE than in GaN, which is suggested to arise from free nitrogen (presumably N2) trapped at the reacted Ni/GaN interface. The accompanying Ga 3d BE shifts indicate SBHs of 1.44 and 1.83 eV respectively for nand p-GaN, assuming that 3.6 ML is sufficiently thick to define the SBH and that SPV is negligible. This places EF at nearly the same position in the gap for both types of contacts. The ideal MottSchottky barriers would be 1.05 and 2.35 eV respectively for n- and p-type GaN, and the fact that EF appears at nearly the same position for both dopant types suggests that the SBH is dominated by defects produced by the interfacial reaction. Maruyama et al. [746] and Hagio et al. [747] studied Ni on MOCVD p-GaN (0001) using AFM, AES and also surface-sensitive Ga 3d XPS (hν = 180 eV) that was facilitated by a synchrotron radiation source. One form of sample preparation, termed "etching", involved ex-situ treatment in what was described as "28% NH3" at 50 °C. It is assumed that this means 28% aqueous NH4OH solution. A second method of sample preparation was IBA (nitrogen ions, 400 °C anneal). The former showed substantial C and O contamination, while the latter showed little or no C and a small amount of O, estimated to be 0.05 ML. On the etched surface, the Ga 3d shows a high-BE satellite due to GaOx that is virtually eliminated by Ni deposition, which indicates that Ni "getters" O from the surface to form NiOx. On the IBA surface, Ni causes a lowBE satellite indicating Ga in a metallic environment, which gains relative intensity upon anneal to successively higher temperatures and indicates an interfacial reaction.

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Barinov et al. [748] performed surface-sensitive photoemission microscopy experiments on Ni/n-GaN (0001) using methods described in connection with their work on Au (Section 5.20). A patch of Ni about 4 ML thick at the center and 15 μm wide was deposited on the clean surface. The edges of the patch were graded in thickness; hence, acquiring data at various positions allowed measurements to be made as a function of θNi. At θNi ≈ 3 ML the SBH has stabilized at 1.18 to 1.20 eV, and SPV effects have become negligible. As in the case of the Au work, the clean-surface Ga 3d shows low- and high-BE satellites associated with surface effects. Beneath the Ni patch, the whole Ga 3d spectrum shifts to lower BE in response to the SBH, and the low-BE satellite is replaced by another, at a still-lower BE relative to bulk GaN, that results from metallic Ga that has been released by the interfacial reaction and alloyed with Ni. The reaction is enhanced by annealing at 300 or 600 °C, which increases the relative intensity of the low-BE feature. The higher-temperature anneal also leads to a pronounced decrease in the SBH, which is attributed to a lowering of the Ni work function due to the presence of dissolved Ga. The N 1s exhibits the same shift to lower BE as a result of the BB change, together with a broadening to higher BE that is ascribed to N that has recombined with Ga in the Ni layer. Such N would not be affected by the BB change that causes the N 1s of the bulk GaN to shift to lower BE. A C-rich defect region was also identified and shown to originate with C contamination in micropipes in the SiC (0001) substrate that propagate through the GaN epilayer. Changes in surface structure and stoichiometry vs. annealing were studied in detail. A 300 °C anneal causes Ni to accumulate at the C-containing defects, where the extent of the Ni-Ga alloying is somewhat greater than in non-defective regions as shown by the

relative intensity of the low-BE Ga 3d satellite. A 600 °C anneal leads to a more homogeneous surface, a decrease in Ni 2p XPS intensity and a shift of the Ga 3d satellite to a BE that is consistent with metallic Ga. This is interpreted to indicate the penetration of Ni into the GaN lattice, which leads to a surface enriched in free Ga. It is also found that the SBH, although sensitive to annealing temperature, remains uniform over the whole surface notwithstanding the structural inhomogeneity for lower-temperature anneals. Aurongzeb et al. [749] used XRD, AFM and magnetic force microscopy (MFM) to study the formation of Ni nanodots (or crystallites) that occurs, as described above [745], when a thin Ni film on GaN is annealed. This was not a UHV study, and no particular surface cleaning or analysis was mentioned. However, given the aforementioned [747] ability of a Ni film to "getter" O contamination from the GaN surface during annealing, the results are quite possibly relevant to work done in a more controlled environment. Ni films 2 nm thick were deposited on GaN (presumably (0001)) and annealed in dry N2 at temperatures in the range of 550–930 °C. The as-deposited films are smooth and uniform, and annealing at 550 °C or above causes the film to coalesce into nanodots (or crystallites) with flat surfaces (Fig. 51). The size, uniformity and RMS roughness of the nanodots all increase with annealing temperature, and, at 930 °C, they are 150–250 nm in lateral size and fairly regularly shaped. The area between nanodots is not completely free of Ni. The temperature dependence of the rate of nanodot formation gives an activation energy of ΔEa = 0.34 ±0.07 eV, which is close to the value for self-diffusion of Ni on the (110) surface. Studies of nanodot lateral size, area and roughness vs. anneal time (at 750 °C) indicate that growth is a diffusion-

Fig. 51. 1 μm x 1 μm images of Ni surfaces on GaN substrates following two different anneals: (a) and (b) combined AFM and magnetic force microscopy (MFM), respectively, following 930 °C for 30 min; (c) and (d) combined AFM and MFM, respectively, following 750 °C for 20 min. Full gray scale ranges are (a) 15.0 nm and (c) 17.8 nm. From Aurongzeb et al. [749] (reproduced with the permission of AIP Publishing).

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limited, or ripening, process. The composition of the nanodots vs. annealing was probed with XRD, which shows the presence of Ni3Ga4 and, after a higher-temperature treatment, NiGa4, which is consistent with a greater reactivity at the interface. In a subsequent study, Aurongzeb et al. [750] formed structured Ni films on GaN (0001) and then used these to catalyze the MOCVD growth of GaN nanowires. For a very thin (0.8 nm) Ni film annealed at 750 °C, SEM and AFM show two kinds of features; namely, irregular mounds and what are termed "antidots", which are Ni-coated depressions about 25 nm across and 2.5 nm deep. For thicker Ni deposits (≥1.4 nm) only the nanodots described above are seen after annealing. It is found that GaN nanowire growth occurs preferentially at the antidots and is promoted by the release of N that occurs due to decomposition at the Ni-GaN interface. The nanowire growth was characterized in some detail, but this lies beyond the scope of the present review. Nörenberg et al. [751] used RHEED, AFM and STM to study the growth of Ni islands when a thin film of Ni on MOCVD GaN (0001) is annealed. The sample was cleaned first in organic solvents and then in situ either by annealing in 2x10-5 Pa (1.5x10-7 Torr) of NH3 vapor or by heating to 700 °C in UHV. The in-situ cleaning procedure was varied in order to produce initial surfaces with different amounts of excess Ga; however, no AES or XPS results were reported. A Ni film of unspecified thickness was annealed at 600– 650 °C, after which Ni (111) islands with mainly a hexagonal shape were observed with sizes in the range of 1-50 nm and a height of up to 2.4 nm. These results are consistent with those of Aurongzeb ̄ et al. [749] described above. The Ni [110] direction lies parallel to the GaN [112̄ 0] direction, and the tops of the islands are flat but ̄ corrugated. The corrugation period is 5 Å (twice the [110] spacing of bulk Ni), which indicates a large degree of relaxation. Grodzicki et al. [752] used UPS, XPS, LEED and STM to investigate Ni/n-GaN (0001). The sample was cleaned by heating in situ at 800 °C, after which only small amounts of C and O contamination were observed. The upward BB and the electron affinity were about 0.6 eV and 3.5 eV respectively, and the LEED pattern was a sharp, low-background (1x1). A 1 nm-thick Ni deposit is disordered, covers the GaN uniformly and shows an SBH of 1.2 eV. In UPS, the features associated with the GaN VB are eliminated; however, these reappear after a 650 °C anneal with the continued presence of emission at EF due to metallic Ni. The LEED pattern of bare GaN (0001) also reappeared but with additional weak spots consistent with a Ni (111)-(2x2) structure. Annealing to 800 °C (again for an initial Ni deposit of 1 nm) gives more-pronounced GaN VB features in UPS, a sharper GaN LEED pattern, only a very slight loss in Ni 2p XPS intensity (~2%) and no significant shift in any Ga or Ni core-level BEs. These results are taken to indicate the annealing-induced coalescence of Ni into islands, as described above, which exposes a large fraction of the GaN surface. Deposition of additional Ni on this surface then leads to a disordered, granular film of bulk Ni with ϕS = 5.1 eV, which is characteristic of polycrystalline Ni [615]. The relatively-high Ni deposition rate (unspecified) was thought to account for the lack of ordering in this thicker Ni layer. Annealing this layer at 650 °C causes a very slight shift of the Ni 2p to lower BE (by about 0.15 eV) and a shift in the relative position of the shake-up satellite. For bulk Ni (i.e., a thick Ni film before annealing), this satellite lies at 5.8 eV below the parent peak; whereas, for the same layer annealed at 650 °C the spacing is 6.2 eV, which is characteristic of a Ni-Ga alloy, possibly Ni3Ga. Annealing a thick layer at 650 °C increases the Ga content seen in XPS, and the Ga 2p3/2 peak is dominated by a low-BE component assigned to Ga-Ni bonding, the BE of which is distinct from that of free metallic Ga. This indicates the segregation of Ga to the surface. Coalescence of the granular film into (111) crystallites is seen in STM, and LEED shows mostly a sharp (√3x√3)R30° pattern with some evidence of a (2x2).

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Similar LEED results were obtained previously (Fig. 50) and ascribed to Ga adsorption on Ni (111). After annealing, ϕS decreases to 4.6 eV and UPS shows VB structure characteristic of Ni3Ga. Annealing the same sample at 800 °C causes further changes. The Ni 2p shake-up satellite now appears at 6.7 eV below the parent peak, the Ga 2p3/2 peak of GaN reappears as a shoulder on the high-BE side of the Ni-Ga peak, ϕS decreases to 4.4 eV, and the LEED pattern is sharp with both (1x1) and (2x2) spots but no (√3x√3)R30°. This is ascribed to the coalescence of the metal film into larger islands, with a higher Ga content, which exposes areas of bare GaN. Pers et al. [753] performed STM studies of Ni-Ga alloy layers on GaN (0001) that were formed either by deposition of Ni at RT followed by annealing at 650 °C or by deposition with the substrate at 650 °C. The resulting bimetallic surface, which is mainly Ni3Ga under these conditions, is of interest as a catalyst for the reduction of CO2 to CH3OH. Prior to deposition the substrates were "degreased" in isopropanol and then annealed in situ at 800 °C. Deposition of Ni followed by annealing leads to 3D islands that are coalesced into meandering chains. On the other hand, deposition onto the surface at high temperature produces a uniform dispersed array of irregular hexagonal grains, which is considered to be more useful in catalysis. González-Hernández et al. [618] reported theoretical results for Ni on GaN (0001) obtained using methods described previously in the discussion of their Cr results. Adsorption at the H3 site is somewhat more favorable than at T4 (ΔEads = -4.474 eV for H3 vs. -4.353 eV for T4) but much more favorable than at T1 (ΔEads = -2.870 eV). The small preference for H3 over T4 is attributed to a weakly-repulsive interaction with the first-underlayer N atom. The magnetic moment of adsorbed Ni is found to be 0.00 vs. 2 μB for the free atom, which is ascribed to the charge transfer of 0.275 |e| from Ni to GaN that reduces the unpaired spin density. Presumably a large contribution to the decrease in magnetic moment derives from the pairing of Ni and Ga DB orbitals to form bonds. The diffusion barrier from H3 to T4 is about 0.46 eV (which is close to the barrier computed for a Ga adatom) and slightly greater than the barrier from T4 to H3 (0.34 eV), which reflects the greater stability of H3 vs. T4. It is suggested that the finite diffusion barrier means that it will be possible to prepare a surface with a stable Ni adlayer. The DOS for one Ni per (2x2) SUC shows no difference between majority- and minority-spin occupancies, which is consistent with the observation of a magnetic moment of zero for θNi = 0.25 ML. González-Hernández et al. [754] reported further theoretical studies of Ni/GaN (0001). This work was done using methods similar to those used in Ref. [618], and the results for adsorption energies and diffusion barriers for one Ni per (2x2) SUC were the same as those described earlier. Increasing θNi up to 1 ML decreases ΔEads for the H3, T4 and Br sites and increases it for the T1 such that, at 1 ML, the values are all similar, ranging from about -3.5 eV for T1 to -3.7 eV for T4. The strongly-exothermic and nearly-equal ΔEads at all sites for 1 ML is consistent with the experimentally-observed growth of uniform Ni layers even at low coverages. The DOS for one Ni per (2x2) cell in an H3 site shows a reduction in the Ga DB occupancy near EF due to electron transfer from Ni to GaN, and fully occupied states localized on Ni appear near the VBM. Subsequent work by González-Hernández et al. [472] considered Ni interacting with a GaN (0001) surface with one Ga adatom per (2x2) SUC in a T4 site, which constitutes a non-metallic surface with no occupied Ga DBs. The methods employed were similar to those described above in connection with other work by the same group. In this case, two types of H3 sites can be distinguished, one of which (labeled "H3a0") is closer than the other to the Ga adatom and is the energetically-favored site for a Ni adatom. Substitution of Ni for surface or subsurface Ga or

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Fig. 52. The most-stable structures for Nb4 clusters on GaN (0001). These are T3_H3 for 3D-Nb4 and T3_2D for 2D-Nb4. Dark, medium and light spheres are Nb, Ga and N respectively. From Wang and Zhu [761] (Copyright 2007 by the American Physical Society).

incorporation of Ni into interstitial sites are all energetically very unfavorable relative to adsorption in the H3a0 site except under conditions that are both Ni- and N-rich. In this case, Ni replacing a Ga in the surface termination layer that is bonded to the Ga adatom, to give a Ni-Gaadatom bond, becomes favorable. This is labeled an "Sp" adsorption site. The DOS shows that adding Ni in the H3a0 or the Sp site leads to a metallic surface since the Ni-free surface is non-metallic. However, the DOS at EF for Ni in the Sp site appears to be very small. In either case, there is also evident overlap between Ni and Ga levels near the VBM that indicates Ga-Ni bonding. In summary, Ni/GaN (0001) appears to be fairly well understood, and a consistent model can be developed on the basis of theory and experiment. At RT, Ni grows uniformly, and reaction is confined to the immediate interface. Annealing causes more extensive reaction leading ultimately to the release of N, to a range of Ni-Ga alloys and to a layer of well-ordered Ni (111) crystallites. The Ni crystallites can be alloyed with Ga and can also exhibit reconstructions resulting from Ga adatoms. The N that is released may desorb as N2 or undergo further reaction with Ga atoms. However, there are to our knowledge no studies addressing the interaction of Ni with other GaN surfaces. 5.28. Niobium Wang and Zhu [761] studied the adsorption of Nb4 clusters on GaN (0001) theoretically. The interest was in determining the properties of stable metal nano-clusters on semiconductor surfaces for possible applications such as catalysis and contact formation. There are two stable forms of adsorbed Nb4, shown in Fig. 52. These are the 2D quadrangle (2D-Nb4) and the 3D tetrahedron (3D-Nb4), both of which are suggested to be very stable closed-shell systems. The calculations used the PAW method and the PW-91 functional, and the 2DPS models consisted of four or six Ga-N bilayers, with the bottom surface terminated in PHs, and (2x2) or (3x3) SUCs. For a (2x2) SUC, the stable adsorption geometries are the T3_H3 for 3D-Nb4 (ΔEads = -6.72 eV per cluster)

and the T3_2D for the 2D-Nb4 (ΔEads = -8.71 eV per cluster). In the 3D structure, the 3 Nb atoms in contact with the surface occupy T4 sites while the fourth Nb in the tetrahedral cluster lies above an H3 site. In the 2D structure, all 4 Nb atoms lie in approximately a T4 site. The 2D structure is lower in energy since all 4 Nb atoms interact with the surface. It is proposed that in either case the partially-filled Ga DBs on the ideally-terminated surface are saturated by adsorption of one Nb4 per (2x2) SUC; however, a DOS was not presented. The barrier for the interconversion of the 2D and 3D species when adsorbed in the respective most-stable configuration (termed a "diffusion barrier" in the original reference) is 41 eV, indicating a high degree of stability. When the larger SUC is used, to reduce the surface coverage, ΔEads increases to -7.59 and -9.64 eV per cluster respectively for 3D-Nb4 in T3_H3 and 2D-Nb4 in T3_2D, and the interconversion barrier also increases. Chargedensity difference plots (CDPs) were used to assess the bonding within each cluster and with the GaN surface. A CDP is the difference in charge density between the adsorbed cluster and the sum of 4 free atoms or between the SUC with Nb4 and the sum of the clean SUC and the free cluster. These show that the clusters do not interact with each other for the (3x3) SUC and that there is a strong interaction with the uppermost Ga-N bilayer. However, in the (3x3) SUC there are too many Ga DBs to be saturated by a single Nb4 cluster, which implies that the surface should be metallic. 5.29. Palladium The interaction of Pd with GaN (0001) has been studied experimentally by Hartlieb et al. [473], Liu et al. [762,763], Nörenberg et al. [751,764] and Grodzicki et al. [765,766] with an interest in understanding contact properties. Liu et al. [762,763] prepared MOVPE GaN surfaces wet-chemically in various acids or in organic solvents followed by Pd deposition in a vacuum of ∼1x10-7 Torr. The resulting samples were assessed for epitaxial growth using 2.0 MeV 4He+ ion backscattering and also a Read x-ray camera. The best epitaxy is found when the GaN surface is first cleaned using boiling aqua regia (3:1 HCl:HNO3), and the epitaxy improves with distance from the Pd/ GaN interface toward the Pd surface. Since surface contaminants interfere with epitaxy, it is inferred that these are minimal after acid cleaning and that recontamination in room air between cleaning and loading into the deposition chamber is not significant. The degree of epitaxy is comparable at deposition rates of 2 and 15 Å sec-1, indicating that the Pd is sufficiently mobile that the higher rate does not impede epitaxy. (For a Pd density of 12.0 gm cm-3, 1 Å = 6.792x1014 Pd cm-2 = 0.598 ML where 1 ML is defined as 1 Pd per surface lattice site.) The Pd (111) plane grows parallel to the GaN (0001) surface, even though the lattice mismatch is 13.75%, but the mechanism whereby epitaxy occurs in spite of this high degree of mismatch has not been determined. Nörenberg et al. [751,764] used STM to study the initial stages of Pd deposition on GaN (0001). The sample preparation and other experimental details were described above in connection with their work on Ni (Section 5.27). Deposition at ∼300 °C followed by annealing at ∼600 °C leads to reaction with excess Ga and incorporation of Pd into the surface to form a disordered Pd/Ga alloy. Repeated deposit/anneal cycles lead to a strained layer consisting of different domains oriented along the GaN [112̄ 0] direction. The surface phase is complex, and it is uncertain whether it constitutes a Pd-rich alloy or a Ga adlayer on top of a strained Pd (111) layer. On a less Ga-rich surface, Pd wets the surface and forms a layer of epitaxial islands. However, the islands do not appear to coalesce into a continuous layer, which is ascribed to the large lattice mismatch between Pd (111) and GaN (0001). When all excess Ga

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on a Ga-rich surface has been consumed in the interfacial reaction, subsequent deposition and annealing leads to formation of Pd (111) nanocrystals with well-defined dimensions that increase upon annealing at 600–650 °C. Hartlieb et al. [473] used UPS, XPS and LEED to study the interface between Pd and p-type MOVPE GaN (0001). A clean surface was prepared first by immersion in a series of organic solvents followed by HCl and then H2O. The sample was then annealed in situ at 825 °C in a flux of NH3 vapor from a doser. The background NH3 pressure was about 9x10-5 Torr, but the BEP might have been as much as an order of magnitude higher. Finally the sample was cooled to 200 °C and transferred into the UHV analysis chamber. Before in-situ cleaning the XPS data indicated an oxynitride surface phase. After cleaning, the surface showed no C above the XPS detection limit of ~0.3 atomic-%, but O was present at a level of ~2 atomic-%. A Ga/N atomic concentration ratio of 1.0 was measured in XPS, and EF was found to lie at 1.7 eV above the VBM. Note should be taken of the substantial SPV effect [440] that enters into XPS and UPS experiments for p-type GaN (Sections 4.7.3.2 and 5.10). This reduces the magnitude of the downward BB on the bare surface and, to some extent, on metal-covered surfaces. The Pd layer growth is described reasonably well as a layer-by-layer (Frank-van der Merwe) process, and the change in BB with Pd coverage (determined using the shift in Ga 3d BE) leads to an SBH of 1.3 eV. The LEED data are consistent with the epitaxial growth described above by Liu et al. [762,763], and there is no indication in any of the data of a chemical reaction at the interface. Grodzicki et al. [765] used UPS, XPS, STM and AFM to study the interface between Pd and n-type GaN (0001). Clean surfaces were prepared by immersion in alcohol and in H2O and then by heating to 800 °C in UHV. No impurities were detected in XPS either on the clean surface or after in-situ Pd deposition. Pd does not wet the surface and no LEED pattern is observed after deposition, both of which results are in contrast with some previous studies, discussed above, that indicate layer-by-layer epitaxial growth. From the Ga 3d BE on the bare surface (20.55 eV) one can deduce that EF-VBM = 2.79 eV using the VBM-Ga 3d separation of 17.76 eV [439]. This agrees well with EF-VBM = 2.75 eV determined directly from UPS, which indicates the absence of any significant contribution from surface states near the VBM of the bare surface. These results indicate an upward BB of about 0.5 eV, assuming that CBM-EF in the bulk is about 0.04 eV (see Fig. 24). The total width of the UPS emission (Section 5.10) gives χ = 3.1 eV for the bare surface. The Pd XPS spectrum does not change with coverage, which indicates a lack of significant chemical interaction at the interface, and an SBH of 1.6 eV is found. Subsequently the same group [766] performed a series of deposit/anneal experiments to observe the effects of elevated temperature on the interface. The bare surface in this case was free of C and exhibited a sharp (1x1) LEED pattern with no evidence of faceting. The surface was, however, described as Ga-rich and showed a small level of O contamination. Also, no surface-state emission was detected above the VBM. In UPS, structure in the VB, shown in Fig. 53, indicates that annealing a 1.5 nm-thick Pd film at 550 °C (800 °C) forms a GaPd2 (GaPd) intermetallic compound. Before annealing, ϕS is 5.0 eV (close to the reference value [615] of 5.12 eV for polycrystalline Pd) and decreases to 4.4 (4.0) eV after formation of GaPd2 (GaPd). The interfacial reactions are also seen to shift the Pd 3d XPS spectrum to successively higher BEs. The combination of LEED and STM showed that the initial Pd deposit is disordered, does not adhere well and exhibits a granular morphology. Annealing to form GaPd2 results in a (1x1) LEED pattern that is less intense and not as sharp as that seen for the bare surface, and STM indicates an array of differently-sized islands. Upon formation of GaPd, the (1x1) LEED pattern (which arises from the GaN

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Fig. 53. UPS valence band spectra taken for: 0 clean GaN(0001) substrate; 1 Pd film ∼1.5 nm thick as deposited at RT on the clean substrate; 2 after annealing the film at 550 °C; and 3 after further annealing at 800 °C. Arrows mark the positions of VB peaks in typical UPS spectra of GaPd and GaPd2. From Grodzicki et al. [766] (with the permission of Springer).

substrate) becomes sharper, with a lower background intensity, and the islands become larger. Subsequent deposition of more Pd, after having annealed the first deposit at 800 °C, yields UPS data with features characteristic of crystalline Pd, and ϕS = 5.5 eV is found, which is close to the value of 5.67 eV recommended [767] for Pd (111). The LEED now shows a somewhat-diffuse (1x1) pattern with a spot spacing corresponding to the lattice constant of Pd (111). Annealing this layer of additional Pd leads to further formation of first GaPd2 and then GaPd as in the first cycle. It was previously noted by Kim et al. [79] that Ga is very soluble in Pd and that annealing the Pd/GaN interface is likely to produce Ga vacancies in the substrate. Although the subsequent deposits of Pd wet the surface, the GaPd2 and GaPd do not and continue to exhibit island formation. None of the treatments gave any evidence, in the form of N 1s XPS lineshape changes, of Pd-N bonding. In summary, Pd/GaN (0001) appears to be another example of a system for which the physical and chemical structure of the interface depends on how the initial bare surface is prepared as well as on how the interface is formed. In particular, the presence of excess Ga before Pd deposition appears to interfere with epitaxial growth, possibly as a result of the formation of alloys and/or intermetallic compounds that are less capable of epitaxy. The behavior of Pd appears somewhat similar to that of Ni (Section 5.27) in that annealing a thin layer in some cases leads to the formation of alloyed islands that can then nucleate a polycrystalline Pd layer during subsequent deposition at RT. 5.30. Platinum The interaction of Pt with GaN (0001) has been studied experimentally by Tracy et al. [474], Wu and Kahn [561], Preble et al. [671], Kim et al. [768], Schäfer et al. [769] and Winnerl et al. [770]. The interest is mainly in the formation and properties of metal contacts. Wu and Kahn [561] used UPS, XPS, AES and LEED to study Pt on GaN of uncertain polarity, which was nominally (0001) Ga-polar.

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The experimental details were summarized above in the discussion of their work with Al (Section 5.1). The interface is found to be abrupt and non-reactive as shown by the absence of any satellite features in the Ga 3d and Pt 4f XPS. For n-GaN, a 20 Å Pt layer increases the upward BB by 0.9 eV; whereas, very little change in BB is seen for p-GaN. (For a Pt density of 21.46 gm cm-3, 1 Å = 6.626x1014 Pt cm-2 = 0.584 ML where 1 ML is defined as 1 Pt per surface lattice site.) The SBH for p-GaN is 0.9 eV; however, none was given for n-GaN, probably because the BB does not appear to have stabilized yet for 20 Å of Pt. Preble et al. [671] performed XPS, HRTEM, SEM, XRD and I-V measurements to study Pt contacts (600 Å thick) formed in situ on atomically-clean GaN (0001). The experimental details were described previously in the discussion of their work with Au (Section 5.20). The metal layer is found to grow in a layer-bylayer, or Frank-van der Merwe, mode [571] and to be crystalline with a (111) orientation and a smooth, featureless and non-reacted interface. The I-V data show the as-deposited contact to be rectifying but that annealing at 600–800 °C leads to Ohmic behavior. However, an 800 °C anneal causes a loss of structural integrity of the interface, which then shows what appear to be holes in SEM. Further analysis of the annealed interface using TEM shows the presence of roughness, reaction products and Pt crystallographic orientations other than (111). The XRD data after an 800 °C anneal show two new peaks that might be due to a Ga2Pt reaction product but could not be conclusively assigned, and the holes seen in SEM are then thought to be caused by the release of N2 during the chemical reaction at the interface. The XRD also shows evidence for annealing-induced compressive stress that was attributed to a difference in thermal expansion coefficients for Pt and GaN. Tracy et al. [474] performed XPS, UPS, I-V and C-V measurements, the experimental details of which were summarized previously in discussing their work with Au. The Pt/GaN interface formed at RT is abrupt and non-reactive, and the upward BB for an n-type GaN substrate increases by 0.8 eV for the first 5 Å of Pt and then remains fixed at higher coverages. The SBH is found to be 1.2 ±0.1 eV from the XPS measurements (but see below), 1.15±0.01 eV from I-V data and 1.24±0.05 eV from C-V experiments. These results are considerably less than the value of 2.6 eV obtained from the Mott-Schottky model for an ideal and defect-free interface, and the authors suggest possible reasons for this effect. As discussed in Section 5.20 in connection with results for Au, the SBH of 1.2 eV given above was obtained by adding the shift in the XPS Ga 3d BE due to contact formation to EF-VBM for the bare surface measured in UPS. If instead one uses the Ga 3d BE of 19.6 eV after Pt deposition to obtain EF-VBM, an SBH of 1.46 eV is found. This value will be used later, in Section 6, in the discussion of SBHs. Kim et al. [768] studied the effects of strain and its reduction via annealing on Pt/p-GaN (0001) contacts using XRD and XPS with MOCVD GaN. Platinum layers (100 Å thick) were deposited at a pressure of o 3x10 -7 Torr on wet-chemicallycleaned substrates. The XRD data show that the Pt forms (111)oriented domains that grow in size upon annealing to 450 °C, which is accompanied by an increase in the degree of alignment and a decrease in contact resistivity. Annealing also causes a reduction in downward BB by 0.21 eV (i.e., a decrease in the p-GaN SBH) and the appearance of a low-BE Ga 3d satellite suggesting Ga-Pt bonding. A high-BE satellite ascribed to Ga-O bonding is also present for all treatments. These annealing effects are attributed to a relaxation of the in-plane biaxial tensile (compressive) strain of +0.9% (-0.9%) in the Pt (GaN) caused by the lattice mismatch. It is proposed that the compressive strain in the unannealed GaN substrate has the effect of increasing E g at the interface, which in turn yields the larger SBH.

Schäfer et al. [769] deposited Pt nanoparticles on n- and p-type MOCVD GaN (0001) and found a dopant-dependent oxidation behavior for the Pt using ambient-pressure XPS (APXPS). The substrate cleaning and Pt deposition were both performed using wet-chemical methods. The Pt 4f XPS shows spin-orbit doublets due to metallic Pt (Pt0), Pt with chemisorbed oxygen (Ptchem-O) and the Pt2+ and Pt4+ oxidation states. The Ptchem-O species is ascribed to a residue from the sample preparation. Differences between nand p-GaN as to the BEs of the different Pt peaks were noted and shown to result from SPV induced by the x-ray source. Either for the as-inserted samples or after reduction in H2 at 800 K, the fraction of the total Pt 4f intensity due to Pt0 is always significantly smaller for n- than p-GaN. Ex-situ-reduced samples were used in APXPS experiments at 725 K and 0.5 mbar (375 mTorr) of O2, and upon admission of the O2 the data show little or no change in the Pt0 intensity for p-GaN but a large decrease for n-GaN. Evacuating the O2 and increasing the temperature to 775 K causes a gradual reduction in the total O content, but the fraction of Pt0 remains much smaller for n-GaN. It is also noted that for n-GaN the BE shifts of all the Pt-O features relative to Pt0 are larger for oxidation during x-ray exposure than for plasma oxidation in the absence of x-rays. The results indicate that O reacts more readily with Pt nanoparticles supported on n- vs. p-GaN. This was explained in terms of a charge-transfer process in which electron-hole pairs created in GaN under x-ray illumination ionize in the space-charge field. The minority carriers, which are holes (electrons) for n- (p-) GaN, are then swept to the surface where they are transferred to the Pt nanoparticles. Thus a Pt nanoparticle supported on n-GaN has a lower electron density under illumination than one on p-GaN. It is, however, not obvious why this lower electron density should enhance the chemisorption of (electronegative) O2. One can speculate that perhaps a somewhat different mechanism is in effect. It is possible that photo-generated holes coming to the n-GaN surface convert adsorbed Oδ− anions to atomic O, which then oxidizes the Pt nanoparticles. This might be termed a "reverse spillover effect" in which active O generated on the semiconductor reacts with supported metal clusters. A similar process involving Oδ− reduction was described briefly in Section 4.7.3.2 in connection with the effects of photostimulated desorption of O on SPV for nGaN (0001). In a further study, Winnerl et al. [770] used conductance and contact potential difference measurements to elucidate the kinetics of photogenerated charges near the surface of GaN (0001) with and without Pt nanoparticles. The work is very noteworthy but is beyond the scope of the present review. 5.31. Ruthenium The interaction of Ru with the GaN (0001) surface has been studied theoretically by Ortega López at al. [771] with an interest in metal contact formation. The calculation used USPPs and the PBE functional. The 2DPS had 4 Ga-N bilayers, with the bottom terminated with PHs, and a (2x2) SUC. In qualitative agreement with results for other metal atoms, adsorption at a T4 site is slightly more stable than at an H3 (by 0.048 eV) but much more stable than at a T1. For either T4 or H3 there is a significant relaxation in the immediate vicinity of the Ru, wherein the 3 Ga nearest neighbors move a few tenths of an Ångstrom toward the Ru, and a barrier of 0.612 eV is found for diffusion between the T4 and H3 sites. The DOS shows the relaxed surface to have metallic character with extensive mixing of Ru d-orbitals with Ga and N orbitals. This mixing is found to be closely related to the relaxation that results from Ru adsorption.

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5.32. Samarium Experimental studies have been performed for Sm interacting with the GaN (0001) surface by Guziewicz et al. [772] and with the (0001̄ ) surface by Guziewicz et al. [773,774] and Orlowski et al. [775]. This work was motivated by the potential use of rare-earthdoped GaN as a dilute magnetic semiconductor in spintronic devices and also, because of the rich luminescence spectrum, as an optoelectronic material. As a clarifying remark, Sm as a free atom has an outer-shell configuration 4d105s25p64f65d06s2, or [Xe] 4f65d06s2, and is commonly referred to as being "divalent" [776]. In the XPS/UPS literature the outer-shell configuration is typically given as 4d104f6(sd)2, which emphasizes the spectroscopicallyrelevant shells. Likewise, in the bulk metal, Sm is in the "trivalent" configuration 4d104f5(sd)3. It appears to be standard practice to label the divalent or trivalent states as "Sm+2" or "Sm+3" with outer-shell configurations 4d104f6 or 4d104f5 whether or not the Sm is actually ionic. Hence, there are references to Sm+2 and Sm+3 appearing in the bulk metal. For Sm deposited on a non-reactive substrate [776], the Sm+2/Sm+3 concentration ratio is known to depend on cluster size and layer thickness. Guziewicz et al. [772] performed RPES experiments using the (0001) surface of a GaN single crystal on which Sm was deposited in UHV, followed in some cases by annealing to promote diffusion into the lattice. Prior to Sm deposition, the surface was cleaned by IBA (600 eV Ar+, 500 °C anneal). For VB photoemission spectra, synchrotron radiation was used to observe resonantly-enhanced excitation of the 4f levels of both divalent (Sm+2) and trivalent (Sm+3) species, which can be described as Sm+24d104f6 + hν(137 eV) → [4d94f7]* → 4d104f5 + e− Sm+34d104f5 + hν(141.8 eV) → [4d94f6]* → 4d104f4 + e− where [...]* represents a transient excited state. These processes are in addition to the normal (not resonantly-enhanced) photoemission. For a Sm coverage of up to 20 ML, Sm+3 is found to be the dominant species; although the Sm+3/Sm+2 ratio varies with coverage. Annealing at 500 °C appears to promote conversion of Sm+2 to Sm+3. Before annealing, a low-BE shoulder appears in the Ga 3d spectrum at an energy that depends on Sm coverage. Leastsquares fitting reveals two components in this shoulder, at BE = 18.1 and 17.4 eV, which is ascribed to an interfacial reaction that results in Ga in two different chemical environments, both of which involve Sm. After a 500 °C anneal, the bulk-GaN component (at BE = 20.2 eV) disappears, leaving only a single peak at BE = 18.2 eV. This indicates that all Ga within the photoemission sampling depth now exists in a single chemical environment in which Sm is present. Guziewicz et al. [773] also studied Sm on the (0001̄ ) surface using samples and surface preparation methods similar to those described in Ref. [772]. At all coverages up to 14.5 ML, VB photoemission is dominated by Sm+3. Above 4.5 ML the spectrum appears metallic (i.e., a Fermi edge is observed); although, Sm+3 remains the dominant surface species. This is in contrast with bulk Sm, which forms Sm+2 at the surface, and is taken as an indication of a reactive interface. The behavior of the Ga 3d with increasing θSm is similar to that seen for the (0001) surface, which is a further indication of interfacial reaction that releases Ga into the Sm layer. In a subsequent and more-detailed study of the (0001̄ ) surface [774] by the same group, both Sm+2 and Sm+3 are seen in VB photoemission. The Sm+2 peak is initially shifted by 0.9 eV to higher BE than in bulk Sm and gradually shifts to lower BE with increasing θSm. Only a fraction of this shift can be ascribed to changes in the GaN BB, and not until a Sm thickness of 20 Å does a well-defined Fermi edge appear and the Sm+2 BE become equal to that on the surface of the bulk metal. This is taken as evidence that

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Sm+2 is chemically interacting with GaN for thicknesses below ∼10 Å. (For a Sm density of 7.52 gm cm-3, 1 Å = 3.012x1014 Sm cm-2 = 0.265 ML where 1 ML is defined as 1 Sm per surface lattice site.) The interface appears to be highly heterogeneous since both the Sm+2 and Sm+3 emissions gain intensity with thickness up to 20 Å; whereas, for a homogeneous Sm film, the Sm+2 would be confined to the surface. An average valence was computed using Vavg = (3I3+2I2)/(I3+I2) where I2 and I3 are the Sm+2 and Sm+3 VB resonant intensities corrected for the relative photoionization crosssection. For bulk Sm, Vavg = 2.7, which indicates a dominance of Sm+3. On the other hand, for Sm/GaN (0001̄ ) Vavg varies with coverage up to about 10 Å and, even at 20 Å, is only 2.62. This is interpreted as an indication that Sm+2 and Sm+3 are both present in the interfacial reaction layer. In the Ga 3d spectrum, two low-BE components appear after Sm deposition as in Ref. [772]. This is ascribed to the presence of two different chemical states for Ga, possibly representing interaction with Sm+2 and Sm+3. For a sequence of Sm depositions up to ~3.8 Å (i.e., 1 ML), the total Ga 3d intensity first increases slightly and then decays slowly, which indicates disruption of the GaN surface by an interfacial reaction. Above 3.8 Å, the Ga 3d signal decays almost exponentially but is still visible in surfacesensitive spectra for a 20 Å layer, which suggests a combination of layer and island growth with Ga diffusion into the Sm. Annealing at 500 °C after 20 Å of Sm leads to the disappearance of Sm+2 from the VB photoemission spectrum, which is ascribed to its conversion to Sm+3 with diffusion into the GaN bulk. The Ga 3d shows one narrow component, at BE = 18.2 eV, which is assigned to Ga interacting with Sm+3 together with a weak shoulder at higher BE due to a small bulk-GaN contribution. Orlowski et al. [775] have also performed RPES experiments for Sm on GaN (0001̄ ) surfaces prepared in the same manner as in Refs. [772–774]. As in the other studies, Sm+2 and Sm+3 both appear at the earliest stages of deposition, with Sm+3 being the dominant species. This is attributed to the fact that Sm+3 can substitute more easily for Ga+3 than can Sm+2. Although this work is somewhat outside the scope of the present review, it is noted in passing that Vézian et al. [777] have grown GaN (0001)-(2x2) on Si (111) using gas-source MBE (with NH3 as the source of N) followed by the growth of SmN using N2, which dissociates catalytically on elemental Sm. Ga is found to segregate to the SmN surface during growth, which is ascribed to the release of free Ga via site exchange at the Sm/GaN interface. 5.33. Scandium The interaction of Sc with GaN (0001) has been studied experimentally by Kaplan et al. [778], and there have also been several theoretical studies. These include investigations of the (0001) surface by López-Perez et al. [779] and by Guerrero-Sánchez et al. [780], the (0001̄ ) by Guerrero-Sánchez et al. [781] and the (112̄ 0) and (101̄0) by González-Hernández et al. [782]. The interest is in the possible use of Sc, a soft hexagonal metal that lattice-matches GaN reasonably well, as a compliant substrate for GaN growth. ScN, which is a semiconductor with the NaCl structure, is also of interest since the (111) surface lattice-matches GaN (0001) quite well. In the experimental work, Sc was deposited in situ on clean MOVPE GaN (0001). The surface preparation was not described, but it probably involved annealing in a flux of Ga metal vapor. The initial deposition on a RT substrate leads to formation of ScN, which is thermodynamically favorable given that ΔHf is reported to be -75 kcal mol-1 for ScN vs. −25 kcal mol-1 for GaN. Above some critical thickness the deposited Sc becomes metallic as further reaction with the substrate is blocked by the ScN reaction-product layer. With increasing substrate temperature during deposition

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(up to 780 °C), the thickness of the ScN layer increases. With increasing θSc at RT, the LEED transitions from the (1x1) characteristic of clean GaN (0001) to a diffuse pattern associated with poorly-ordered ScN to finally a sharp hexagonal pattern due to Sc metal. Thus a well-ordered layer of Sc can be grown on top of the ScN layer. López-Perez et al. [779] performed theoretical studies for the (0001) surface using the PAW method and the PBE functional, with the 3d electrons of both Sc and Ga included as valence states. The 2DPS comprised a (2x2) SUC with 4 Ga-N bilayers of which the bottom two were fixed in the ideal bulk-lattice configuration and the N DBs saturated with PHs. The most stable adsorption site is the T4 followed by H3 and T1, with ΔEads of -4.45, -4.25 and -2.62 eV respectively, and the preference for T4 over H3 is attributed to an attractive interaction between Sc and the first-underlayer N. The diffusion barrier from T4 to H3 is 0.77 eV and 0.57 eV in the reverse direction. Incorporation of Sc was also studied, and it was found that substitution for a single surface Ga is exothermic by 2.54 eV; whereas, forming an interstitial or substituting for N is endothermic by 1.20 or 2.66 eV respectively. With increasing θSc, incorporation via Ga substitution in the uppermost 2 Ga-N bilayers is favored over incorporation deeper into the bulk. This is attributed to the high ΔHf of ScN, which stabilizes the reaction-product layer. (Presumably the third bilayer of the four in the 2DPS was also allowed to relax when considering incorporation beyond the second bilayer.) A phase diagram was also computed that shows a wide region of stability for ScN, which is ascribed to the good lattice match between GaN (0001) and ScN (111). Calculations of the DOS shows that the bare (0001) surface is metallic, due to partially-filled Ga DBs, but these are saturated when one Sc adsorbs per (2x2) SUC in the T4 position, which is in accord with the ECR. The (2x2) SUC comprises 4 Ga atoms, each with 3/4 |e| excess electron density. Hence, adsorption of one Sc, with 3 valence electrons, forms three 2-electron Ga-Sc bonds and leaves an empty DB on the remaining Ga. Moving the adsorbed Sc to a substitutional site in the uppermost Ga layer restores the partially-filled Ga DBs and leads to the return of a metallic state, which persists for increasing substitution. Guerrero-Sánchez et al. [780] performed similar calculations for Sc on GaN (0001), presumably using USPPs since a low PW cut-off energy (30 Ry) was specified. The 2DPS (which was also composed of 4 Ga-N bilayers) in this case had only the lowermost bilayer fixed in the bulk-lattice configuration. For the ideally-terminated (0001) surface, adsorbing one Sc in a (2x2) SUC shows that the T4 site is more favorable than the H3 (T1) by 0.19 (1.81) eV, in good agreement with the results of López-Perez et al. [779]. Site exchange between adsorbed Sc and a terminatinglayer Ga is energetically favorable, and in the most stable such configuration the displaced Ga occupies a T4 site in which it bonds only to other Ga atoms in the terminating layer. For a full ML of Sc, site exchange between all Sc atoms and Ga atoms in the terminating layer is more favorable than the chemisorbed phase by about 2.00 eV per (2x2) cell. Similar calculations were done for very Ga-rich conditions, in which the Ga terminating layer is covered with a bilayer of Ga. For a single Sc in a (2x2) SUC, adsorption at a T4 site on the terminating layer (i.e., underneath the Ga bilayer) is again more stable than the H3 but only by 0.08 eV, and the T4 → H3 diffusion barrier decreases from 0.58 eV on the ideally-terminated surface to 0.12 eV for the Ga bilayer structure, which indicates a surfactant effect on the part of the Ga bilayer. For very Ga-rich conditions, site exchange is most favorable when Sc replaces Ga in the terminating layer of the lattice, rather than in the metallic Ga bilayer. This is due to the stability of the resulting Sc-N bonds, and the same is found to apply for a full ML of Sc. Relative energies were computed for Sc/GaN interaction

under N-rich, moderately Ga-rich and very Ga-rich conditions. The most-stable configuration for the N-rich surface has N adatoms adsorbed in H3 sites, and adsorption of a single Sc per (2x2) SUC leads again to substitution for a Ga in the lattice-terminating Ga layer. Continued adsorption of Sc on the N-rich surface leads to a Sc-N bilayer with an overlayer of Ga formed by displacement from the outermost Ga layer. Thus Sc-N bonding is favored under all conditions from N-rich to very Ga-rich when a full ML of Sc is deposited, and evidence is presented that it is the wurtzite and not the cubic form of ScN that is produced. Calculations of the DOS show that the surface is metallic under all conditions, due to partially-filled DBs on either Sc or Ga. Guerrero-Sánchez et al. [781] have performed calculations for Sc on GaN (0001̄ ) using methods similar to those in Ref. [780]. In this case the 2DPS consisted of 3 Ga-N bilayers, with an additional adlayer of Ga to model the (0001̄ ) under Ga-rich MBE conditions, and a (2x2) SUC. Thicker slabs, with 5 or 7 Ga-N bilayers, gave the same results for the quantities of interest as did the thin slab, which justifies the use of the 3-bilayer 2DPS. The structure of the Sc-free surface is a (1x1), with the Ga adatoms directly on top of the terminating-layer N atoms. The most favorable adsorption site for a single Sc in a (2x2) SUC is as a bridge (Br) between 2 Ga adatoms, but this is lower in energy than H3 and T4 by only 0.07 and 0.08 eV respectively. The T1 site, however, is 1.36 eV higher than the Br. Relative to the Br structure, site exchange between Sc and adlayer Ga is exothermic by 1.52 eV when the displaced Ga occupies a T4 site in which it bonds only to other Ga. This is only slightly (by 0.02 eV) more stable than for the displaced Ga occupying an H3 site (again bonded only to other Ga). When θSc is increased to a full ML adsorbed above the Ga adlayer, T4 becomes the most favorable Sc site. It is then energetically favorable for all the Ga to be displaced, leading to a Sc-N bilayer beneath a layer of Ga atoms lying in T4 sites (i.e., above N atoms in the Sc-N bilayer). Under N-rich conditions, for which there is no Ga adlayer, the Sc-N bilayer becomes even more stable. The DOS shows the surface with a Sc-N bilayer to be metallic under both N-rich and Ga-rich conditions. González-Hernández et al. [782] obtained theoretical results for Sc on the non-polar (112̄ 0) and (101̄0) surfaces using models and methods similar to those in their study of Cu on these surfaces (Section 5.14). For either surface a wide range of different adsorption sites, shown in Fig. 54, was considered (see also Fig. 2). The most stable Sc adsorption for either surface occurs in one of the possible bridge sites. This is the Br3 on (112̄ 0) and the Br2 on (101̄0), with ΔEads = -4.302 and -4.293 eV respectively for one Sc per SUC. In either case, the Sc forms a bridge between surface Ga and N atoms. As in other studies, substitution of Sc for Ga (N) is exo-(endo)thermic, and substitution for Ga is energetically more favorable than adsorption. The incorporation of Sc was studied for the full range of μGa, and, with increasing Sc concentration, incorporation occurs in first- and second-layer Ga sites. At the highest Sc concentration, the most stable configuration for the (112̄ 0) or (101̄0) surface has two or one Sc per SUC, respectively, in each of the three outermost layers. 5.34. Silicon The interaction of Si with the GaN (0001) surface has been studied experimentally in Refs. [714,717,783–788], and Lee et al. [786] have also studied Si on the (0001̄ ) surface. Theoretical work for the (0001) surface has been performed by Lee et al. [786], Rosa et al. [789–791] and Ji et al. [792] and for the (0001̄ ) by Ji et al. [792]. Neugebauer [687] has also presented a review of the theory of Si surfactant effects in GaN growth. The interest is in the use of Si as an n-type dopant and also in its effects on GaN growth and morphology.

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Fig. 54. Ball and stick models of GaN (a) (112̄ 0) and (b) (101̄0) surfaces. The blue (gray) balls represent Ga (N) atoms. The top views show model Sc adsorption sites, labeled top (T), hollow (H) and bridge (Br). The side views show the layer labels (l1, l2, l3). From González-Hernández et al. [782] (Copyright 2014, reproduced with permission from Elsevier).

Munkholm et al. [783,784] observed the surfactant effect of a low θSi during MOCVD growth using in-situ grazing-incidence xray scattering. These results, which are only briefly noted here, show that Si adsorption during growth changes the mode from step-flow (which leads to 3D growth) to layer-by-layer (2D growth) over a wide temperature range. Evidence is also found for surface segregation of Si in heavily-doped material at high temperature, which will be discussed later in this section. The surfactant effect appears to saturate at θSi = 0.07 ML, and excess Si that does not incorporate into the GaN "floats" on the surface during growth. Chen et al. [785] studied the effects of CVD deposition of Si on GaN (0001). The substrates were prepared by ultrasonic cleaning in organic solvents followed by immersion in first boiling 50% HCl in H2O then HF solution, after which Si was deposited at 630 °C using SiH4 in a low-pressure CVD reactor at 7 mTorr (base pressure = 10-5 Torr). The Si films showed good crystallinity and a (111) orientation in XRD. Sputter profiling combined with AES showed a low level of C and O impurities with evidence for interdiffusion of Si and N (i.e., Si in the GaN and N in the Si layer). This was ascribed to the loss of surface N from GaN via reaction with H released by SiH4 decomposition, which resulted in NHx mixing with the reagent flux. Electrical measurements showed a high concentration of donors in the interfacial region, which is consistent with heavy Si doping, and the Si 2p and N 1s XPS confirmed the presence of SiNx in the interfacial layer. Although not stated by the authors, these results would also be consistent with the possibility of a reactive Si/GaN (0001) interface, i.e., a direct reaction between Si and GaN. Lee et al. [786] used STM, RHEED and AES to investigate surface

reconstructions caused by Si deposition on GaN (0001) and (0001̄ ). The samples were prepared and studied in situ in an MBE growth chamber, and Si depositions were done at substrate temperatures in the range of 300–350 °C. No structural change is seen in RHEED when Si is deposited on the (0001)-"(1x1)" (or pseudo-(1x1)) surface, with a laterally-contracted Ga bilayer. On the (5x5) surface, with a lower Ga adlayer coverage, Si induces a (2x2) reconstruction that disappears above 300 °C, which suggests a metastable structure. For subsurface incorporation of Si, as suggested by theoretical work described below, θSi ≈ 0.63 ML is estimated for the (2x2) structure. Continued exposure to Si at 300 °C results in an increased density of small "(1x1)" domains, which suggests that Ga displaced by site exchange with Si remains adsorbed and reforms the metallic-Ga bilayer associated with the "(1x1)" structure. At a Si coverage of ∼1 ML a (4x4) pattern appears after a brief 350 °C anneal. Annealing at higher temperature leads to this pattern disappearing and a purely-"(1x1)" reappearing, which is ascribed to the incorporation of all Si at subsurface sites with the displaced Ga then reforming a metallic bilayer. The effect of Si on the smooth-to-rough transition, which is observed during MBE growth when the Ga/N flux ratio decreases below unity, was also investigated. No significant effect is seen for the (0001) surface; whereas, an immediate roughening is observed for the (0001̄ ). The proposed explanation, based on the above results, is as follows. During normal MBE growth under Garich conditions, the (0001) surface is covered by a Ga adatom bilayer through which Si diffuses easily and displaces Ga from GaN lattice sites. This leaves the Ga bilayer intact and capable of promoting surface diffusion of Ga and N. On the other hand, the (0001̄ ) surface is covered by a single Ga ML during Ga-rich growth.

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Si displaces Ga in this layer and thus disrupts any effect it has on aiding Ga and N diffusion, which leads to the observed roughening. This constitutes an anti-surfactant effect of Si on the (0001̄ ) surface. Lee et al. [786] also performed theoretical studies of Si on GaN (0001) as part of the experimental work described above. This aspect will be discussed in more detail later in this section. Schmidt et al. [714,717,787] used XPS with high spatial resolution to study the surface segregation of Si from the GaN bulk. Surfaces of samples grown by MOCVD with Si concentrations of either 2.5x1018 or 1x1019 cm-3 show stripes that are roughly 1 μm wide and up to tens of μm long. The stripes are found to represent faceted grooves in the GaN surface and are thought to occur as a result of the tensile stress generated by Si incorporation. Comparison of the relative intensity of the Si 2p and Ga 3p3/2 XPS peaks, which are close in BE, shows that the whole surface is enriched in Si, especially the stripes. For a uniform dopant density of 1x1019 cm-3, the Si/Ga concentration ratio would be ∼10-4, and no Si should be detectable in XPS; thus, surface segregation must be occurring. Quantitative determination of θSi gives 4.5x1014 Si cm-2 (0.40 ML) at the facet edges and a lower value, by a factor of about 2.54, in the flat areas between facets. The possible contribution of

SiOx, resulting from the oxidation of surface-segregated Si dopant, to persistent low levels of O impurity on GaN surfaces was noted in Section 3.5. Markurt et al. [788] used HRTEM to study the anti-surfactant effect of a high θSi that occurs for growth on the (0001) surface under N-rich (MOCVD) conditions. As an anti-surfactant, Si inhibits surface diffusion and thus promotes 3D (island) vs. 2D (layer) growth. The sample was prepared by depositing SiNx on MOCVD GaN (0001) in order to produce a δ-doped Si layer that is relevant to growth in a high Si flux. This was done by replacing the Ga supply (presumably Ga(CH3)3) with SiH4 at the end of the GaN growth run, and it was verified that GaN growth does not occur directly on top of the SiNx. The interest then is in the structure and composition of the SiNx, and it was shown that it has the stoichiometry SiGaN3 and forms together with one VGa per unit cell to give a (√3x√3)R30° structure. Ab initio theoretical modeling was also performed to examine the reason why GaN growth is inhibited on the surface of a SiGaN3 region, which is beyond the scope of the present review. Rosa et al. [789] extended the theoretical work described briefly in Ref. [786] in a study of Si on GaN (0001) using the LDA

Fig. 55. Upper: Schematic side view of the energetically-favorable structures for bare and Si-covered GaN (0001) surfaces. (a) N terminated with a Si subsurface, (b) Ga bilayer, (c) Ga bilayer with a subsurface Si, (d) Ga adatom, (e) N adatom, (f) Ga adatom with a subsurface Si, and (g) 2 MLs of Si. Lower: Phase diagram showing the energetically stable structures as a function of both Si (μSi) and N (μN) chemical potentials. The atomic geometries of these structures correspond to those in the upper panel, and the shaded area shows the region where all structures are unstable against the formation of Si3N4. From Rosa et al. [789] (reproduced with the permission of AIP Publishing).

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and a 2DPS with nine GaN layers (presumably nine Ga-N bilayers) terminated on the bottom face with PHs. The bare surface was modeled with a (2x2) SUC, while the "(1x1)" (or pseudo-(1x1)), with a laterally-contracted Ga bilayer, was modeled with a (√3x√3) SUC, and the Si coverage was in the range of 0 to 2 MLs. Fig. 55 shows the various structures considered together with a phase diagram indicating which is the most stable under different conditions. For low μSi, incorporation of Si is unfavorable, and one sees only the different clean-surface GaN (0001) structures on progressing from N-rich to Ga-rich conditions. With increasing μSi, various Si-induced reconstructions occur, all of which are thermodynamically unstable against Si3N4 formation. The Si-induced (2x2) seen [786] on the (0001) surface under MBE conditions is explained by a process in which Si displaces one surface Ga per (2x2) SUC, which remains as an adatom, and also incorporates at a subsurface Ga site (Fig. 55f). The resulting structure is, however, less stable than the (1x1) shown in Fig. 55a, from which it is concluded, in agreement with experiment, that a Si-induced (2x2) is metastable. Under Ga-rich conditions, a high μSi favors the incorporation of Si in the lattice-terminating layer under a metallicGa bilayer (Fig. 55c). The phase diagram shows that Si remains in the surface layer under the N-rich conditions typical of MOCVD, where it eventually forms Si3N4 islands. These islands block 2D growth of GaN, which means that Si in this case acts as an antisurfactant. On the other hand, under the Ga-rich conditions typical of MBE, Si incorporates easily, leaving the Ga bilayer intact and continuing to function as a surfactant. This work was extended by Rosa and Neugebauer [790] to include a study of bulk doping by Si, which is beyond the scope of the present review, and also a more detailed investigation of Si adsorption. For the bare (0001) surface under Si-rich conditions, adsorption is unfavorable at all sites, all coverages up to 1 ML and all allowed values of μN except for θSi = 0.25 ML at a T4 site. This reduces the number of DB electrons per (2x2) SUC from three to one. On the other hand, for the (0001) surface with an ML of N adsorbed at T1 sites, which is a highly-unstable structure, Si adsorption is favorable for all θSi in both HCP (T4) and FCC (H3) sites, either of which maximizes Si-N bond formation. The ΔEads in this case is highly exothermic due to the high density of N DBs on the Si-free surface, and adsorption at T4 and H3 has essentially the same ΔEads. It is concluded that N-rich conditions favor the formation of Si-rich structures; whereas, Ga-rich conditions favor little or no adsorption of Si. To gain insight into the experimentally-observed (2x2) reconstruction induced by Si adsorption, various models were constructed in which Si replaces some or all Ga in a (2x2) SUC to form mixed Ga-Si surface layers, followed by adsorption of Si or Ga on these mixed surfaces. Under Si- and N-rich conditions, replacing all Ga with Si, gives the most stable surface. For more Ga-rich (and still Si-rich) conditions, the most stable structure has 3 of the 4 Ga atoms replaced by Si; whereas, for very Ga-rich conditions, the most stable surface has 1 Ga replaced by Si. The results confirm the conclusion stated above, that N-rich conditions favor a high concentration of surface Si. These results were obtained with the restriction that Si remains as an adatom or in the outermost Ga-N bilayer. When, under conditions that are both Si-rich and moderately Ga-rich, this constraint is removed it is found that the most exothermic (2x2) structure has Si incorporated into the first and second Ga-N bilayers with a Ga adatom in a T4 site back-bonded to 3 Ga atoms (Fig. 55f). However, as discussed previously [789], this structure is metastable with respect to the (1x1) structure in Fig. 55a. For very N- and Si-rich conditions, adsorption of an ML of Si on top of this structure (Fig. 55g) is favored. In either case maximizing the number of Si-N bonds leads to the most stable structure. When subsurface Si is considered under very

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Ga-rich conditions, the most stable structure is found to be 1/ 3 ML of Si in the outermost Ga-N bilayer underneath a bilayer of metallic Ga (Fig. 55c). These results and others are summarized in a phase diagram that is similar to that in Fig. 55, and the conclusions regarding the implications for GaN growth are those discussed in the preceding paragraph. It is noteworthy, in view of the surface-segregation studies of Schmidt et al. [714,717,787], that the present results indicate that the N-rich conditions that pertain to MOCVD favor accumulation of Si at the surface. Rosa and Neugebauer [791] have also reported a theoretical study of polarity inversion due to Si, in which the growth of a (0001) surface becomes one of a (0001̄ ). As discussed above, under conditions that are Si-rich but not highly Ga- or N-rich, the most favorable (0001) structure has an ML of Si in T1 sites and, above that, an ML of N in T4 sites (Fig. 55a). This converts a Ga-terminated to an N-terminated surface. Bond-length considerations show that the high degree of stability of this structure is not the result of any unusual bonding geometry. However, calculation of the surface band structure shows that, for the structure in Fig. 55a, Si donates electron density into the partially-filled N dangling orbital, which stabilizes the surface. Ji et al. [792] computed the structure and optical properties of the (0001) and (0001̄ ) surfaces of Si-doped GaN. For either surface polarity, the 2DPS had six Ga-N bilayers with the lowermost three fixed in the bulk-lattice configuration and the bottom surface terminated in PHs. One Ga per (2x2) unit cell was replaced with Si in the first, third and fifth Ga-N bilayer starting at the (0001) or (0001̄ ) surface. Thus the surface and bulk were uniformly doped with one-eighth of the Ga replaced with Si. The functional used was not stated, but it involved the GGA. After relaxation, ϕS = 3.204 and 6.313 eV were found for the (0001) and (0001̄ ) surfaces respectively vs. 4.2 eV for the undoped surface, which was attributed to an increased partial negative charge on surface N atoms. Si donates more electron density to N than does Ga so that on the (0001), where N lies below the surface plane, an outward-pointing dipole is created that leads to a decrease in ϕS; whereas, the reverse occurs on the (0001̄ ). Band structures and optical dielectric constants in the 0 to 20 eV range were computed with a view toward the use of Si-doped GaN for UV detection. In summary, Si substitutes only for Ga and not for N, and the most stable structures are ones that maximize the number of Si-N bonds. Si adatoms are unstable against incorporation into the GaN lattice, and, except under very Ga-rich, all structures due to incorporation of individual Si atoms are unstable against Si3N4 formation. The absence of Si3N4 during actual MBE growth is attributed to the fact that Si incorporates so easily that the surface concentration never reaches a level where Si3N4 formation is feasible. Under highly Ga-rich conditions, the most stable structure has Si in a Ga site in the GaN surface layer under a Ga adatom bilayer, in agreement with experiment. 5.35. Silver The formation of Ag layers on GaN (0001) has been studied experimentally by Maffeis et al. [124], Tracy et al. [474], Wu et al. [793] and Bakhtizin et al. [794], and Ag on non-polar surfaces was studied by Walker et al. [676]. The interest is in the structure of the interface and how it relates to contact formation. There has also been a theoretical study of Ag/GaN [678], but that was for the (001) surface of the cubic form and will not be discussed here. Another theoretical study, by Song et al. [795], used ab-initio results for Ag/GaN (0001) to develop an interfacial potential function. Kampen and Mönch [702] deposited Ag in situ on atomicallyclean GaN (0001) prepared as described above (Section 5.24) in

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connection with their results for Pb. An SBH of 0.82 eV was found using ex-situ I-V measurements, but the interface was not further characterized. Maffeis et al. [124] used XPS and I-V measurements to study Ag contacts on n-GaN. Samples grown via MBE were cleaned in dilute aqueous HF solution and then in situ using a series consisting of deposition of 40 Å of Ga at 600 °C, annealing in UHV at 700 °C, annealing in UHV at 775 °C, another 40-Å Ga deposition at 775 °C and finally annealing in UHV at 775 °C. Presumably the Ga thickness corresponds to the amount deposited on a QCO at RT. Surface-sensitive Ga 3d XPS data were obtained using excitation at hν = 66 eV. The final surface before Ag deposition shows an increase in upward BB of 0.7 eV relative to the untreated, as-received sample and also Ga 3d satellites at higher and lower BE that probably arise from GaOx contamination and residual free Ga respectively. Deposition of 30 Å of Ag produces no additional BB, which indicates that the Fermi level is pinned. The result for EFVBM is 2.2±0.2 eV on the nominally-clean surface, which, in view of the lack of any detectable change in BB with Ag deposition, corresponds to an SBH of 1.1±0.2 eV vs. the I-V value of 0.77 eV. The latter agrees well with the I-V result of Kampen and Mönch [702], noted above, who also used Ga cleaning. It is noted here that Maffeis et al. appear to equate the 0.7 eV change in BB due to cleaning with the total BB on the nominally-clean surface, which assumes that there is no significant BB on the untreated surface. This in turn leads to an estimated SBH of 0.7 eV. Were this correct then the 0.7 eV increase in BB would yield EF-VBM ≈ 2.6 eV on the clean surface (for CBM-EF ≈ 0.04 eV in the bulk) vs. the observed value of 2.2 eV. This suggests that there is a small but finite BB of ∼0.4 eV on the untreated, as-received surface. Tracy et al. [474] performed XPS, UPS and I-V measurements, the experimental details of which were described previously in discussing their work with Au (Section 5.20). For 10 Å of Ag, the BB increases by 0.20 eV with no indication of mixing or reaction at the interface, and no further change in BB is seen for thicker layers. (For a Ag density of 10.501 gm cm-3, 1 Å = 5.863x1014 Ag cm-2 = 0.517 ML, where 1 ML is defined as 1 Ag per surface lattice site.) From the photoemission experiments the SBH is found to be 0.6 ±0.1 eV, which is in good agreement with the I–V result of 0.58 ±0.01 eV. These values are considerably smaller than the prediction of 1.3 eV based on the Mott-Schottky model for an ideal and defect-free interface, and the authors suggest possible reasons for this effect. As discussed in Section 5.20 in connection with results for Au, the SBH of 0.6 eV given above was obtained by adding the shift in the XPS Ga 3d BE due to contact formation to EF-VBM measured in UPS for the clean surface. If instead one uses the Ga 3d BE of 20.3 eV after Ag deposition to obtain EF-VBM, an SBH of 0.77 eV is found. This value will be used later, in Section 6, in the discussion of SBHs. Wu et al. [793] and Bakhtizin et al. [794(abstract only)] performed in-situ STM experiments on samples grown by MBE, which were first formed with a pseudo-(1x1) surface terminated in a metallic Ga bilayer and then annealed at 700 °C to remove the Ga adlayer. The surface is poorly ordered since the bare, ideally-terminated (0001)-(1x1) surface is unstable. Silver was then vapordeposited on the RT substrate at a slow or fast rate (0.8 or 60 ML' min-1 respectively) where 1 ML' is defined in this study as 1.38x1015 Ag cm-2, which is the Ag (111) packing density. (This equals 1.22 ML for an ML defined as 1 Ag per surface lattice site.) At the slow rate, growth occurs in a Stranskii-Krastanov mode [571]. At low coverage (θAg ≈ 0.8 ML'), Ag forms a uniform array of small 3D clusters resembling a disordered wetting layer; whereas, at a somewhat higher coverage (2.4 ML') growth of large 3D islands becomes apparent. The surface diffusion of Ag, which promotes 3D island formation, was effectively overcome by use of a very fast deposition rate, which results in a smooth and

continuous Ag layer. A subsequent 200 °C anneal of this smooth layer results in a breakdown leading to the formation of large Ag islands with a few MLs remaining on the GaN surface between the islands. Further step-by-step anneals up to 500 °C result in islands interspersed by locally-ordered regions exhibiting Ag-induced reconstructions, which were noted but not described in detail. A 600 °C anneal results in a well-ordered (1x1) surface that is ascribed to a full coverage of Ag adsorbed in T1 sites. Walker et al. [676] studied Ag on (101̄0) and (112̄ 0) surfaces prepared by cleaving in situ. The actual surfaces were designated as (011̄0) and (1̄21̄0), but these should be equivalent to the (101̄0) and (112̄ 0) respectively. The methods employed were described in Section 5.20 in connection with their results for Au on the same surfaces. Only preliminary data for rough surfaces formed by "bad" cleaves were presented. As was seen for Au, for which data were obtained for both "good" and "bad" cleaves, Ag deposition on a badly-cleaved surface leads to only a slight change in BB, which indicates that EF is pinned. Song et al. [795] performed ab-initio calculations for Ag/GaN for the purpose of parameterizing interatomic potentials to describe the interface. Adsorption energies (termed "adhesion energies") of about -1.5 and -1.0 eV were found for the (0001̄ ) and (0001) surfaces respectively for Ag in either T1 or Br sites. For the H3 site, both surfaces gave ΔEads ≈ -1.2 eV. The T4 site was apparently not considered, and the ab-initio calculations were not described in detail. (The values quoted here were obtained from the graphical results in Fig. 6 of this paper, and those for adsorption at the Br site appear to be mislabeled as "T1".) 5.36. Sulfur The adsorption of S on the GaN (0001̄ ) surface was studied by Plucinski et al. [436] using XPS and ARUPS, with an interest in understanding the passivation of GaN surfaces via wet-chemical sulfide treatment. Passivation of GaN surfaces using solutions of ammonium sulfide ((NH4)2S), termed "sulfur passivation", has been extensively studied (see, e.g., Refs. [796–798] for some early work) but is beyond the scope of the present review. The use of such solutions in the wet-chemical cleaning of GaN was also mentioned briefly in Section 3.1. The n-type samples were grown by MBE, cleaned in dilute HCl and H2O and then outgassed at 850 °C in UHV. The final cleaning involved cycles of IBA with nitrogen ions and 850 °C anneals after which a sharp, low-background (1x1) LEED pattern was observed. The surface was believed to be terminated in an adlayer of Ga based on the appearance of characteristic surface states in UPS. Molecular sulfur (presumably Sn clusters, with n unknown) was deposited in situ using an electrochemical cell and data obtained for two sets of conditions. In the first, the sample was exposed at RT to 40 L of S, while the second involved an additional 400 L followed by annealing at 300 °C. The exposure in Langmuirs was deduced from the pressure rise during dosing, which is useful only as an indicator of the relative exposure. The latter treatment gave a very stable S adlayer such that the clean surface could be regenerated only by IBA. As part of this work, the sample was also exposed to 5x103 or 1x104 L of O2 either with or without preadsorbed S, and the stable S adlayer is found to inhibit chemisorption of O2. Structure in the Ga 3d XPS was analyzed in detail and evidence presented that the high-BE shoulder, commonly assigned to Ga-O bonds involving impurity O, is actually an intrinsic feature due to Ga 3d-N 2s hybridization (Section 4.7.1). The clean surface showed an upward BB of ∼1.3 eV, which was reduced to ∼0.9 eV with the stable S adlayer or ∼0.64 eV for a 1x104 L O2 exposure. The clean surface was also found to be very sensitive to the adsorption of contaminants from the UHV background, which indicates that, unlike in the case of MOCVD material [398], the

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present n-GaN (0001̄ ) surface was not passivated by adsorbed H via diffusion from the bulk. This would be consistent with a lower concentration of H in the bulk of MBE vs. MOCVD GaN. The high degree of surface reactivity could also be a result of the metallicGa adlayer that is found to cover part of the (0001̄ ) surface after cleaning by IBA (Section 4.7.1.2). 5.37. Titanium The interaction Ti with GaN (0001) and (0001̄ ) surfaces has been studied experimentally in Refs. [561,764,799–802] and by Kowalik et al. [803] respectively. Theoretical results for (0001) have been reported by González-Hernández et al. [618] and by Ortega-Lopez et al. [804]. The main point of interest was in contact formation. Wu and Kahn [561] used UPS, XPS, AES and LEED to study Ti on GaN of uncertain polarity, which was nominally (0001) Ga-polar. The experimental details were summarized previously in the discussion of their Al work (Section 5.1). The results regarding reaction at the interface are very similar to those for Al; however, the dependence of BB on metal coverage is different. This is ascribed to the fact that the AlN reaction product formed at the Al/GaN interface is a wide-band-gap insulator; whereas, the TiN interfacial reaction product is a metal. Hence, the BB increases with θTi as the metallic layer develops, as expected for the formation of a standard metal/semiconductor Schottky barrier. For both n- and p-type GaN, Ti deposition pins EF at 2.0 eV below the CBM, and the similarity of the two results was taken to suggest the importance of MIGS (Section 6) in determining the SBH. Annealing at 900 °C in situ promotes further Ti/GaN reaction but does not significantly affect the position of EF. The possible influence on the SBH of any difference in work function between Ti and TiN was not discussed. Barinov et al. [799] used surface-sensitive XPS data, obtained via a synchrotron light source, to study the dependence of the SBH on lateral inhomogeneities at the Ti/n-GaN (0001) interface. The method of GaN growth was not stated but is assumed to be MBE based on contemporaneous work for other metals by the same group. Clean surfaces were prepared by IBA (0.6 keV nitrogen ions, 850 °C anneal). The Ga 3d on the clean surface shows a high-BE satellite ascribed to band dispersion and a low-BE satellite that is assigned to a SCLS. Both these effects were discussed in Section 4.7.1; however, the Ga 3d satellite might instead be the result of Ga adatoms [638] rather than a true SCLS. One can deduce that the BB on the clean surface is ~0.55 eV based on the bulk Ga 3d BE (20.5 eV) and the VBM-Ga 3d separation of 17.76 eV [439], assuming a CBM-EF separation in the bulk of ∼0.04 eV (see Fig. 24). The observed BB is probably reduced by 0.1-0.2 eV relative to the "in the dark" value by SPV. For an average Ti thickness of 5 Å, photoelectron microscopy shows inhomogeneous regions where the metal deposit is thicker due to the presence of reactive macroscopic defects on the bare surface. These are in addition to the dominant regions wherein the Ti thickness is uniform. (For a Ti density of 4.5 gm cm-3, 1 Å = 5.662x1014 Ti cm-2 = 0.499 ML where 1 ML means 1 Ti per surface site.) The Ti/GaN interface is reactive even in the absence of defects as shown by the appearance of satellite features in both the Ga 3d and Ti 2p XPS data and by the presence of N in the Ti layer. This indicates a ternary TiNxGay phase that varies in composition between different surface regions. In particular, the Ga 3d shows a new low-BE satellite due to Ga in a metallic environment, and the BE is lower and the intensity higher for this feature in inhomogeneous vs. uniform regions. Annealing up to 800 °C causes more extensive reaction, leading ultimately to a TiN-like phase from which essentially all the free Ga has been eliminated by desorption. The Ga 3d spectrum then returns to an appearance similar to that on the clean surface. Shifts in the bulk Ga 3d with

115

annealing temperature were obtained for both uniform and inhomogeneous regions and used to determine BB after correction for SPV induced by the XPS excitation source. The important result is obtained that the BB and its temperature dependence are the same for all regions of the surface. This is explained in terms of a homogenization effect wherein potential differences between various regions are virtually eliminated by lateral charge redistribution. Kim et al. [800] used surface-sensitive XPS data, obtained via a synchrotron light source, to study the formation of Ohmic Ti/ntype GaN (0001) contacts. Clean surfaces were prepared on MOCVD material by cycles of nitrogen ion bombardment and annealing at 800 °C, after which no C was detected and the O contamination was reduced to an unspecified level. Ti was deposited in situ to a thickness of 12.7 Å and verified to be essentially uniform using AFM. The Ti 2p XPS shows reaction at the interface to form Ti-N bonds as well as Ti-O, which results from O contamination either on the bare surface or incurred during deposition. One notes that Ti is widely used as a getter in UHV systems due to its high reactivity with O-containing species. Annealing at 800 °C increases (decreases) the relative intensity of the Ti-N (Ti-O and metallic Ti) features. Annealing also increases ϕS by 0.65 eV, which indicates that the work function of TiN is 0.65 eV higher than that of polycrystalline Ti metal (4.33 eV [615]). The appearance of Ohmic behavior after annealing, in spite of the large SBH, was explained in terms of a greatly-reduced depletion width relative to the unannealed interface. This effect is ascribed to the formation of a degenerate n-type layer at the interface as a result of the high concentration of N vacancies produced by reaction with Ti. Electron tunneling is enhanced by the small depletion-layer thickness, which leads to Ohmic behavior. It is noted here that the same mechanism was proposed by Wu and Kahn [562] to account for annealing-induced Ohmic behavior in Al/n-GaN (0001) contacts (Section 5.1). Lin et al. [801] and Naono et al. [802] also used XPS and I-V data to investigate further the relationship between N vacancies and annealing-induced Ohmic behavior in Ti/n-GaN (0001) contacts. The results obtained provide further support for the proposed mechanism based on a reduced thickness of the depletion layer. Nörenberg et al. [764] used STM to study the initial stages of Ti deposition on MOCVD GaN (0001) following methods described above in connection with their work on Pd (Section 5.29). Deposition of Ti at ∼300 °C leads to the formation of irregular 2D islands of TiN with the (111) face parallel to the GaN surface, which suggests epitaxial growth. Deposition at RT, on the other hand, produces small clusters of either TiN or Ti metal. Upon annealing at ∼600 °C the Ti metal reacts to form irregular TiN islands, which become more regular when annealed in 2x10-5 Pa (1.5x10-7 Torr) of NH3 vapor. Kowalik et al. [803] investigated Ti on the (0001̄ ) surface of bulk single-crystal GaN using RPES facilitated by the use of synchrotron radiation. The sample polarity was verified by etching in aqueous KOH solution (Section 4.2.1), and clean surfaces were prepared by IBA (600 eV nitrogen ions, 500 °C anneal). A (1x1) LEED pattern of unspecified quality was seen for the clean surface, but no other surface characterization was reported. In transitionmetal compounds, RPES is used to determine the contribution of metal states to the VB. This may be envisioned as a two-step process of the form Ti 3p63d2 + hν → [Ti 3p53d3]* → Ti 3p63d1 + e− where [...]* indicates a transient state. The final state is the same as for direct excitation of a 3d electron, but the RPES process is strongly enhanced when hν equals the 3p → 3d transition energy (∼46 eV). The VB for a 2.6 Å-thick Ti layer is characteristic of TiN, with Ti 3d states at EF and Ti-N bonding states at 6.2 eV below EF. Mild annealing, at 150 °C, promotes further TiN formation. Data recorded off-resonance (hν = 38 eV) can be subtracted from those

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obtained on-resonance to cancel the GaN contribution and reveal clearly that from the Ti 3d states. These results, and also changes in the Ga 3d lineshape and intensity, suggest a model in which Ti reacts to form TiN and a layer of metallic Ga that remains at the TiN/GaN interface. This is consistent with the higher ΔHf of TiN (-347 kJ mol-1) vs. GaN (-118 kJ mol-1). González-Hernández et al. [618] reported theoretical results for Ti on GaN (0001) obtained using methods described previously in the discussion of their Cr results (Section 5.12). Adsorption is strongly favored at the T4 site (ΔEads = -4.849 eV), where Ti can interact with a first-underlayer N. In contrast, ΔEads = -4.360 (-2.682) eV for an H3 (T1) site. A charge transfer of 0.071 |e| occurs from the GaN to the Ti, and the Ti magnetic moment in a T4 site is 0.98 μB. The barrier for diffusion from H3 to T4 is about 0.59 eV and 1.04 eV in the reverse direction, which reflects the greater stability of T4 vs. H3. For one Ti in a (2x2) SUC, the surface is semiconducting with the majority and minority spins present on both Ti and surface Ga atoms. Ortega-Lopez et al. [804] performed theoretical studies of Ti adsorption and incorporation on GaN (0001) using the PBE functional with USPPs. The 2DPS consisted of 4 Ga-N bilayers of which the lower two were fixed in the bulk configuration and the bottom surface terminated with PHs. For one Ti in a (2x2) SUC, ΔEads = -4.22, -4.13, -2.88 and -2.50 eV respectively for Ti in T4, H3, Br and T1 sites. These are in qualitative agreement with the results of González-Hernández et al. [618]; although, the T4-H3 difference is smaller in the present study. Ti in a T4 site is more stable than Ga in a T4 (ΔEads = -3.83 eV) from which it is inferred that Ti could improve contact adhesion at the GaN surface. The effect of increasing θTi up to 1 ML was studied by successively adding Ti to T4 or H3 sites in the (2x2) SUC. The T4 is the more stable at all coverages, but the H3 remains close in energy. For either site, ΔEads decreases in magnitude with increasing θTi, which indicates a repulsive interaction between adatoms. The incorporation of Ti was studied by substituting Ti in the upper two bilayers. It is found that Ti substitution for Ga is strongly favored over substitution for N and that Ti tends to accumulate in the outermost two Ga layers. Apparently the deeper bilayers remained fixed during substitution, and it is not clear the extent to which this might have affected the energetics. The computed phase diagram shows that Ti incorporation is favorable under moderately- to highly-Ti-rich conditions, in which case substitution for all Ga in the uppermost two bilayers produces the most stable structure. This high degree of substitution is attributed to a good match in symmetry and lattice constant between the GaN (0001) and rocksalt TiN (111) planes. The total DOS and partial DOS were also obtained for several modes of substitution, and it is found that the surface is metallic for all structures with, however, a varying density of states at EF. 5.38. Vanadium The interaction of V with the GaN (0001) surface has been studied theoretically by González-Hernández et al. [618,805]. The methods used in Ref. [618] have been described previously in the discussion of the corresponding Cr results (Section 5.12). Vanadium adsorption is most stable in the T4 site (ΔEads = -3.691 eV) vs. H3 or T1 (ΔEads = -3.428 and -2.093 eV respectively). The preference for T4 is attributed to an interaction between V and N, which lies below the T4 site. The magnetic moment per (2x2) cell with one V in the T4 site is reduced to 2.05 μB from the free-atom value of 3 μB, which is ascribed to the transfer of 0.037 |e| from the GaN to the V. The H3→T4 diffusion barrier is fairly small, about 0.18 eV, while the reverse barrier is about 0.46 eV, which reflects the greater stability of T4 vs. H3. The DOS shows no states at EF, which indicates that V in the T4 site saturates the partially-filled Ga DBs on the bare (0001) surface; however, strongly spin-

polarized states localized on V are found in the gap above the VBM. This work was extended by González-Hernández et al. in Ref. [805] using methods similar to those in Ref. [618] except that only the lowermost Ga-N bilayer of the 4-bilayer 2DPS was fixed during relaxation. Up to θV = 1 ML, T4 remains the preferred adsorption site, and ΔEads per V increases slightly in magnitude, which indicates a weakly-attractive V-V interaction. At θV = 1 ML, T4 is only slightly more stable than H3. Incorporation of V proceeds via substitution for Ga; whereas, either substitution for N or interstitial formation leads to an unstable structure. At all coverages up to 1 ML, substitution into the first Ga-N bilayer is energetically most favorable; however, for low (0.25 ML) or high (1.0 ML) coverages, substitution into the second bilayer is almost equivalent in energy. The preference for the outermost bilayers is attributed to the formation of strong V-N bonds, as suggested by the larger ΔHf for VN (-2.25 eV) vs. GaN (-1.14 eV). Results were given for the relative formation energies of different phases, from which a phase diagram was constructed. For Vpoor conditions the normal behavior for GaN (0001) is observed; namely, N adsorption at an H3 site, then Ga adsorption at T4 followed by Ga bilayer formation as the conditions progress from Nrich to Ga-rich. Under V-rich conditions, V incorporation with 4 atoms per (2x2) SUC in the uppermost Ga-N bilayer is found except under highly Ga-rich conditions, for which a Ga bilayer on the clean surface becomes the most stable configuration. The results indicate that growth of V-doped GaN is most easily done under Nrich conditions. More details were given regarding the DOS, which for 1 V per (2x2) SUC in a T4 site shows a semiconducting surface with a gap of ∼0.4 eV. New states appear between EF and the VBM, which for the majority spin are localized mainly on V (accounting for the large magnetic moment of 2.05 μB) while those for the minority spin are mainly associated with Ga DBs. With 4 V per (2x2) SUC substituting for Ga, the majority-spin states (which are due to V) cross EF; whereas, the minority states (also due to V) lie above EF, which suggests semi-metallic behavior. 5.39. Zirconium The deposition of Zr on GaN (0001) has been studied by Idczak et al. [806,807] using LEED and XPS. The interest was in the formation of ZrO2 high-k gate dielectric layers and ZrN/Zr/GaN Schottky contacts to n-type GaN. The samples were cleaned in alcohol and H2O prior to insertion into the UHV chamber followed by annealing in situ at 800 °C [806] or 700 °C [807], and O contamination was detectable on the nominally-clean surface. In the first of the two studies [806], Zr layers were deposited in situ followed by annealing at 700 °C. For up to 9 Å of Zr, four Zr 3p spin-orbit doublets are seen in XPS with the aid of least-squares fitting. (For a Zr density of 6.52 gm cm-3, 1 Å = 4.305x1014 Zr cm-2 = 0.379 ML where 1 ML is defined as 1 Zr per surface lattice site.) In order of increasing 3p3/2 BE these are assigned to metallic Zr and/or ZrN (329.6 eV), ZrOx (x o 2) (331.0 eV), ZrNxOy and ZrOx (332.5 eV) and ZrO2 (334.4 eV). With increasing thickness it appears that O diffuses into the GaN substrate while N moves out, into the overlayer, to form ZrN. Eventually the Zr 3p spectrum becomes dominated by features associated with the ZrNxOy oxynitride and with ZrOx. The LEED pattern for the nominally-clean surface was a sharp (1x1) at Ep = 80 eV, but at other energies additional beams were detected that were ascribed to "terraces". This phenomenon has been analyzed elsewhere [145–148] in terms of faceting (Section 3.3.1), and it has been noted previously [491] that Ep ≈ 80 eV minimizes the intensity of the faceting features in LEED. After Zr deposition and annealing the (1x1) LEED pattern (at Ep = 80 eV) persisted but with varying intensity, which was taken to indicate formation of an ordered layer.

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Table 5 Summary of Schottky-barrier data for as-deposited (i.e., unannealed) metal/n-GaN (0001) interfaces from photoemission measurements. In most cases the bare surface is atomically clean, or nearly so, and well-ordered (although possibly faceted), and in all cases the metal deposition is in situ in UHV. In nearly all cases a wet-chemical treatment, which is not mentioned here, was performed prior to in-situ cleaning. All energies are in eV. Values have been selected for inclusion on the basis of the consistency of the measurement method. Metal

ΦBexpt

Ag

1.1 0.77 0.8 0.61 1.3 1.16 1.15 0.98 0.90 0.81 0.66 1.3 0.84 1.5 1.44 1.4 1.2 1.46 1.46 1.3 1.05

Al Au

Ce Cu Gd Ni

Pd Pt Ti

a

Φ0

b

1.1 0.66 0.75 0.45-0.85 0.75 0.66 2.2 0.45-0.85 0.56 0.56 0.66 0.5 0.9 0.9 0.7 0.2 0.6 0.51 0.66 0.75 0.55

ΦBexpt-Φ0

ΦM

0 0.10 ∼0 ∼0 0.55 0.50

4.26

0.96

4.28

0.98

5.1

1.8

2.9 4.65 3.1 5.15

-0.4 1.35 -0.2 1.85

5.12 5.65 4.33

1.82 2.35 1.03

∼0.3 0.34 0.25 0 0.8 ∼0 0.6 0.74 1.2 0.6 0.95 0.80 0.55 0.5

c

ΦBMS

d

Growth/Surface Prep.

Ref.

MBE/Ga adsorb-desorb CVD/NH3 anneal CVD/IBA MBE/In-situ growth CVD/IBA CVD/NH3 anneal CVD/UHV anneal MBE/In-situ growth CVD/UHV anneal MOVPE/UHV anneal MOVPE/Ga adsorb-desorb CVD/IBA MOVPE/H-atomþ Ga-anneal CVD/IBA CVD/UHV anneal MBE/IBA CVD/UHV anneal CVD/UHV anneal CVD/NH3 anneal CVD/IBA MBE/IBA

[124]e [474]f [561] [564]g [561] [474]f [668]h [564] [330]f [126]f [126]f,i [598] [623] [613] [331] [748]j [752] [765]f [474]f [561] [799]f,k

a

Experimental SBH Band bending on the bare surface c Polycrystalline metal work function, from Ref. [615]. d SBH from the Mott-Schottky relationship ΦBMS ¼ (ΦM-χ) where χ ¼ 3.3 7 0.1 eV is the electron affinity of clean GaN (0001), Section 5.10. e ΦBexpt was obtained from the position of the VBM seen in UPS after depositing 30 Å of Ag (EF-VBM ¼ 2.2 eV). The Ga 3d data show no change in BB relative to the surface before deposition, whence ΦBexpt-Φ0 ¼ 0. The SBH tabulated here differs from that given in the reference (0.77 eV) on the basis of I-V data. f These values have been determined using data provided for the Ga 3d BE vs. metal coverage. In the case of Ref. [474], the tabulated values are ∼0.25 eV larger than those in the original reference. See Section 5.20 for a discussion. For Ref. [765] the tabulated value is 0.14 eV smaller. g The SBH depends on the thickness of the GaN MBE layer (tMBE). It is 0.417 0.1 eV for tMBE E 20 nm and 0.617 0.06 eV for tMBE Z 100 nm. h This point, which shows a very large clean-surface BB that decreases when Au is deposited, is considered an "outlier". i The Au in this case is found to alloy with Ga, which could affect ΦBexpt by changing ΦM. This point is considered an "outlier". j Φ0 in this study may have been reduced by the SPV effect. Only the data for the Ni-covered surface were reported as having been corrected for SPV. k The method of growth was not stated but is assumed to be MBE based on contemporaneous work by the same group. b

The latter of the two studies [807] provides additional LEED and STM data. Deposition of 0.8 ML of Zr followed by annealing at 700 °C eliminates the terrace, or facet, features seen in LEED at Ep = 124 eV. The resulting (1x1) pattern then suggests epitaxial growth. It is recalled here that a similar facet-elimination effect was observed in the case of Al on GaN (0001) [559] from which it was inferred that reaction at the interface consumes, or etches away, the faceted surface to leave a relatively smoother interface. The STM results show an increase in terrace width, which implies a lower density of terrace edges, and in terrace height and further suggest that Zr forms what are described as conglomerates of different chemical composition. In this case a thicker (2.2 ML) Zr layer, presumably after a 700 °C anneal, showed no long-range ordering in LEED.

6. Metal contacts Many of the studies reviewed in the previous section involve metals and include a measurement of the SBH. Because of its importance (and complexity) the Schottky barrier has been the subject of intensive and on-going study that has been reviewed in several publications, among them those of Brillson [808] and Tung [809,810]. A brief but very informative review has also been given by Eller et al. [5]. It has been seen that the SBH depends to a significant extent on the details of how the metal contact and the bare GaN surface are prepared. Here a brief review will be given of some general results relating to the SBH for well-characterized metal/GaN interfaces formed under atomically-clean conditions, focusing largely on the effects of surface preparation rather than

on the physics of contact formation. Table 5 summarizes SBH results from Section 5 together with additional data. To aid the comparison by eliminating as many variables as possible, only photoemission data for as-deposited (i. e., unannealed) n-type GaN (0001) surfaces are given since these are the most widely-available UHV results. For some metals, SBH values have also been obtained using I-V or C-V methods for contacts prepared under UHV conditions. These are generally close to those found using photoemission, which is a more direct measure of the position of EF, but are not included in Table 5. Data for p-GaN, in addition to being somewhat less common for atomically-clean substrates, may also be influenced by the large SPV effect [440] which can affect the apparent position of EF, at least for low metal coverages [525,526]. The effect of SPV is less important, but perhaps not entirely negligible, for n-GaN. In a further effort to reduce extraneous differences among the data sets, a common procedure has been adopted for obtaining the SBH, which is given by SBH = Eg - (CBM-EF)bulk - [(EF-Ga 3d)surf - (VBM-Ga 3d)] = CBMsurf CBMbulk (9) where Eg = 3.39 eV at RT [24] and (CBM-EF)bulk ≈ 0.08 eV is the energy of the CBM relative to EF in the bulk, which can be computed [811] using values for the carrier concentration (typically ND ≈ 1x1017 cm-3) and the electron effective mass (m* = 0.20 me, Ref. [812]). This is given by (CBM-EF)bulk = kT·ln(NC/ND) where NC = 2(2πm*kT/h2)3/2 = 2.24x1018 cm-3 at RT is the DOS at the CBM. The Ga 3d BE after contact formation is (EF-Ga 3d)surf, and the Ga 3d energy relative to the VBM, which is independent of BB,

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is (VBM-Ga 3d) = 17.76±0.03 eV [439]. In some cases the SBH obtained in this way differs somewhat from the value given in the papers cited, and further details can be found in the subsections that discuss the various metals. The SBH obtained via Eq. (9) is independent of any measurement for the clean surface and is unaffected by SPV if the metal layer is sufficiently thick, which can be assumed to apply when the SBH becomes independent of metal coverage. The subset of references selected for inclusion in Table 5 consists of those that provide sufficient information (i.e., the Ga 3d BE after contact formation) to allow the use of Eq. (9) and that also give a value for Φ0, the BB on the clean surface, which is necessary for the following discussion. Where necessary, Ga 3d BEs were obtained from graphical data plotted in figures. Data for Mg [561,703] have been omitted from Table 5 in view of the uncertainty concerning the BB contributions from hole doping vs. contact formation. In one study [703] a large increase in upward BB is seen during deposition of the first ML, before the Mg layer appears metallic. Because of the high vapor pressure of Mg, a thin metallic layer can be desorbed at a low temperature (520 K) after which there is very little reversal (∼0.1 eV) in the BB change. A similar effect has been reported [575] when a layer of Sb, deposited in situ on p-GaN (0001), is thermally desorbed. This suggests that most of the Mg-induced BB change results from a high concentration of acceptors caused by Mg incorporation rather than from contact formation. The ∼0.1 eV shift in EF-VBM when metallic Mg is desorbed can then be taken as an estimate of the effect of contact formation. Another study [561] observed no doping effect but also only a small change in BB with Mg deposition on n-GaN, which again indicates a small effect from contact formation. Also omitted from Table 5 is an Au result [669] (ΦBexpt = 1.4 eV, Φ0 = 0.7 eV) for what was probably the (0001̄ ) surface. The metal work functions (ΦM) in Table 5 are those for the polycrystalline materials [615]. In cases (e.g., Ni), where an ordered metal layer forms, values for single-crystal surfaces [767] might be more appropriate, and several metals show a variation in ΦM of as much as ∼20% among the different low-index surfaces. Another factor affecting ΦM is alloying with Ga as a result of interfacial reaction. The alloy ΦM may be more relevant to the SBH than is that of the pure bulk metal. Evidence for a Ga alloying effect on contact properties was found by Maffeis et al. [126] for Au/n-GaN (0001) where the clean surface had been prepared by Ga deposition and desorption. Barinov et al. [669] accounted for annealinginduced changes in the SBH for this system in terms of the replacement of pure Au with a AuGa2 intermetallic compound. A discussion of the measurement of the GaN electron affinity (χ), which is also relevant to the SBH, has been given in Section 5.10 in connection with Cs adsorption and NEA behavior. Since all contacts listed in Table 5 were formed by in-situ vapor deposition on surfaces that were atomically clean or nearly so, the main difference among the various studies probably lies in the procedures used for preparing the clean substrate. The effects on contact properties of the surface treatment before metal deposition have been well documented. However, less attention has been given to the effects of in-situ cleaning on contacts formed in UHV than to "practical" contacts wherein the substrate is cleaned ex situ and then transported through room air to a moderate-vacuum (∼10-5 Torr) metal deposition system. General discussions of this subject have been given in the reviews by Liu and Lau [32] and by Pearton et al. [36]. Several studies have described the effects on the SBH of interfacial oxide [63,87,813], defects [76,84] and excess Ga [126], all of which relate to surface cleaning. Bell et al. [814] have studied the effect on the Au/n-GaN (0001) SBH of annealing the GaN substrate prior to Au deposition and found a strong dependence for temperatures up to ~600 °C that appears to parallel that seen [123] for the BB change with annealing for a bare ionbombarded substrate. These results indicate that, in addition to

other factors, the thermal history of the substrate is also important. Damage incurred during metal deposition is a potential issue that can complicate the interpretation of SBH data. Hasegawa et al. [815] have reported a novel approach in which a GaN surface is cleaned and a metal contact deposited, both electrochemically, which is an example of in-situ cleaning and contact formation in a wet-chemical environment instead of in UHV. The resulting contacts show properties that are superior to those obtained using conventional vacuum-deposition methods, which is attributed to a lesser degree of damage in the electrochemical deposition. For other III-V materials, it is known that energetic metal atoms arriving from a thermal evaporation source can cause damage, which led to the development of the so-called "soft-landing" method [816,817]. Here the clean semiconductor surface at ∼60 K is covered with a layer of condensed Xe onto which a metal layer is deposited in the form of clusters. The thermal energy is dissipated in the rare-gas layer, which is then allowed to evaporate to form the contact. To our knowledge this has not yet been done for GaN. Although "soft landing" may not be practical for routine contact fabrication it is potentially valuable in a study of fundamental mechanisms. Part of the variation in ΦBexpt shown in Table 5 for different experiments using the same metal can be accounted for qualitatively by differences in Φ0. This can be seen by comparing trends in ΦBexpt and Φ0, which show that in most cases the two quantities vary together. The Au results provide a good example if one omits the "outlier" values in Ref. [126], where the surface was cleaned by Ga deposition and desorption (see below), and in Ref. [668] where a decrease in BB was seen after Au deposition (Section 5.20). Here ΦBexpt varies over a range of ∼0.50, but ΦBexpt-Φ0 varies by only 0.30. The same qualitative trend with ΦBexpt and Φ0 changing together is generally seen, albeit with some scatter, for other metals (Ag, Al, Ni and Ti) for which more than one datum point is available. Thus variations in Φ0 that result from preparation of the bare surface can contribute to differences in ΦBexpt. The mean value of Φ0 in Table 5 for all types of samples and methods of surface preparation is 0.71 eV (corresponding to EF-VBM ≈ 2.59 eV) with a variance of ±0.18 eV. This omits one very large (2.2 eV, Ref. [668]) and one very small (0.2 eV, Ref. [748]) value. The result for EF-VBM is close to the EF pinning position (2.55 eV above the VBM, Ref. [440]) for GaN (0001) surfaces that were cleaned by IBA and studied using XPS at elevated temperature to avoid SPV. This pinning position is believed to result from partially-filled Ga DBs (Section 4.7.3). Implicit in the above proposal is the assumption that whatever causes BB on the bare surface is relatively unaffected by metal deposition so that the BB resulting from contact formation simply adds to that initially present on the bare surface. In other words, Φ0 is assumed to depend only on the clean-surface preparation and not on the metal. This might appear to be a poor approximation in the presence of reaction and/or strain at the interface. Reaction is typically observed when nitride-forming metals are deposited after in-situ cleaning, and strain has been shown [768] to affect the Pt/n-GaN SBH, which might also occur for other metal/GaN contacts. The results for Au in Ref. [668], for which ΦBexpt o Φ0, provide a clear example of a case where this approximation is invalid. Bermudez [818] attempted to quantify this description using an entirely phenomenological approach, based on the Cowley-Sze theory, which posits that ΦBexpt - Φ0 = S(ΦM - χ) + K for n-GaN. Here χ = 3.3 eV is the GaN electron affinity, and S (the "slope parameter") is a fitting parameter between 0 and 1. The K term was originally expressed as K = -SΦ0 and was included to assure the proper limiting behavior for S = 1 (a perfect Mott-Schottky contact) and S = 0 (a contact with EF completely pinned). This term

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might better be viewed as a quantity, which should be small compared to Φ0, that accounts for effects other than the initial BB and the contact formation, such as a thin insulating contamination layer [63,87,813] or a dipole layer [474] at the interface. Like Φ0, K is assumed to be independent of the metal. In practice, Φ0 will necessarily be small in a hypothetical case where S = 1 since a low density of surface states in the gap is required for S = 1. Hence, the proper limiting behavior is assured for S = 1 as long as K remains less than Φ0. Another implicit assumption is that bound polarization charges, and the external surface charges that are present on the bare surface to compensate these charges, are unaffected by contact formation. Thus it is assumed to be possible, in principle, to have Φ0 = 0 (i.e., flat bands) and S = 1 in a situation where the polarization charges are compensated entirely by external effects. The approach outlined above was shown [818] to be capable of fitting ΦBexpt vs. ΦM, giving linear behavior and a reasonably small K, for data that were all obtained in the same laboratory using nominally-identical samples and surface preparations. The model is less able to account quantitatively for variations in SBH between different laboratories, and it fails completely for metals with a very low ΦM, such as Ce and Gd. It has been suggested [598,613] that the SBH in such cases is dominated by interfacial reaction. Nevertheless, Table 5 shows that ΦBexpt-Φ0 for a given metal generally exhibits less of a spread than does ΦBexpt, omitting the "outlier" Au results, which indicates that variations among data from different sources are reduced. A tentative conclusion based on the limited amount of data in Table 5 is that clean surfaces prepared by Ga deposition and desorption lead to poor contacts, as already suggested by Maffeis et al. [126]. For the three metals where data are available for such surfaces (Ag, Au and Cu), ΦBexpt ≈ Φ0, which for a high-ΦM metal suggests a very defective contact (i.e., one with a small slope parameter, S). This is consistent with evidence cited in Section 3.2.1 indicating that a metallic Ga layer in contact with GaN (0001) at high temperature enhances decomposition. It is unknown whether the same applies when GaN is heated in a flux of Ga vapor, which is also effective in surface cleaning but avoids the accumulation of a thick layer of metallic Ga. Work by Eyckeler et al. [512] indicates that a careful procedure involving annealing in a Ga flux can produce a clean and well-ordered n-GaN (0001) surface with a fairly small BB (EF-VBM = 2.94 eV at 150 K with ND = 5x1016 cm-3, which corresponds to a BB of ∼0.5 eV). It is also unknown whether the effect of Ga cleaning on the SBH is the result of defects or the possible presence of excess free Ga remaining from the final annealing step. In the case of Ag [124], free Ga is clearly seen in the Ga 3d XPS before deposition, and it is possible that thorough removal of free Ga would result in better contacts. A further observation is that ΦBexpt ≈ Φ0 is seen for Al in two studies in which Ga cleaning was not employed and also for Ag after annealing in NH3. The same does not seem to occur for other metals, even those that can react with GaN (e.g., Ni and Ti). Brudnyi [819] has given a general discussion of metal/n-GaN SBHs in terms of the charge neutrality level (CNL). An expression of the form ΦBexpt = (Eg - ICNL) + S(ΦM - ICNLabs) was applied, where ICNL is the energy of the intrinsic CNL relative to the VBM and ICNLabs = Eg + χ - ICNL. This can be recast in the form ΦBexpt = (1-S)(Eg - ICNL) + S(ΦM - χ) = (1-S)Φ0 + S(ΦM - χ), which is the same expression employed in Ref. [818] if Φ0 (the clean-surface BB) is equated to Eg-ICNL. Here Brudnyi used ICNL = 2.7 eV, which is a theoretical value for the CNL that is close to the experimental position of EF on the clean (0001) surface (2.55 eV above the VBM, measured "in the dark") as discussed above and in Section 4.7.3. A theoretical value was also used for S together with χ = 4.1 eV for GaN, which is larger than the accepted value (for the clean (0001) surface) of 3.3 eV (Section 5.10). With this, a good fit was found for a range of metal/n-GaN contacts (with ΦM ≥ 4.2 eV) prepared and

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Fig. 56. Energy-level diagram used in the MIGS model for a metal contact on an ntype semiconductor. W represents energy, and WC, WF and WV are the CBM, Fermi level and VBM respectively. ΦM is the metal work function, and δi is the thickness of the interfacial dipole layer with a potential difference of Δ. Wbp is the energy of the branch point below (above) which the MIGS are donor- (acceptor-) like, and ΦBn and Φbp are the SBH and the zero-charge-transfer barrier height. These two barrier heights are equal if there is no difference in electronegativity between the metal and the semiconductor (i.e., no charge transfer). ΦSD is the semiconductor work function, defined here as the difference between the vacuum level of the bare material and Wbp. Adapted from Mönch [820] (reproduced with the permission of the American Vacuum Society).

measured under various conditions. Next we summarize a more rigorous approach to the SBH. Mönch [820,821] developed the MIGS model (Fig. 56) as a unified description of SBHs for well-prepared contacts, i.e., those that are intimate, unreacted, laterally homogeneous and free of contamination and extrinsic defects. This requires careful in-situ contact formation on atomically-clean surfaces. "Defect" in this context includes any reconstruction of the bare semiconductor surface, which alters the surface charge distribution relative to that of the ideally-terminated bulk lattice. The basis for the model is that the tails of the wave functions of metal electrons extend into the semiconductor in an energy range lying between WV and WF and thus constitute intrinsic interface states, which are the MIGS. Below some branch-point energy Wbp the MIGS are donorlike; whereas, above Wbp they are acceptor-like, and the net charge in the intrinsic interface states is negative, zero or positive depending on whether Wbp lies below, at or above EF. Thus Φbp = Wci-Wbp, where Wci is the energy of the CBM at the interface, would correspond to the SBH for a hypothetical metal contact for which no charge transfer occurs in either direction. Invoking the concept of partially-ionic metal-semiconductor bonding, the MIGS model predicts that ΦBn will be smaller than (greater than) Φbp if XM is less than (greater than) XS, where XM and XS are the electronegativities of the metal and the semiconductor. The end result is ΦBn = Φbp + SX(XM-XS), where SX is a slope parameter. All parameters in ΦBn are defined in terms of quantities that can be either measured or computed using ab-initio methods. As shown in Fig. 57a, the theory gives a good quantitative description of SBHs for contacts that are well prepared as defined above, for which MIGS are the dominant source of interface states.

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Fig. 57. (a) Barrier heights of laterally homogeneous GaN Schottky contacts as a function of the difference between the metal and GaN electronegativities. The MIGS line is drawn with Φbp ¼ 1.1 eV and SX ¼ 0.29 eV/Miedema-unit. From Mönch [820] (reproduced with the permission of the American Vacuum Society). (b) n-GaN Schottky barrier heights vs. metal work function for contacts formed by the conventional vacuum deposition and in-situ electrochemical processes. The results show the superior contacts (i.e., higher slope parameter, S) obtained for electrochemical cleaning and deposition vs. vacuum deposition on substrates cleaned in NH4OH solution prior to contact formation. From Hasegawa et al. [815] (Copyright 1999 The Japan Society of Applied Physics).

Results for a wider range of metals on n-GaN (0001) are also given in Ref. [821]. Alternatives to the MIGS theory have been proposed, as described in the reviews by Tung [809,810]. One of these is the disorder-induced gap state (DIGS) model of Hasegawa (Ref. [815] and works cited). This approach appears better able to account for the strong dependence of SBH on the method of contact fabrication. Here the magnitude of the slope parameter SX is associated with disorder and damage at the metal/GaN interface, and the higher SX observed for contacts formed by in-situ electrochemical cleaning and metal deposition (Fig. 57b) is attributed to there being a lower level of stress and disorder than in conventional vacuum-deposited contacts.

7. Adsorption of inorganic and organometallic molecules Some of the comments that appear in the introductions to Sections 3–5, particularly in regard to comparisons between theory and experiment, also apply here. 7.1. Ammonia (NH3) The interaction of NH3 with GaN surfaces has been studied extensively due to its importance in MOCVD growth. The use of NH3 vapor in the in-situ cleaning of GaN surfaces was discussed in Section 3.2.2. Here the focus is on adsorption and reaction with clean GaN surfaces under well-controlled conditions. Experimental results have been given by Chiang et al. [822], Shekhar and Jensen [823], Bartram and Creighton [824] and Bermudez [825]. Theoretical results are given for the (0001) and (0001̄ ) surfaces in Refs. [94,141,213,216,383,659,826–840] and [368,841] respectively

and for (101̄0) and (112̄ 0) in Refs. [212,368,841] and [368,841] respectively. Chiang et al. [822] studied NH3 adsorption using TOF-SARS, which is a form of ISS that can detect surface atoms, including H, with high sensitivity [842]. The samples were grown by MBE on Si (100) and, after mounting in UHV, were cleaned by IBA (Ar+ ions of unspecified energy, annealing at 800 °C). The surface orientation and polarity were not stated; however, the TOF-SARS signal from Ga is much stronger than that from N, from which one might infer that the sample is at least Ga-terminated if not Ga-polar. There appears to be little or no sign of C or O impurities in the TOF-SARS data. NH3 is very reactive with the surface, based on the temperature dependence of data for surfaces exposed to H (Section 7.3) vs. NH3 and on the effect of NH3 on pre-adsorbed D. Reaction leads to the formation of Ga-NHx (xo3), Ga-H and N-H sites. The thermal desorption of H after NH3 exposure is similar to that seen when the surface is exposed to atomic D, which indicates a partial dissociation of NH3 leading to surfacebound H. Furthermore, pre-adsorbed D is displaced by H as a result of NH3 adsorption, which is another indication of NH3 dissociation. Shekhar and Jensen [823] used TPD to study the reaction of ND3 with GaN (0001). The deuterated species was used in order to avoid complications due to the presence of H2 in the UHV background. The sample was cleaned in organic solvents and then in situ by IBA (1 keV Ar+, 1000 K anneal). After ND3 exposure at RT, TPD up to ∼850 K showed only 20 (ND3), 14 (N) and 4 (D2) atomic mass units. The possibility of exchange of N between GaN and NH3, or of decomposition of the GaN as a source of N-containing species, was excluded using 15NH3. Exposure to NH3 of a surface with pre-adsorbed D shows desorption of NHxD3-x and HD, which indicates that NH3 partially decomposes, recombines with adsorbed D and desorbs as molecular ammonia. A surface exposed to 15 NH3 was annealed to 550–650 K to generate adsorbed 15NHx

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fragments and then exposed to atomic D. The TPD yield of 15NH2D was larger than that of 15NHD2 by a factor of ∼3.5, which indicates that a large fraction of the NHx is in the form of NH2. It also follows from these experiments that most, if not all, of the NH3 seen in TPD arises from recombinative desorption of NH2 and H rather than from desorption of intact NH3. Bartram and Creighton [824] used LEED and TPD to study the interaction of NH3 with GaN (0001). No details regarding surface preparation were given, but the starting surface exhibited a (1x1) LEED pattern with sharp spots and a low background. NH3 adsorbs only reversibly on this surface, which is signaled by the appearance of intact NH3 in TPD. However, prior high-temperature exposure to D2 (2 Torr, 120 sec, 1200 K) alters the surface in such a way that steps (or facets) are evident in LEED, and some NH3 adsorption is then irreversible (i.e., completely dissociative, resulting in N2 desorption). Exposure of such a faceted surface to 15 NH3 leads to 15NH2D in TPD, indicating partial decomposition of adsorbed NH3 to form NH2, which then recombines with adsorbed H or D to yield NH3 or NH2D. However, no 14NH3 desorption is detected in experiments with 15NH3, which excludes the GaN lattice as a source of N. These results are generally consistent with those of Shekhar and Jensen [823] noted above; although, only

Fig. 58. Upper: UPS data for (a) an NH3-saturated surface, (b) the same surface after a brief thermal desorption ("flash") of the chemisorbed species at 800 ºC and (c) the difference spectrum [ΔN(E) ¼ (a) minus (b)]. In (a) and (b), linear extrapolation of the valence band edge to the baseline shows the apparent shift to higher BE due to the removal of surface states by adsorbed NH3. Vertical dashed lines indicate the two edge positions, and the negative-going feature near 3 eV in (c) is due to removal of surface states. Lower: (a) ΔN(E) for NH3 (same as in upper panel), (b) ΔN (E) for adsorbed H, (c) schematic representation of the spectrum of molecular NH3 condensed on Si (100) at 80 K and (d) schematic representation of the spectrum of -NH2 chemisorbed on Si (100) at 300 K. In (b), the feature at  19 eV may be due to a slight miscancellation of the strong Ga 3d emission. The labels "1e" and "3a1" indicate the corresponding NH3 molecular orbitals. The relative intensity of (a) and (b) is not quantitative. From Bermudez [825] (Copyright 2000, reproduced with permission from Elsevier).

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reversible adsorption was observed in that work. Irreversible desorption is detected by the appearance of 15N2, 15N14N and 14N2 in TPD. The overall conclusion is that on a stepped or faceted surface, where NH3 dissociation occurs to form NH2 and NH, an excess of adsorbed H promotes recombinative desorption of NH3; whereas, a deficiency of H induces further irreversible decomposition leading to N2 production. Bermudez [825] used UPS to study the species formed when NH3 adsorbs on GaN (0001). The aim was to obtain spectroscopic information for the adsorbed NHx species that were found in the TPD studies described above. The MOCVD sample was cleaned by nitrogen-ion bombardment followed by annealing in a flux of NH3 from an pinhole molecular-beam doser [617]. This was done in an effort to minimize the density of N vacancies, which can form during UHV annealing. Further details regarding this process are given in Ref. [123]. NH3 has a long residence time in UHV chambers and adsorbs readily on a clean GaN (0001) surface, which makes it difficult after annealing in NH3 to reduce the background to a level at which a clean surface can be obtained. This can be done (Fig. 58) by flashing off the adsorbed NH3 and quickly recording data, from which a ΔN(E) spectrum is obtained that shows features due the adsorbed species. The apparent shift in the VBM results from the removal of surface states that occurs when NH3 adsorbs on the clean surface, since little or no change in BB is detectable in the Ga 3d BE in XPS. The fairly narrow and intense peak in the NH3 ΔN(E) at BE = 10.5 eV is assigned to N-H bonding orbitals since a similar feature appears for condensed NH3 and for Si-NH2 on Si (100). The broad peak at BE ≈ 8.5 eV appears to coincide with a feature in ΔN(E) for adsorbed H, which supports assignment to a Ga-H bond. The deeper-lying peak in ΔN(E) for adsorbed H may also contribute intensity in the region of the N-H bonding feature seen for NH3. The peak at ∼4.5 eV in the NH3 ΔN(E), which is absent in ΔN(E) for H, appears to coincide fairly well with the 3a1 peak in NH3 and SiNH2, which is due to the NBLP orbital on N. This suggests a surface covered with Ga-NH2 and Ga-H. However, based on a simple Ga10N12H12 cluster-model calculation at the RHF level using semiempirical methods, it was argued that this feature is instead due to a Ga-N bonding orbital involving adsorbed NHx. It was further concluded that the UPS data are best described in terms of Ga-H and a Ga-N(H2)-Ga bridge with four-fold-coordinated N. It is noted that H and bridging NH2 add a total of 4 |e| so that 3 bridging NH2 and 3 H are needed per (4x4) SUC, which gives an NH3 coverage of 3/16 ML. However, the adsorbate coverage was not determined in this study. This still leaves a total of 6 |e| distributed among 7 Ga DBs so that, in addition, two 3-fold-coordinated Ga or N adatoms or two VGa per (4x4) cell are needed to satisfy the ECR. Ga adatoms can reasonably be expected to result from the in-situ cleaning method employed. The resulting (4x4) cell then has only empty Ga DBs. An alternative NH2+H dissociation process would be to start with a clean surface having one three-fold-coordinated Ga adatom per (2x2) SUC, which constitutes a passive surface. Inserting NH2 into a Ga-Ga back-bond as a bridge and forming a Ga-H bond either at the vacant Ga (2x2) surface site or at the Ga adatom would also satisfy the ECR and give an NH3 coverage of 1/4 ML. Pignedoli et al. [826] performed theoretical studies of the stability of GaN (0001) surfaces with Ga-NH2 and N-H species formed by NH3 decomposition using the PW approach with the LDA and soft (Troullier-Martins) PPs. The Ga 3d electrons were included in the PPs; however, NLCC [197] was employed to avoid the necessity for treating the Ga 3d electrons explicitly. The 2DPS consisted of 4 Ga-N bilayers with a (2x2) SUC and the bottom surface terminated in PHs. A clean surface under Ga-rich (N-rich) conditions was modeled with one Ga (one N) adatom per (2x2) SUC in a T4 (H3) site, both of which satisfy the ECR, while adsorption was modeled

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using surfaces with no adatoms. Adsorption of H was modeled using the bare surface and adsorption of NH3 by forming one VGa per (2x2) SUC, which satisfies the ECR and makes available three N DBs as adsorption sites for H. Under N-rich and very H-rich conditions, the most stable structure identified in this study for co-adsorbed NH3 and H has one Ga-NH2 with three N-H groups surrounding the VGa. It is noted here that this structure, as it is described in the original reference, does not satisfy the ECR since it results in a total of 2 |e| occupying the two remaining Ga DBs per (2x2) cell. An alternative structure, with one Ga-NH2 and one N-H per (2x2) cell, was also described. This does satisfy the ECR since the end result has the two remaining Ga DBs empty and the two remaining N DBs in the vacancy doubly occupied. Under Ga-rich and very H-rich conditions there are three Ga-H, with no NH2, in the most stable phase. This latter structure, which satisfies the ECR, is also the most stable over a wide range of H and N richness. Ab-initio MD calculations were also done that show that adsorbed NH2 is mobile and moves between vacant Ga sites. The possibility of Ga-N(H2)-Ga bridges was not explicitly considered in this study. In a subsequent study, Pignedoli et al. [827] extended their earlier work with some modification. A (4x4) SUC was used in order to treat lower coverages, structures with and without VGa were considered and bridging NH2 was included as a possible adsorbate structure. Stable phases that were modeled include 0.75 ML of H (i.e., 12 Ga-H per SUC), 1 Ga-NH2 and 11 Ga-H per SUC and 4 Ga-N(H)2-Ga bridges per SUC. The first two satisfy the ECR since the adatom species together contribute a total of 12 |e| that combine with the 12 |e| of unpaired electron density in the bare, ideally-terminated (4x4) SUC to form 12 Ga-H and/or Ga-NH2 bonds. The 4 bridges together also contribute 12 |e|, but the ECR is not satisfied since a total of 2 |e| remain in the DBs on the two vacant Ga atoms per (2x2) sub-unit. However, if a Ga-Ga dimer bond were to form between the two vacant Ga atoms then the ECR would be satisfied. Other combinations of H, terminal NH2 and bridging NH2 that satisfy the ECR are also possible, while still other stoichiometries that do not are unstable. The results reveal a tendency for cluster formation at higher terminal-NH2 coverages. In other words, for equivalent coverages of H and terminal NH2, those structures that place NH2 groups closer together are energetically favored. It was suggested that the driving force derives from the formation of a local region resembling a patch of GaN (0001). A terminal NH2 replacing 3 H atoms (which does not satisfy the ECR) remains terminal and does not relax to form a Ga-N (H2)-Ga bridge. A phase diagram was constructed showing the ranges of μH and μN over which those structures considered in the calculation are energetically favored, and the implications of these results for GaN growth were discussed. Van de Walle and Neugebauer [213,216] performed theoretical studies of the GaN (0001) surface under varying pressures of H2 and N2 as a function of temperature. Although this study did not involve direct exposure to NH3, the results are relevant here because adsorbed NHx (x≤3) and H are formed. Under extremely Hrich conditions (T = 0 K and 760 Torr of H2), the most stable structure except at very high μGa has one Ga-NH3 and three GaNH2 per (2x2) SUC. At the Ga-rich extreme, one Ga-NH3 and three Ga-H per cell becomes the most stable configuration. Both structures satisfy the ECR, with the NBLP orbital on NH3 forming a GaNH3 dative bond with the empty Ga DB. The situation is very different at a typical MOCVD temperature of 1300 K. Here a (2x2) cell with one NH adsorbed via three Ga-N back-bonds in an H3 site together with one Ga-NH2 is the most stable structure under very N-rich conditions, with Ga-NH2 being replaced by Ga-H for moderately N-rich to moderately Ga-rich conditions. Both structures satisfy the ECR. At still higher μGa, first a bare Ga adlayer and then a Ga bilayer are formed. Similar results at other temperatures and

pressures give the phase diagram shown in Fig. 7. Lu et al. [828] conducted theoretical studies of NH3 adsorption on GaN (0001) using the B3LYP functional and a cluster model of the form Ga13N13H18 with two Ga-N bilayers. The H atoms saturate DBs at the edges of the cluster, and because real H (not PH) is used the electron occupancies in surface DBs will differ from those in a 2DPS calculation. This can potentially affect results for ΔEads. Various basis sets were used; namely, 6-31G(d) for NH3, 3-21G for N and H in the lattice and LANL2DZ or LANL2MB pseudopotentials for Ga. Molecular NH3 adsorbs in a T1 site via a Ga-NH3 dative bond. The most stable mode of dissociative adsorption forms a GaN(H2)-Ga bridge and a Ga-H site, which is lower in energy than a terminal Ga-NH2 plus a Ga-H and is exothermic by 0.95 eV relative to molecular adsorption. Doi et al. [829] studied NH3 adsorption on the (0001) surface using the PBE functional for model consisting of a (2x2) SUC with a single Ga-N bilayer. The bottom (N) layer was terminated with adsorbed GaH3, and only the top (Ga) layer and the adsorbed NH3 were allowed to relax. For one, two or three NH3 per SUC adsorbed in T1 sites, ΔEads = -1.27, -1.94 and -0.72 eV per SUC respectively, with a full ML being endothermic. It is noted here that this can be understood in terms of the ECR. Two NH3 per (2x2) SUC can form Ga-NH3 dative bonds with empty Ga DBs. Adsorbing the third NH3 requires that an electron be promoted to the CB from one of the remaining Ga DBs. The fourth Ga DB is then doubly-occupied and incapable of forming a dative bond to NH3. Krukowski et al. [830–832] studied the interaction between NH3 and GaN (0001) using the PBE functional with NCPPs to represent atom cores and local basis sets (double-ζ plus polarization) to treat valence electrons. The 2DPS consisted of 5 Ga-N bilayers with a (3x3) SUC and with the bottom surface terminated with H atoms (presumably θH = 0.75 ML, to satisfy the ECR) and the top 2 bilayers free to relax. For the bare surface, NH3 adsorbs molecularly with ΔEads = -3.5 eV while on a surface with all Ga sites in the SUC occupied by H, other than the NH3 adsorption site, ΔEads = -2.6 eV. NH3 is also strongly adsorbed (ΔEads = -3.2 eV) even when the surface is completely saturated with pre-adsorbed H, in which case an H atom is detached from a Ga-H site to form an adsorbed • NH4 radical. The nature of the bonding of this species was not described in detail, and the calculations appear to have been spinrestricted. A complete kinetic and thermochemical analysis of the system under MOVPE growth conditions was also given. Uhlrich et al. [94] and Grabow et al. [141] studied the adsorption of NH3 on the (0001) surface theoretically as part of a combined experimental and computational investigation of the thermochemistry of NH3 cleaning. The calculations used the PW91 functional and a 2DPS with four Ga-N bilayers and a (3x3) or (2x2) SUC. A dipole correction was applied (Fig. 6), and the uppermost two bilayers and the adsorbate were allowed to relax during geometry optimization, but the method used for terminating DBs on the bottom surface was not mentioned. Ultra-soft PPs were used with the Ga 3d electrons included as valence states. For one adsorbed species per (2x2) cell, ΔEads = -1.66, -4.11 and -5.98 eV respectively for NH3 in a T1 site, NH2 bridging two Ga atoms and NH in an FCC (H3) site bonded to three Ga atoms [141]. Here the reference state in each case is the bare surface with the adsorbate species (NH3, NH2 or NH) in the gas phase, and therefore the ΔEads results for NH2 and NH are not easily applicable to dissociative adsorption of gas-phase NH3. The calculations were apparently not spin polarized (except for those relating to O2, which are described in Section 7.8). With zero-point energy corrections of 0.06, 0.19 and 0.19 eV respectively, ΔH0 = -1.60, -3.92 and -5.79 eV are obtained. The ΔEads for NH2 and NH become less exothermic with increasing coverage, which indicates a repulsive interaction between adsorbates and/or differing degrees of stability due to partial filling

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of surface DBs. The potential energy surface was obtained for the step-by-step process of NH3 adsorption, decomposition and desorption as N2 and H2. Decomposition of NH is unfavorable in terms of both kinetics (large ΔEa) and thermodynamics (endothermic reaction energy). Although decomposition of NH2 to form adsorbed NH is more favorable, at least at low coverage, the large repulsive interaction between NH sites inhibits the formation of a high coverage of such species. It is thus suggested that bridging NH2 is likely to be the dominant N-containing species under normal conditions. These results were used to simulate and analyze the TPD experiments [823,824] described above. Vibrational modes, including hindered translations and rotations, were also obtained for all NHx species. Mode assignments are not given but in some cases are obvious through comparison with those of free NH3. The theoretical work of Grabow et al. [141] is exceptional in that it gives mode frequencies for several atoms and small molecules adsorbed on GaN (0001), which would be valuable in the analysis of spectroscopic data. Won et al. [833] performed calculations for NH3 interacting with the GaN (0001) surface modeled using a Ga13N13H24 cluster, with H used to saturate DBs on the edges and at the bottom of the cluster. This differs from the Ga13N13H18 cluster used by Lu et al. [828] in that a Ga (N) in the lower bilayer that is bonded to only two N (Ga) atoms is compensated with two H rather than one, presumably in order to make this bilayer appear more bulk-like. The comments made above regarding DB occupancy in connection with the former cluster also apply here. The B3LYP functional was used with the LANL2DZ effective-core PP for Ga and 6-31G(d) basis sets for N and H. The Ga 3d electrons are included in the PP rather than in the valence states. NH3 adsorbs molecularly at a T1 site via a Ga-NH3 dative bond, with ΔEads = -33.0 kcal mol-1, and dissociates to form a Ga-N(H2)-Ga bridge and a Ga-H site. Relative to molecular adsorption, this is exothermic by 54.7 kcal mol-1 (2.37 eV). These results are in qualitative agreement with those of Lu et al. [828]; although, ΔEads for dissociation is significantly larger in the present case. Relative to molecular adsorption, dissociation to form terminal Ga-NH2 and Ga-H is endothermic by 8.5 kcal mol-1 and is the transition state in the reaction that forms a Ga-N(H2)-Ga bridge. Relative to bridging NH2, further dissociation to form NH backbonded to three Ga atoms and a Ga-H site is exothermic by 9.6 kcal mol-1, with a barrier of 16.8 kcal mol-1, if NH occupies an H3 site. On the other hand, placing NH in a T4 site, where it can interact with a lattice N atom, is endothermic by 2.4 kcal mol-1 and involves a barrier of 45.1 kcal mol-1. In these calculations, the adsorbed H resulting from the initial NH3 dissociation is removed from the model under the assumption that, in a real system, it will have diffused away from the reaction site. Further dissociation, to form adsorbed N and H, is endothermic by 21.8 kcal mol-1 with a barrier height of 57.2 kcal mol-1. Again the adsorbed H resulting from NH2 dissociation is removed from the model before treating NH dissociation. An alternative NH dissociation mechanism exists wherein NH first moves to the higher-energy T4 position. The dissociation is then less endothermic and has a lower barrier than does dissociation of NH in the more-stable H3 site. The surface diffusion of adsorbed NH, N and H were also considered. Based on the barrier heights obtained above, dissociation of adsorbed NH appears to be the rate-limiting step in the production of atomic N from NH3 under MOCVD growth conditions. The diffusion barriers obtained were 34.4, 38.8 and 66.8 kcal mol-1 respectively for NH, H and N for the minimum-energy paths. Suzuki et al. [834] studied the adsorption and subsequent decomposition of NHx (0≤x≤3) on GaN (0001) under Ga-rich growth conditions using a 2DPS with four Ga-N bilayers and a (2x2) SUC. The revised PBE functional was used, and the bottom of the slab was terminated with PHs. For the full range of μGa under H-rich

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conditions, the most stable species are NH3 and NH2 adsorbed at T1 and Br sites respectively, with the energy of NH3 being only 0.04 eV higher. On the other hand, NH and N (both in H3 sites) are higher in energy by 0.26 and 1.72 eV respectively. Cardelino and Cardelino [835] performed calculations for a cluster model with 44 Ga-N pairs in a wurtzite configuration for which it was noted that there were no unpaired electrons in Ga or N DBs. Although not explicitly stated, this implies that unpaired electron density in DBs on the Ga face was transferred to DBs on the N face during electronic relaxation to give an "auto-compensated" system with empty Ga and doubly-occupied N DBs. The model is thus an approximation to a 2DPS representation of an ideally-terminated GaN surface. Adsorption was analyzed using a hybrid approach in which the adsorbate (NH3) was treated at a "high level" (ab-initio DFT with the B3LYP functional) while the cluster was included at a "low level" (PM6 semi-empirical theory). This procedure, termed "ONIOM" [843], is designed to reduce computational cost without sacrificing a great deal of chemical accuracy. Calculations were performed in order to obtain thermochemical quantities and rate constants for various surface and gas-phase reactions. These results will not be described in detail here, as they are somewhat removed from the main focus of this review. Walkosz et al. [836] investigated the adsorption of NH3 on GaN (0001) theoretically using the PAW method with the PW-91 functional for geometry optimization and the HSE functional for DOS calculations. The latter is a hybrid functional that, although more computationally expensive, gives more accurate band gaps [200] than do pure-GGA functionals. The 2DPS consisted of a (2x2) SUC with 6 layers of GaN (presumably 6 Ga-N bilayers) with the bottom surface terminated with PHs and the top 2 layers (presumably bilayers) allowed to relax. NH3 and H are found to bind strongly to T1 sites and N and NH to H3 sites, in agreement with other studies. NH2 is most favorable as a Ga-N(H2)-Ga bridge unless the T1 site of either Ga is already occupied, in which case NH2 occupies a vacant T1 site to form a terminal Ga-NH2. In order to construct a phase diagram appropriate to the surface under MOCVD growth conditions, which involves many possible structures, a phenomenological model was used to describe the energies of different configurations. Here

BE =

∑ εi + ∑ εi, j + εECR i

i, j

(10)

Fig. 59. Calculated phase diagrams for GaN (0001) surfaces as a function of the chemical potentials of Ga and NH3. The labels describe the adsorbates and their corresponding binding sites (in parentheses). The axis on the right shows the temperature corresponding to the NH3 chemical potential on the left axis at a pressure of 1 bar (750 Torr). The dashed line marks the computed enthalpy of formation of GaN (-1.20 eV) at standard conditions. From Walkosz et al. [836] (Copyright 2012 by the American Physical Society).

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where BE is the binding (or adsorption) energy of each structure, εi is the adsorbate-substrate interaction for adsorbate i, εi,j is the energy of interaction between adsorbates i and j and εECR = |n|u± is a penalty for violation of the ECR. For a (2x2) SUC, the ECR requires the addition or removal of 3 electrons per SUC. The deviation from this requirement is given by n = 3 - n(NH2) - 2n(NH) - 3n(N) - n(H) where m·n(X) represents the contribution from the number n of adsorbed species X per SUC. Thus n is the number of electrons per (2x2) cell that are not involved in 2-electron bonding orbitals or in a NBLP orbital on N. For example, NH contributes 4 valence electrons, three of which form Ga-N bonds to leave n = 1 unpaired electron per (2x2) SUC. One NH2 in either a bridging or terminal configuration leaves two electrons not in bonding or in N NBLP orbitals. The term u± means either u+ or u−, depending on the sign of n, and represents the energy penalty per electron if there is an excess (+) or deficit (−) of electrons. The various terms in Eq. (10) were obtained by fitting to the results of the 2DPS calculations described above. The resulting phase diagram is shown in Fig. 59 where Ga-rich (NH3-rich) conditions correspond to μ = 0 on the horizontal (vertical) axis. Under NH3-poor conditions, for example, one sees the well-known progression from adsorbed N (H3) to adsorbed Ga (T4) to Ga bilayer as one progresses from Ga-poor to Ga-rich conditions. For NH3-rich conditions and moderate temperatures, one NH3 and three NH2 (all in T1 sites) is preferred for any μGa. In one region of the phase diagram an isolated NH, which violates the ECR, is the favored structure, and this constitutes a potential source of defects capable of n-type doping. Kempisty et al. [659,837–840] performed theoretical studies of NH3 adsorption on GaN (0001) with a focus on the effects of doping and EF pinning. This work has been extensively described in Ref. [840], which will serve as the basis for the present discussion. The calculations used NCPPs to replace core electrons and localized basis sets of different quality for the valence orbitals of bulk, surface and adsorbate atoms, together with either the PBE or the Wu-Cohen GGA functional. For a small (1x1) SUC the 2DPS consisted of 20 Ga-N bilayers, while for a (4x4) SUC the slab involved 8 bilayers. In all cases the bottom surface was terminated with PHs and a dipole correction applied. The background charge method was used to simulate bulk doping, in which a single positive or negative charge is smeared over the whole slab unit cell. This also affects the occupancy of DBs on surface atoms, which shifts the pinning position of EF. Several combinations of adsorbed H, NH2 and NH3 were used to test the calculation, and it was confirmed that the resulting EF pinning position at the surface was consistent with the ECR. Varying coverages of pre-adsorbed NH3 were used (Fig. 60) to test the effect on adsorption of the pinning position of EF. Dissociative adsorption to form NH2 and H is more favorable than molecular adsorption at all coverages of pre-adsorbed NH3. For up to 0.3 ML of pre-adsorbed NH3, the formation of bridging NH2 is more favorable; whereas, the terminal (Ga-NH2) species is favored at higher coverage. Above 0.625 ML of pre-adsorbed NH3 on ptype GaN, ΔEads decreases abruptly for either form of adsorption, which was explained in terms of a shift in EF and its effect on charge transfer. Alternatively, one can understand this by noting that with 5/8 ML of NH3 adsorbed via Ga-NH3 dative bonds there is also 3/8 ML of doubly occupied Ga DBs. This violates the ECR but nevertheless represents a passive surface that, for p-GaN, would be stabilized by a large downward BB. Further molecular adsorption of NH3, in this case, beyond 5/8 ML requires emptying of a doublyoccupied Ga DB. For n-type GaN the abrupt decrease in ΔEads occurs at an NH3 coverage just below 5/8 ML, which reflects the instability of the doubly-occupied Ga DBs on a surface with upward BB. The transition, with increasing NH3 coverage, from bridging to terminal NH2 formation can also be understood in

terms of the ECR and the number and occupancy of Ga DBs. An et al. [383] performed calculations for the adsorption of NH3 on GaN (0001) using a 2DPS with 5 Ga-N bilayers and a (2x2) SUC. The bottom surface was terminated with PHs, and the lowermost 3 bilayers were fixed in the bulk-lattice configuration. Allowing the middle bilayer to relax was found to have a negligible effect on the results. The calculations, which used the PBE functional, included a dipole correction (Fig. 6) and were spin-unrestricted in order to allow for the possibility of paramagnetic reaction intermediates. Relaxing the spin-restricted constraint is something that was not typically done in earlier calculations for NH3 dissociative adsorption. The PW-PP approach was used with Ga 3d electrons included in the PP rather than in the valence states. The PPs were presumably ultra-soft since a low (400 eV) PW cutoff energy was used. For the bare (0001) surface it was found that an inward displacement of half the Ga atoms in the (2x2) SUC lowers the surface energy by 0.13 J m-2 (8.1 meV Å-2) in agreement with results of Kempisty et al. [381] and Chen and Kuo [382]. The displaced Ga atoms lie slightly below, and form sp2 bonds to, the N atoms in the surface bilayer. The predicted (2x1) reconstruction of the bare surface was discussed in Section 4.6.1. NH3 adsorbs at a T1 site (ΔEads = -32.75 kcal mol-1) and dissociates to form a Ga-N(H)2-Ga bridge and a Ga-H with a barrier of 13.61 kcal mol-1. It was not stated which of the two inequivalent types of Ga atoms on the (2x1)-reconstructed surface is favored in NH3 adsorption. The Ga-N(H)2-Ga bridge (ΔEads = -89.70 kcal mol-1) is favored over terminal Ga-NH2 (ΔEads = -84.17 kcal mol-1) and dissociates with a barrier of 21.68 kcal mol-1 to form NH in an H3 site and Ga-H. The H3 site (ΔEads = -129.83 kcal mol-1) is favored over T4 (ΔEads = -114.15 kcal mol-1) for the NH, which dissociates to N in an H3 site and Ga-H with a barrier of 70.79 eV. These results are qualitatively consistent with those of the cluster-model calculations of Won et al. [833], particularly in the conclusion that NH dissociation is the rate-limiting step in the decomposition of adsorbed NH3; although, the magnitudes of the reaction energies and barriers are quantitatively different in some cases. As in the work of Won et al., the Ga-H produced in each dissociation step is removed before proceeding to the next step. The previous ΔEads and barrier results all apply to 0.25 ML, i.e., one adsorbate per (2x2) SUC. As such, the ECR is not always satisfied. For example, forming a Ga-N(H)2-Ga bridge and a Ga-H adds 4 electrons to the (2x2) SUC, leaving 1 unpaired electron in a Ga DB if there is no available mechanism for filling or emptying this partially-filled DB. Barrier heights for surface diffusion were also obtained. For NH2, the barrier for hopping between bridge sites via a T1 (terminal Ga-NH2) intermediate site is 6.23 kcal mol-1. For NH, the barrier for hopping between H3 sites via a T4 intermediate site is 17.53 kcal mol-1. Both barriers are sufficiently low that these processes can be expected to occur at significant rates below ∼100 °C; however, the barriers for diffusion of N and H are somewhat higher (27.90 and 20.98 kcal mol-1 respectively). To summarize the discussion thus far, TPD data clearly indicate that NH3 adsorption is partially dissociative on GaN (0001), i.e., NH3 → NHx + (3-x)H, and that NH2 is the dominant species at RT. However, other than one UPS experiment (which indicated a Ga-N (H2)-Ga bridging structure), there has been no experimental attempt to identify spectroscopically the NHx species or to establish how it is bonded. Under conditions appropriate to UHV experiments such as TPD and UPS, cluster-model and 2DPS calculations seem to agree that bridging NH2 is favored. This level of consensus between the cluster and 2DPS calculations is somewhat encouraging since the former method generally does not correctly model the occupancy of Ga DBs on the bare (0001) surface. On the other hand, 2DPS calculations designed to model MOCVD growth conditions (i.e., high temperature and NH3 pressure) indicate that a terminal Ga-NH2 species is dominant. The clear implication is that

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the bonding configuration of adsorbed NH2 is coverage-dependent, as has been pointed out by Kempisty and Krukowski [840]. Fritsch et al. [368,841] have performed a theoretical study of the interaction of NH3 with the GaN (0001̄ ) surface using the LDA with NCPPs to replace core electrons and localized atomic orbitals representing valence levels. The Ga 3d electrons were included in the PP rather than as valence states. The 2DPS comprised a (2x2) SUC with five Ga-N bilayers with nothing used to terminate DBs on the bottom surface. For the bare surface under very or moderately N-rich conditions the most stable surface has one VN per SUC, which satisfies the ECR. Dissociative adsorption of NH3 was modeled using MD at a temperature of about 500 K for which an N-H bond breaks leading to NH2 bridging two Ga atoms at the VN site and H bonding to N at an adjacent T1 site, which also satisfies the ECR. For one NH3 per (2x2) SUC, ΔEads for dissociative adsorption is -2.05 eV with an activation energy of ΔEa ≤0.5 eV. Fritsch et al. [368,841] have reported theoretical results for the interaction of NH3 with the GaN (101̄0) surface using methods described in the previous paragraph, except that the 2DPS comprised four Ga-N bilayers and a (1x2) SUC. Dissociative adsorption is exothermic by 1.56 eV for one NH3 per (2x1) SUC (i.e., 0.5 ML) and results in a Ga-NH2 and an N-H site. At a coverage of two NH3 per (2x1) cell, ΔEads = -1.95 eV (presumably per NH3). Northrup et al. [212] have studied the interaction of NH3 with GaN (101̄0) using the LDA with soft (Troullier-Martins) PPs. The Ga 3d electrons were treated as valence states, and the 2DPS comprised 12 GaN layers (presumably 12 Ga-N bilayers) with a (1x1) SUC. The slab is symmetric, and H and/or NH2 were adsorbed on both faces. Dissociative adsorption of NH3 to form Ga-NH2 and N-H by reaction with a surface Ga-N dimer is exothermic by 2.08 eV per NH3. Vibrational frequencies for the adsorbed species were also obtained. Fritsch et al. [368,841] performed a theoretical study of NH3 adsorption on GaN (112̄ 0) using methods described above in connection with their work on (0001̄ ) and (101̄0). The 2DPS in this case comprised four Ga-N bilayers. Dissociative adsorption of NH3 to form Ga-NH2 and an adjacent N-H is exothermic by 1.0 eV. 7.2. Hydrazine (N2H4) An et al. [383] and Cardelino and Cardelino [835] have reported theoretical studies of the reaction of N2H4 with GaN (0001), motivated by an interest in the potential use of N2H4 as a low-temperature MOCVD reagent or by its possible importance as an MOCVD reaction intermediate. The approach used by Cardelino and Cardelino [835] was described above in connection with their NH3 results. Ab-initio calculations were performed in order to obtain thermochemical quantities and rate constants for various surface and gas-phase reactions. These results, although important, will not be described in detail here since they are somewhat removed from the main focus of this review. The approach used by An et al. [383] was described above in connection with their NH3 results. Molecular N2H4 adsorbs via GaN bonds at T1 and Br (bridge) sites with ΔEads = -33.44 and -38.05 kcal mol-1 respectively for one N2H4 per (2x2) cell. In the T1 structure, one Ga-N bond forms, and the N-N bond is tilted away from the surface. In the Br structure, the N-N bond lies parallel to the surface with each N bonded to a Ga atom. It was not stated which of the two inequivalent types of Ga atoms on the (2x1)reconstructed bare surface (Section 4.6.1) is favored in adsorption. It is noted that, for one N2H4 per (2x2) cell, neither structure satisfies the ECR. Dissociation of the Br structure occurs to form two NH2 in T1 sites with a ΔEa of 1.15 kcal mol-1 and an energy release of 50.96 kcal mol-1. The barrier is lower and the reaction energy more exothermic than for the dissociation of adsorbed NH3 to form Ga-NH2-Ga and Ga-H, which suggests that N2H4 should be a

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very effective reagent for GaN MOCVD. It is noted here that this application is contingent on the availability of sufficiently pure and anhydrous reagent. 7.3. Hydrogen (H and H2) The interaction of atomic H or D with GaN (0001) has been extensively studied experimentally [123,228,229,443,445, 494,495,704,822–824,844–852]; although, fewer results have been reported for the (0001̄ ) [146–148,228,229,387,398]. Theoretical results have been given for (0001), (0001̄ ) and (101̄0) in Refs. [141,213,214,216,365,366,380,381,383,433,853–857], [215,365,366, 858] and [212] respectively. Akiyama et al. and Ito et al. have rē [380,419] ported theoretical results for H adsorption on the (1011) and on the (112̄ 0) and (112̄ 2) [380,855] surfaces. Feenstra et al. [3] and Neugebauer [687] reviewed the experimental and theoretical aspects of the effects of H on GaN growth. There are several points of interest in this work, among them the use of adsorbed H as a structural probe, the effects of co-adsorbed H on the uptake of other species, the exchange of H between the surface and the bulk and the potential use of H in processing reactions such as lowenergy electron-enhanced etching [859,860]. Most of the work discussed here involves the adsorption of atomic H or D, which is generated by back-filling the UHV chamber with H2 or D2 with the sample a few cm away from a W filament resistively heated to 1700–1900 °C. This dissociates, or "cracks", a small percentage of the molecules. The exact flux of atoms hitting the surface is difficult to determine, and it is customary simply to report the exposure to H2 or D2 using the pressure recorded by an ionization gauge. Thus "an H exposure of 100 L" means "an H2 exposure of 100 L in the presence of a hot W filament". This is sufficient for an estimate of relative atomic exposures, assuming that the filament temperature, sample-to-filament distance, etc. remain constant, but the atomic-H exposure corresponding to a given H2 exposure is not easily transferable between laboratories. Radiative heating of the sample by the hot filament can present a problem in some experiments, and the reader is referred to the book on experimental techniques by Yates [861] for a discussion of methods for H-atom production. See particularly Ref. [862] in regard to avoiding excessive sample heating. Chiang et al. [822] employed TOF-SARS [842] to study D desorption from GaN (0001) using samples and methods described in Section 7.1 in connection with their NH3 work. No D adsorbs unless a hot W filament is used to dissociate the D2. The coverage of adsorbed D remains approximately constant up to about 250 °C whereupon recombinative desorption begins and is nearly complete at ∼500 °C. The small remnant at 500 °C, which desorbs at or below 600 °C, is thought to originate with a minority N-D species; whereas, the majority of the desorption occurs from Ga-D sites, based on a comparison with TPD data for GaAs and on bond-energy considerations. The desorption process is better described by second- than by first-order kinetics with an activation energy of roughly 7 kcal mol-1. It is proposed that desorption results from a slow diffusion process where two D atoms come together to form D2 that quickly desorbs. Shekhar and Jensen [823] performed TPD experiments following exposure of GaN (0001) to D atoms using samples and methods described in Section 7.1 in connection with their NH3 results. As in previous work [822], no D adsorption was seen unless the D2 was dissociated with a hot W filament. The sample was nominally at RT, but the temperature rose by 50 K during D adsorption due to radiative heating by the filament. No ND3 was observed in TPD, which would indicate etching of the surface. For very small exposures the D2 peak appears at ∼770 K. With increasing θD another peak appears at about 660 K, which gains in intensity and shifts to 625 K. Above 750 K only a negligible amount of adsorbed D

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Fig. 60. Adsorption energy for NH3 on GaN (0001) vs. coverage. Upper: molecular; Lower: dissociative. From Kempisty et al. [840] (used in accordance with the Creative Commons Attribution license).

remains. The decrease in the peak temperature with increasing θD indicates a second-order desorption process, which is consistent with the results of Chiang et al. [822]. Dhesi et al. [443,445] performed ARUPS experiments for H adsorption on GaN (0001) using methods described in Section 4.7.1 in connection with their clean-surface studies. The surface state seen near the VBM on the clean surface is removed by H adsorption, which also introduces new states below the bulk VBM and decreases the upward BB on the n-type sample by ∼1.0 eV based on the H-induced shift in the Ga 3d BE (Fig. 60). Bermudez et al. [123] reported UPS and ELS results for MOCVD GaN (0001) after a saturation exposure to H atoms for a sample prepared by IBA (1 keV nitrogen ions, 850 °C anneal). The sample polarity was not known at the time and was suspected to be N-polar but was later determined to be Ga-polar. The UPS data in Fig. 61 show the ΔN(E) difference spectrum, which reveals the change in the VB region due to H adsorption. In addition to the H-induced (positive-going features) below the VMB there is a negative structure near the bulk VBM indicating the removal of surface states present on the clean surface. These results will be discussed later in this section and also in Section 7.8. Exposing the clean surface to H atoms causes a decrease of ∼0.3 eV in the upward BB, which is less than the ∼1.0 eV shift seen by Dhesi et al. [443]. Fig. 61 shows ELS data that indicate the highly-efficient ESD of H by the primary electron beam. Exposure to H atoms attenuates a loss feature at about 3.4 eV and causes changes near 7 and 20 eV; although, it is difficult to determine from these data whether the latter two effects arise from the addition of new features or the attenuation or broadening of clean-surface structure. The 3.4 eV loss corresponds to a transition between filled and empty surface

states, and the 20 eV loss occurs in the region expected for Ga 3d excitation. These data will be revisited in Section 7.8 in the discussion of O2 adsorption. All of these H-atom effects are rapidly reversed by exposure to the ELS primary beam (90 eV, ∼60 μA cm-2). Thus a single scan from a ΔE of 40 to 0 eV, which lasts about 120 sec, shows little if any effect of H on the 3.4 eV feature since most of the H is desorbed before the scan reaches ΔE o 5 eV. Instrumental limitations prevented a reverse scan (0 to 40 eV loss energy); however, a rapid (∼10 sec) scan from ΔE = 10 to 0 eV shows a significant H effect that is lost after another 60 sec of irradiation. The ESD of H from GaN (0001) appears to be much more rapid than from Si (100), where the effects of adsorbed H can easily be detected in ELS (e.g., Ref. [863]). An indepth discussion of ESD in surface science is given in the review by Ramsier and Yates [864], and further results concerning the ESD of H from GaN (0001) will be presented later in this section. Bartram and Creighton [824] performed TPD experiments for D adsorbed on GaN (0001) using samples and methods described in Section 7.1 in connection with their NH3 results. It is recalled that D was introduced by exposure to unexcited D2 at a high temperature and pressure (1200 K, 2 Torr), which also led to a faceted surface as seen in LEED (Section 3.3.1). It is not known whether the faceting was strictly an effect of the temperature or if the D2 was somehow involved. Following this treatment, HD and D2 desorb with peaks at 825 K, and there is also a small Ga peak at about 1000 K. The HD is ascribed to outdiffusion of bulk H remaining from MOCVD growth. The appearance of Ga desorption at a lower temperature after treatment than before suggests that D (or H) can lower the temperature at which GaN decomposes, which is a wellknown effect in high-pressure H2 (e.g., Refs. [246–249]). However, no conclusive evidence was found for ND3 formation. Yang et al. [704] performed photoemission microscopy studies of H on GaN (0001) using methods described above in connection with their work on Mg adsorption (Section 5.25). The results suggest that adsorbed H changes the angular distribution of Ga 3d photoelectrons (excited by hν = 130 eV photons) so as to increase the emission in the surface-normal direction. The mechanism whereby this happens remains uncertain. Bellitto et al. [494,844–847] and Yang et al. [848] performed an extensive series of experiments for H on GaN (0001) using primarily LEED, HREELS, ELS, TPD and ESD. Samples grown by MOCVD were cleaned in organic solvents followed by in-situ IBA (1 keV nitrogen ions, 1173 K anneal). No evidence of contamination was found in AES data after sample cleaning, but the detection limit was only 0.05 ML due to the use of a retarding-field (LEED/ Auger) electron energy analyzer with electronic modulation to obtain the first-derivative AES spectrum (d[N(E)]/dE). The LEED pattern was a sharp, low-background (1x1), but satellite spots indicating faceting (Section 3.3.1) appeared at some values of Ep. Longer anneals at lower temperature, down to 873 K, gave a weak, high-background (1x1) pattern but without faceting. The raw HREELS data [844,846,848], with a resolution of 55 cm-1, show intense FK phonon losses (Section 4.8) at integer multiples of 700 cm-1, which make it difficult to detect weak features due to adsorbates. The FK losses other than the fundamental were effectively eliminated by a numerical deconvolution procedure as shown in Fig. 62. Exposure to unexcited H2 up to 103 L has no detectable effect, but even a small H-atom exposure leads to features due to Ga-H stretching (Fig. 62). The 1880 cm-1 peak that appears after H exposure is assigned to the Ga-H stretching fundamental, while higher-energy losses are ascribed to combinations of this mode and integer multiples of the FK phonon. No N-H stretching mode, expected near 3300 cm-1, is found, which indicates that the surface is Ga terminated. Assignment of a 3280 cm-1 loss peak to N-H stretching was excluded in an experiment using D instead of H. Heating briefly to 380 °C eliminates the H-

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Fig. 61. Left: (a) HeII UPS data for a clean GaN (0001) surface and after a 200 L exposure to H2 in the presence of a hot W filament. The edge of the Ga 3d, the N 2s shallow core level and the Ga 3d "ghost" excited by the 48.4 eV satellite in the He II emission are indicated. Higher-energy satellites contribute some Ga 3d "ghost" intensity to the peak near -9 eV. The position of the VBM after H adsorption is estimated by linear extrapolation of the edge to the baseline. The relative intensity of the two spectra is not quantitative. (b) Difference spectrum obtained by scaling and shifting the clean-surface spectrum so as to cancel approximately the Ga 3d and N 2s features. The negative feature at the VBM results from removal of surface states by adsorbed H. Right: Surface-sensitive first-derivative ELS data in the range of valence and plasmon excitations. The elastic peak is shown on a reduced vertical scale at the zero of loss energy, and the arrow heads mark features that are affected by H adsorption or desorption. The cleansurface spectrum was averaged for eight scans but the H-exposed for only one. The inset shows results of a single scan over the 0–10 eV range (a) after dosing and (b) after a further ∼60 sec of primary-beam irradiation. Scans begin at the high loss-energy end of the spectrum. Relative intensities of different spectra are not quantitative. From Bermudez et al. [123] (Copyright 1998, reproduced with permission from Elsevier).

induced losses via recombinative desorption of H2, consistent with earlier TPD results [823]. Measuring the TPD directly [848] using a mass spectrometer and adsorbed D shows desorption over the range of about 250-500 °C with a peak at 410 °C. The first-derivative ELS data [494,844] for an H-saturated surface show a broadening of the structure near 20 eV (see Fig. 61), which may indicate the growth of an additional peak, and also subtle changes in the 12-15 eV range. These effects are complete after an H exposure of ∼100 L, and further exposure leads to no significant changes. To make the small H-atom effects more apparent, a difference spectrum (ΔN(E) = N(E)H - N(E)clean) was obtained. which shows that H adsorption removes peaks at about 3.5 and 6.6 eV and adds structure at 11.7 and 18.1 eV. The 3.5 eV feature is assigned to a transition between filled and empty surface states lying close to the bulk band edges. The 6.6 and 11.7 eV transitions are assigned together, based on UPS [123,443] and IPES [450] data reported by others. The initial state of the former is the surface state near the VBM and is thus removed by H adsorption, while the initial state of the latter is a Ga-H bonding orbital seen in UPS. Both transitions terminate in a state at ∼2 eV above the CBM that was identified in IPES data. The 18.1 eV structure is interpreted as the surface plasmon, which is at ∼16 eV on the clean surface, that is shifted to higher energy by H adsorption. The possible effect on these data of ESD of H by the primary electron beam was noted. The previously-reported [123] rapid ESD of H from GaN (0001) was quantified by Bellitto et al. [845,847] using ELS (Fig. 63). The data were recorded in the form of N(E), with ip set as low as possible (50 μA cm-2), and ΔN(E) obtained as the difference between N(E) of the H- (or D-) exposed and the clean surfaces. As

discussed in the preceding paragraph, features in the 3 to 7 eV range of loss energy are attenuated by adsorbed H and restored as ESD removes H. Hence, the integrated intensity in this range can be used as a measure of H coverage. As noted above, adsorbed H also leads to the appearance of loss structure at 11.7 and 18.1 eV. The former loses intensity when ESD removes H, but the 18.1 eV peak is relatively unaffected, which suggests that it is related to subsurface adsorption sites. From fitting the dependence of the 3 to 7 eV integrated intensity on the total electron beam exposure at Ep = 90 eV (Fig. 63), ESD cross-sections of σ = 2x10-17 (7x10-18) cm2 per electron are found for H (D). These are larger by a factor of 102 to 104 than those found, at a comparable Ep, for H or D on Si (100). Based on the HREELS data discussed above, the H that is being desorbed is initially bonded to Ga. With the assumption of one H or D per surface Ga at saturation, these σ values correspond to one H (D) desorbed per ∼30 (100) incident electrons. Interestingly, σ (D) is smaller than σ(H) by a factor of only ∼3 for GaN (0001) vs. ∼50 for Si (100). Typically σ(D) o σ(H) because the velocity of the escaping D is less than that of H, assuming that the KEs are the same, which allows more time for the electronically-excited system to relax and the D to be readsorbed [864]. The relatively small isotope effect for GaN implies either that the excited state leading to desorption has a long lifetime or that the KE is so high that even reducing the velocity of the escaping particle by a factor of √2 does not greatly reduce the desorption rate. Grabowski et al. [495,849] used HREELS to study H adsorbed on MOVPE GaN of unknown polarity (either (0001) or (0001̄ )). The sample was prepared by immersion in aqueous HF solution followed by in-situ cleaning using deposition of Ga metal, which was thermally desorbed at 800-850 °C. Only a trace of C was seen in

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Fig. 62. Left: HREELS data for (a) clean GaN (0001) and following exposure to (b) 5 L, (c) 25 L, (d) 50 L and (e) 500 L of H* (H2 in the presence of a hot W filament). Peaks at 2580, 3280, and 3980 cm-1 are assigned to combinations of the Ga-H stretch and one, two and three FK phonons respectively. Right: HREELS data for (a) H-saturated GaN (0001) and (b) following deconvolution to reduce multiple FK losses. The intensity scales are not the same for the original and deconvoluted spectra. The peak at 1880 cm-1 is assigned to the Ga-H stretching vibration. From Bellitto et al. [846] (Copyright 1999, reproduced with permission from Elsevier).

AES after cleaning, and LEED showed a (1x1) pattern with extra spots indicating steps or faceting (Section 3.3.1). The HREELS data were recorded with a resolution of 56 cm-1, and apparently no numerical processing was employed to reduce the intensity of the FK phonon losses. Before adsorption of H or D, only multiple FK phonon losses are seen, as in earlier work [146,844,846,848], together with a weak Ga-C stretch at 583 cm-1. After H-atom adsorption, Ga-H and N-H stretching modes are seen at 1900 and 3255 cm-1 respectively together with combinations of these modes with a single FK phonon (700 cm-1). The assignment of the N-H mode was verified using D instead of H, and the presence of both Ga-H and N-H modes on the same surface is attributed to the existence of steps, or facets, which expose both types of atoms (bearing in mind that the surface polarity is unknown). This result differs from that of the HREELS study by Bellitto et al. [844,846,848] who observed no N-H on a faceted (0001) surface. Impurity-related modes are also seen at 805 cm-1 (N-OH stretching), 3650 cm-1 (O-H stretching) and 1645 cm-1, which is most likely due to O-H bending. These are attributed to an H2O contamination during Hatom exposure since H2O is known to be highly reactive with clean GaN (0001) and (0001̄ ) surfaces (Section 7.10). With increasing exposure the intensities of the Ga-H and N-H modes initially increase and then decrease somewhat. This is ascribed to a process in which first GaH and NH sites form, followed by GaH2 and NH2 and then by volatile GaH3 and NH3, which leads to etching and a loss of intensity. With increasing coverage, a shift to higher energy is seen in the Ga-H (but not the N-H) mode, which is taken as evidence for unresolved contributions from different species, e.g., GaH and GaH2. Yang et al. [850,851], continuing the work of Bellitto et al. [494,844–848], employed TPD and ESD to study the adsorption of D on GaN (0001) surfaces prepared as described previously [494]. In the TPD of D2 after exposure to atomic D [850], the desorption peak varies from 380 to 570 °C as the heating rate is changed from

0.05 to 8 °C sec-1. The peak shape also changes, revealing the existence of overlapping peaks at about 320 and 410 °C. This indicates the existence of two (or perhaps more) desorption sites or mechanisms with different kinetic parameters. Presumably the change in the peak temperature with heating rate results from a variation in the relative intensity of the two peaks due to the kinetic differences. Furthermore, the relative area of the two peaks depends on sample history, with the lower-temperature feature gaining intensity with repeated IBA cycles, which leads to a betterordered but more-faceted surface. With the assumption of the standard pre-exponential factor for desorption of 1x1013 sec-1, an activation barrier for D2 desorption of ΔEades = 2.0±0.1 eV is determined from a first-order-kinetic analysis of the main (higher-temperature) peak. The definitions of the various quantities discussed here are illustrated in Fig. 64. The estimated Ga-D and D-D bond energies are |ΔEads| = 2.8 eV per D and ED2 = 4.5 eV respectively, both based on molecular data. The activation barrier (per D2) for dissociative adsorption is then given by ΔEaads = ΔEades - (2·|ΔEads| - |ED2|) with the assumption that there is no metastable precursor to desorption. This leads to ΔEaads = 0.9 eV = [2.0 - (2x2.8 - 4.5)] eV per D2 and also implies that the reaction D2 + 2·Gasurf → 2(Ga-D)surf is exothermic by ½[2·ΔEads ED2] = 0.55 eV per D. Since recombinative desorption should be a second-order process, the appearance of first-order behavior indicates that two D atoms do not recombine directly but instead have to overcome a diffusion barrier (a first-order process), which dominates the kinetics. It is noted that Chiang et al. [822] proposed a similar mechanism but observed second-order kinetics, as did Shekhar and Jensen [823]. The variation of the peak TPD temperature with heating rate and sample history that was documented in this study may account for some of the differences among the results of different studies. Yang et al. [851] also used TPD to follow the ESD of adsorbed D

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Fig. 63. Left: (a) Solid line, ELS data in the form of N(E) for clean GaN (0001). Dotted line, first spectrum following a saturation exposure to H Atoms. (b) Solid line, ΔN(E) ¼ N (E)H - N(E)clean for the H-saturated surface. Dotted line, ΔN(E) for the same surface after 20 min of electron-beam impact. Right: Integral of ΔN(E) from the hydrogenated (deuterated) surface following various electron exposures. The region from 3 to 7 eV was integrated to calculate each point. The data are fitted with f(x) ¼ A þ Bexp(-sx), where s is the desorption cross section (cm2 per electron) and x is the electron exposure (electrons cm-2). From Bellitto et al. [845] (Copyright 1999 by the American Physical Society).

Fig. 64. Schematic diagram (not to scale) showing the definition of various quantities used in discussing the adsorption and desorption of H and H2. ΔEaads and ΔEades are, respectively, the activation barriers for adsorption and desorption of H2.

for 90 eV electron doses of 21, 42 and 170 μA hr cm-2 (0.47, 0.94 and 3.8x1018 electrons cm-2). The heating rate was not specified but was presumably chosen so that the high-temperature TPD peak dominates. Following the highest dose, TPD shows that all but a small fraction of the D has been removed through ESD. The peak desorption temperature (400 °C) is independent of coverage, which is consistent with a first-order process as noted above. The previous ESD study by this group [845,847] showed that 90 eV electron doses smaller than those used here are sufficient to reverse all D-induced effects in ELS except the presence of the 18.1

eV loss peak. Hence, the residual TPD peak at 400 °C after ESD can be correlated with this feature, which is assigned to a volume plasmon shifted by incorporation of subsurface D. The 90 eV ESD cross-section for this subsurface D is estimated to be ∼9x10-19 cm2, considerably smaller than the value of 7x10-18 cm2 found above for surface D based on the restoration of ELS intensity in the 3 to 7 eV range. Wampler and Myers [852] used nuclear reaction analysis (NRA) to study the outdiffusion and desorption of D from clean, wellorder GaN (0001) surfaces. The D concentration was measured to a depth of ∼1 μm using an 800 keV 3He beam to promote the reaction 2H(3He,1H)4He. The sample was Mg-doped p-type MOVPE GaN in which bulk H remaining from growth was replaced with D by annealing in vacuo at 900 °C and then in 0.88 bar (660 Torr) of D2 at 700 °C. Clean surfaces were prepared by 2 keV nitrogen-ion bombardment after which the level of C and O seen in AES was o0.05 ML. The amount of D remaining in the sample vs. time at various annealing temperatures (700, 800 or 900 °C) exhibits second-order kinetics, which suggests recombinative desorption, and comparison with data for samples without in situ cleaning shows that surface contamination does not significantly impede D2 desorption. Thus the high temperature needed for the release of H from Mg-doped GaN is an intrinsic property of the material and not the result of surface impurities. Following an 800 or 900 ° C anneal of the ion-bombarded sample, a sharp and low-background (1x1) LEED pattern was obtained with no evidence of faceting. The release of D2 (or H2) was modeled as a sequence of four steps: (1) (2) (3) (4)

+ (Mg-H)bulk → Mg− bulk + Hbulk + + Hbulk → Hsurf − H+ surf + e → Hsurf Hsurf → ½H2

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the last of which is recombinative desorption. The description in terms of H+ is based on the higher stability of the cationic species in the bulk of p-GaN [401]. However, recalling the large downward BB on the p-GaN (0001) surface in the dark (Section 4.7.3), it is noted here that H− may be the most stable charge state near the surface. The energetics of this process at T = 0 was analyzed using results from experiment and from ab-initio DFT. A value of ΔEads = -2.22 eV per H is found for the adsorption of an H atom from vacuum, and ΔEa = 0.90 and 0.96 eV per H are obtained for the H2 recombinative desorption and dissociative adsorption barriers respectively. The latter is about a factor of two higher than that found by Yang et al. [850] (∼0.9 eV per H2), the difference being mainly the result of the value used for ΔEads for an H atom (-2.8 eV in the work of Yang et al. vs. -2.22 eV in that of Wampler and Myers). The slightly smaller desorption barrier (0.90 vs. 1.0 eV per H) used by Wampler and Myers also contributes to the difference. The present results also lead to the conclusion that the reaction H2 + 2·Gasurf → 2(Ga-H)surf is endothermic by 0.06 eV per H vs. exothermic by 0.55 eV per H in the study by Yang et al. It is concluded in the present work that recombinative desorption at the surface, and not diffusion from the bulk, is rate-limiting in the removal of D from the bulk of p-type GaN (0001) and that H on the surface is much less stable than MgH in the bulk. Losurdo et al. [228,229] used XPS, SE, AFM and Kelvin-probe microscopy to study the effects of a hydrogen plasma on GaN (0001) and (0001̄ ) surfaces with the sample temperature maintained below 650 °C in order to avoid thermal decomposition. Under the conditions used, only H2 and atomic H are incident on the surface. Furthermore, the H2 is in the electronic ground state since no optical emission due to excited H2 is detected. This work lies outside the scope of subjects reviewed here but is noteworthy due to the finding that atomic H appears to adsorb on the (0001) surface and stabilize it but to etch the (0001̄ ). To summarize the experimental results for H (or D) on GaN (0001), TPD and HREELS data indicate a dependence on surface

preparation, which may be related to faceting. In particular, TPD in most, but not all, experiments can be analyzed in terms of secondorder kinetics. On this surface, H is not detected in HREELS unless H atoms are deliberately introduced, indicating that H2 does not dissociatively adsorb under typical conditions. However, dissociative adsorption of D2 has been observed at high temperature and pressure (1200 K and 2 Torr). In terms of electronic structure, ELS and UPS show that H adsorption removes surface states above the VBM, decreases the upward BB on n-GaN and introduces new states below the VBM due to Ga-H and/or N-H bonding. The very efficient ESD of adsorbed H (in an as-yet-unknown charge state) has been well documented but remains unexplained. Etching by H atoms does not appear to be important on the (0001), which suggests that H-atom cleaning might be useful for this surface. Ahn et al. [387] and Sung et al. [398] performed TOF-SARS [842] and LEED studies of H adsorbed on the GaN (0001̄ ) surface. The TOF-SARS data were analyzed using classical ion trajectory simulations. The MOCVD sample was cleaned by IBA with 1 keV nitrogen ions. After annealing at ∼815 °C a faint (1x1) LEED pattern was seen, which developed into a sharp (1x1) after a ∼920 °C anneal; whereas, a higher-temperature anneal (1000 °C) led to faceting. No impurity C or O was detected in TOF-SARS, but H always appeared on surfaces with a sharp (1x1) LEED pattern. The sample was not intentionally exposed to H atoms; hence, the surface H results from outdiffusion from the bulk. The TOF-SARS experiment is highly surface sensitive, and typical data (Fig. 65) show a surface terminated in N with a high coverage of adsorbed H and only a small signal from the first-underlayer Ga. A scan of the H intensity vs. azimuthal angle (δ) reveals a series of maxima and minima due to shadowing effects. The data can be fitted with a model consisting of 0.75 ML of H adsorbed as N-H, which is consistent with the ECR. To our knowledge, this is the only experimental example of a polar GaN surface in UHV that is stabilized in a (1x1) structure by adsorbed H at a coverage of 0.75 ML . Sloboshanin et al. [146], Tautz et al. [147] and Starke et al. [148] reported HREELS data for H on MOCVD GaN (0001̄ ) surfaces prepared by IBA (1 keV nitrogen ions, 950 K anneal), after which no contamination was detected in XPS data. The LEED pattern for the

Fig. 65. Left: Plan view of the ideal bulk-terminated GaN (0001̄ ) surface showing the azimuthal angle (δ) assignments. Another domain is obtained by 180° rotation about the surface normal. Open circles, first-layer N atoms; large solid circles, second-layer Ga atoms. The sizes of the circles are proportional to the atomic radii. Right: TOF-SARS spectrum of 4 keV Ar þ scattering from a GaN (0001̄ ) surface with the ion beam aligned at a random δ setting. Incident angle α ¼ 6°; scattering angle θ ¼ 40°, both with respect to the surface plane. The labels "R" and "S" refer to "recoiled" and "scattered" respectively. From Sung et al. [398] (Copyright 1996 by the American Physical Society).

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Fig. 66. Schematic top view of prevalent (2x2) reconstructions for GaN (0001) surfaces under different conditions of μH and μGa. Large white circles represent Ga atoms, black circles N, and small white circles H. "VGa" is a Ga vacancy, and "Nad-H" is an N-H group adsorbed in an H3 site. From Van de Walle and Neugebauer [213,214] (reproduced with the permission of the American Vacuum Society).

clean surface was (1x1) with additional spots due to faceting. The HREELS data indicate the presence of N-H bonds after IBA cleaning but before intentional exposure to H atoms, which is consistent with the results of Ahn et al. [387] and Sung et al. [398] for the (0001̄ ) surface. Exposure to H-atoms leads to the appearance of both Ga-H (227 meV) and N-H (403 meV) modes. The presence of — Ga-H is ascribed to that of (1012)-oriented facets, which expose both Ga and N. Both modes gain intensity with increasing exposure, but there is no degradation of the LEED pattern under these conditions, which would indicate etching of the surface. However, it was noted that exposing a faceted (0001̄ ) surface to a sufficiently large dose of atomic H removes the faceting [147], which suggests an etching effect that smoothes the surface. Etching of the (0001̄ ) by atomic H was noted above in the discussion of the results of Losurdo et al. [228,229]. The Ga-H mode shifts to higher frequency with increasing θH, in agreement with results of Grabowski et al. [495,849], which could arise from a resonant dipole-dipole interaction [865], a change in force constant caused by chemical effects or the presence of overlapping and unresolved modes due to different GaHx sites. In the area of theoretical work for H on GaN (0001), Elsner et al. [365,366] found that under N-rich conditions θH = 0.50 or 0.75 ML of adsorbed H are the most stable surface structures; whereas, a Ga ML is favored under Ga-rich conditions. The 0.75 ML surface is semiconducting, in keeping with the ECR, and is slightly more stable than the metallic θH = 0.50 ML phase. Van de Walle and Neugebauer [213,214,216] presented a theoretical analysis of H on GaN (0001) under equilibrium growth conditions using methods described in Section 4.1.2. The DFT part of the calculation made use of the LDA and a 2DPS with at least 4 Ga-N bilayers terminated on the bottom with PHs. The SUC was either (2x2) or (√3x√3), and the lower half of the slab was kept fixed in the bulk-lattice configuration during geometry optimization. The results are summarized in the phase diagram shown in Fig. 7. Under H-poor (low-μH) conditions the usual (0001) surface structures are seen with increasing μGa; namely, N adsorbed in an H3 site, followed by Ga in a T4 site and then a laterally-contracted Ga bilayer. With increasing μH a variety of structures involving adsorbed N, H and/or NHx are seen, which are illustrated in Fig. 66. All these structures are based on a (2x2) SUC and obey the ECR. For example, in Nad-H+NH2 the NH and NH2 contribute 4 |e| and 1 |e| respectively. Of this, 3 |e| pair with the 3 |e| per (2x2) SUC in Ga DBs on the ideal surface to form 3 Ga-NH back-bonds, and 2 |e| are used to form a Ga-NH2 bond at the remaining Ga site. The results

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appear to agree with an experimentally-observed [866] structural transition during MOCVD growth. Bermudez [433] reported theoretical results for H adsorbed on GaN (0001). The 2DPS consisted of 5 Ga-N bilayers with the bottom surface terminated in either 0.75 ML of H as N-H sites or 0.25 ML of Ga adatoms in H3 sites back-bonded to 3 N atoms, both of which satisfy the ECR. No PHs were available in this study. No dipole correction was needed in this case because Bloch functions constructed from localized basis sets were used, which means that the 2DPS was isolated and not periodically repeated in the surfacenormal direction. Geometry optimization was done at the RHF level using PPs to replace Ga and N core electrons with small basis sets to represent valence electrons. The Ga PP was large-core and included the 3d electrons. It was shown that, for the bulk lattice, this procedure yields structural parameters equivalent to those obtained for geometry optimization using a more computationally-expensive approach with the B3LYP functional and large allelectron basis sets. The DFT adsorption energies were obtained using the PW-91 functional together with the RHF electron density to compute an electron correlation energy a posteriori. The DFT calculation of the DOS was done using the RHF-optimized structure together with the B3LYP functional and all-electron basis sets. Due to program limitations (for the version used at the time), only the adatom positions (Ga and/or H) were relaxed. It is noted that the point of interest in geometry optimization was the relative energies for different adatom placements within the (2x2) SUC. The DOS computed for 0.75 ML of adsorbed H in the form of Ga-H does not agree well with UPS data (Fig. 61) for a saturation coverage of H on GaN (0001) prepared by IBA for which annealing was performed at 850-900 °C. The 0.75 ML model, which satisfies the ECR, is the simplest model for an H-stabilized surface. Hightemperature annealing is known (Section 4.5) to desorb N faster than Ga, and UPS data show that the surface is non-metallic even before H adsorption. This led to a model in which the H-free surface is stabilized by 0.25 ML of Ga adatoms in T4 sites backbonded to 3 surface Ga sites, which satisfies the ECR. The DOS for this structure shows a surface state due to the Ga-Ga back-bonds at about 1.8 eV above the VBM and another such state, with a lower DOS "intensity", that is localized on the adatom and lies about 0.5 eV below the VBM, in agreement with other results [459]. If one of the 3 Ga-Ga back-bonds is broken then 0.5 ML of H can be adsorbed as Ga-H without violating the ECR. The most stable such structure has the sp2-hybridized Ga adatom, with two empty DBs, bridging two Ga sites in the surface plane and the two H atoms per (2x2) SUC forming Ga-H bonds on the two other such sites. This removes a large part of the surface-state contribution to the DOS and results in a broad distribution of H-induced states extending throughout the VB. These results are in good agreement with UPS data (Fig. 61) showing the removal of surface states by H adsorption and the accompanying changes in the VB. The ΔH0 was found to be quite large (4.2 eV per Ga-H bond) vs. 2.25 eV per H for the H2 bond. It was suggested that a contributing factor might be the release of strain when one of the Ga-Ga back-bonds breaks, allowing the adatom to relax into a planar sp2-hybridized configuration as in GaH3. To our knowledge, this type of structure (2 H adatoms plus a two-fold Ga adatom) has not been considered in other theoretical studies. Suzuki et al. [853,854] performed theoretical studies of the effect of an H2 atmosphere on GaN (0001) and (0001̄ ) surface decomposition. This work lies outside the scope of the present review and is mentioned only in passing. Various models were constructed for the H-covered surfaces and energies computed for desorption of GaH and NH3, which are the most favorable decomposition products. Grabow et al. [141] performed theoretical studies of the

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adsorption of H and H2 on GaN (0001) using methods described above in connection with their work on NH3. An H2 molecule adsorbs at a T1 site (in an unspecified configuration) with ΔEads = -0.61 eV relative to free H2, and an H atom adsorbs at T1 with ΔEads = -3.41 eV relative to free H. For atomic H, ΔEads increases slightly from -3.41 eV per H at θH = 0.25 ML to -3.54 eV at 0.50 ML and then decreases to -3.24 eV at 0.75 ML and -2.67 eV at 1 ML. The decrease for 0.75 vs. 0.50 ML is unexpected since 0.75 ML satisfies the ECR and should give the most stable surface. This suggests a substantial repulsive interaction between Ga-H sites. The ΔEads values are larger than that found by Wampler and Myers (-2.22 eV per H) from an analysis of kinetic measurements [852]; although, the difference is not very great at 1 ML. As noted by the authors, the exothermic ΔEads for H2 appears to conflict with experimental data that show no molecular H2 adsorption on GaN (0001) at RT. However, such adsorption might be detectable at a somewhat lower temperature. The reaction H2 (gas) + 2Gasurf → 2(Ga-H)surf is found to be exothermic by 2.25 eV per H2 (or 1.12 eV per H) at θH = 0.5 ML. This differs significantly from the finding by Wampler and Myers that the reaction is endothermic by 0.06 eV per H. In the present work this energy was equated to the barrier to recombinative desorption, ΔEades (Fig. 64), and a kinetic model was derived and applied to an analysis of TPD data [823,824,850,852]. This ΔEades can be compared with values obtained from kinetic measurements by Yang et al. [850] (2.0±0.1 eV) and by Wampler and Myers [852] (1.80 eV per H2), both of which were discussed earlier in this section. It is noted here that equating ΔEades with the energy for dissociative adsorption of gas-phase H2 implies that ΔEaads, as defined in Fig. 64, is zero. However, Grabow et al. find that adsorbed molecular H2 is 0.61 eV lower in energy than gas-phase H2. Hence, the barrier to dissociation of adsorbed H2 is 0.61 eV in the present study. This is a fairly small barrier, and in fact the authors describe the dissociation as "spontaneous", which appears to conflict with experiments showing no adsorption of H without "cracking" of the H2. Ito et al. [380] and Akiyama et al. [855] reported theoretical studies of H adsorption on GaN (0001) under growth conditions. The PW-PP approach was used with the PBE functional, NCPPs for Ga and H and a USPP for N. The Ga 3d electrons were included in the PP, not in the valence states, and the PW cut-off energy (28 Ry) was somewhat lower than is normally used with NCPPs. The 2DPS consisted of four Ga-N bilayers with a (2x2) SUC and the bottom terminated in PHs. The results agree qualitatively with those of Van de Walle and Neugebauer [213,214] except that these latter authors found that NH3 forms under conditions that are rich in both N and H. Over a wide range of μGa and μH, the most stable structure in the present study consists of Ga-H and Nads-H, where Nads means N adsorbed at an H3 site and back-bonded to three Ga atoms. Under N-rich and moderately to very H-rich conditions, GaNadsH2 and Nads-H form; whereas, under Ga-rich and very H-rich conditions a surface with three Ga-H per (2x2) cell is favored. All these structures satisfy the ECR. A phase diagram was constructed to show the surface composition as a function of μGa and temperature (derived from the temperature dependence of μH, as in Eq. (5) and Fig. 7) for a typical MOCVD H2 pressure of 76 Torr. Kempisty et al. [381,856,857] conducted theoretical studies of H and H2 interacting with the GaN (0001) surface using methods described in Section 7.1 (Ref. [840]) in connection with their NH3 results. This work also describes at length the (2x1) reconstruction of the bare surface, which was discussed in Section 4.6.1. For comparison, another approach was also used based on the PAW method with PWs and the PBE functional. The 2DPS comprised eight Ga-N bilayers with a (2x2) SUC and included a dipole correction. The position of EF at the surface of the 2DPS was controlled by varying the electron density on the 1 ML of PHs

terminating the bottom surface, which gives rise to a phenomenon described by the authors as the "surface Stark effect". Below θH = 0.75 ML, which corresponds to a passive surface with no occupied Ga DBs, ΔEads for an additional H atom is in the range of -3.4 to -3.2 eV and is essentially independent of both θH and the position of EF at the surface. At θH = 0.75 ML, ΔEads decreases abruptly, becoming about -1.0 eV at θH = 0.90 ML. For clarity, in interpreting the graphical results plotted in this paper we have assumed that, for example, ΔEads at θH = 0.75 ML pertains to adsorption on a surface that already has a coverage of 0.75 ML rather than to the step that increases θH to 0.75 ML. The abrupt decrease in ΔEads arises from the fact that an electron must be promoted from the VBM to an empty Ga DB near the CBM in order to adsorb H beyond θH = 0.75 ML. An et al. [383] reported theoretical results for H on GaN (0001) obtained using methods described in Section 7.1 in connection with their NH3 work. The main focus was on intermediate species involved in MOCVD growth using NH3 or N2H4. The only stable adsorption site is T1 (i.e., a Ga-H bond) for which ΔEads = -75.18 kcal mol-1 (-3.26 eV) at θH = 0.25 ML with a barrier to diffusion between T1 sites of 20.98 kcal mol-1 (0.91 eV). The result for ΔEads is in good agreement with that of Grabow et al. [141] (-3.41 eV) at θH = 0.25 ML. It is also noteworthy that the computed diffusion barrier is close to the recombinative desorption barrier (0.90 eV per H) found experimentally by Wampler and Myers [852], which suggests that the transition state is the same in either case. This implies a scenario in which an H atom, having reached the top of the barrier, either recombines with a near-by H or, if none is available, moves to a vacant T1 site. Elsner et al. [365,366] reported theoretical results for H on GaN (0001̄ ). For the H-free surface the most stable structure, except under very Ga-rich conditions, involves an adlayer with 1 ML of Ga as described in Section 4.6.2. With adsorbed H, θH = 0.75 ML on the N terminating layer, which satisfies the ECR, is the most stable structure under N-rich conditions; whereas, the H-free Ga adlayer continues to be the most stable form in a less N-rich environment. In this study, MOCVD conditions we simulated with T = 1300 K and 760 Torr of H2. Northrup and Neugebauer [215] performed a theoretical study of H on GaN (0001̄ ) using the PW-PP method and the LDA with a 2DPS consisting of five Ga-N bilayers having a (2x2) SUC with the bottom surface terminated in PHs. For μGa mid-way between Gaand N-rich and for any value of μH, the lowest-energy structure for adsorbed H has a coverage of 0.75 ML, which satisfies the ECR. Under MOCVD (high H2 pressure) growth conditions (Fig. 8), this structure is lower in energy than any H-free surface for any value of μGa. This is also true for MBE (low H2 pressure) growth under Nrich conditions, but with increasing μGa the (1x1) Ga adlayer and (3x3) adlayer+adatom structures associated with the H-free (0001̄ ) surface become the most stable. Thus the (0001̄ ) surface has a high affinity for H, in agreement with the experimental results of Sung et al. [398] discussed earlier in this section. The computed phase diagram indicates that formation of the theoretically-predicted (2x2) Ga adatom structure on the (0001̄ ) surface requires very N-rich and H-poor conditions and also that, under MBE conditions, the (0001̄ ) may be covered with adsorbed H (from H2 in the background) even if none is intentionally introduced. This implies that the (0001̄ ) surface can dissociate H2 under these conditions. The stability of the H-terminated surface is suggested as an explanation for the slow growth of the (0001̄ ), which is passivated by adsorbed H. Ptasinska et al. [858] carried out a theoretical study of H on GaN (0001̄ ) using the PAW approach with the PBE functional and USPPs. A 2DPS with 4 Ga-N bilayers and either a (2x2) or (3x3) SUC was used, and a dipole correction (Fig. 6) was applied. For a coverage of θH o 0.75 ML, EF is located near the VBM due to the

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unpaired electron density in N DBs. For θH = 0.75, which satisfies the ECR, EF begins to move toward mid-gap, and for θH 4 0.75 EF is near the CBM as a result of excess electron density occupying previously-empty CB states. The ΔEads per H (about -5.8 eV) is nearly independent of coverage from the lowest value (1/9 ML, or 1 H per (3x3) SUC)) up to 0.75 ML and then decreases sharply, reaching about -3.1 eV at a full ML. This change of ∼2.7 eV in ΔEads is close to the PBE value for Eg, which is consistent with the idea that the change reflects the energy involved in electron transfer from H to GaN. Thus adsorption is less exothermic when the electron transfer is into a state near the CBM (θH 4 0.75 ML) vs. one that is near the VBM (θH ≤ 0.75 ML). With an H2 bond energy of about 4.6 eV, the results predict that H2 dissociation should be energetically (although not necessarily kinetically) favorable on the (0001̄ ) surface at any θH for which there are available sites to bind the H. This is consistent with experimental and theoretical observations, noted earlier in this section, that the (0001̄ ) surface has a high affinity for H. These results are also consistent with those of Grabow et al. [141] that show a decrease (although smaller than that found in the present study) in ΔEads with increasing θH for GaN (0001). In summary, theoretical results indicate a rich and complex behavior on the part of the polar GaN surfaces with regard to H2 under growth conditions. These predictions are difficult to evaluate due to the lack of relevant experimental data, the work of Munkholm et al. [866] being the exception. Similarly, predictions for H adsorption under UHV conditions are also difficult to test as a result of the dearth of experimental methods capable of direct detection of adsorbed H. A vibrational spectroscopy such as HREELS is very useful in this regard, but such data have been limited by uncertainty as to substrate polarity and the surface structure following in-situ cleaning. However, the general theoretical result that only Ga-H forms when H adsorbs on the (0001) appears to be supported by experimental results discussed earlier in this section. This in turn implies the absence of an H-atom etching effect on this surface. Northrup et al. [212] reported theoretical results for H on GaN (101̄0) obtained using methods described in Section 7.1 in connection with their study of NH3 on the same surface. For low-tomoderate values of μH the bare surface is the lowest-energy structure; whereas, at higher μH a surface saturated with Ga-H and N-H bonds is the most stable. Vibrational frequencies were computed for Ga-H stretching and bending (250 and 123 meV respectively) and for N-H stretching and bending (429 and 127 meV respectively). For N-D the stretching frequency shifts to 312 meV. At T = 0 the surface energy of the fully H-terminated surface is 1.93 eV per (1x1) cell lower than that of the bare surface, which indicates that ΔEads = -1.93 for 2 H atoms. Ito et al. [380] and Akiyama et al. [855] performed a theoretical study of the adsorption of H on GaN (112̄ 0) and (112̄ 2) under growth conditions using methods described above in connection with their results for the (0001) surface. The 2DPS consisted of eight atomic layers, and the SUCs were (1x1) and c(2x2), respectively, for the (112̄ 0) and (112̄ 2) surfaces. The bottom surface was terminated in PHs, and the lower four layers remained fixed in the ideal bulk-lattice positions. The non-polar (112̄ 0) surface is less reactive with H than is the (0001) since the DBs on the (112̄ 0) are auto-compensated. On the ideally-terminated surface, the excess electron density in the Ga DB matches the electron deficiency in the N DB; hence, after electronic relaxation, the Ga (N) DB is empty (doubly occupied) thus satisfying the ECR. Under low-to-moderate μH conditions, the bare Ga-N surface dimers are stable except under Ga-rich conditions, for which a Ga adlayer forms. Under more H-rich conditions, Ga-NadsH2 + N-H (Ga-H + N-H) forms under N-rich (Ga-rich) conditions, where Nads means an adsorbed N atom. In this case the NH2 is terminally bonded, i.e., there is only

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one Ga-NH2 bond. The semi-polar (112̄ 2) surface consists of two-fold-coordinated Ga and three-fold-coordinated N (Fig. 3a,b). Here a phase composed of N-H (i.e., H bonded to surface N) and both Ga-Nads(H)-Ga and Ga-Nads(H2)-Ga bridges between surface Ga forms under a wide range of conditions except those that are either very H-poor or very Ga-rich, in which case various H-free Ga adatom and adlayer structures occur as described in Section 4.6.4.3. With adsorbed H, each Ga forms one bridge of each type (NadsH or NadsH2) to a neighboring Ga. Applying the ECR here leads to the following. There is a total of 11/2 |e| per SUC in DBs, and 9 |e| are supplied by 2 H, 1 NadsH and 1 NadsH2. The two N-H bonds at surface N sites use 4 |e|, 2 |e| go to the NBLP orbital on the bridging NadsH and 8 |e| are used to form 4 Ga-Nads back-bonds, which leaves 1/2 |e| in excess. This could be addressed by doubling the size of the SUC (to give an excess of 1|e|) forming a (2x1) cell, breaking one Ga-Nads(H2)-Ga bridge per cell and adding H to give a terminal Ga-NadsH2 (with a NBLP orbital) and a Ga-H. Under conditions that are rich in both Ga and H the surface consists of Ga-H and N-H. The Ga-H bonding was not described in detail, but presumably the Ga is sp2-hybridized with the Ga-H bond essentially normal to the surface. Phase diagrams were constructed to show the surface composition as a function of μGa and temperature (derived from the T-dependence of μH, as in Eq. (5) and Fig. 7) for a typical MOCVD H2 pressure of 76 Torr. Feenstra et al. [3] reported theoretical results for H on GaN ̄ Under conditions that are relatively richer in H than in Ga, (1011). a structure forms with nine N-H bonds in a (2x1) supercell formed from the (1x1) non-primitive cell (Fig. 3c,d). With four each of two-fold- and three-fold-coordinated N per cell, there is a total of twelve N DBs with a net unpaired electron population of 15 |e|. This structure can be passivated by forming nine N-H bonds and three NBLP orbitals on the twelve surface N atoms and is expected to form under MOCVD growth conditions. At a greater relative Ga/ H richness, as in MBE, this structure gives way to an H-free Ga adlayer. Akiyama et al. [419] and later Ito et al. [380] performed theoretical ̄ using methods described in Sections studies for H on GaN (1011) 4.6.4.1 and 5.25 in connection with their work on the clean surface and on Mg adsorption respectively. The ideal surface is terminated in two- and three-fold-coordinated N atoms (Fig. 3c,d). Under conditions of high μH, as in MOVPE, the most stable structure is the so-called "4NH+Ga-H" in which one H bonds to each three-fold N, Ga-Ga dimers form in place of the two-fold N (which are all eliminated) and one H bonds to one of the dimerized Ga atoms. This presumably breaks the Ga-Ga dimer bond, but this point is not clear in the discussion provided. This description is based on a (2x1) supercell, formed from the (1x1) non-primitive cell, which has four three-fold N atoms and four Ga-Ga dimers after removal of the four two-fold N atoms, which in this study are unstable except under Ga-rich or extremely N-rich conditions. Apparently 4N-H+Ga-H is the only stable surface with adsorbed H that exists under the range of conditions considered; whereas, under low-μH conditions, the H-free structures described in Section 4.6.4.1 are observed. These results appear to differ significantly from those of Feenstra et al. [3]. 7.4. Hydrogen chloride (HCl) and gallium monochloride (GaCl) The interaction of HCl with GaN surfaces has been studied theoretically by Uhlrich et al. [94], Okamoto et al. [867] and Krukowski et al. [830,868], motivated by an interest in understanding etching reactions and in the use of HCl as a Ga transport reagent in hydride VPE. Krukowski et al. [830] also briefly discuss the adsorption of GaCl in the same context. Suzuki et al. [834] reported theoretical results for GaCl interacting with the (0001̄ ) surface. Okamoto et al. [867] used a very small cluster model, Ga(NH2)3,

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to represent the local environment on (0001) and (101̄0) surfaces. The calculations were RHF, which neglects electron correlation, but were checked using second-order Møller-Plesset (MP2) theory, which gave qualitatively similar results. Successive reactions were considered that lead to the overall process Ga(NH2)3 + 3·HCl → GaCl3 + 3·NH3 via a series of transition states in which each HCl forms Gaδ+–Clδ− and Nδ−–Hδ+ bonds followed by dissociation of the Ga-N and H-Cl bonds to give Ga-Cl and NH3. The ΔEa decreases with each successive step due the increasing fractional positive charge on Ga as Cl replaces NH2. The barrier is small even for the first step (9.3 kcal mol-1), which suggests a facile reaction. The RHF reaction energies are -29.0, -24.6 and -20.1 kcal mol-1 at each step, indicating that the overall process is highly exothermic. Uhlrich et al. [94] performed theoretical studies of HCl interacting with the ideally-terminated (0001) surface using methods described in Section 7.1 in connection with their NH3 work. Molecular adsorption is found to be exothermic with ΔH0 = -0.69 eV for one HCl per (2x2) cell; although, the adsorption geometry was not described. Dissociation to form adsorbed H and Cl is exothermic with ΔH0 = -3.49 eV relative to the bare surface and free HCl, and neither type of adsorption exhibits any significant activation barrier. For different Cl binding sites (T1, Br and H3), ΔEads is the same to within 0.1 eV, and there is a repulsive interaction between Cl atoms that results in a decrease in ΔEads with increasing θCl up to 1 ML. Adding one N atom per (2x2) cell destabilizes Cl adsorption. Although not discussed in detail, θN = 0.25 yields a (0001) surface that satisfies the ECR, which is expected to be less reactive than the ideally-terminated surface. Dissociation of H2O on a surface with pre-adsorbed Cl is found to be less favorable than on one that is Cl-free. This is consistent with experimental results in this study and in Refs. [60,64] that show a (0001) surface cleaned in HCl solution to be less susceptible to recontamination when exposed to room air. Krukowski et al. [830,868] used a 2DPS with five Ga-N bilayers with the bottom surface terminated with H atoms and the lowermost three bilayers frozen in the bulk-lattice geometry. The calculations used NCPPs with local (i.e., not PW) basis sets and either the LDA or the GGA approach (the latter with the PBE functional). Both (2x2) and (3x3) SUCs were used, and it was noted that the (2x2) is not sufficiently large for convergence of ΔEads in these calculations. To simulate Ga- or N-rich growth conditions, the (0001) Ga atoms were terminated with, respectively, H or NH2. In the former case, HCl approaching the surface forms a weaklybound physisorbed state (ΔEads = -0.4 eV) with the Cl about 4 Å from the surface and then dissociates with a small barrier (ΔEa ≈ 0.5 eV) to form Ga-Cl at a T1 site and adsorbed H2. Relative to free HCl, ΔEads ≈ -3.0 eV, and the Ga-Cl distance is ∼2.0 Å. The nature of the H2 adsorption bond was not described in detail. For NH2 termination the physisorption minimum is more shallow (-0.2 eV) and occurs at a greater distance (∼4.9 Å), and the dissociation barrier is much higher (ΔEa ≈ 2.0 eV). This is ascribed to repulsion between the partial negative charges on the NH2 and the Cl; however, it is noted here that an alternative explanation for the higher barrier might be a greater Ga-NH2 vs. Ga-H bond energy. Although not explicitly stated, the dissociative reaction in the case of NH2 termination presumably leads to a Ga-Cl bond and NH3. Direct desorption of Cl is found to be very difficult (ΔEa = 4.5 eV); however, desorption as HCl via reaction with H diffusing up to the surface from the bulk is much easier (ΔEa ≈ 0.6 eV). Suzuki et al. [834] studied GaCl interacting with the ideallyterminated (0001̄ ) surface theoretically using methods described in Section 7.1 in connection with their results for NH3, etc. on the (0001). The most favorable structure has the Ga-Cl bond vertical with Ga downward and occupying an H3 site, which gives ΔEads = -3.53 eV. A Ga atom adsorbs at the same site with ΔEads = -4.37 eV.

7.5. Nitric oxide (NO) Grabow et al. [141] performed theoretical calculations (spin-restricted) for the adsorption of NO on GaN (0001) using methods described above in connection with their work on NH3. Adsorption occurs with the NO lying flat at an FCC (H3) site with ΔEads = -3.33 eV. Vibrational modes, including hindered rotations and translations, were given but without assignment, and the nature of the chemisorption bond was not discussed. 7.6. Nitrogen (N and N2) There are, to our knowledge, few experimental studies within the range of topics covered here that deal with the interaction of N2 and/or N with GaN surfaces. An exception is the work of King et al. [869]. Theoretical results for GaN (0001), (0001̄ ) and (112̄ 2) surfaces have been given in Refs. [141,344,372,566,576,577,654– 657,661,833,869–873], Refs. [654–657,662] and Ref. [426] respectively. Theoretical results for the non-polar (101̄0) and/or (112̄ 0) surfaces have also been reported in Refs. [576,577,656,663,664]. The interest is in understanding how adsorption and diffusion of N affect GaN growth. King et al. [869] used STM and STS, together with theoretical work described below, to study the interaction of N atoms with the GaN (0001)-"(1x1)" surface covered with an adsorbed Ga bilayer. Samples were grown by MBE and a fractional ML of N atoms adsorbed in situ at 300 °C using a plasma source to generate atomic N as during growth. Four distinct types of islands are observed after N adsorption, which are termed "bright-edged", "center-depressed", "striped" and "flat". Only the last of these has a height equal to a bilayer spacing (2.60 Å), which is consistent with the GaN crystal structure. However, with continued STM imaging, a morphological change occurs whereby the other three are converted to flat-type islands. The STS results indicate that the DOS after conversion is the same as that of the "(1x1)" terraces; whereas, differences are seen before conversion. The theoretical analysis of these results is discussed below. Zywietz et al. [654] performed theoretical studies of the diffusion of N on the bare GaN (0001) surface (i.e., with no metallicGa adlayer). The 2DPS consisted of at least 9 layers of GaN (presumably this means Ga-N bilayers) with a (2x2) SUC and the bottom surface terminated in PHs. The Ga 3d electrons were included in the PP and not in the valence states but were treated using NLCC (Section 4.1.1), which was found not to affect the results significantly. The most stable adsorption site is an FCC (H3), with a barrier of 1.4 eV for hopping between FCC sites via an HCP transition state. The HCP (T4) site is unstable due to a repulsive interaction with the underlying lattice N atom. At low coverage the T1 site is highly unfavorable, lying about 3.3 eV above the H3; however, T1 must be the most stable site at high coverage since this is effectively the lattice site in bulk GaN. It was suggested that this may be a source of kinetic limitation for growth on the (0001) surface. Smith et al. [344] obtained theoretical results for N on GaN (0001) as part of a larger study of the correlation between surface stoichiometry and reconstruction. The approach made use of PWs and the LDA with a 2DPS containing 8 layers of GaN (presumably this means 8 Ga-N bilayers) and terminated on the bottom with PHs. Under very N-rich conditions, an N atom at an H3 site in a (2x2) SUC is stable and is about 0.7 eV lower in energy than at a T4 site. The three Ga atoms bonded to the N adatom undergo a large relaxation displacement, and the Ga-N bond length for the adatom is 2.01 Å vs. 1.94 Å computed for the bulk, which indicates a degree of tensile stress at the surface. Nakamura et al. [655] and Murata et al. [656] studied N adsorption on the ideally-terminated (0001) surface (termed "(0001)

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Ga-terminated") using NCPPs with the PW-91 functional. No details regarding the 2DPS model were provided. The energy minimum occurs when N occupies an FCC (H3) site at a distance of 1.038 Å above the surface [655]. In a later study [656] the distance was revised to 1.439 Å. Ishii et al. [870–872] performed theoretical studies of the adsorption of N on the (0001)-(2x2) surface with θGa = 0.25 ML in a T4 site. The calculations employed the GGA with NCPPs and a 2DPS consisting of eight GaN layers (presumably Ga-N bilayers rather than atomic layers) with the uppermost four layers and the adatoms allowed to relax. The DBs on the bottom layer were saturated, presumably with PHs. For a single N adatom, the most stable site is an H3 adjacent to the Ga adatom. This structure then rearranges to one in which the initial Ga adatom moves to a position above the N adatom where it forms a Ga-N bond. The next most stable site for an N adatom is a T1 (termed "L" in this study) that is adjacent to the Ga adatom. This structure rearranges to one in which the Ga adatom rises above the T4 site and bonds to the N adatom. This energy difference between these two structures (0.8 eV) is significantly smaller than the H3-T1 difference (3.0 eV) without the Ga adatom present (i.e., on the bare ideal surface). A second N adatom occupies another H3 site adjacent to the Ga adatom, and rearrangement in this case leads to displacement of the Ga adatom to a position above the N adatoms where it bonds to both. The authors note that neither of these H3 structures leads directly to the wurtzite lattice, which means that they are not conducive to growth. However, with two Ga and one N adatom per (2x2) cell, the N occupies a T1 site where it bonds to a Ga in the lattice-terminating layer and the two Ga adatoms (originally in T4 sites) then separate from the terminating layer and bond to the N adatom, forming a structure resembling a wurtzite lattice site. The results show that excess Ga plays a critical role in MBE growth in that it prevents N from occupying a very-stable H3 site, as it does under Ga-poor conditions, which is inconsistent with the growth of a wurtzite lattice. The nature of the bonding in these structures was not described in detail. Dai et al. [873] reported theoretical results for N on Ga-rich (0001)-"(1x1)", which is terminated in a bilayer of metallic Ga. The 2DPS comprised 8 Ga-N bilayers with a (2x2) SUC and the bottom surface terminated in PHs. The calculations used PWs and USPPs with Ga 3d electrons included in the valence states. The Ga atoms in the first adlayer are in T1 sites and those in the second (outer) adlayer can be in either H3 or T4 sites, with the latter being lower in energy by less than 0.01 eV (presumably this is the energy is per SUC). For adsorption of N on top of the metallic bilayer, the T1 site is found to be the most favorable, and relaxation of the fluid-like outer Ga adlayer has a large effect in reducing the total energy. The H3 site is 0.14 eV higher in energy, and the bridge and T4 sites are higher still. The lowest-energy diffusion path is T1 → H3 → bridge → T1, for which the barrier is 0.65 eV. This is much lower than the barrier on the bare (0001) surface. It is stated that the higher N mobility on the Ga bilayer makes recombinative desorption of N2 less likely, but it is not obvious that this should be the case unless N incorporation is also enhanced or there is a repulsive interaction between adsorbed N atoms. Takeuchi et al. [657] studied the effects of Ga coverage and of electronic excitation of the GaN on adsorption and diffusion of N on the (0001) surface using methods described in Section 5.18 in connection with their work on Ga adsorption. This was motivated by experimental indications that irradiation with high-energy electrons during MBE growth can improve the material quality. In the absence of excitation, the most favorable site for N on the bare (0001) surface is H3; whereas, the T4 and bridge sites are higher by 0.76 and 1.12 eV respectively. The H3-T4 energy difference for a (2x2) SUC is in good agreement with that obtained previously by Smith et al. [344]. For the (0001)-"(1x1)", which is terminated in a

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laterally-contracted bilayer of metallic Ga, adsorbed N occupies a position between the two adlayers where it is coordinated to three Ga atoms in the lower adlayer and to one in the top adlayer to form a tetrahedral configuration in a (√3x√3) SUC. The diffusion barrier for N incorporated in this manner is 0.76 eV vs. 1.12 eV for N adsorbed on the bare (0001) surface. Adsorption of N on top of the Ga bilayer occurs most favorably at an H3 site, but this is 0.13 eV higher in energy than the structure formed by incorporation of N into the bilayer. These results differ from those of Dai et al. [873], discussed above, who studied adsorption of N on top of the bilayer and found that the T1 site is most favorable. However, the diffusion barriers found in either study (0.65 vs. 0.76 eV) are very similar. To study the effects of electronic excitation, the bare (0001) surface with a (2√3x2) SUC was used, which gave somewhat higher energies for T4 and bridge sites relative to H3 than did the (2x2) SUC. These differences are 0.89 and 1.26 eV respectively vs. 0.76 and 1.12 eV for the higher-coverage (2x2) SUC, which might suggest an attractive interaction between adsorbed N in T4 or in bridge sites. Excitation is seen to reduce the diffusion barrier (from 1.26 to 0.92 eV for a single excitation) by lowering the energies of the bridging and T4 sites relative to H3, which results from the promotion of an electron into an anti-bonding state. Although not explicitly considered in this study, it is possible that the experimentally-observed improvement in material quality due to electron irradiation during growth might result instead from ESD of impurity O atoms introduced by dissociative adsorption of H2O in the UHV background (Section 7.10). Timon et al. [372,566] performed theoretical studies of N adsorption on the ideally-terminated GaN (0001) surface using methods described above in connection with their work on Al adsorption (Section 5.1). This study was part of a larger investigation of the co-adsorption of various other atoms together with N. A full ML of N adsorbed in T1 sites is energetically unfavorable for any value of μN. However, for such a surface three of the N atoms form a trimer with an N-N distance of 1.46 Å. A single N adatom per (2x2) cell in an H3 site, which satisfies the ECR, is the most stable structure under N-rich conditions, in keeping with many other studies of this type of surface. In the case of N on the (0001)-"(1x1)", with a laterally-contracted bilayer of metallic Ga, a (√3x√3) SUC was employed in the calculation. Here a structure with one N per SUC substituting for Ga in the uppermost layer of the bilayer is more stable under Ga-rich conditions than is the bare (0001) surface with one N adatom per (2x2) cell but less stable than the N-free Ga bilayer. Apparently the incorporation of N between the Ga layers or in the lower layer of the bilayer was not considered. Gokhale et al. [576,577] presented theoretical results for N on GaN (0001) that were obtained using methods described in Section 5.2 in connection with their work on Sb. For θN = 0.25 ML, N adsorbs in an FCC (H3) site with ΔEads = -5.39 eV (relative to the bare surface and a free N atom) and a diffusion barrier of ΔEa = 0.99 eV, which is lower than the barrier of 1.4 eV obtained by Zywietz et al. [654] using the LDA approach. For N2, ΔEads = -0.55 eV is found. The N2 adsorption site was not specified, but it is presumably H3 as for atomic N. Recombination of two N in a (2√3x√3)R30° SUC to form adsorbed N2 is exothermic by 1.48 eV, but the barrier is ΔEa = 1.88 eV, which is much higher than ΔEa for N-atom diffusion. To our knowledge, the predicted adsorption of molecular N2 has not been observed experimentally in UHV, but this might require a low-temperature experiment. King et al. [869] performed calculations, in conjunction with their STM and STS experiments described above, for N interacting with the (0001)-"(1x1)" surface with a laterally-contracted bilayer of metallic Ga. A (√3x√3) SUC was used together with the FLAPW method, but no further details were given. The most energetically-

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favorable site is described as a subsurface T1 between the Ga adlayers. Presumably this means that the N is bonded to one Ga in the lower adlayer and to three in the top adlayer, which would be the reverse of the structure found by Takeuchi et al. [657]. This gives a tetrahedrally-coordinated N with the Ga layers spaced about 0.6 Å apart in agreement with the experimental result of 0.48±0.12 Å. The different types of islands seen in STM are ascribed to different distributions of N between the two Ga layers, which is supported by a comparison of observed (STS) and calculated DOS results. The model proposed to describe the evolution of surface structures begins with N insertion as described above. Electron tunneling during STM then causes a process wherein N moves into the inner adlayer and bonds to three Ga atoms in this layer and one in the terminating Ga layer of the lattice, which then produces a new Ga-N bilayer. Grabow et al. [141] reported theoretical results for N on GaN (0001) obtained using methods described in Section 7.1 in connection with their NH3 work. This study extends earlier work by Gokhale et al. [576,577]. Atomic N adsorbs at an FCC (H3) site with ΔEads = -5.36 eV, relative to the free atom, for θN = 0.25 ML. With increasing coverage, ΔEads decreases nearly monotonically from -5.91 eV at θN = 1/9 ML to -2.82 eV at θN = 1 ML. Molecular N2 adsorbs at a bridge site with ΔEads = -0.72 eV relative to free N2; however, the nature of the bonding was not described in detail. It was further found that the barrier to N2 formation increases strongly with θN as a result of the repulsive interaction between adsorbed N atoms. Vibrational frequencies for adsorbed N and N2 were also reported. Won et al. [833] reported theoretical results for the diffusion of N on GaN (0001) using the cluster model described in Section 7.1 in connection with their results for NH3 decomposition. A barrier height of 66.8 kcal mol-1 was found, which suggests that adsorbed N is relatively immobile under growth conditions (in the absence of a metallic-Ga bilayer). However, the barrier to recombinative desorption as N2 is very low, only 5.6 kcal mol-1; hence, any significant mobility on the part of N will lead to facile desorption. This is much lower than the barrier of 1.88 eV (43.4 kcal mol-1) found by Gokhale et al. [576,577] for 2 N atoms in a (2√3x√3) R30° SUC (θN = 1/3 ML). However, the barrier is strongly dependent on θN, increasing to 95.0 kcal mol-1 for 2 N in a (2x2) cell (θN = 1/2 ML) [141]. For the cluster model used by Won et al., two adsorbed N atoms gives a coverage of 2/7 ML. Chugh and Ranganathan [661] performed extensive theoretical studies of N on GaN (0001) using methods described in Section 5.18 in connection with their work on Ga adsorption. For θN = 0.25 ML (i.e., a (2x2) structure), ΔEads = -2.43, -4.90 and -5.67 eV respectively are found for N in on-top (T1), HCP (T4) and FCC (H3) sites. The overall trend and the FCC energy concurs with other results discussed above as does the observation that ΔEads becomes more exothermic with decreasing θN. The surface relaxation in response to adsorption, the charge density distribution and the dipole moment of the SUC were all analyzed in detail. Adsorption of N in the FCC site causes a significant amount of distortion, with the three Ga atoms to which it back-bonds shifting laterally toward it by 0.18 Å and upwards by 0.63 Å. With a smaller SUC (i.e., a higher θN), the lattice cannot relax fully after N adsorption; hence, ΔEads becomes more exothermic with increasing SUC size even up to (5x5), for which ΔEads = -7.20 eV in an H3 site. The analysis of these effects and of the implications for reconstruction of the clean surface were discussed in Section 5.18 in connection with similar results for Ga adsorption. Zywietz et al. [654] performed theoretical studies of the diffusion of N on the GaN (0001̄ ) surface terminated in a single adlayer of metallic Ga in T1 sites using methods described above in connection with their work on the (0001). The FCC (H3) site is the most favorable but is only about 0.2 eV lower than the HCP (T4),

and the barrier to hopping (for which T4 is the transition state) is only 0.9 eV vs. 1.4 eV on (0001), which is ascribed to a weaker interaction between N and the substrate in the case of Ga-terminated (0001̄ ). The authors suggest that the high N diffusion barrier on either surface imposes a kinetic limit on the recombinative desorption of N. This process is energetically favorable but limited by the slow rate at which N atoms come together to form N2. For either surface, Ga is much more mobile than N, and the implications of this for GaN growth were discussed. Tsai [662] reported an ab-initio MD study of the adsorption and diffusion of N on GaN (0001̄ ) covered with one ML of metallic Ga to simulate MBE conditions. The 2DPS consisted of 3 Ga-N bilayers (and the Ga adlayer) with the bottom terminated with H and a (2x2) SUC. Presumably the terminating species was real H, not PH, but the coverage was not stated. Only the Γ-point of the BZ was included. The N atom was given an initial velocity, toward the surface in the surface-normal direction, corresponding to a temperature of 1000 K, and a 0.13 fsec time step was used in obtaining trajectories. In a trajectory of 600 fsec, N impinging at a bridge site first recoils from the Ga adlayer then penetrates through this layer and back out again before eventually entering a state where it translates along the adlayer surface. In contrast, when impinging at a T1 site the N eventually escapes back into vacuum. Nakamura et al. [655] and Murata et al. [656] studied N adsorption on the ideally-terminated (0001̄ ) surface using NCPPs with the PW-91 functional. No details regarding the 2DPS model were provided. The energy minimum occurs when the N is at about 0.50 Å above the surface, and the energy at this point is essentially the same for the FCC (or H3) and HCP (or T4) sites. Takeuchi et al. [657] performed theoretical studies of N adsorption on the GaN (0001̄ ) surface, terminated in an ML of metallic Ga, using methods described above in connection with their work on the (0001). The FCC (H3) and HCP (T4) sites have equivalent energies for N adsorption, due to the fact that the metallic Ga adlayer effectively isolates the N from the underlying GaN surface. The bridge site lies higher in energy by 0.73 eV, which defines ΔEa for diffusion. Electronic excitation of the GaN is seen to have no significant effect on N adsorption energies, unlike in the case of the bare (0001) surface discussed above. Akiyama et al. [426] have studied the interaction of N with the (112̄ 2) surface using the PW method with USPPs and the PBE functional. The 2DPS consisted of 7 Ga-N bilayers with the bottom surface terminated with PHs. Two different surface structures were considered. One consists of a c(2x2) SUC with one Ga adatom (Fig. 20c) and the other an ML of adsorbed Ga with a (1x1) SUC. As discussed in Section 4.6.4.3, these are stable surface structures for the (112̄ 2). For the c(2x2), placing an N adatom near a three-foldcoordinated surface N leads to N-N bond formation and desorption of N2, which is exothermic by 0.48 eV. This suggests that the full Ga adlayer is needed for surface stability during growth. In the presence of a Ga adlayer, N penetrates the adlayer and adsorbs in a tetrahedral configuration bonded to Ga atoms in the adlayer and in the lattice terminating layer where it is stable against desorption under growth conditions. Gokhale et al. [576,577] have presented theoretical results for N on the non-polar (112̄ 0) surface obtained using methods described in Section 5.2 in connection with their work on Sb. A ΔEads of -2.28 eV is found for one N per (1x1) SUC (relative to the bare surface and a free N atom) with very high diffusion barriers of ΔEa = 2.63 and 2.85 eV, respectively, parallel and perpendicular to the [0001] direction. The ΔEa for 2Nads→(N2)ads is only 0.77 eV, which means that the high diffusion barrier limits the rate of recombination. For N2, ΔEads = -0.11 eV in a (2x1) SUC; however, the adsorption geometry was not described for either N or N2. Murata et al. [656] have reported theoretical results for N on the (101̄0) and (112̄ 0) non-polar surfaces. The most-favored sites are respectively the so-

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called "s4" and "s5", which unfortunately are not clearly depicted in the illustrations provided. Lymperakis and Neugebauer [663] attempted to study the diffusion of N on the (101̄0) and (112̄ 0) surfaces using methods described in Section 5.18 in connection with their results for Ga. In either case, placing an N adatom close to a surface N leads to N-N bonding and desorption of N2, indicating that neither surface is stable when exposed to atomic N. Jindal and Shahedipour-Sandvik [664] studied N diffusion on the (101̄0) surface theoretically using methods described in Section 5.18 in connection with their Ga work. Results were also obtained for N diffusion on the ideallyterminated (0001) and (0001̄ ) surfaces. For the former, the FCC (H3) is the lowest-energy adsorption site, in agreement with previous studies, with the T4 (termed "H2 hcp" in this study) being 0.29 eV higher. Diffusion occurs from H3 to T4 with ΔEa = 0.66 eV and then from T4 to another H3 with ΔEa = 0.37 eV. On the (0001̄ ), N adsorption occurs in a T1 site (termed "H1 hcp" in this study) via a strong N-N bond with ΔEa = 2.43 eV for diffusion through an FCC (H3) transition state. For the (101̄0) surface, multiple energy minima with different configurations (not described in detail) are found for adsorption, with N close to a surface N and with ΔEa = 1.7 and 2.3 eV respectively for diffusion perpendicular and parallel to the [0001] axis. The (101̄0) results appear to differ significantly from those of Lymperakis and Neugebauer [663]. To summarize, the general understanding for N on the more heavily-studied (0001) surface is that, in the absence of a Ga adlayer, N adsorbs in an H3 site. This is already well established from studies (Section 4.6.1) of the (0001) surface under N-rich conditions. In the presence of a Ga bilayer, there is a pronounced tendency for N to penetrate into the bilayer so as to form a tetrahedral structure where it bonds to Ga in both layers. 7.7. Nitrous oxide (N2O) The interaction of N2O with GaN (0001) has been studied theoretically by Hu et al. [874] with an interest in understanding the surface oxidation mechanism. The 2DPS comprised 3 GaN bilayers with the lowermost fixed and the bottom surface terminated in N-H bonds. Although not explicitly stated this presumably involved θH = 0.75 ML, which gives a passive surface according to the ECR. Spin-unrestricted calculations were done using the PW91 functional and an ideally-terminated (3x2) SUC. Presumably USPPs were employed since a low PW cutoff (30 Ry) was used. Adsorption geometries in which the N2O lies parallel to the surface are much more stable than those in which it is vertical with either N or O alone interacting with the surface. In the most favorable parallel geometries, dissociation occurs to give O adsorbed in an FCC (H3) site and N2 bonded via one N in either an HCP (T4) site or as a bridge between two Ga atoms. These two reactions have a nearly-identical ΔEads of about -437.2 kJ mol-1; whereas, placing the N2 with one N in an FCC site leads to desorption and a ΔEads of -422.3 kJ mol-1 for the overall reaction. Presumably a substantial fraction of ΔEads derives from the stability of the N2 product. The DOS of the bare surface shows metallic character, due to the partially-filled Ga DBs, which is diminished by the adsorption of O. The DBs on those Ga atoms that bond to O form filled bonding and empty antibonding Ga-O orbitals, while those on other Ga atoms in the SUC remain partially filled and appear at EF. An NEB calculation was also done to identify the transition state and to analyze the energetics of the dissociation reaction. Beginning with a reactant state (RS) in which N2O lies roughly parallel to and 3.5 Å above the surface (i.e., too far for bond formation), the reaction proceeds through a weakly-bound physisorbed state (PS) and then to a transition state (TS) that is only ΔEa = 0.11 eV above the PS. In the transition from RS to TS the N2O gradually becomes more vertical and moves closer to the surface.

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An abrupt decrease in total energy is then seen as dissociation occurs to give adsorbed O and N2. The small ΔEa suggests that N2O is a very efficient oxidation reagent for GaN (0001). 7.8. Oxygen (O and O2) and ozone (O3) The interaction of O2 with GaN has received a great deal of attention due to the importance of native-oxide formation in practical applications. Experimental results for O2 on the (0001) and (0001̄ ) surfaces are given in Refs. [184,185,192,491,493,506,875–881] and Refs. [388,436,511] respectively. Of these, Refs. [184,185,192,506,511,878] address native-oxide formation in room air while the others concern in-situ O2 chemisorption. Theoretical studies are described in Refs. [141,881–887] for the (0001) and (0001̄ ) surfaces, in Refs. [193,888– ̄ and in Ref. [421] for the (1011). ̄ Also, Jackson and 891] for the (1010) Walsh [892] have performed an ab-initio analysis of the thermodynamics of GaN oxidation. Results for O3 on GaN (0001) have been reported in one study, by Sivasubramani et al. [893]. In this section the focus is on chemisorption and oxidation involving O2 at nominal RT, which includes native-oxide formation in air; whereas, oxidation by thermal, wet-chemical or electrochemical means lies beyond the scope of the present review. For the interested reader, a recent study of the thermal oxidation of GaN (0001) in dry O2 has been reported by Yamada et al. [894]. It is noted that some of the studies of H2O adsorption discussed in Section 7.10 also provide information about adsorbed O, which can form as a result of complete dissociation. Bermudez [491] reported data for the initial adsorption of O2 on n-GaN obtained using AES, UPS, XPS and LEED for MOCVD samples cleaned by IBA (1 keV nitrogen ions, annealing at ∼900 ° C). The sample polarity was unknown at the time but was later found to be (0001). The initial chemisorption phase, which was the main focus of this study, saturates at an O2 exposure of ∼200 L, at θO = 0.40 ML, with little or no further change up to 3x103 L. The O2 in this study (as in almost all others) can be described as "excited" due to the use of a hot-filament ionization gauge to measure the O2 pressure during exposure, which promotes a fraction of the O2 to the long-lived and highly-reactive 1Δg electronic state. The effect of O2 excitation on chemisorption on, for example, III-V semiconductors has been examined in detail elsewhere [895]. A clear (1x1) LEED pattern is seen after 3x103 L O2 with beams that are significantly more diffuse than for the clean surface, which suggests a partial disordering of the surface. In ELS (Fig. 67) a transition is seen at ΔE = 3.4 eV (i.e., at close to the bulk Eg) that is highly sensitive to O2, which indicates a transition between surface states lying close to the band edges. Other more subtle changes due to O2 are seen near ΔE ≈ 20 eV, in the region of Ga 3d excitation. In UPS, O2 eliminates an occupied surface state close to the VBM. This results in an apparent shift in the VBM, due to the loss of surface-state intensity, but little change in BB, as evidenced by the absence of a significant shift in the Ga 3d "ghost" emission. The electron affinity increases by ∼0.58 eV following a saturation exposure to O2, from which a surface-normal dipole moment (negative end outward) of 0.40 D was estimated (Section 5.10). A small decrease in upward BB, by 0.1 to 0.2 eV, is seen after a 200 L O2 exposure. This suggests a small passivating effect during initial O chemisorption but could also result from an increase in SPV, which would also yield an apparent decrease in BB. Prabhakaran et al. [875] investigated the native oxide on GaN (0001) using primarily AES and XPS combined with ion bombardment and with wet-chemical etching in warm aqueous NH4OH solution. Samples were grown by MBE and then exposed to room air for several hours to form the oxide. The results suggest that the native oxide is mainly Ga2O3 with some additional oxynitride component, which might arise from insertion of O into GaN back-bonds.

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Fig. 67. Upper: First-derivative ELS vs. O2 exposure (primary beam: Ep ¼ 90 eV, ip E 0.8 μA incident normal to the surface) for GaN (0001). The elastic peak (0.7 eV full width at half maximum) is shown on a compressed vertical scale at the zero of loss energy. The spectra have been displaced vertically for clarity, and relative intensities are not quantitative. Lower: HeII-excited UPS (resolution ¼ 0.8 eV). The peak labeled "Ga 3d ghost" arises from Ga 3d excitation by the 48.4 eV satellite of the main 40.8 eV line. Likewise, the clean-surface peak at about -9.5 eV is due in part to unresolved Ga 3d ghosts excited by higher-energy satellites. Adsorption of O adds another component at slightly higher binding energy, causing an apparent shift of this feature. The relative intensity of the two spectra is not quantitative. Straight lines, least-squares fitted to the band edges, indicate the O-induced shifts. From Bermudez [491] (reproduced with the permission of AIP Publishing).

Tsuruoka et al. [493] studied adsorption of O2 on MOCVD nGaN (0001) using HREELS and LEED with sample cleaning by annealing in UHV at 900 K. No impurities were detectable in HREELS; however, the strong FK losses (Section 4.8) at integer multiples of 702 cm-1 might have obscured much weaker losses due to adsorbed C or O. Exposure to O2 in the 300-700 K range leads to a shift to higher energy and an asymmetric broadening of the FK fundamental, which is attributed to the formation of first Ga2O and then to a mixture of Ga oxides and oxynitrides. Following a 1070 K anneal in UHV the HREELS returns to that of the initial surface, which suggests that O-containing species are eliminated by desorption and/or indiffusion. The surface band gap increases from 3.4 to 4.4 eV in response to high-temperature O2 exposure, which is consistent with oxide formation, and the (1x1) LEED pattern becomes more diffuse. Watkins et al. [876] studied the effects of very large O2 exposures, up to 1014 L at RT, on GaN (0001) using XPS with steps taken to minimize O2 excitation during exposure. It is noted here that an interpretational difficulty with such very large exposures is

Fig. 68. Upper: Oxygen coverages on GaN (0001) vs. O2 exposure at RT as determined using XPS and AES. The dotted and dashed lines are least-squares fits of model functions. Lower: Normalized AES coverages for exposure to unexcited and to excited O2. Data shown as □ and O are for excited O2 from Ref. [491], and the dashed line is taken from the upper panel. In the original reference the surface was designated as "{0001}" since the polarity was not determined conclusively. From Janzen et al. [877] (Copyright 1999, with kind permission of The European Physical Journal (EPJ)).

the possible effect of trace contaminants. For example, if the O2 contains 1 part in 106 of H2O then a 1014 L O2 exposure (equivalent to ∼36 hours in 760 Torr of pure O2) is also a 108 L exposure to H2O. The sample was grown on a GaAs (100) substrate using MBE and then capped with As before transport to the surface-analysis chamber, at which point the As was thermally desorbed to generate the bare GaN surface. However, some O 1s intensity was detectable even before intentional O2 exposure. The O 1s intensity remains approximately constant up to about 105 L and then increases abruptly and reaches a saturation coverage of about 0.9 ML at ∼108 L, which is much lower than on GaAs (100) exposed under identical conditions. There is little or no obvious change in the O 1s XPS lineshape during this entire process, but an asymmetric broadening to higher BE is seen in the Ga 3d, which is consistent with Ga-O bonding. The different behaviors of GaN vs. GaAs with regard to the exposure dependence of coverage and XPS lineshapes is ascribed to the formation of only a single oxide phase on GaN vs. a more complex, multi-phase structure for GaAs. It is proposed that O2 adsorption on GaAs causes significant strain at the surface, which promotes subsurface oxidation. Such an effect is much less prominent on GaN (0001), for which adsorption appears to cease once all available surface sites are filled. Janzen et al. [877] used AES, XPS and LEED to study the oxidation of GaN at RT for exposures of up to 1015 L, which is equivalent to about 15 days in 760 Torr of pure O2. The comments

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made in the preceding paragraph regarding very large O2 exposures also apply here. The polarity of the sample ((0001) or (0001̄ )) was unknown. The MOVPE samples were cleaned ex situ in buffered HF solution and in situ using either Ga deposition followed by desorption at 850 °C or IBA (nitrogen ions at an unspecified energy, 850 °C anneal), and exposures were done, for comparison, both with and without excitation by a hot-filament ionization gauge. The clean surfaces showed a (1x1) LEED pattern with additional structure indicative of facets (Section 3.3.1). The XPS results for O coverage vs. unexcited O2 exposure (Fig. 68) show two stages. The first begins at the lowest exposure (0.3 L) and saturates at ∼103 L, while the second starts at ∼108 L and appears not to reach saturation even at 1015 L. Similar trends are seen in AES data, which, significantly, are essentially the same for both methods of in-situ surface preparation. These results differ from those of Watkins et al. [876] who observed only one stage of adsorption that saturated at ∼108 L. The (1x1) LEED pattern remains intact up to 1015 L but with blurring of the spots and an increased diffuse background. Very different behavior is seen for a surface with an ML of metallic Ga. Here little or no O is detected in AES up to about 100 L after which θO increases rapidly and, at ∼3x104 L, reaches a level exceeding that of the stoichiometric surface for 1015 L. The major difference between the AES and XPS results lies in the absolute θO values (Fig. 68), which are about a factor of two higher in XPS. This is ascribed to ESD of O by the primary beam in AES. A quantitative model for O uptake was proposed that involves dissociative chemisorption in the first stage ( o103 L) and fieldassisted (or Mott-Cabrera) oxidation in the second ( 4108 L), and the resulting fits to the XPS data are shown in Fig. 68. Fitting the first stage gives a sticking coefficient of 0.12±0.08 and a saturation coverage of 0.79±0.01 ML, which is close to the XPS saturation of coverage of 0.9 ML obtained by Watkins et al. [876]. Janzen et al. also investigated the uptake of excited vs. unexcited O2 (Fig. 68), and no significant difference was found. This is attributed to the high reactivity toward O2, even in the electronic ground state, exhibited by GaN (0001). A brief further comment is in order regarding ESD and its effect on the measurement of θO in electron-excited AES. In their UPS study of H2O adsorption on GaN (0001), which will be described in Section 7.10, Bermudez and Long [896] also performed a 500 L O2 exposure (sufficient to saturate the initial chemisorption phase) and obtained θO = 0.40 ML using AES. With an awareness of the work of Janzen et al., this was done by recording N(E) vs. E in pulse-count mode using a 3 keV electron beam of ip ≈ 40 nA focused to a 100 μm spot. Photons of a sufficient energy for O 1s XPS were unavailable in this study. This is the same θO obtained previously [491] in analog-detection (d[EN(E)]/dE vs. E) mode with ip ≈ 4 μA in a 100 μm spot. This suggests that ESD of some form of O from GaN (0001) is a very efficient process, as it is for adsorbed H (Section 7.3), since reducing the current density by a factor of 102 does not lead to any significant increase in the measured θO in AES. In other words, the additional O seen in XPS is not detected in electron-excited AES even at a greatly-reduced primary-beam current density. The results also suggest that there are two (or more) forms of adsorbed O or adsorption sites. One undergoes very rapid ESD and can be detected only in XPS, while the other is relatively immune from ESD and can be observed using standard electron-excited AES. Electron-beam damage in AES is a wellknown effect and has been discussed at length in Ref. [114]. Gupta et al. [878] studied the growth of native oxides in air at RT on GaN (0001). Samples were grown by MBE, characterized using RHEED, removed from the chamber, exposed overnight to clean room air and then reloaded into the chamber for further RHEED study. The results indicate that under these conditions oxidation does not occur to an extent detectable in RHEED.

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Thoms et al. [879] used AES, ELS, LEED and HREELS to investigate the adsorption of O2 on n-GaN (0001) at RT. The MOCVD samples were first cleaned in organic solvents and then subjected to IBA (1 keV nitrogen ions, 900 °C anneal). The initial chemisorption saturates at an exposure of about 200 L, with no further increase in θO up to 103 L, and results in an increased diffuse background in LEED. The ELS data in undifferentiated (N(E) vs. E) form show that O2 causes the removal of transitions at 3.5 and 6 eV and a gain in intensity near 18 eV, in qualitative agreement with the results in Fig. 67. The HREELS spectra showed an O2-induced asymmetric broadening similar to that described previously [493]. Hashizume et al. [184,185] studied native-oxide growth using n-type samples that were grown by MBE and then exposed to room air. The surface polarity was not explicitly stated, but it can be assumed to be (0001) based on the appearance of a (2x2) RHEED pattern during growth. Before air exposure the as-grown surface shows an upward BB of about 0.6 eV, which increases to 1.3-1.4 eV after exposure. The oxide is found to be essentially Ga2O3, which can be largely removed by immersion in NH4OH solution at 50 °C; however, chemically reducing the oxide coverage has little or no effect on the BB. This suggests that acceptortype defects remain after removal of the native oxide. Dong et al. [880] used STM, STS, LEED and AES to study O2 chemisorption and oxidation on GaN (0001) samples grown in situ by MBE. The initial surface was the "(1x1)" with a laterally-contracted bilayer of Ga metal on top of the Ga terminating layer of the substrate. The free-Ga coverage is found to be 2.3±0.5 ML, and the O coverage (after a saturation exposure of 2x105 L at RT) is 2.1 ±0.5 ML, which suggests a stoichiometry between those of Ga2O and Ga2O3. It is uncertain whether higher O2 exposures were used in search of a second stage of adsorption. Due to the possible influence of ESD, noted by Janzen et al. [877] and mentioned above, the θO determined via AES may constitute a lower limit. It is also worth recalling the finding of Janzen et al. that O uptake on GaN (0001) with a metallic-Ga adlayer is much more rapid, and reaches a higher coverage, than on a stoichiometric surface. This suggests that a significant fraction of the O uptake observed by Dong et al. occurs within the Ga adlayer itself. In AES, the surface-sensitive, low-energy Ga structure in the 40-110 eV range exhibits lineshape changes consistent with Ga oxidation. In STM, smooth and nearly-featureless terraces are seen on the clean surface; whereas, after 2x105 L O2 at RT, the terraces appear disordered with a corrugation of about 0.1 nm. Annealing at 550 °C after O2 exposure results in two different ordered structures. One is a (3√3x3√3)R30° seen in LEED and STM, and the other is a somewhat-disordered (2x2). The Ga and O coverages in either case are both 2.0±0.5 ML, essentially unchanged from the values before annealing. First-principles theoretical results are cited that show the most stable surface to have an O/Ga ratio of 8/5, which is close to that of Ga2O3. This is larger than the AES ratio of ∼1.0, which could be explained if the measured θO were reduced by ESD. It is proposed that an amorphous Ga2O3-like phase forms at RT and that ordering occurs at higher temperature. The STS data show the bare surface to be metallic; whereas, after 2x105 L O2, a band gap of 2 eV is found. In a further study, Dong et al. [881] used AES, LEED, STM and STS to study the (3√3x3√3)R30° ordered structure formed by reacting the "(1x1)" surface with O2 at 550 °C or by annealing at this temperature after exposure at RT. The work was supported by ab-initio theoretical results that will be described later in this section. Mixtures of smooth and rough regions are seen in STM, both of which show a band gap of about 3 eV in STS with EF near the CBM. The Fermi level is unpinned, since its position varies with tip bias during STS, which indicates a very low density of interface states in the GaN band gap. Garcia et al. [506] used XPS to study the effect of native oxide

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formation on BB, as discussed in Section 4.7.3.1, for n-type GaN (0001) samples grown by MBE and then exposed to room air. The degree of upward BB is seen to increase linearly with the XPS O/Ga atomic ratio, and extrapolation to zero O content gives EF - VBM = 2.70±0.1 eV (i.e., an upward BB of about 0.6 eV). This result is consistent with those found by others (Section 4.7.3.1) for atomically-clean surfaces in UHV. Various factors that might contribute to the BB are also discussed. In light of the work of Dong et al. [881] discussed in the preceding paragraph, these results suggest that oxidizing the GaN (0001) surface itself leads to a high density of interface states in the gap; whereas, oxidizing the "(1x1)" Ga bilayer gives an oxide with a low density of gap states at the oxide/ GaN interface. These results may indicate a favorable method for forming gate oxides on GaN devices. Mishra et al. [192] used UPS, XPS, SEM and AFM to investigate the effect on native oxide formation of pits on GaN surfaces of unspecified orientation and polarity. Samples were grown by MOCVD at various temperatures and were not intentionally doped; hence, they were probably n-type due to unintentional O doping as is typical in MOCVD GaN. After growth the samples were exposed to room air, cleaned in acetone and mounted in UHV. The average density and depth of surface pits, as well as the surface roughness, increases with growth temperature, which correlates with an increased native oxide coverage. It is inferred from this that such pits are favorable sites for oxidation. As mentioned in Sections 3.5 and 4.3, other experimental [149,191] and theoretical [193] work indicates a tendency for the GaN native oxide to accumulate at macroscopic defects. Beach et al. [388] used UPS and XPS to study the adsorption of O2 on the GaN (0001̄ )-(3x3) surface prepared by in situ MBE. The clean-surface Ga 3d shows a low-BE satellite corresponding to a coverage of about 1.1 ML of metallic Ga, which is consistent with the "adlayer+adatom" structure of this surface (Section 4.6.2). This satellite is attenuated by O2 exposure as is a shoulder extending from the bulk VBM to EF, which is also due to the metallic-Ga layer. The O coverage was observed up to about 1.5x104 L and saturates at about 1x104 L at θO = 1.3±0.2 ML. This corresponds to a Ga/O atomic ratio of ∼0.85 if one assumes that only adlayer Ga is bonded to O. The O 1s peak shifts to higher BE with increasing coverage, which may indicate the presence of two unresolved peaks with varying relative intensity. Plucinski et al. [436] used ARUPS to study the adsorption of O2 on n-GaN (0001̄ ). The experimental details were described in Section 5.37 in connection with their results for the adsorption of sulfur. A surface state is seen at about 1.5 eV above the VBM that is removed by O2, and the upward BB of 1.4 eV on the clean surface is reduced to 0.7 eV after 104 L of O2, which indicates the O2 chemisorption partially eliminates surface and/or defect states in the gap on the (0001̄ ). Choi et al. [511] grew an n-type (0001̄ )-(3x3) surface via MBE and used SE to observe the effects of exposure to room air. The surface was found to be highly reactive, more so than the (0001), as evidenced by changes in the complex pseudo-dielectric constant o ε4 that indicate a higher adsorbate coverage. The measurement and interpretation of oε 4 was described previously in Section 5.22 in connection with the results of Choi et al. [681] for In adsorption. It was also found that the clean surface could be restored by Ga deposition and desorption (termed "Ga flash-off" in the original reference) and that air exposure caused a decrease in BB. It is noted here that the results are consistent with oxidation of the metallic-Ga "adlayer+adatom" that is known to define the (0001̄ )-(3x3) surface (Section 4.6.2). In summary, in the experimental work for O2 adsorption at RT it appears to be generally agreed that there is an initial "fast" chemisorption stage that begins immediately, with little or no induction period, and saturates within ∼200-1000 L (possibly

depending on surface polarity) and that any surface states are removed during this initial adsorption. For this stage at least, there is little or no dependence of O uptake either on electronic excitation of the O2 or on the method of in-situ surface cleaning (i.e., IBA vs. Ga deposition and desorption). However, any Ga adatoms that may be present are especially susceptible to rapid Ga-O bond formation. Although the adsorbate layer formed during this first stage is not, itself, well-ordered, there is little or no gross disordering of the substrate. This would be consistent with the absence of significant penetration of O into the terminating layer during the first stage. Beyond this there may be a slower second stage that involves oxidation (i.e., formation of a Ga2O3-like phase) and/or the insertion of O into Ga-N back-bonds. This stage is lesswell understood and not always observed, and it is controversial whether or not saturation occurs at large O2 exposures. There is also evidence for a significant ESD effect that perturbs the measurement of θO using electron-excited AES. Oxidizing a metallic-Ga adlayer, as opposed to the GaN itself, yields an oxide/GaN interface with a relatively low defect density. Elsner et al. [882] performed theoretical studies of atomic O adsorption on GaN (0001) and (0001̄ ) surfaces using the DFTB approach with a (4x4) SUC and a 2DPS with five Ga-N bilayers for which the bottom surface was terminated with PHs. Except under very O-rich or O-poor conditions, the most stable structure for the ideally-terminated (0001) with adsorbed O has θO = 3/8 ML, which satisfies the ECR and is semiconducting. Each surface Ga has 3/4 |e| in a DB, and the (4x4) SUC, with 16 Ga atoms, thus has a total of 12 |e| in DBs which can be used to adsorb 6 O atoms as Ga-O-Ga bridges leaving 4 empty Ga DBs per SUC. Elsner et al. found that a more stable variation has 4 of the 6 O in 3-fold-coordinated H3 sites, which uses an empty Ga DB and a NBLP orbital on the O. There is little change in energy when some of the H3 O atoms are moved to T4 sites; hence, the adsorbate layer is expected to be disordered in practice with a random mix of O in H3 and T4 sites and a high-background (1x1) LEED pattern in agreement with experiment. It is also found that under very O-rich conditions the ideally-terminated surface with a full ML of O in T1 sites becomes stable. The O atoms form O-O dimers with each O bonded to a single Ga. This can be described as a peroxo structure (O2−2), and we speculate here that this might be the species described above that is seen only in XPS and is subject to rapid ESD during electron-excited AES. The peroxo and also the superoxo (O2−) species could perhaps be identified in a UPS experiment [897,898]. For a (0001) surface terminated in a full ML of adsorbed Ga on top of the Ga terminating layer of the lattice, the most stable surface with adsorbed O involves θO = 1 ML with O above the Ga adlayer in 3-fold-coordinated sites. This surface satisfies the ECR if two Ga-Ga bonds are broken per (4x4) SUC. The structure is thought to constitute an inchoate form of β-Ga2O3, the most stable phase of Ga2O3, which would account for its stability. Applying the ECR formalism here, 16 Ga adatoms per (4x4) cell contribute a total of 48 |e|, 20 of which combine with the 12 |e| in Ga DBs in the lattice terminating layer to give 16 Ga-Ga back-bonds with 28 |e| remaining. Breaking two of the Ga-Ga back-bonds then gives a total of 32 |e| in DBs, which is exactly sufficient to adsorb 1 ML of O atoms. For the (0001̄ ) surface, which is thought to be covered with a full ML of Ga adatoms in T1 sites on top of the N termination layer (Section 4.6.2), a so-called "75%O+25%N" structure is lowest in energy under moderately or strongly O-deficient conditions. Here θO = 0.75 ML and θN = 0.25 ML adsorb on the Ga adlayer, which satisfies the ECR. Of the 48 |e| in the (4x4) Ga adlayer, 12 |e| combine with the 20 |e| in DBs in the N terminating layer to form 16 Ga-N back-bonds. The remaining 36 |e| are exactly sufficient to adsorb 12 O atoms (using 24 |e|) and to form 3 Ga-N bonds to each of 4 N adatoms (using 12 |e|). The DB on each N is doubly occupied, and each O occupies at T4 or H3 sites and uses one NBLP orbital to

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give a total of 3 O-Ga back-bonds. The source of the N adatoms was not described in detail but was suggested to be diffusion from the bulk. Under O-rich conditions a "100%O" phase is the most stable, in which 2 Ga-O bonds per (4x4) SUC in Ga-O-Ga bridges are broken and the Ga and O DBs left doubly occupied. This is needed to accommodate the 4 |e| that remain from the 36 |e| after 16 O atoms are adsorbed per (4x4) SUC. Under less O-rich conditions this structure is unstable since filling DBs on the electropositive Ga atoms produces energetic states in the band gap. Zywietz et al. [883] performed theoretical studies of atomic O adsorption on GaN (0001) and (0001̄ ) surfaces using the LDA with soft PPs. The 2DPS was described as having at least nine layers of GaN, which presumably means nine Ga-N bilayers, and a (2x2) SUC was used. It is noted here that θO = 3/8 ML cannot be treated using a (2x2) SUC since a minimum of 8 Ga per SUC is needed. The (0001) was modeled using the ideally-terminated surface, while a full Ga adlayer in T1 sites was used for the (0001̄ ). For a low coverage (θO = 0.25 ML), the most stable adsorption occurs in an FCC (H3) site with ΔEads ≈ -3.2 and -2.9 eV per O, relative to free O2, for the (0001) and (0001̄ ) respectively. On the (0001̄ ) however, O in H3 and T4 sites have nearly the same energy. With increasing coverage on the (0001), the T1 site becomes the favored O site for θO 4 0.5 ML, and adsorption rapidly becomes less exothermic and even endothermic above 0.8 ML. One notes that this can be understood by the fact that at θO = 3/8 ML the Ga DBs are empty. Further adsorption of O beyond this point then requires that a Ga DB near the CBM be occupied by an electron promoted from a filled surface state near the VBM. On the other hand, H3 is always slightly favored over T4 on the (0001̄ ), and ΔEads becomes more exothermic, reaching about -3.5 eV per O at 1 ML on this electronrich surface. The authors explain this different behavior in terms of the relaxation of O into the Ga adlayer on the (0001̄ ) surface, which acts to screen the anionic adsorbate. This process does not occur on the (0001), which leads to a repulsive interaction between O atoms. A DOS was obtained for either surface both clean and with a full ML of adsorbed O, which may provide insight regarding the effects of O2 exposure on BB that were mentioned in Section 4.7.3.1. The gap is found to be nearly free of states after O adsorption on the (0001) surface, but this is less the case for the (0001̄ ). The effect of Ga adatoms on O adsorption was also investigated, using (2x2) or (3x3) SUCs, in order to simulate processes that might occur during growth. Presumably "growth" refers to MBE, which is typically done under Ga-rich conditions. "Adatom" here refers to Ga adsorbed on the bare (0001) surface (1 per (2x2) cell) or on the Ga adlayer (1 per (3x3) cell) in the case of (0001̄ ). On (0001) the adatom greatly reduces ΔEads for θO, from -3.2 to -1.5 eV per O at θO = 0.25 ML; whereas, a much smaller reduction (by ∼0.2 eV per O) occurs on (0001̄ ). It is noted here that this can be explained by the fact that 1/4 ML of Ga on the (0001) yields a surface with no electrons available in DB orbitals; whereas, the (0001̄ )-(3x3) is still electron-rich. Hence, adsorption of O on the adatom-stabilized (0001) requires that an electron be promoted from a filled surface state near the VBM to the empty Ga DB surface state lying near the CBM, which reduces ΔEads by approximately the LDA value of Eg (∼1.7 eV) as discussed by Kempisty et al. [840]. It is thought that, under growth conditions, there is a kinetic barrier to Ga desorption and that, therefore, excess Ga will always be present, which will suppress the uptake of O on (0001) but not on (0001̄ ). It is not clear whether this study also included the possibility of Ga-O bond formation involving the Ga adatom itself. Lu et al. [884] performed DFT calculations, using the B3LYP functional and localized basis sets, for both O2 and atomic O interacting with GaN (0001) modeled using a Ga13N13H24 cluster as discussed above in connection with NH3 adsorption (Section 7.1, Ref. [833]). The (0001) surface was modeled as ideally-terminated

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Fig. 69. Phase diagram for surfaces formed by exposing the (0001)-"(1x1)" to O2 followed by annealing at 550 °C. The most stable structures are indicated as a function of the Ga and O chemical potentials. The regions labeled "2 ML oxygen" and "1.25 ML oxygen" correspond respectively to the trilayer þadatom and O-terminated structures shown in the insets. These two surfaces could coexist with Ga2O3 precipitates in the O-rich limit. The μO ¼ 0 limit corresponds to the energy per atom of molecular O2 and the μGa ¼ 0 limit to the energy per atom of bulk Ga. From Dong et al. [881] (reproduced with the permission of the American Vacuum Society).

while the (0001̄ ) was constructed with a Ga adatom above every surface N atom. The O2 was constrained to remain in the triplet state, which is the ground state of the free molecule. On (0001), the most favorable configuration for adsorbed O2 (ΔEads = -4.43 eV for the fully-relaxed structure) is lying flat and forming a bridge between two Ga atoms. The charge transferred to the O2 is 0.98 |e|, and the O-O distance is 1.49 Å vs. 1.21 Å in the free molecule, which suggests a superoxo O2−-like species with an O-O bond that is weakened relative to the free molecule. The barrier to dissociation is 0.7 eV; although, the transition-state spin was not indicated. For atomic O the most-favorable adsorption site on either surface is the FCC (H3) with ΔEads = -6.38 and -5.06 eV per O2 respectively, relative to free O2, for (0001) and (0001̄ ). These values (-3.19 and -2.53 eV per O) are in reasonable agreement with those of Zywietz et al. [883] as is the finding that O lies higher above the (0001) surface than the (0001̄ ), which suggests the possibility of incorporation into the latter. Dong et al. [881] reported a theoretical study of the (3√3x3√3) R30° ordered-oxide phase that forms on the (0001) surface as described earlier in this section. Few details were given regarding methods, but the model and approach appear to be the same as those described [371] in Section 4.6.1 in connection with the clean surface. Three stable phases, with θO = 0.25, 1.25 and 2.0 ML, are found in the phase diagram for various O/Ga ratios (Fig. 69). The θO = 0.25 ML structure is the adatom model discussed by Zywietz et al. [883]. For 1.25 ML, a single Ga-O bilayer forms above the Ga terminating layer of the lattice with 1 N per (2x2) SUC in the outermost Ga-N bilayer replaced by O. In the 2.0 ML structure, which is stable over a wide range of μGa and μO, an O-Ga-O trilayer forms on top of the Ga terminating layer of the lattice with Ga adatoms above the top O layer. This could be seen as the oxidation of the "(1x1)" metallic-Ga bilayer. The Ga adatoms (one per (2x2) SUC) are three-fold coordinated to O, and the Ga atoms within the

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trilayer are six-fold coordinated. The Ga adatoms have a doublyoccupied DB, which is unusual for surface cations in a compound semiconductor, but the associated surface state lies very close to the bulk VBM, and no surface or interface states appear in the band gap. Based on the trilayer+adatom model, the (3√3x3√3) R30° structure can be derived using seven Ga adatoms per (3√3x3√3)R30° SUC, each of which is three-fold coordinated to O. This leaves only 1/4 |e| per SUC in unpaired electron density, which arises from the slight excess of adatom Ga in this structure vs. the (2x2). In other words, the model (3√3x3√3)R30° SUC comprises 27/4 = 6.75 (2x2) SUCs but has 7 Ga adatoms. In an extension of the work reported in Ref. [884], Hu et al. [885] performed theoretical studies of O2 adsorption and dissociation on GaN (0001) and (0001̄ ) surfaces using the PW-PP approach with the PW-91 functional and with the inclusion of spin polarization. Presumably USPPs were employed since a low PW cut-off energy (30 Ry) was used. The bare Ga-terminated surface was used to model the (0001), while the (0001̄ ) was modeled with a full ML of Ga adatoms. The 2DPS comprised eight layers of GaN (which presumably means eight Ga-N bilayers) with a (2x2) SUC and the bottom surface terminated in H. It is noted that a full ML of real H (not PH) would not satisfy the ECR. The lowermost three layers (or Ga-N bilayers) were fixed during optimization. With one O2 per SUC on the (0001), a flat-lying configuration leading to dissociation is much more favorable than a vertical one, which results in molecular adsorption. The dissociative ΔEads per O2 is in the range of -680.2 to -683.5 kJ mol-1 (∼3.53 eV per O), depending on the position of the incident O2 with respect to the SUC, and the two O atoms occupy FCC (H3) sites following dissociation. There is only a small barrier to dissociation. The most favorable site for molecular adsorption, with ΔEads = -218.3 kJ mol-1, places the O2 vertically above an FCC site. For the (0001̄ ) surface, the flatlying (vertical) structures are again dissociative (molecular), but one exception is a vertical configuration with O2 directly above a Ga adatom, which is also dissociative. The energies for dissociative adsorption are close to those found for the (0001) surface. In either case θO = 0.5 ML, and other coverages were not investigated; although, previous work [882,883] indicates that ΔEads depends significantly on coverage. The DOS for (0001) with two O per SUC shows a partially-filled O orbital at EF, indicating a metallic surface; although, the corresponding results for (0001̄ ) are less clear. Sun et al. [886] performed theoretical studies of the effects of electronic excitation of GaN on the adsorption of O on the (0001) and (0001̄ ) surfaces. This was done in order to obtain a quantitative understanding of the experimentally-observed reduction in O incorporation during MBE growth in the presence of high-energy electron impact. The calculations used the PW-PP approach with USPPs and the PBE functional. For the electronic ground state, the 2DPS comprised six Ga-N bilayers with the bottom surface terminated in PHs, the lowermost three bilayers fixed and (2x2) or (√3x√3) SUCs. For treating electronic excitation, a 2DPS with eight bilayers and a (2x2√3) SUC was employed. A bare (0001) surface was used to model the Ga-polar surface during growth under moderately Ga-rich conditions. For more Ga-rich conditions a "(1x1)" model terminated in a laterally-contracted bilayer (θGa = 2.33 ML) of metallic Ga was used. The (0001̄ ) surface was taken to be terminated in a full ML of metallic Ga as is typical during MBE. In the absence of excitation, O adsorbs in H3 sites on the bare (0001) surface with ΔEads (relative to O2) decreasing from -3.69 eV per O at 0.25 ML to -2.2 eV at 1.0 ML. It is again noted that θO = 3/ 8 ML, which is the lowest-energy coverage on the ideal (0001) according to the ECR [882], cannot be modeled with a (2x2) SUC. For θO ≥ 0.5 ML a structural change occurs in which N-N bonds form due to the weakening of Ga-N bonds caused by formation of stronger Ga-O bonds, which is consistent with experimental

observation of trapped N2 in disordered GaN with a high concentration of bulk O. For (0001)-"(1x1)", ΔEads for O adsorption is much lower (about -2.50 eV at θO = 0.33 ML) than for the ideallyterminated (0001), which is consistent with the experimental observation of less O incorporation under Ga-rich conditions. On (0001̄ ) terminated with a Ga ML, ΔEads is similar for H3 and T4 sites and increases from -3.06 eV at 0.25 ML to -3.50 eV at 1.0 ML in agreement with Zywietz et al. [883]. The incorporation of O via substitution for N was investigated for several different configurations and O concentrations. For the bare (0001) this process is endothermic by 0.67 eV, relative to O as an adatom, when the substitution occurs in the outermost bilayer and becomes even more unfavorable for deeper bilayers. For (0001)-"(1x1)" the energy differences between different Ga-N bilayers with regard to incorporation become smaller, indicating less of a tendency toward surface segregation. On the (0001̄ ) terminated in a Ga adlayer, O can incorporate into the first Ga-N bilayer under the adlayer up to θO = 0.5 ML. At higher coverage, incorporation of some O into the second bilayer becomes favorable. Phase diagrams were constructed to show the energies of different modes of adsorption and O incorporation under growth conditions as a function of μGa in the O-rich limit. For the (0001), the most stable structures in order of increasing μGa are first 0.25 ML of adsorbed O, then 1 ML incorporated into the first Ga-N bilayer and finally 0.33 ML (one O per (√3x√3) SUC) in the first Ga-N bilayer underlying the metallic-Ga bilayer. For the (0001̄ ) the most stable structure at any μGa is a full ML of O adsorbed on the Ga adlayer, in agreement with Elsner et al. [882] and Zywietz et al. [883]. Compared to the ground state, electronic excitation of GaN at an energy density of 0.01 eV Å-2 is found to reduce the energy cost for incorporating O into the second Ga-N bilayer relative to the first bilayer; although, the process remains overall endothermic. Similar effects are seen on both the (0001) and (0001̄ ) surfaces. Thus the effect of excitation is to make it less unfavorable for adsorbed O to migrate into the bulk, which is in contrast to the apparent experimental observation. However, it is found that these results can be reconciled with experiment by noting that electronic excitation of GaN also reduces the diffusion barrier for O adatoms, which should make recombinative desorption of O2 easier. It is noted here that the observed effect of electron irradiation in reducing the concentration of bulk O might instead result from ESD of adsorbed O impurities. This is a well-known phenomenon [114,864], particularly for oxides and halides, that is induced by the excitation of core levels and/or bonding orbitals and would be consistent with previous results [877] suggesting that some O adatoms on GaN are very susceptible to ESD. Grabow et al. [141] reported theoretical results for O and O2 on GaN (0001) obtained using methods described above (Section 7.1) in connection with their NH3 work. The O2 calculation was spinpolarized. For θO = 0.25 ML, ΔEads = -4.37 eV (-7.17 eV) with respect to free O2 (a free O atom). The FCC (H3) site is the most stable and remains so up to θO = 1 ML with, however, a strong repulsive interaction leading to a decrease in ΔEads as in previous work. No value for an O2 dissociative adsorption barrier was given. As noted above, the repulsive interaction, which is inferred from the decrease in ΔEads with increasing θO, can be understood by the fact that at θO = 3/8 ML the Ga DBs near the CBM are empty. Further adsorption of O beyond this point requires that a Ga DB be occupied by an electron promoted from a filled surface state near the VBM [840]. Coan et al. [887] performed cluster-model calculations to study the interaction of O2 with the GaN (0001) surface. The clusters, based on the illustrations provided, had a composition of either (GaN)20 or (GaN)24 with surfaces centered on a Ga, an N or an H3 site and with DBs at the edges terminated with H. The calculations were spin polarized and used the B3PW91 hybrid functional

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together with LANL2DZ PPs for all atoms. It was found that the most energetically-favorable interaction leads to dissociation and the formation of two Ga-O-Ga bridges. In summary, most of the theoretical work for oxygen adsorption on the GaN (0001) and (0001̄ ) surfaces involves atomic O and not O2 in the 3Σg electronic ground state. Some studies of O adsorption also find evidence for the possible formation of O2− and/or O22− species in addition to chemisorbed O. Comparisons are most often made among the ideally-terminated (0001)(1x1), the (0001)-"(1x1)" with a metallic Ga bilayer and the (0001̄ )-(1x1) with a single Ga adlayer. Under conditions that are moderately O-rich, the most stable structure formed by the ideal (0001) involves 3/8 ML of O, which satisfies the ECR. However, obtaining this structure requires a (2x4) or larger SUC, and studies using a (2x2) cell find θO = 0.25 ML to be more stable than θO = 0.5 ML. Such studies also find that adsorption on the (0001)(1x1) becomes less exothermic with increasing θO but more exothermic on the (0001̄ )-(1x1), which reflects the relative ease of O adsorption on the electron-rich Ga adlayer. Under sufficiently O-rich conditions, a full ML of adsorbed O can form on any of the surfaces studied. Oxidizing the (0001)-"(1x1)" Ga bilayer produces a system with little or no density of states in the GaN band gap, which suggests this approach (rather than oxidizing the GaN substrate itself) as a viable means of forming a highquality gate oxide. Proceeding now to other surfaces, Jones et al. [193], Elsner et al. [888] and Gutiérrez et al. [889] performed theoretical studies of O on the non-polar (101̄0) surface using the DFTB approach. The most stable structure is one in which a surface VGa is surrounded by three O atoms replacing three N atoms, designated VGa-(ON)3. Each O has one more electron than the N it replaces, and the charge balance is maintained by removing the central Ga with its three valence electrons. The defect is electrically and chemically inert and is more stable at the surface than in the bulk by 2.2 eV. The formation of the defect is exothermic by 1.7 eV, relative to the defect-free surface, under Ga-rich growth conditions with O in equilibrium with Ga2O3. These defects have a strong tendency to accumulate at the surface during growth where they eventually block growth and lead to the formation of nano-pipes with (101̄0) walls covered with Ga oxide. Northrup [890] studied the adsorption of O on the GaN (101̄0) surface using the PW-PP method with a 2DPS having 10 atomic layers. The calculations employed (1x1) or (2x2) SUCs and Troullier-Martins soft PPs. Under O-rich conditions, the most stable structure for any permissible value of μGa is one where all N in the top two layers is replaced by O, which is labeled the "2(ON) surface". It is also found that formation of a layer of Ga adatoms on the 2(ON) is energetically unfavorable. For almost any allowable combination of μO and μGa, the stable phase is the bare surface or the 2(ON) or Ga2O3. A significant tendency toward surface segregation is found in that O is always more stable when located closer to the surface. Since O has one more valence electron than N, the extra electron density fills the DB on surface Ga sites (in violation of the ECR), which then changes from sp2 to p3 hybridization. This in turn leads to a band of surface states that splits off from the bulk VBM in parts of the BZ. Ye et al. [891] studied the incorporation of O in the GaN (101̄0) surface theoretically using PWs and USPPs with the PW-91 GGA functional and a 2DPS having eight Ga-N bilayers. The 2DPS is symmetric, and the outermost two bilayers on either face were allowed to relax. It was proposed initially that the most stable structure for adsorbed O should be the VGa-(ON)3 defect identified by Elsner et al. [888], in which a VGa is surrounded by 3 O replacing 3 N, and not the 2(ON) described in the preceding paragraph. Unlike the 2(ON), this does not produce a band of surface states derived from filled DBs on Ga surface sites. However, it is found

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that, except under very N-rich conditions, 2(ON) is in fact the most stable structure. This was explained by a lowering in total energy that occurs when the Ga DBs become filled in the 2(ON) structure. Zhu et al. [421] performed theoretical studies for O on the ̄ surface using methods described in Section 4.6.4 semi-polar (1011) in connection with their work on the clean surface. For low-μO conditions only the various clean-surface structures are stable. With increasing μO a (2x1) structure forms (Fig. 3d) with all the three-fold- and half the two-fold-coordinated N replaced with O and the other two-fold N atoms removed to form vacancies. Higher μO leads to a (1x1) structure with all N on the bare surface replaced by O, and at still higher μO Ga2O3 precipitates. Jackson and Walsh [892] have developed a first-principles thermodynamic model for the GaN-O2-N2 system, which was then applied to the oxidation of GaN. This involved the calculation of energies and enthalpies for oxidation and defect formation under practical conditions where "defect" refers to O substituting for N. It is concluded that both defect formation and complete oxidation to Ga2O3 are thermodynamically favorable and that, therefore, the resistance of GaN to oxidation must be kinetic in nature. It is also found that defect formation during high-temperature oxidation can be inhibited by a high N2:O2 ratio. Although this study lies outside the range of topics covered here, the results are nevertheless potentially useful in understanding GaN surface oxidation under the conditions of a typical UHV experiment. For example, it is shown that bulk O incorporation is exothermic under a wide range of conditions but that the free energy change depends on temperature, O2 pressure and defect concentration. Finally, Sivasubramani et al. [893] cleaned MOCVD GaN in HF solution and then exposed the sample at 400 °C to O3 (ozone) insitu in an atomic layer deposition reactor attached to a UHV surface-science chamber. This gave a 1.5-2 nm-thick Ga oxynitride layer with evidence for both Ga-O and N-O bonding. This work is in the nature of a thermal oxidation, which has been excluded from the present review, but is noted because of the unique use of O3. 7.9. Trimethylgallium (Ga(CH3)3), triethylgallium (Ga(C2H5)3), etc Lam and Vohs [899] studied the interaction of Ga(CH3)3 (TMG) with GaN (0001) using TPD, HREELS, AES and RBS. In theoretical work, An et al. [383] and Cardelino and Cardelino [835] studied TMG reacting with GaN, and An et al. [383] have also investigated Ga(C2H5)3 (TEG). Won et al. [833] investigated the interaction of monomethylgallium (GaCH3, MMG), a TMG decomposition product, with GaN. These studies, all done for the GaN (0001) surface, were motivated by a desire to understand the mechanism of MOCVD growth of GaN. León-Plata et al. [900] have reported theoretical results for the interaction of trimethylaluminum (TMA) and tetrakis(ethylmethylamino) hafnium (TEMAH), [(CH3)(C2H5) N]4Hf, with the OH-terminated (hydroxylated) surface. This work is relevant to the growth of Al2O3 and HfO2 on GaN using atomic layer deposition but is beyond the scope of the present review. In their experimental work, Lam and Vohs [899] used an n-type GaN (0001) MOCVD sample that was first cleaned in solvents and in H2O then mounted in UHV and processed using IBA (1 keV Ar+, annealing at 850-950 K). The resulting surface showed no C or O in AES and a diffuse (1x1) LEED pattern. Following TMG exposure at ∼110 K, only molecular TMG is seen in TPD up to 250 K. In the 250450 K range, desorption of MMG and/or dimethylgallium (Ga (CH3)2, DMG) is detected, accompanied by desorption of H2, CH3 and CH4, which indicates partial decomposition of some of the adsorbed TMG. Kinetic analysis of the TPD peaks associated with MMG or DMG leads to a desorption energy of 18-24 kcal mol-1, which is close to the bond energy (19 kcal mol-1) in the gas-phase (CH3)3Ga:NH3 Lewis acid-base adduct. It is inferred from this that

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Fig. 70. Fourier-deconvoluted HREELS data for (a) the clean GaN (0001) surface dosed with 10 L of TMG at 300 K and after heating to (b) 550, (c) 650, and (d) 800 K. From Lam and Vohs [899] (Copyright 1999, reproduced with permission from Elsevier).

the MMG and/or DMG fragments are bonded to surface N atoms. Presumably the accessibility of N atoms on the (0001) surface would require some form of defect or step edge. Following a series of TPD experiments, C and excess Ga are detected on the surface via AES and RBS, which is consistent with TMG decomposition. Dehydrogenation of adsorbed CH3, which on the basis of a kinetic analysis of the TPD is thought to be bonded to surface Ga, is responsible for C deposition. This process begins at ∼300 K, which suggests that the GaN surface is fairly active in dehydrogenation reactions. After TMG exposure at 110 K, HREELS data show evidence of electron depletion at the surface (i.e., an increase in upward BB) in the form of increased intensity of the GaN phonon loss peaks. The increased intensity results from the reduction in the screening of the phonon dynamic dipole by free electrons. The vibrational modes of molecular TMG are also observed, and annealing to 285 K to desorb molecular TMG leads to the appearance of Ga-H and N-H stretching modes together with peaks due to C-H stretching and CH3 deformation. Exposure at RT (Fig. 70) gives HREELS data similar to those obtained after annealing following low-temperature exposure but with higher resolution. These data show a Ga-C stretch, in addition to the features described above, together with a C-H stretching band that is partially resolved into the symmetric and asymmetric modes of CH3. Annealing in stages to 800 K leads to the gradual disappearance of the CH3 modes with, however, the continued presence of weak Ga-H and N-H features up to at least 950 K. The intensity of the hydride modes increases with successive exposure/anneal cycles, which, together with their resistance to desorption, suggests the possibility of subsurface diffusion of H. Based on these results a sequence of reactions leading to complete decomposition of adsorbed TMG was proposed. Won et al. [833] performed calculations for MMG interacting with the GaN (0001) surface modeled using a Ga13N13H24 cluster and following an approach discussed above (Section 7.1) in connection with the adsorption of NH3. Here MMG is found to adsorb intact as a bridge between surface Ga sites with ΔEads = -65.3 kcal

mol-1 vs. -33.0 kcal mol-1 for NH3 adsorbing in a T1 configuration. The ΔEa for decomposition to form Ga adsorbed at a T4 site and release a CH3 radical is quite high (64.5 kcal mol-1). A barrier of 27.5 kcal mol-1 is found for the diffusion of adsorbed Ga, which is somewhat higher than that typically found in 2DPS calculations (about 0.40 eV = 9.2 kcal mol-1, as discussed in Section 5.18). Cardelino and Cardelino [835] performed theoretical calculations for TMG reacting with GaN using the approach described in connection with NH3 (Section 7.1). It is seen that Ga(CH3)2, with an unpaired electron, adsorbs more readily than do the closed-shell species Ga(CH3)3 and Ga(CH3), the latter having a Ga NBLP orbital. It is also found that the largest contribution to ΔEads derives from the change in energy of the substrate rather than from bond formation or from stabilization of the adsorbate. Unlike adsorption, dissociation of adsorbed Ga(CH3)x is found to be endothermic, with an energy close to that of the corresponding gas-phase moiety. An extensive thermochemical analysis of processes occurring in the gas- and adsorbed phases was given. An et al. [383] performed a theoretical study for TMG and TEG on GaN (0001) using methods similar to those discussed (Section 7.1) in connection with their NH3 work. Because of the larger sizes of TMG and TEG vs. NH3, a larger SUC was used with 8 surface Ga sites. The work dealt with TMG and TEG reacting with a surface having six Ga-NH2 per SUC, which satisfies the ECR and models a likely intermediate stage in MOCVD growth using N2H4. Initially TMG adsorbs by forming a weakly-bound Lewis acid-base adduct (ΔEads = -5.51 kcal mol-1) with the NBLP orbital on an NH2. Successive reactions then occur in which Ga(CH3)x abstracts an H from an NH2 to eliminate CH4, and the remaining Ga(CH3)x-1 fragment forms a Ga-N bond. The highest energy barrier (42.54 kcal mol-1) occurs for the conversion of DMG to MMG. The final CH3 elimination requires a gas-phase H atom since the geometry of adsorbed MMG places the CH3 too far from an adjacent NH2. With TEG there is the possibility of, besides direct elimination of C2H6 via H abstraction, a β-hydride elimination, Ga-CH2CH3 → GaH + H2C=CH2. The results suggest that, while β-hydride elimination is not clearly favored over direct elimination, it may occur in parallel with the direct process, especially at the first stage of Ga-C bond breaking. 7.10. Water (H2O and OH) Zhang and Ptasinska [182] have performed XPS studies for GaN (0001) at H2O pressures up to 0.1 mbar (75 mTorr) and temperatures up to 773 K. Experimental results have also been reported by Lorenz et al. [456] and by Bermudez and Long [896] for H2O interacting with GaN (0001) near RT under UHV conditions. Sloboshanin et al. [146] and Starke et al. [148] observed the interaction of the (0001̄ ) surface with H2O that was present as an impurity in the UHV background. Here we will omit experimental work done in liquid H2O that focuses on electrochemistry or photocatalysis, which, although important, lies outside the scope of the present review. Theoretical results for H2O on the (0001), (0001̄ ) and (101̄0) surfaces are given in Refs. [94,141,382,887,901– 907], Ref. [902] and Refs. [907–913] respectively. In related work, [94,141,382,914] theoretical results have also been given for OH on GaN (0001). Some of the theoretical work is concerned mainly with processes involving liquid H2O but will be described briefly since insight is also provided into fundamental GaN surface reactions. Bermudez and Long [896] used mainly UPS to study the adsorption of H2O on an n-type MOCVD GaN (0001) surface prepared by IBA (1 keV nitrogen ions, annealing at 850-900 °C), after which the sample was exposed to H2O at ∼50 °C using a pinhole molecular-beam doser [617] in order to minimize the level of H2O in the UHV background. Synchrotron radiation provided excitation

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Fig. 71. (A) UPS data for (a) clean and (b) H2O-saturated surfaces and (c-e) the saturated surface after successive anneals in UHV at the indicated temperatures. The spectra have been displaced vertically for clarity. (B) UPS data for (a) clean, (b) H2O-saturated and (c) O2-saturated surfaces. Here "O2-sat." refers to saturation of the initial chemisorption phase. The vertical bars give schematic representations of UPS data for solid H2O and for Ga-OH on GaAs(110). The symmetry labels 1b2, etc. refer to molecular orbitals of H2O. Linear extrapolations of the VB edge to the baseline are shown in (b) and (c) to locate the VBM. The vertical line labeled ‘Ga 3d’ shows the VBM determined from the position of the Ga 3d. Relative intensities of different spectra are not quantitative, and the spectra have been displaced vertically for clarity. (C) Upper: HeII UPS for clean (red) and H2O-saturated (blue) surfaces. Both spectra are normalized to the height of the HeIIβ-excited Ga3d peak at 12.5 eV. The blue spectrum is shifted 0.5 eV to lower BE to compensate for the reduction in upward BB. Lower: Difference spectrum showing the reduction of two surfaces states S1 and S2 and the formation of two O-related states O1 and O2. In all spectra, binding energies are referenced to the Fermi level. (A) and (B) from Bermudez and Long [896] (Copyright 2000, reproduced with permission from Elsevier); (C) from Lorenz et al. [456] (Copyright Wiley-VCH Verlag GmbH & Co. KGaA. Reproduced with permission.).

energies of hν = 40.8 and 60.8 eV for surface-sensitive spectra of the VB and Ga 3d respectively. Dissociative adsorption occurs with a sticking probability of 4 0.45 and saturates at θO = 0.46 ML, as determined using AES. For comparison, the sticking probability for O2 is lower but the saturation coverage (θO ≈ 0.40 ML) is about

the same. An upward BB of 0.66 eV is seen for the clean surface, which decreases to 0.52 eV after H2O saturation. However, the measurement is complicated by the possibility of an increase in SPV after H2O adsorption (Section 4.7.3.2), which would also cause a decrease in upward BB. Surface states just above the VBM are

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removed by H2O adsorption, but a weak tail extending into the gap remains, which is ascribed to subsurface defects that are relatively unaffected by H2O. The VB UPS (Fig. 71A,B) was studied as a function of annealing up to 500 °C and also compared with data for O2 exposure and with results from the literature for solid H2O and for chemisorbed OH. It is concluded that after a saturation exposure near RT the surface consists of a mixture of Ga-O and Ga-OH bonds that is converted by a ∼200 °C anneal to essentially a purely oxide-like phase dominated by Ga-O bonding. The change in electron affinity (δχ) relative to the bare surface is +0.08±0.08 eV for a saturation exposure of H2O and +0.42±0.04 eV after annealing, vs. δχ ≈ +0.50 eV after an O2 exposure sufficient to saturate the initial chemisorption phase. Both the magnitude of δχ and the dependence on annealing are consistent with a thermally-induced conversion of Ga-OH to Ga-O. Lorenz et al. [456] performed UPS and XPS experiments for H2O on n-type GaN (0001) grown by MBE and transferred under UHV conditions into the analysis chamber. A (2x2) reconstruction is seen in RHEED and ascribed to the presence of N adatoms in H3 sites. The clean surface is highly sensitive to adsorption of background contaminants, which leads to the disappearance of surface-state features in UPS within about 2 hours. Exposures were performed by back-filling with H2O vapor with pressure measurement via a hot-filament ionization gauge, which can be a source of molecular excitation. In O 1s XPS, a weak peak (labeled "A") first appears at BE = 530.5 eV after a very low exposure (0.2 L). For higher exposures this is replaced by a stronger feature ("B") at 532.2 eV, which exhibits a weak shoulder ("C") on the high-BE side. An initial sticking coefficient of 0.3 and a total saturation coverage (for all states of O) of 0.9 ML is estimated from the O 1s intensity. The latter is larger than that obtained by Bermudez and Long [896] using electron-excited AES (0.46 ML). This is attributed to ESD of O by the AES primary beam, even though the primarybeam current density was low due to the use of pulse-count detection. A similar pronounced ESD effect was discussed in Section 7.8 in connection with O2 adsorption. The UPS data show a reduction of 0.5 eV in upward BB as a result of a saturation exposure (∼20 L). Since the upward BB on the clean surface is only 0.4 eV this indicates essentially a flat-band condition after saturation, which implies that empty or partiallyfilled surface states in the gap have been removed. The UPS data after saturation (Fig. 71C) also show the removal of two surface states (S1 and S2) that are seen on the clean surface. Note that the Ga 3d HeIIβ peak, at BE ≈ 12.8 eV, is a satellite feature (hν = 48.4 eV) due to the use of non-monochromatized HeII radiation. The state with the lower BE (S1) is very sensitive to H2O and is believed to be linked directly to the (2x2) reconstruction; whereas, S2 disappears more slowly with increasing exposure up to 20 L. It is suggested that the initial O 1s peak (A), like S1, may also be characteristic of the (2x2) surface, based on the similar sensitivity of both features to small H2O exposures. On the other hand, the main O 1s peak (B) is ascribed to chemisorbed O since the same feature is observed following O2 exposure. The UPS data also show two features (O1 and O2) associated with adsorbed O. These do not correlate well with either adsorbed H2O or OH but are similar to structure seen after O2 exposure. This, together with the absence of any detectable OH in HREELS, indicates an oxide- (rather than hydroxide-) like phase. Except for the difference is θO at saturation (which is a consequence of ESD incurred during electron-excited AES, as discussed in Section 7.8) and in the magnitude of the BB change, the results reported in the two experimental studies are in reasonable agreement in spite of the very different surface-preparation methods (i.e., IBA vs. in-situ growth). There is, however, a difference in interpretation as to the relative importance of Ga-OH vs. Ga-O bonding after a saturation exposure near RT.

Zhang and Ptasinska [182] performed XPS experiments on GaN (0001) in H2O vapor at pressures up to 0.1 mbar (75 mTorr). The samples were prepared by IBA (0.5 keV nitrogen ions at a 45° angle of incidence, 1173 K anneal in 3x10-7 mbar (2.3x10-7 Torr) N2), which resulted in a sharp (1x1) LEED pattern with no C or O detectable in XPS. It is noted here that annealing in N2 rather than UHV has, to our knowledge, been used by only one other group [181] who also obtained good LEED results. The Ga 2p3/2, N 1s and O 1s XPS data were obtained using Al Kα excitation (hν = 1486.7 eV) in 0.1 mbar of H2O from RT to 773 K. At RT, Ga-OH, Ga-O-Ga (oxide) and adsorbed H2O are seen. With increasing temperature more hydroxyl and oxide forms, and evidence for N-O bonding (i. e., an oxynitride) is found. Since the surface is Ga-polar, N-O bonds would arise either from insertion of O into Ga-N back-bonds or from adsorption at defects. Ga-H and N-H bonds are not directly detectable in XPS but are assumed to form when H2O dissociates to produce OH. The effects of H2O on surface electronic properties were monitored by observing the BEs of the VBM and the Ga 3d. As a result of the high Al Kα photon energy the VBM of the clean surface is unaffected by surface states; however, there appears to be some inconsistency between EF-VBM measured directly vs. by analysis of the Ga 3d BE. Sloboshanin et al. [146], Tautz et al. [147] and Starke et al. [148] reported HREELS data for H2O on faceted GaN (0001̄ ) surfaces prepared as described in Section 7.3 in connection with their results for H adsorption. These studies focused mainly on the structure and properties of faceted surfaces; however, HREELS data recorded as part of this work showed facile reaction of the clean surface with H2O in the UHV background. This is evidenced by the appearance of N-H and O-H stretching modes at 403 and 453 meV respectively that gain in intensity as the sample stands in UHV at RT. Uhlrich et al. [94] and Grabow et al. [141] reported theoretical studies of the adsorption of H2O on GaN (0001) using methods described in Section 7.1 in connection with their work on NH3. Molecular adsorption at a T1 site via a Ga-OH2 dative bond is exothermic with ΔEads = -1.53 eV. Dissociation into adsorbed H and OH is exothermic (ΔH0 = -1.41 eV, relative to adsorbed H2O) with an activation energy of ΔEa = +0.05 eV. The dissociation is thus essentially spontaneous, which is consistent with the experimentally-observed [456,896] high sticking coefficient for the dissociative adsorption of H2O on GaN (0001). The potential energy surface for complete dissociation to adsorbed O and H shows every step in the process to be exothermic with the result that O is strongly bound and difficult to remove, which is also consistent with experiment. Vibrational modes, including hindered rotations and translations, were also obtained. Mode assignments were not given but are obvious in some cases through comparison with those of free H2O. Hu et al. [901] performed theoretical calculations for H2O on GaN (0001) using a 2DPS with 3 Ga-N bilayers for which the bottom surface was passivated with H (presumably with θH = 0.75 ML to satisfy the ECR). The PW-91 functional was used with all-electron localized basis sets for all elements except Ga, for which an effective-core PP was employed. The calculations were spin-unrestricted in order to include possible paramagnetic transition states in the dissociation process. A (3x3) SUC was used, but which of the 3 bilayers were free to relax was not specified. Molecular adsorption occurs via dative-bond formation between an O NBLP orbital and a Ga DB orbital with the H2O lying approximately parallel to the surface. The two H atoms can be oriented either toward the same nearest-neighbor N atom or each toward a different N, both of which are bonded to the active Ga site. The ΔEads values are -28.06 and -28.58 kcal mol-1 respectively. Dissociation is exothermic, with ΔEads = -27.72 kcal mol-1 relative to molecularlyadsorbed H2O, and forms Ga-H and Ga-OH with the O-H bond

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oriented toward an adjacent N atom. The energetics of adsorption and dissociation were studied using NEB calculations. Molecular adsorption occurs with no barrier, but dissociation to form Ga-H and Ga-OH incurs a small barrier (7.13 kcal mol-1). These results are generally consistent with those of Uhlrich et al. [94] and Grabow et al. [141] noted above, who find ΔEads = -35.3 and -32.5 kcal mol-1 respectively for molecular adsorption and for dissociation of adsorbed H2O; although, the previous work finds a smaller dissociation barrier (∼1.2 kcal mol-1). Further dissociation to form a Ga-O-Ga bridge and two Ga-H sites is exothermic by 22.55 kcal mol-1, relative to the first dissociation step, but involves a barrier of 73.99 kcal mol-1. Relative to the second dissociation step, breaking the two Ga-H bonds and desorbing H2 is endothermic by 34.87 kcal mol-1 and presents a barrier of 85.18 kcal mol-1. These results suggest that the stable surface formed near RT should consist of adsorbed H and OH. P.-T. Chen et al. [902] reported theoretical studies of the adsorption and dissociation of H2O on GaN (0001). A 2DPS with 6 Ga-N bilayers with a (2x2) SUC and the bottom bilayer fixed in the bulk-lattice configuration. The PW-91 functional was used, and the PW-PP calculations were spin-unrestricted in order to treat transition states, which were identified using the NEB method. The lowest-energy configuration for adsorbed H2O has the O forming a bond to a Ga with one O-H nearly parallel to the surface and oriented toward a nearest-neighbor Ga and the other oriented away from the surface. The ΔEads of -1.68 eV (-38.74 kcal mol-1) is somewhat more exothermic than that determined by Hu et al. [901] (-28.58 kcal mol-1) who also found a different lowest-energy configuration for adsorbed H2O. Dissociation of H2O to form Ga-H and Ga-OH is exothermic with ΔEads = -1.22 eV relative to (H2O)ads, in good agreement with Hu et al., and a barrier of 0.10 eV. Relative to this state, the second dissociation step (to form adsorbed O and adsorbed H2) is endothermic by 0.94 eV with a barrier of 1.42 eV. This is consistent with the results of Hu at al. who found a reaction energy of (-22.55 + 34.87) kcal mol-1 = +0.53 eV for the same process. Subsequent desorption of adsorbed H2 is endothermic by only 0.01 eV. It was proposed, with the aid of DOS results, that photocatalytic dissociation of water occurs via an electron transfer process that facilitates the reaction Ga-H → ½H2, the Ga-H having been formed easily in the first dissociation step. Tan et al. [903,904] performed DFT studies of H2O interacting with GaN (0001) for the purpose of developing a mechanical force-field model for subsequent use in MD studies of the liquidH2O/GaN interface. The DFT work used the PAW method with the PW-91 functional and a 2DPS with 6 Ga-N bilayers. The bottom surface was terminated with PHs, and a (2x√3) orthorhombic SUC was used. A dipole correction (see Fig. 6) was also applied. However, the DFT results were not discussed in detail, and the forcefield model does not include the possibility of dissociative chemisorption of H2O. Coan et al. [887] performed cluster-model calculations to study the interaction of H2O with the GaN (0001) surface using methods described in Section 7.8 in connection with their results for O2. The most energetically-favorable interaction leads to half-dissociation with the formation of Ga-OH and Ga-H. Ye et al. [905] performed theoretical studies of the coverage dependence of H2O adsorption on the ideally-terminated GaN (0001) surface using the PAW approach with the PW-91 functional and a 2DPS with 6 Ga-N bilayers and the bottom surface terminated with PHs. A dipole correction was included, and NEB calculations were used to identify transition states. For a full ML coverage (i.e., one H2O per surface Ga) with a (1x1) structure, the most stable mode of molecular adsorption occurs via a Ga-OH2 dative bond with ΔEads = -0.08 eV per H2O. The plane of the H2O makes an angle of ∼44° with the surface such that the O-H bonds are oriented toward vacuum. The small ΔEads results from the

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Fig. 72. Upper: Top-down and side views of the (2x1) reconstructions of (a) molecular and (b) dissociative adsorption of H2O on GaN (0001). Here "(2x1)" refers to a reconstruction of the adlayer and not the GaN surface. Lower: (a) Adsorption energy of molecular (black squares), half-dissociative (red circles), and fully dissociative (blue triangles) H2O on GaN(0001) with respect to increasing coverage, beginning at 1/9 ML. The background color is utilized to distinguish the coverage ranges with different stable adsorption morphologies. Positive energies correspond to exothermic processes. The insets display some representative adsorption geometries and structures near the transition from one mode of adsorption to another. For the structures shown, 1/6 ML and 1/2 ML are the highest coverages possible for full- and half-dissociation respectively. From Ye et al. [905]. (Copyright 2013, American Chemical Society. Reprinted with permission.).

energy-raising effects of intermolecular repulsion and intramolecular distortion that counteract the energy-lowering H2OGaN bonding interaction. These competing effects are further analyzed in terms of electron transfer from GaN to H2O, which in turn is related to the tilt angle noted above. A much more stable 1 ML phase is formed by a (2x1) reconstruction of the molecular H2O layer (Fig. 72a) for which ΔEads = -0.902 eV per H2O. Here one H2O per SUC is adsorbed as for the (1x1), and the other is Hbonded to the adsorbed molecule. Dissociation of this structure to give a (2x1) phase with two Ga-OH and one weakly-adsorbed H2 per SUC (Fig. 72b) is exothermic with ΔEads = -0.967 eV per H2O relative to the isolated reagents. The barrier for this dissociation is 0.23 eV, and desorption of the H2 leaves a surface with a full ML of Ga-OH which remains in a (2x1) structure due to H-bonding between OHs. Larger SUCs, up to (2x3) with a 1-ML coverage, were considered but led to no additional adlayer structures. The processes described thus far all begin with a full ML of molecular H2O adsorbed on an otherwise ideally-terminated surface, which is an idealized situation. Adsorption at sub-ML coverages, down to 1/9 ML = 1 H2O per (3x3) SUC, were also studied, and molecular, fully-dissociative

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(Oads+2Hads) and half-dissociative ((OH)ads+Hads) phases were considered together with different adsorption sites. The results, summarized in Fig. 72, show that full dissociation to form threefold-coordinated O (in an H3 site) and two Ga-H bonds is the energetically-favored process. However, the barrier for full dissociation, which is determined by the breaking of the GaO-H bond, is high (ΔEa = 1.47 eV). For the fully-dissociated structure shown, which involves five Ga sites, 1/6 ML of H2O (one per (2x3) cell) is the maximum possible coverage. At intermediate coverages (1/6 ≤ θ ≤ 1/2 ML) half-dissociation is lower in energy than molecular adsorption, which is possible (i.e., exothermic) although not necessarily favored, at all coverages. For half-dissociation, which occupies two Ga sites, 1/2 ML of H2O is the maximum coverage, and the barrier is only 0.14 eV. The sequence of events proposed for adsorption on the bare surface at RT begins with half-dissociation to form Ga-H and GaOH. Full dissociation, although thermodynamically favored, is kinetically limited under these conditions. Above ∼0.5 ML, molecular adsorption becomes dominant, wherein H2O forms H-bonds to this reacted surface layer. The balance among the different modes of adsorption can be affected by temperature, the chemical state of the surface (e.g., the presence of defects) and by the rate of arrival of H2O from the ambient (i.e., the H2O pressure). Oue et al. [906] performed theoretical studies of H2O dissociation on stepped and kinked GaN (0001) surfaces using a PWPP approach with the PBE functional. Presumably USPPs were used since a low PW cut-off (25 Ry) was used for the wavefunctions. Transition states were located using the NEB technique. A stepped surface, namely the (0001) inclined off-axis toward the (101̄0), was approximated using the (221) surface of zinc-blende (cubic) GaN, i. e., a (111) surface with a high step density. The ideal zinc-blende (111) and wurtzite (0001) surfaces are structurally similar and are expected also to be energetically similar. The stepped (111) surface was represented using a 2DPS with 4 Ga-N bilayers and the bottom surface terminated with PHs, and a kinked surface was modeled by removing every other Ga from a step edge and saturating the resulting N DBs with H. This again is an approximation since a real kinked surface presumably has a lower density of missing Ga atoms. Since the main interest of this study was in etching reactions in aqueous media, the first issue addressed was the Ga-terminated ideal GaN (111) surface, and it is found that Ga-OH is more favorable than Ga-H at any coverage from 0.25 to 1.0 ML. One infers from this that any Ga-H would be rapidly hydrolyzed to Ga-OH + H2 in an H2O-rich environment. The ΔEads per OH (termed the "differential ΔEads" in this study) is nearly constant at about -2.0 eV up to θOH = 0.75 ML for a dissociative process in which H2 is desorbed. Above 0.75 ML ΔEads per OH decreases abruptly, which is expected on the basis of the ECR since 4 surface Ga atoms, each with 3/4 |e| in a DB, can be passivated with 3 OH radicals. For a surface with 0.75 ML of Ga-OH, molecular adsorption of 0.25- ML of H2O is very favorable (ΔEads = -1.93 eV) since a NBLP orbital on the O can form a dative bond with the empty Ga DB on the vacant Ga site. A surface with 0.75 ML of OH and 0.25 ML of H2O on the terraces defines the initial surface used in subsequent calculations. Two modes of dissociative adsorption were considered for stepped and kinked surfaces: (a) A "side-bond process" in which OH is bonded to Ga at a step edge (with or without a kink), and H is bonded to N at the step edge. (b) A "back-bond process" in which OH is bonded to Ga at a step edge (with or without a kink), and H is bonded to N at a terrace site. The reader is referred to Ref. [906] for "ball-and-stick" models showing the initial, transition and final states for each of these processes. Of the four reactions, all of which involve breaking a

Ga-N back-bond, only the back-bond reaction at a kink site is energetically favorable (ΔEads = -0.04 eV relative to the initial state); whereas, the others are endothermic by 0.34 eV or more. This reaction also has the lowest barrier (ΔEa = 0.81 eV) vs. 0.95 eV for the others. For each process, the redistribution of electron density that occurs during the reaction was analyzed by observing changes in the DOS. In particular, the broken Ga-N bond in the transition state is detected by the appearance of an N non-bonding orbital at the VBM. It appears from these results that H2O dissociation at step edges is substantially less exothermic than on the ideal (111) surface. Y.-W. Chen and J.-L. Kuo [382] reported theoretical results for the adsorption of the first ML of H2O on GaN (0001) using a 2DPS with 6 Ga-N bilayers and the bottom surface terminated with PHs. The bottom 4 bilayers were fixed in the ideal bulk-lattice configuration during geometry optimization, and the SUC was an orthorhombic cell constructed from 16 hexagonal (1x1) SUCs. The PAW approach was used with the PW-91 functional, and a dipole correction was included. Charge distributions were analyzed using the Bader Atoms in Molecules (AIM) theory and also the ECR. (An informative pedagogical discussion of Bader's AIM theory has been given by Popelier [915].) The calculations were spin-unrestricted, and the results also show how PH termination makes the charge distribution in the interior of the 2DPS appear more bulk-like. In this study a (2x1) reconstruction of the bare surface is found to be more stable by 0.06 eV per Ga than the unreconstructed (1x1). This reconstruction, which takes the form of a small alternating up-down displacement of surface Ga atoms in the surfacenormal direction, was discussed in Section 4.6.1. As in previous studies, 3 modes of adsorption are considered; namely, molecular, half-dissociative ((OH)ads + Hads) and fully-dissociative (Oads + (H2)ads). It should be noted that in some studies full dissociation is discussed in terms of 2Hads rather than (H2)ads. Hence, differences in the reported values for ΔEads will reflect the difference between the H-H bond energy for (H2)ads vs. ΔEads for two Ga-H sites. For 1,

Fig. 73. Electron transfer (based on Bader AIM theory) and energy results for 8 H2O molecules and each GaN double layer, with the first being the surface layer. For the horizontal axis, "8w_n" means "8 H2O adsorbed per (4x4) SUC, of which n dissociate to Ga-OH and Ga-H". Here n ¼ 6 corresponds to 0.375 ML of dissociated H2O. The black line ( ) gives the total energy (not per H2O) with more-positive values indicating a more-stable surface. The lines labeled "1st", "2nd", etc. indicate the electron charge donated to the adsorbate from each bilayer, and the blue line shows the total charge received by the adsorbate. Results for the 3rd, 4th and 5th bilayers have been omitted. The horizontal line at -5.8 |e| represents the total excess charge on the bare (2x1) surface, most of which is localized in the surface layer. From Chen and Kuo, Ref. [382]. (Copyright 2013, American Chemical Society. Reprinted with permission.).

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2 or 4 H2O per SUC, ΔEads for half-dissociation varies from -1.35 to -1.43 eV per H2O relative to the corresponding molecularly-adsorbed state; whereas, ΔEads for full dissociation lies in the range of -0.19 to -0.45 eV per H2O. The main focus of this study was on the first wetting layer, which is a mixture of molecular and half-dissociated H2O. Many different coverages, adsorption models and fractions of total H2O coverage undergoing dissociation were considered. The end result is that the most stable wetting layer, in terms of ΔEads per H2O, has 0.375 ML (6 H2O per SUC) of half-dissociated H2O with any coverage beyond that in molecular form. Electron transfer between GaN and the wetting layer was also analyzed, and it is found that half-dissociation is limited by the availability of transferable electrons near the surface. Most of this electron density is localized in DBs on the first bilayer and is entirely consumed in the half-dissociation of 0.375 ML of H2O, as shown in Fig. 73. This is consistent with the ECR since H• and [OH]• each contribute a single electron. With 3/4 |e| in each Ga DB, dissociation of 0.375 ML of H2O leaves a passivated surface with no partially-filled DBs. These effects are also seen in the DOS, which shows a reduction in the density of DB states in the gap as the coverage of dissociated H2O increases to 0.375 ML. For dissociation at a higher coverage, the surface becomes p-type (i.e., EF near the VBM) due to the transfer of more electron density than is available in the Ga DBs alone. Ga-H is present on the surface as a dissociation product and can desorb H2 to make more sites available for OH (or perhaps react with H2O to form Ga-OH and release H2). This process was considered in an effort to relate the computed OH coverage to the θO observed experimentally by Lorenz et al. [456]. The most stable such surface has all Ga-H replaced by Ga-OH to give a total OH coverage of 0.75 ML. This agrees exactly with the coverage of the dominant species observed by Lorenz et al. [456], which was discussed earlier in this subsection, but overlooks the fact that the experimental results were interpreted in terms of predominantly oxide with little or no OH. In fact, any OH coverage between 3/8 and 3/4 ML can be considered to be consistent with the theoretical results if only a fraction of the Ga-H is replaced with Ga-OH. Y.-W. Chen et al. [907] performed theoretical studies of the mobility of H2O and its dissociation products on the GaN (0001) surface using methods similar to those described in previous work [382]. For an isolated intact H2O the barrier for hopping between Ga sites is 0.40 eV for a (4x4) SUC; however, the presence of coadsorbed OH (from dissociation of other H2O molecules) is expected to stabilize adsorption through H-bonding and therefore to raise the barrier. The barrier for hopping of the H dissociation product between Ga sites varies from 0.8 to 1.0 eV, depending on the nature of the co-adsorbed OH, vs. a barrier of 0.2 to 0.35 eV for the recombination of H and OH to reform adsorbed H2O. The most stable site for an O atom is in an H3 site where it bonds to 3 surface Ga atoms. The hopping barrier for an isolated O atom between such sites is about 1 eV, and the transition state has the O atom in a T4 site. For higher θO, ΔEa for hopping varies between 0.59 and 1.81 eV. The highest ΔEa corresponds to θO = 3/8 ML, which gives the most stable surface structure according to the ECR. Sixteen surface Ga atoms per (4x4) cell provide a total unpaired electron density of 12 |e| in DBs, which fills the valence shells of 6 O atoms to give θO = 6/16 = 3/8 ML. For those structures considered, the lowest ΔEa is found for θO = 7/16 ML (i.e., slightly in excess of 3/8 ML) for which the additional O is relatively weakly bound. The barrier is also affected by a tendency of adsorbed O atoms to avoid each other, which leads to a high barrier for θO = 5/ 16 ML. Adsorbed OH is found to be mobile, with hopping barriers in the range of 0.11 to 0.31 eV depending on the coverage of coadsorbed H and OH. These are much lower than the barrier for OH dissociation (0.73 to 0.93 eV); hence, OH can easily diffuse between empty Ga sites or else hop to a Ga-H and then recombine to

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form H2O. To summarize the theoretical work for H2O on GaN (0001), almost all the results have been obtained for the ideally-terminated surface. It is generally agreed that molecular adsorption via a GaOH2 dative bond is exothermic, although to a degree that decreases with increasing coverage, and that half-dissociation to form Ga-OH and Ga-H is exothermic relative to molecular adsorption and involves a low activation barrier. The Ga-H can desorb H2 to make more surface sites available for OH (or perhaps react with H2O to form more Ga-OH and release H2), and H2O adsorption occurs mainly by half-dissociation at low coverage and by H-bonding to Ga-OH at higher coverage. Beyond that, the issue of full dissociation to form adsorbed O appears to be somewhat controversial; although, it is generally agreed that the activation barrier is higher than for either molecular adsorption or half-dissociation. A factor contributing to the uncertainty is the question of the fate of the H released in the reaction (i.e., Hads, (H2)ads or free H2). To our knowledge, there are at present no experimental data available to resolve this issue. P.-T. Chen et al. [902] performed theoretical studies of the adsorption and dissociation of H2O on ideally-terminated GaN (0001̄ ) using methods described above in connection with their work for the (0001) surface. The lowest-energy configuration for molecular H2O has the two H atoms interacting with 2 N atoms and the O atom oriented away from the surface, giving ΔEads of -1.13 eV. Dissociation to form N-H and N-OH is exothermic (ΔEads = -2.09 eV relative to molecularly-adsorbed H2O) with a barrier of 0.34 eV. Relative to this state, the second dissociation step (to form O adsorbed via an N-O bond and adsorbed NH2, where an N-Ga bond has been broken) is endothermic by 1.54 eV with a barrier of 1.73 eV. Relative to this second state, decomposition of NH2 (to form adsorbed H2 and reform the broken N-Ga bond) is endothermic by 2.23 eV with a barrier of 2.56 eV. Subsequent desorption of adsorbed H2 is endothermic by only 0.04 eV. Due to the significantlyhigher overall barrier for H2 production and removal for (0001̄ ) vs. (0001), the former is thought not to be effective in the photocatalytic dissociation of H2O using terrestrial solar radiation. Shen et al. [908] performed theoretical studies of H2O interacting with the non-polar GaN (101̄0) surface using a symmetric 2DPS with 5 Ga-N bilayers and H2O on both faces. The middle bilayer was fixed during geometry optimization, and the calculations used the PW-PP method with the PBE functional and USPPs. Dissociation energy barriers were obtained using the NEB method, and several different modes of molecular and dissociative adsorption were considered. For a full ML restricted to a (1x1) SUC, the most favorable process is dissociation to form Ga-OH at all Ga sites and N-H at all N sites with the H in Ga-OH oriented toward the O of a nearest-neighbor Ga-OH, which gives ΔEads = -2.18 eV per H2O. If the (1x1) restriction is lifted for a full ML, it is then possible to form mixed phases with dissociated and molecular H2O, but none is lower in energy than the fully-dissociated (1x1) structure. For a (1x1) ML the most stable structure for molecular adsorption (ΔEads = -0.74 eV per H2O) has Ga-OH2 dative bond formation with the H2O plane lying roughly parallel to the surface. One O-H bond is oriented toward the coordinatively-unsaturated N nearest neighbor and the other toward the O atom on a neighboring H2O. If this is viewed as a precursor to dissociation, the barrier height is only 1.0 meV so that there is effectively no barrier to dissociation. At a lower H2O coverage (0.25 ML) the dissociated structure described above is still the most favorable, but ΔEads is reduced to -1.71 eV per H2O, which indicates that inter-adsorbate interaction stabilizes the high-coverage surface layer. The contributions of strain (both in the GaN surface and in the adsorbate layer) and intermolecular interaction to the total ΔEads were analyzed in detail and found to depend in a complex manner on adsorption coverage and geometry.

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In a subsequent study of the (101̄0) surface, Shen et al. [909] employed ab-initio MD. The calculations used a 2DPS with 5 Ga-N bilayers and a (4x3) SUC, for which there were 94 H2O molecules in the liquid layer contacting the SUC on either face of the bilayer. Thus both sides of the 2DPS were "wet" with liquid H2O having a density of 0.95-0.98 gm cm-3. The PBE functional was used together with localized basis sets for valence electrons and core electrons replaced by PPs with the Ga 3d electrons included in the valence states (in the PP) for surface (bulk) atoms. In equilibrium at a temperature of 340 K, 83% of the surface Ga and N form Ga-OH and N-H via H2O dissociation while the remaining Ga sites form Ga-OH2 dative bonds to molecular H2O. The rapid formation of the dissociated-H2O layer is consistent with the small dissociation barrier reported previously [908]. It is also found that 50% of the Ga-OH sites form H-bonds to molecular H2O in the liquid rather than to each other, which constitutes a disruption of the H-bonded network formed by the Ga-OH layer in the absence of liquid H2O. In order to study the reaction mechanism further, the authors employed cluster models and the B3LYP hybrid functional. "Small" ([GaN]15) and "large" ([GaN]21) clusters were used for which DBs were passivated with H atoms. The models included 4 H2O molecules to account for explicit solvent effects such as H-bonding, while longer-range effects were represented by a polarizable continuum. Additional details regarding the construction and testing of the models, the choice of basis sets and the computation of thermochemical quantities are given in the original reference. The "water-splitting" reaction occurring in a liquid-H2O ambient was represented as a cyclic 4-step process: (1) (2) (3) (4)

[+]-OH− → [+]-O•− + H+ + e− [+]-O•− + H2O → [+]-OOH− + H+ + e− [+]-OOH− → [+]-O2•− + H+ + e− [+]-O2•− + H2O → [+]-OH− + O2 + H+ + e−

where [+] represents the cluster cation that, together with the active OH− site, forms the initial cluster, and O•− and O2•− are spindoublet radical anions. The Gibbs free energy changes for the reactions were computed and analyzed in detail, with the result that the first step is rate limiting. Liu et al. [910] reported theoretical results for H2O on the GaN (101̄0) surface. This was described as the "wurtzite (100)" surface, which is an alternative term (Section 2) for the (101̄0). The calculation used the PW-PP method with the LDA and a 2DPS having 4 atomic layers, but the size of the SUC was not explicitly stated. The NEB approach was applied to identify reaction transition states. The most stable mode of molecular adsorption (ΔEads = -0.95 eV per H2O) is via Ga-OH2 dative-bond formation with the plane of the molecule perpendicular to the surface and parallel to the Ga-N surface dimer bond. Adsorption of a second H2O at a first-, second- or third-nearest-neighbor surface Ga site gives respectively ΔEads = -0.75, -0.85 and -0.76 eV per H2O. (In the original reference, ΔEads is given as a positive quantity for an exothermic process.) One infers from this oscillatory behavior that a distance-dependent balance exists between attractive and repulsive interactions (including strain in the surface layer). In the first dissociation step, Ga-OH is formed at the original H2O adsorption site, and the most favorable location for H is at a site between the Ga-OH and a next-nearest-neighbor N, which is the N atom belonging to the neighboring Ga-N surface dimer in the [0001̄ ] direction. The nature of the bonding for H at this site was not described. This process is found to be endothermic by about 2.4 eV, relative to the molecularly-adsorbed state, with a barrier of 2.74 eV. These results for half-dissociation are very different from those obtained by other groups for the (101̄0) surface, possibly due to the use of pure LDA and/or to the fact that the 2DPS was only two bilayers thick.

Y.-W. Chen et al. [907] performed theoretical studies of the mobility of H2O dissociation products on the GaN (101̄0) surface (abbreviated as the (100)) using methods described above in connection with their work on the (0001). In general, the results for the two surfaces are quite different. Barriers were computed for the hopping of H, OH and O in the [001] and [010] directions, which are parallel and perpendicular to the Ga-N surface dimer bond respectively (Fig. 2). The hopping of molecular H2O was not considered, due to the rapid dissociation to form Ga-OH and N-H. The barrier for H hopping between N sites is high (42 eV) in either direction; however, the barrier to the formation and desorption of H2 is even higher (about 5 eV). The mediation of H diffusion via an H-bonded network, formed by adsorbed molecular H2O H-bonded to Ga-OH, was investigated and found not to be effective. These results indicate that H adsorbed via H2O dissociation as N-H on the (101̄0) surface is both stable and immobile. The barrier to O-atom hopping is somewhat lower (ΔEa = 1.54 and 1.68 eV respectively in the [001] and [010] directions), but the barrier to recombinative desorption as O2 is even lower (1.1 eV). The barrier to OH hopping between Ga atoms is highly asymmetric, being ∼2 eV in the [001] direction but only 0.31 eV in the [010]. The latter is less than the computed H-bond energy between Ga-OH and H2O, and the low barrier height suggests that OH will diffuse easily along [010]. On the other hand, dissociation of OH into O and H has a high barrier (3.36 eV) on the (101̄0). Three ab-initio MD studies have been reported that deal primarily with the liquid-H2O layers in contact with the GaN (101̄0) surface. This subject lies beyond the range of topics covered here; hence, these works, although important, will be mentioned only in passing. Wang et al. [911] investigated this system using methods described above in connection with an earlier study [909]. The dynamics of diffusion and of H+ transfer were determined, which led to the conclusion that the surface catalyzes H2O dissociation, retaining OH− while releasing H+, and is thus very acidic (pKa = 3.0 ±0.1). It is also found that the OH− HOMO lies about 0.5 eV above the bulk VBM and is therefore potentially effective as a hole trap in photocatalytic processes. Akimov et al. [912] also carried out a non-adiabatic ab-initio MD study, focusing mainly on photodissociation processes relevant to "water splitting". This work characterized the dynamics of hole relaxation, the hole transfer from GaN to H2O and the resulting proton-transfer events. Ertem et al. [913] performed combined ab-initio MD and cluster calculations to analyze photoelectrochemical water splitting. Kinetic and mechanistic factors involved in the proton-coupled electron transfer processes were investigated in detail, and the deprotonation of surface Ga-OH sites is determined to be the rate-limiting factor. Moving on now to the topic of OH (rather than H2O) adsorption, Uhlrich et al. [94] and Grabow et al. [141] performed a theoretical calculation for the adsorption of OH on GaN (0001) using methods described above in connection with their work on NH3. This was part of a larger study on the thermochemistry of the use of NH3 cleaning to remove O-containing surface species. Adsorption occurs at a T1 site with ΔEads = -4.78 eV relative to the bare surface and the free [OH]• radical. The calculation was apparently not spin polarized, and the OH geometry was described as "tilted" but no details were given. ΔEads decreases significantly with increasing coverage above 0.5 ML. It is noted here that this implies a strong repulsive interaction since one expects the most exothermic ΔEads to occur at θOH = 0.75 ML, which satisfies the ECR. Vibrational modes, including hindered rotations and translations, were also obtained. For dissociation of adsorbed OH into adsorbed O and H, ΔH0 = -1.20 eV and ΔEa = +1.06 eV were found [94]. Yokoyama et al. [914] reported theoretical results for OH on GaN (0001) with a (1x1) SUC as part of a study of the catalytic effects of Pd and S co-adsorbed on an OH-terminated surface. The

V.M. Bermudez / Surface Science Reports ∎ (∎∎∎∎) ∎∎∎–∎∎∎ Table 6 Summary listing of experimental and theoretical studies addressing the adsorption of organic species on GaN surfaces, some of which are discussed in Section 8. References dealing with AlxGa1-xN, with III-N materials other than GaN or with non-reactive organic/GaN interfaces are not included here. Molecular Species

References

Alcohols Alkanes Alkenes and Alkynes Amines Azophenylcarbazoles Biomolecules, Biomaterials, etc. Grignard Reagents Organometallics Peptides Porphyrin Phosphonic and Phosphoric Acids Silanes Thiols

[916] [917,918] [919–924] [925–928] [929] [930–939] [940] [941–945] [946–953] [954] [955–963] [964–969] [970,971]

calculation used the LDA with the PAW method for a 2DPS with 10 atomic layers (i.e., 5 Ga-N bilayers) and the bottom surface terminated with PHs. A single OH (presumably a radical) adsorbs in an H3 site with ΔEads = -4.94 eV. Y.-W. Chen and J.-L. Kuo [382] studied OH adsorption using methods described above in connection with their work on H2O. The most stable surface has a coverage of 3/4 ML, in keeping with the ECR, with an average ΔEads of -1.52 eV per OH, defined as the reaction energy for [(Bare Surface) + mH2O → m(Ga-OH) + (m/2)H2]/m.

8. Adsorption of organic molecules There is an extensive literature on the adsorption of organic molecules on GaN and on surface functionalization, i.e., the covalent attachment of such species. This work has been motivated mainly by an interest in the synthesis and properties of hybrid organic/semiconductor electronic devices and in the use of functionalized semiconductors as active elements in chemically-specific sensors. The sample preparation in most cases involves wet-chemical methods. Therefore it is often not clear whether what is being functionalized is the GaN itself or the native-oxide layer (possibly OH-terminated) that results when the clean surface is exposed to ambient air or to H2O either in vapor or liquid form. For some applications, where the goal may be to modify and control the chemical properties of a surface that is exposed to a biological medium, this distinction may be irrelevant. However in other situations, where the electronic properties or the chemical stability of the interface itself may be important, the presence of an intervening contamination layer could be significant. The approach taken in the present section, bearing in mind the overall focus of this review, is to discuss in some detail only those studies for which the organic species (X) is demonstrably bonded directly to the GaN surface via, for example, a Ga-X or Ga-O-X bond. This category includes experimental work done entirely in UHV on atomically-clean surfaces or for which the absence of significant contamination (C and/or O) has been documented before and after functionalization using, e.g., XPS. It also of course includes any theoretical work. Other studies are simply listed in Table 6 as an aid to the interested reader. Excluded from the present discussion are references that deal with contact properties and interfaces between GaN and organic polymers, as used in organic electronics, since these generally do not involve functionalization as the term is used here. Also omitted are studies that focus on the development of GaN-based chemical and biochemical sensors rather than on the functionalization aspect itself or that deal with AlxGa1-xN or

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with III-N materials other than GaN. As indicated in Table 1, there are already reviews of work in these other areas. 8.1. Alcohols Calzolari et al. [916] have performed theoretical studies of the ̄ interaction of catechol (1,2-dihydroxybenzene) with the GaN (1010) surface using a PW-PP approach with the PBE functional, USPPs and a 2DPS with 6 Ga-N bilayers and a (2x3) SUC. The molecule can be described as a derivative of benzene in which two adjacent C-H groups are replaced by C-OH. Adsorption occurs via a process in which both O-H bonds dissociate to form 2 Ga-O bonds. This releases 2 H atoms to form 2 N-H bonds, which then form N-H–O hydrogen bonds to the O atoms. The reaction, which is qualitatively similar to that discussed for H2O in Section 7.10, gives a ΔEads of -3.07 eV. The DOS results show that some surface states in the band gap on the bare surface, which involve filled N and empty Ga DBs, are affected by the formation of chemisorption bonds and that other states, which are localized on the molecule, appear in the gap. 8.2. Alkanes Li et al. [917] have reported experimental and theoretical results for the aromatization of light alkanes catalyzed by GaN. Here GaN powder is found to catalyze the conversion of CH4, H3C-(CH2)n-CH3 (n = 1, 2, 4) and C6H12 (cyclohexane) to benzene (C6H6). The material was cleaned by heating under moderate vacuum for 2 hrs at 550 °C after which it was cooled under vacuum to 450 °C and the reagent admitted. The powders where characterized using HRTEM, XRD and XPS, and a Brunauer-Emmett-Teller surface area of 6.73 m2 gm-1 was measured using N2 adsorption at 77.4 K. Reaction products were analyzed using gas chromatography. The exposed ̄ powder surfaces consist mainly of the (1010), (0001) and (0001̄ ) planes, and the Ga 3d XPS reveals little or no evidence of either free Ga or GaOx. The Ga 3d peak does, however, show some indication of unresolved structure on the low-BE side, which was not discussed, and a finite O 1s intensity is detected in XPS. Repeated catalytic cycles appear to have little or no effect on the crystal structure, the surface composition or the catalytic activity. The effect is believed to involve the (101̄0) plane on which the C-H bond can be weakened by one or both of two mechanisms. Either C interacts with a surface Ga and H with a surface N or the reverse (i.e., Ga–H and N–C). The former is found to be energetically more favorable in ab-initio calculations using the B3LYP functional and a free-standing cluster (not described in detail) with peripheral DBs terminated with H. Experimentally, it was found that oxidizing the surface by heating in air led to a reduction in catalytic activity, which is consistent with the bare surface being the active component. Work by Lam and Vohs [899] (Section 7.9) also indicates that GaN surfaces may be active in dehydrogenation reactions. This work has also been extended [918] to the photo-induced conversion of CH4 to C6H6 on the surface of GaN nanowires. 8.3. Alkenes and alkynes Kim et al. [919] performed experimental studies of the reaction of alkenes with the GaN (0001) surface using XPS and TEM, and theoretical results have been reported by Hu et al. [920,921]. In both theory and experiment, the reacting surface is terminated with essentially a full ML of Ga-H bonds. Kim et al. [919] prepared H-terminated GaN (0001) surfaces by wet-chemical cleaning followed by exposure to an H plasma, after which a small C 1s peak was detectable in XPS. A weak GaOx satellite was possibly also present in the Ga 3d data, as evidenced by a small degree of asymmetry to higher BE in the raw data. The

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Fig. 74. Reaction scheme for the attachment of DNA to GaN surfaces. From Kim et al., Ref. [919]. (Copyright 2006, American Chemical Society. Reprinted with permission.).

reagent (Fig. 74) was a 10-carbon chain terminated at one end by a -C(H)=CH2 group and at the other by -NH2, which was initially protected from unwanted side reactions by converting it to a trifluoroacetamide (TFA), F3C-C(=O)-N(H)-. The object was to attach the chain covalently to the GaN surface, via reaction of -C(H)=CH2 with H-Ga to form -CH2-CH2-Ga, and then to deprotect by converting the TFA back to an -NH2 group that could subsequently be used to attach DNA. This was accomplished by UV irradiation of the GaN sample at λ = 254 nm (hν = 4.89 eV) in direct contact with the liquid reagent followed by removal of unreacted material using organic solvents. Successful functionalization was demonstrated using XPS. Hu et al. [920] analyzed the mechanism and kinetics of the reaction of Ga-H with -C(H)=CH2 on the (0001) surface theoretically. The calculations employed a 2DPS with 3 Ga-N bilayers, a (3x3) or (4x4) SUC and the bottom surface terminated with a full ML of H atoms. This termination does not yield a passivated surface, according to the ECR, but the model was justified by comparison with results for PH termination. Localized basis sets were used for the valence orbitals with PPs for the core states, and the NEB approach was employed to locate transition states. The calculations were spin-unrestricted to account for the possibility of paramagnetic reaction intermediates. The reagents studied were 5-amino-1-pentene (H2N(CH2)3C(H)=CH2) and also smaller molecules of the form H2C=C(H)(X) where X = H, CH3, CF3 and NH2. The 5-amino-1-pentene, which is a smaller version of the molecule used by Kim et al. [919], weakly physisorbs (ΔEads = -5.027 kcal mol-1) with the C=C bond lying close to the surface. In the proposed model, the function of the UV irradiation in the

experimental work of Kim et al. [919] is to desorb H from a Ga-H site to leave a bare Ga site with a partial positive charge. The first transition state (with a barrier of ΔEa = 8.786 kcal mol-1) involves the breaking of the C=C π-bond, the rehybridization of the terminal carbons from sp2 to sp3 and the beginning of Ga-C bond formation between the end C and the bare Ga. This is followed by an intermediate state, at ΔEads = -15.483 kcal mol-1 relative to the isolated reagents, involving a paramagnetic Ga-CαH2-+CβH-R (R = -CH2CH2CH2NH2) species with an unpaired spin density of 0.107 μB on the Cβ atom and smaller densities (≤0.021 μB) on other atoms. The next step is an H-atom extraction, the lowest barrier for which (ΔEa = 7.933 kcal mol-1) results from reaction with an adjacent GaH site lying along a direction defined by the GaC-C bond. Rotation about the Ga-C bond to extract H from a different Ga-H site increases the barrier by 6.711 kcal mol-1. The final state, with a GaCH2-CH2-R linkage and a partial positive charge on the Ga from which the H was abstracted, lies at ΔEads = -31.224 kcal mol-1 relative to the isolated reagents. From an analysis of the atom-specific unpaired spin densities and fractional charges, in comparison to the same reaction on the Si (111) surface, it was shown that the GaN (0001) reaction can be described as an electrophilic addition, as opposed to a radical addition as in the case of Si(111). This was further demonstrated by varying the electrophilic nature of substituents on the Cβ atom using calculations for a series of molecules of the form H2C=C(H) (X) where X = H, CH3, CF3 and NH2. The stability of the Ga-CH2-+C (H)(X) intermediate increases with increasing electron-donor behavior for X. In other words, ΔEads for the intermediate increases in magnitude in the order CF3 o H o CH3 o NH2, which is consistent with an electrophilic mechanism but the opposite of what is expected for a radical intermediate. An analogous correlation is seen wherein the barrier to H-atom abstraction increases with the electron-donor character of X, which allows the partial positive charge on the Ga-CH2-+C(H)(X) intermediate to delocalize thus making it less effective in abstraction. In a companion study, Hu et al. [921] performed similar calculations for ethylene (H2C=CH2), acetylene (HC≡CH), styrene (PhC(H)=CH2) and phenylacetylene (Ph-C≡CH) where "Ph" represents a phenyl group, C6H5. The methods used were essentially the same as in Ref. [920]. Ethylene and styrene react in a manner similar to that described above for other alkenes; although, the exact values for reaction energies and barriers depend on the substituent. The Ga-CH2-+C(H)(X) intermediate is more stable, but the H-abstraction barrier higher, for X = Ph than for X = H, which can be understood in terms of a greater degree of charge delocalization in the former. In the case of HC≡CH there is a very small barrier (1.11 kcal mol-1) to formation of the intermediate, in which the π bond undergoes a donor-acceptor interaction with the DB on an H-free Ga site. Here the Ga is weakly bonded to both C atoms for which the interatomic distance is then slightly elongated (by ∼0.01 Å) relative to free C2H2. The barrier between this and the final state, in which H is abstracted from an adjacent Ga-H to form Ga-C(H) =CH2, is 14.29 kcal mol-1. This is higher than the barrier for desorption of C2H2 (11.23 kcal mol-1), which means that desorption is more likely than the formation of a stable adsorbate. For Ph-C≡CH, the barrier to formation of the intermediate (5.88 kcal mol-1) is higher than for C2H2, but it is more stable (ΔEads = -17.64 vs. -12.08 kcal mol-1). Furthermore, the structure of this intermediate (Ga-C (H)=+C-Ph, with a C=C distance between that of free C2H4 and C2H2) resembles that of the alkene intermediates and is different from that of the C2H2 intermediate. The barrier to H abstraction, which forms Ga-C(H)=C(H)(Ph), is only 3.83 kcal mol-1. 8.4. Amines Bermudez performed experimental studies of the adsorption of

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Fig. 75. Left: ELS (Ep ¼ 90 eV, ip E 0.3 μA cm-2) obtained in pulse-counting mode for (a) clean GaN (0001) and (b) after a dose of 3.8x1015 aniline cm-2 at RT. Right: (a) UPS difference spectrum (after aniline minus before) obtained with HeII excitation; (c),(d) computed spectra for different model structures. The spectra have been aligned at the deep-valence peak at BE ¼ 18 eV. The strong emission at low BE in (a) is due to HeI excitation (hν ¼ 21.2 eV), which is much more intense than the HeII, and the weak emission above the VBM is due to higher-energy satellites in the HeII source emission. In (a), the Ga 3d effectively cancels in the difference spectrum. From Bermudez, Ref. [925] (Copyright 2002, reproduced with permission from Elsevier). The molecular structures are those of, from left to right, aniline, 3-pyrroline, pyridine and 4-chloroaniline.

aniline [925], 3-pyrroline [926] and 4-chloro- and 4-iodoaniline [927] on GaN (0001). The molecular structures are shown schematically in Fig. 75. Preliminary data for the adsorption of pyridine were also reported in Ref. [926]. The techniques employed were ELS, UPS, XPS and XAES supported by quantum-chemical modeling. The sample was prepared by IBA (1 keV nitrogen ions, ∼900 °C anneal), after which the level of impurity O was at or below the AES detection limit (∼0.03 ML) and LEED showed a (1x1) pattern with little or no faceting. Exposure to the reagents was done using a pinhole molecular-beam doser [617]. Aniline, 3-pyrroline and pyridine are liquids, while the 4-haloanilines are solids with sufficiently high sublimation pressures that dosing is feasible. The interest was in the facile functionalization of the (0001) surface with N-containing compounds and also in the use of such reagents to lower the effective electron affinity of GaN. Fig. 75 shows surface-sensitive data ELS and HeII UPS data for aniline, a representative primary amine. Adsorption, which saturates at a dose of ∼6x1015 aniline per cm2, removes the surfacestate loss at about 3.4 eV and introduces a π→π* transition at 6.5 eV due to the phenyl ring. The sticking coefficient is estimated to be ∼0.05 and the saturation coverage ∼0.28 ML, the latter being limited by the large size of the phenyl ring. In contrast, a larger benzene dose (∼3.5x1016 cm-2) has little or no effect on the surface state and yields no significant π→π* intensity, which indicates that aniline adsorption involves the NH2 group and not the phenyl ring. Analysis of the C 1s XPS further indicates that the ring undergoes

little or no chemical interaction with the surface. The UPS ΔN(E) spectrum was compared with data obtained elsewhere for an aniline multi-layer condensed at low temperature. The two spectra correspond closely except that the free-molecule HOMO is missing for the adsorbate as is a deeper-lying feature that appears prominently at BE ≈ 12 eV below EF for condensed aniline. The HOMO corresponds to the NBLP orbital on N, while the deeper-lying feature is associated with an NH2 bonding orbital. Quantum-chemical calculations were performed for a very simple model, using the B3LYP functional, in which the N atom was bonded to different combinations of H and GaH3 groups in order to approximate the local chemical interaction at a (0001) surface site. The best agreement with the UPS ΔN(E) data occurs for C6H5-NH bridging two Ga atoms, as shown by (d) in the righthand panel of Fig. 75, which accounts for the absence of the two prominent peaks in the condensed-aniline spectrum noted above. This structure is analogous to the NH2 bridge proposed for the adsorption of NH3. In order to maintain a closed-shell system, the C6H5-N(H)(GaH3)2 molecule was modeled as an anion with an overall net charge of -1. On the real surface, the added electron density would come from other partially-filled Ga DBs. Experimentally, the electron-donor character of aniline leads to a surface dipole layer of the form Gaδ−-Nδ+, which reduces the effective electron affinity by δχ = -0.55±0.13 eV. This leads to an estimate of μ⊥ = 0.72 D for the surface-normal dipole moment, after correction for screening due to adsorbate polarizability,

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which is somewhat less than the dipole moment of the free molecule (∼1.07 D). The reduction in χ is potentially useful in making Ohmic contacts to p-type GaN, which is problematic due the high ionization potential (IP = Eg+χ ≈ 6.7 eV) for bare GaN (0001). Although not done as part of this study, such contacts can be fabricated without significant damage to the organic layer using methods reported elsewhere [972]. A subsequent study [926] focused on 3-pyrroline as a representative secondary amine. The ELS data are similar to those for aniline, with the π→π* transition appearing at 7.2 eV and a sticking coefficient and saturation coverage of about 0.05 and 0.34 ML respectively, which are close to the corresponding aniline values. The presence of the π→π* transition shows that the C=C bond remains intact. A reduction in χ by 0.92 eV is found, which is even larger than that for aniline, and from this μ⊥ = 0.92 D is estimated for the Gaδ−-Nδ+ surface-normal dipole moment after correction for the adsorbate polarizability. Comparison of the UPS ΔN(E) spectrum with results computed for different models was also performed, as described above for aniline. Although the comparison is less clear in this case, the best agreement appears to result for a structure in which the N atom loses H and then adsorbs as a bridge between two Ga sites. Some data were also obtained for pyridine as part of this study. The π→π* transition appears at 7.0 eV in ELS, vs. 7.2 eV for the free molecule, which again indicates that the ring remains intact. The UPS difference spectrum in this case shows only poorly-resolved structure and appears as a very broadened version of the free-molecule data. Somewhat paradoxically, this suggests that adsorption has a large effect on the electronic structure of the molecule, even though the π bonding appears to remain intact. In general, the UPS data appear to be more complex when the N atom is part of the ring (3-pyrroline and pyridine) than when the ring is present only as a ligand (aniline). The photochemistry of 4-chloro- and 4-iodoaniline adsorbed on GaN (0001) was investigated in Ref. [927]. The goal was to adsorb a 4-haloaniline via the NH2 group and then to determine whether an organic layer could be synthesized "from the bottom up" by photochemically cleaving the carbon-halogen bond to form a radical species for subsequent reaction with a second reagent. Two types of photochemical excitation sources were used. One was the near-UV emission from a Hg arc, which passed through DI H2O to remove IR radiation. The other was a so-called "Tanaka discharge" in H2, which emits mainly in the 7.5-12.4 eV range. In either case the radiation entered the chamber through a CaF2 window. The photochemistry of 4-chloro- (and also 4-fluoro) aniline is known to involve mainly heterolytic cleaving of the carbon-halogen bond to form a carbene cation and a halogen anion, which requires a polar solvent and is not expected to occur easily in UHV. Thus data for this species serve as "baseline" measurements for an inert system; whereas, homolytic cleavage to form radical species is considered more likely for 4-iodo- (and perhaps also 4-bromo-) aniline. Consistent with this, UV irradiation has little or no effect on adsorbed 4-chloroaniline. On the other hand, similar treatment of the iodo species causes a small loss in the iodine XAES intensity and a subtle change in the ELS structure near the π→π* feature at about 6 eV. By comparing computed UPS data for the free molecules with experimental results reported elsewhere, it was possible to identify peaks at low BE that are due to the Cl 3p or I 5p orbitals. Analysis of UV-irradiation effects in UPS again showed essentially no change for the chloro species and small but reproducible changes for the iodo compound. These take the form of a partial loss of C-I bonding and an concomitant appearance of Ga-I bonding. The proposed model involves a self-limited process in which I released by photochemical cleaving of the C-I bond is captured at vacant Ga sites, with termination of the process

occurring once all available Ga sites are filled with I. Only a fraction of the 4-iodoaniline can be photochemically modified in this manner before the process terminates. The photochemistry appears to involve direct excitation of the adsorbed molecule, rather than the transfer of excited carriers from the substrate, since no difference was seen for n- vs. p-type GaN. 8.5. Grignard reagents Grignard reactions on GaN (0001) have been studied experimentally by Peczonczyk et al. [940] using primarily XPS and H2O contact-angle measurements. When such a procedure, which is well known in synthetic organic chemistry, is applied to GaN, surface Ga sites are first terminated with a halogen (typically Cl) and then exposed to a Grignard reagent of the form RMgCl to yield a Ga-R bond and MgCl2. Here "R" can be any of a number of functional groups, such as an alkyl chain. The GaN samples were first wet-chemically cleaned and then exposed to PCl5 in solution to chlorinate the surface, and XPS data showed only a very low impurity-carbon coverage after this treatment. The oxygen contamination level was not discussed; although, the surface was described as "unoxidized". It is possible that PCl5 might remove impurity C and O by forming volatile CCl4 and Cl2O, and it is known [60,64,94] that adsorbed Cl impedes the oxidation of GaN (0001) during exposure to room air. Also, the XPS data provided give no indication of a significant P residue. The chlorinated sample was then reacted with (C6H4F)MgBr in solution to attach the fluorophenyl group (C6H4F) and release MgClBr, which resulted in a chemically-stable functionalized surface. 8.6. Peptides Peptides are biomolecules formed when the amine group of one amino acid reacts with the carboxylic acid group of another to form an amide bond. These structures take the generic form R-N (H)-CH2-C(=O)-N(H)-R' where R and R' are organic ligands and the -C(=O)-N(H)- linkage is the amide group. Makowski et al. [950] have used XPS to study the attachment of peptides to the GaN (0001) surface via a series of wet-chemical procedures. Strictly speaking, it is not the peptide itself that is bonding to the surface. Rather, the interest is in synthesizing a molecule on the surface with a peptide functionality, which is potentially of value in biosensor applications. Surfaces were first H-terminated and then converted to Cl termination, at which point there appeared to be only a small amount of C impurity. No O 1s data were given, but surface-sensitive Ga 2p3/2 showed no obvious indication of a GaOx satellite. A Grignard reaction (Section 8.5) was used to attach an alkyl chain terminated at the free end with an alkene (-C(H)=CH2) group. Next, an organometallic (Grubbs) catalyst was used to attach to the alkene group another alkyl chain terminated at the free end with a carboxylic acid group. At this point, the surface is ideally covered with Ga-CH2-C(H)=C(H)-(CH2)4-C(=O)OH species. Subsequent processing then leads to an amide group or to a peptide structure. The work is a clear example of a "bottom-up" synthesis in which a complex organic structure is built through a series of surface reactions beginning with a "simple" H termination. 8.7. Phosphonic acids A phosphonic acid has the generic form R-P(=O)(OH)2, where R is an organic ligand. The P-OH groups can react with, for example, Ga-OH to form P-O-Ga bonds and release H2O. The interaction of phosphonic acid derivatives with GaN (0001) and (101̄0) surfaces has been studied experimentally by Wilkins et al. [960,961] using XPS, AFM, PL, XRD, Raman and H2O contact-angle measurement.

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Inductively-coupled plasma mass spectrometry (ICP-MS) was also used to determine the amount of Ga leached into various aqueous solutions in contact with surfaces before and after functionalization. In the first study [960], a novel in-situ wet-chemical approach was described in which the functionalization reagent was mixed into an etching solution (aqueous phosphoric acid, H3PO4, at 40 or 100 °C) in order to OH-terminate surface Ga sites and thereby promote reaction with the organic species, which also limits the extent of etchant-induced oxide formation. The reagents used were (3-bromopropyl)phosphonic acid (Br-CH2CH2CH2-P(=O) (OH)2) and propylphosphonic acid (CH3CH2CH2-P(=O)(OH)2). Both bulk and thin-film GaN samples were used and were wet-chemically cleaned before use. The bulk sample was also subjected to CMP before cleaning. The results demonstrate the efficacy of functionalization in inhibiting oxide formation during exposure to H3PO4. In a subsequent study [961], Wilkins et al. used various longchain substituted phosphonic acids as functionalizing reagents for GaN (0001). These include: (I) HS-(CH2)11-P(=O)(OH)2, (II) F3C(CF2)5-CH2CH2-P(=O)(OH)2 and (III) (HO)2P(=O)-(CH2)8-P(=O) (OH)2, which were added to aqueous solutions of H3PO4. The sample was a free-standing wafer that had been separated from the sapphire growth substrate and then processed using CMP and wet-chemical cleaning. Functionalization and, to varying degrees, the suppression of oxide formation were demonstrated using XPS. Wilkins et al. [962] have also used XPS, H2O contact-angle measurement and AFM to study the stability in liquid H2O of GaN (0001) functionalized with Reagent (II). In addition, the amount of Ga leached into solution was determined using ICP-MS. The results show the adverse effects on the stability of the functionalized surface of unreacted Ga-OH, which promotes oxide formation upon prolonged contact with H2O. This is an important consideration when functionalizing a GaN surface that is not initially oxide free. Much of the work on the simultaneous use of etching and functionalization reagents to modify GaN surfaces has been reviewed recently by Pearce et al. [963], and the reader is referred to this work for a thorough discussion. 8.8. Silanes To our knowledge, all studies to date of silane functionalization of GaN (see Table 6) have involved surfaces that were either intentionally formed with a thin oxide layer or else were processed in a way that such a layer was highly likely. Representative silanes include species such as trichlorosilanes (R-SiCl3) and triethoxysilanes (R-Si(OCH2CH3)3) where R is an organic ligand. Most strategies for semiconductor functionalization using silanes are based on the very facile reaction of these species with OH groups to form, for example, Ga-O-Si linkages on a surface terminated with Ga-OH. One such study will be noted briefly here. Arisio et al. [968] have demonstrated that the instability in H2O of a siloxane SAM on GaN is due to dissolution of Ga oxide at the interface. This illustrates the point mentioned in the introduction to this section regarding the possible effects on chemical stability of a structure in which it is the native oxide and not the GaN itself that is being functionalized.

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studied theoretically by Hu et al. [971]. The experimental work [970] showed no evidence for degradation of the thiol layer during x-ray exposure due to secondary electrons, which is a well-known problem in studies of SAMs on metal surfaces. The C KLL/N KLL relative intensity in XAES was computed for a model in which the octane chains in an all-trans configuration make a finite angle (φ) with the surface normal. From this it was estimated that, at the saturation coverage of ∼0.28 ML (based on the (S 2s)/(Ga 3s) XPS relative intensity), φ is in the range of 70-90°. Thus the chains lie essentially flat on the GaN surface, and a true SAM is probably not formed under the conditions employed. For comparison, φ ≈ 57° is reported elsewhere for a SAM formed by adsorption of H3C(CH2)16CH2SH on GaAs (100). It was suggested that forming a SAM on GaN (0001) might necessitate either a higher coverage or perhaps a longer alkyl chain. The reduced vapor pressure makes alkanethiols much larger than 1-octanethiol difficult to use in a UHV dosing experiment. Annealing up to 450 °C causes a loss of much, but not all, of the C intensity in XPS and XAES, together with loss of a smaller fraction of the S XPS intensity, which is ascribed to a combination of desorption and decomposition. It appears that forming a wellordered SAM on GaN (0001) requires a higher thiol coverage than can be obtained using UHV-compatible techniques. Hu et al. [971] performed a theoretical study of CH3CH2SH on GaN (0001) using a 2DPS with 3 Ga-N bilayers for which the bottom surface was terminated with H and the bottom 3 atomic layers fixed in the bulk configuration. A (3x3) SUC was used together with the PW-91 functional, a PP for Ga (with Ga 3d orbitals included as valence electrons) and all-electron basis sets for the other atom species. The most stable adsorption geometry (ΔEads = -88.58 kcal mol-1) places the S in an FCC (H3) site where it forms a Ga-S-Ga bridge with the C-C chain making a tilt angle of 56.4° with the surface normal. In a slightly less-stable structure (ΔEads = -86.10 kcal mol-1), the S sits in a T1 site with the S-C-C essentially normal to the surface (C-C tilt angle of 10.5°). In either case the H atom released from the S-H bond adsorbs at an adjacent Ga site. Results for H3C(CH2)2CH2SH show that increasing the chain length from 2 to 4 carbons increases the tendency of the chain to tilt away from the surface normal. A calculation of ΔEads per molecule was done up to a coverage of 1 ML, which shows this quantity to become slightly more exothermic up to 0.33 ML and then less exothermic at higher coverages, which suggests that 0.33 ML is effectively the saturation coverage. The C-C chain tilt angle also becomes smaller toward higher coverage, which suggests the onset of SAM formation as the packing density increases. The energetics of decomposition and desorption of the thiolate were also considered. The barrier to dissociative adsorption, i.e., SH bond breaking, is very low (4.9 kcal mol-1) but very high (92.4 kcal mol-1) for recombinative desorption. The barrier for C-S bond breaking is moderate (21.5 kcal mol-1) and leads to S bonded to 3 Ga atoms in an FCC site with the CH3CH2 fragment bonded to a single Ga, which can then undergo β-hydride elimination resulting in H2C=CH2 desorption. These results (saturation coverage, tilt vs. chain length and the combination of desorption and decomposition) are generally consistent with the experimental results and interpretation [970].

8.9. Thiols

9. Concluding remarks and future prospects

Bermudez reported experimental results [970] for the adsorption of 1-octanethiol (H3C(CH2)6CH2SH) on GaN (0001) obtained using primarily UPS, XPS and XAES. The methods used were essentially the same as those described above (Section 8.4) in connection with similar work involving amines. The adsorption and decomposition of ethanethiol (CH3CH2SH) on GaN (0001) has been

It is clear from the foregoing review that some elements and compounds have been investigated in great detail as adsorbates on GaN while others have received little or no attention. It is equally clear that fundamental questions remain unanswered, even for the heavily-studied systems. What follows are a few suggestions, in no particular order, for potentially-valuable areas for future research.

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These are mainly a reflection of the author's personal interests and should not be regarded as complete and all-inclusive. Several of these issues are closely related, which further adds to the challenge in designing an experimental program. (1) Dependence of interfacial reaction on clean-surface preparation. For some elements discussed in Section 5, such as Al, Fe and Ni, there are clear indications that interfacial reactivity is enhanced when the bare surface has been annealed at elevated temperature as part of the cleaning process. The reactions in all cases are exothermic, based on the standard heats of formation of the nitride species involved, and theory generally concurs with the reactivity that is observed in some studies. This implies that thermal pretreatment is effective in overcoming some sort of kinetic barrier that limits reaction on the pristine surface. As discussed in Sections 3.2, 3.3 and 4.5, the annealing temperatures typically involved in in-situ cleaning are such that N is lost faster than Ga. Hence the enhanced reactivity might result from excess Ga, N vacancies or some other type of defect. The reactions, when they occur, appear to extend beyond the outermost surface layer and to continue past the point where one might think that all surface defect sites have been consumed. This hints at what might be described as an autocatalytic process. Annealing-induced defects initiate the reaction, which then makes more defects, and the process continues until a sufficiently-thick interfacial layer of reaction products is formed, at which point diffusion through this layer then limits further reaction. This apparent dependence of interfacial reaction on clean-surface preparation is a worthwhile subject for systematic study. (2) Surface accumulation of H. Some of the results discussed in Section 7.3 clearly indicate that bulk H remaining from MOCVD growth can diffuse to, and accumulate on, the (0001̄ ) surface, but not the (0001), of n-GaN. The possible accumulation of H can have consequences in any study of adsorption on MOCVD material subjected to elevated temperature, as in in-situ cleaning, and a clear understanding of this phenomenon could rightly be considered a prerequisite for any such investigation. It is possible that the effect does not occur for MBE material since the H2 pressure during growth, and presumably the density of bulk H, is typically much lower than in MOCVD (see Fig. 8). As noted in Section 4.7.1.2, Ryan et al. [475] studied the (0001̄ ) surface of p-type MBE material and found, through the observation of H-sensitive surface states, that the clean surface was not already saturated with H. The accumulation of H might be influenced by the presence of bound polarization charges (Section 4.2.2), which are negative on the (0001) and positive on the (0001̄ ) surface, and by the charge state of H in the bulk, which is H+ for p-GaN and H− for n-GaN [401,973]. It would be very useful to study H accumulation on polar vs. nonpolar surfaces and its dependence on doping type. Techniques such as TPD or HREELS could be employed in such a study as methods for detecting adsorbed H. Another aspect of the charge state of H should be mentioned. As shown in Fig. 17, H− is predicted to be the stable form of H when EF-VBM 4 2.1 eV, which describes n-GaN both in the bulk and at the (0001) surface, for which the typical clean-surface upward BB of ∼0.7 eV equates to EF-VBM ≈ 2.6 eV. For EF-VBM o 2.1 eV, as in the bulk of p-GaN, H+ is more stable. However, there is a large downward BB at the p-GaN (0001) surface "in the dark" [440,512] (i.e., in the absence of SPV, Section 4.7.3.2) for which EF-VBM ≥ 2.5 eV. This raises the possibility of a different charge state for H in the bulk vs. at the (0001) surface of p-GaN and of switching the charge state at the surface from H− to H+ by using the SPV effect to reduce the BB. Such effects could be important in the accumulation of surface H under some conditions. An interesting possibility (Refs. [244,974] and works cited) is the use of highly-charged ions (Ar+8 or higher) at a grazing angle of incidence to sputter H selectively. These ions are described as

"slow" in the original references, but the energy used is 2.5q keV where +q is the ion charge. The removal of H occurs through an electronic process termed "potential sputtering", rather than via direct impact, and is reported to cause minimal damage. However, to our knowledge, the absence of damage has not been thoroughly documented yet using, e.g., LEED. This approach, if feasible without the introduction of significant disorder, would permit a systematic study of the effect of removing H from a (0001̄ )-(1x1) surface that is stabilized by 3/4 ML of adsorbed H [398]. In combination with SIMS, it would also provide a means for quantifying H coverage. (3) H-atom cleaning. Another issue related to surface H is that of H-atom cleaning (e.g., Ref. [188]). This method has been successfully applied to several III-V and other materials but, to our knowledge, has not been extensively evaluated for the in-situ cleaning of GaN in surface-science experiments. One exception is the work of Dumont et al. [623] in which H atoms generated by a plasma source were used. A potential complication is that, as discussed in Section 7.3, H atoms appear to etch the (0001̄ ) surface but probably not the (0001). H-atom exposure may be promising as a simple, low-temperature in-situ cleaning method and for that reason could usefully be evaluated more thoroughly in this regard. A further intriguing aspect of H-atom cleaning is the possibility that surface roughness features, including facets, can be etched away by this means. This has been demonstrated [147] for the (0001̄ ) but to our knowledge has not yet been explored for other surfaces. (4) Systematic study of O2 adsorption. Some of the experiments discussed in Sections 7.8 and 7.10 point to complex behavior in the adsorption of O2 on GaN (0001). A saturation coverage for the initial chemisorbed phase of θO ≈ 0.8-0.9 ML is consistently found using XPS; whereas, θO ≈ 0.40 ML is consistently found using electron-excited AES, even at a reduced value of the primary-beam current density. This suggests the presence of two forms of adsorbed O (or two adsorption sites), one of which is highly susceptible to ESD. It is noted that θO = 3/8 = 0.375 ML on the (0001) surface satisfies the ECR since the 6 |e| coming from DBs on eight Ga atoms are exactly sufficient to adsorb 3 O atoms. This may be taken as circumstantial evidence that the ∼0.40 ML seen in AES represents the saturated chemisorption phase while the additional ∼0.5 ML seen only in XPS is something else, possibly the result of adsorption on top of the chemisorbed layer. The identity of the O species and the mechanisms for formation are of interest. Understanding this phenomenon would perhaps be aided by a study of the dependence of O2 adsorption on different surface orientations and reconstructions, all performed with the same methods and experimental conditions. Given the high reactivity of H2O with GaN surfaces (Section 7.10), attention will have to be paid to the possible effects of trace H2O contamination in the O2 and/or the UHV background when performing experiments involving large O2 exposures (4 105 L). This includes the production of H2O by any hot-filament ionization gauges operating in O2. Electronic excitation of the O2 by hot-filament gauges [895] will also have to be considered and possibly avoided through the use of a cold-cathode ionization gauge. As discussed in the following, the GaN doping type may also be an important factor to consider. A useful approach [975] might be to condense a thin layer of O2 on the surface at cryogenic temperatures and then, using UPS, to observe the bonding and dissociation of the O2 as the temperature is raised in stages. This affords the possibility of identifying intermediate species that might be short-lived at RT. With a condensed layer of O2, attention will have to given to avoiding photo-enhanced chemisorption caused by the photoemission excitation source. To this end, it would perhaps be advantageous to use n- rather than p-type GaN. The upward BB commonly found on n-GaN will cause photogenerated holes

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to be swept to the surface, which should have less of an effect on promoting reaction with O2 than the photogenerated electrons that will be brought to the surface in the case of p-GaN. On the other hand, the SPV work of Foussekis et al. [535] and the photoreflectance and PL work of Behn et al. [550] (Section 4.7.3.2) show that intense UV irradiation of an air-exposed n-GaN (0001) surface in vacuo causes the rapid desorption of oxygen. Such a photodesorption effect may not be significant for the lower photon fluxes typically employed in UPS and XPS, but a similar process might occur as a result of secondary electrons produced in electron-excited AES. This could explain the difference in θO for AES vs. XPS, and it is likely that this type of process occurs more readily for n- vs. p-GaN. Electron-hole pairs created by inelastic scattering of secondary electrons will ionize in the spacecharge field, and the holes will be swept to the n-GaN surface where they can be captured by O anions to produce O2 that desorbs. Another possibility, which was mentioned in Section 7.8, is that the entity responsible for the higher coverage might be a peroxo (O2−2) or superoxo (O2−) species that forms on top of the chemisorbed O layer (0.40 ML). Theoretical studies [882,884] have found possible evidence for O2−2 or O2− when O2 adsorbs on the (0001) surface, and such species are known to form when O2 adsorbs on transition-metal oxides [976,977] or on defective alkaline-earth oxides [978]. Oxo species should be identifiable in a UPS experiment [897,898] or perhaps in HREELS if the interference from multiple FK phonon excitations can be eliminated by numerical means (Section 4.8). It is also possible that the O that is easily removed by ESD is in the form of OH rather than in an oxide-like environment. Evidence for such an effect is found [979] in the oxidation of Si (111). (5) Optimizing IBA. In spite of the large amount of research that has been done relating to IBA cleaning of GaN, the process has not yet been optimized. A very useful approach would be to investigate the effects of the key parameters, which are the total ion dose, the sample temperature during ion bombardment and the annealing time and temperature. Based on the discussion in Section 3.3 it can be taken as well established that the optimum process in terms of minimizing damage would involve nitrogen ions of ≤500 eV that are incident at ≥60° with respect to the surface normal and that careful outgassing of the GAN is necessary as a first step. The figures of merit would be the quality of the LEED pattern (i.e., spot width and contrast relative to the diffuse background), the Ga/N atomic ratio in AES or XPS and also the surface roughness as seen in AFM. An important part of such a study would be a comparison of the relative merits of annealing in UHV, in NH3 or in N2 as discussed in Section 3.3.4. It is recalled that one study, of the N-polar face [733], found that IBA can lead to the same reconstructions that are seen in in-situ MBE. (6) Surface structure after IBA. Theoretical studies of adsorption on surfaces prepared by IBA, which describes a large fraction of GaN surface work, have been severely hampered by the lack of a detailed and systematic understanding of the physical and chemical structure of such surfaces. Theoretical work necessarily requires a specific and well-defined surface model; hence, such research has concentrated almost entirely on the types of surfaces grown by MBE and studied in situ. Once the IBA process has been optimized and is reproducible and well understood, it will then become feasible to characterize the surface structure and composition using STM, PED, LEED I-V analysis, etc. This in turn should remove some of the variability between different experimental studies of the same adsorbate using surfaces prepared by IBA and will also make such results more suitable for theoretical modeling. Of particular interest is an understanding of the relative importance of Ga adatoms and N vacancies after high-temperature (above ∼800 °C) annealing in UHV, which is involved in most forms of in-situ cleaning. Above this point, N is lost faster than Ga

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(Section 4.5), and either or both types of defects are possible in principle. For example, the surface states seen just above the VBM in UPS after IBA have been interpreted in terms of Ga adatoms (Section 4.7.1.1). On the other hand, ordered arrays of N vacancies have been seen [298,299] in STM for a (0001) or (0001̄ ) surface after heating in UHV to 900 °C. (7) Sample dependence of faceting. Results discussed at several points indicate a wide variability in the extent to which faceting is observed for nominally-similar in-situ cleaning treatments of the (0001) and (0001̄ ) surfaces. Some studies report distinct and obvious faceting while others find little or none. Even allowing for the well-documented (Section 3.3.1) dependence on Ep of the intensity of facet beams in LEED, this suggests the importance of some hidden factor(s) involved in sample growth or preparation. Research on GaN surfaces would be greatly aided by an elucidation of the root causes of faceting and of procedures for sample growth and/or surface cleaning that can reproducibly avoid this effect. One suggestion [123] is that faceting is a process that relieves strain and, therefore, that careful uniform heating during annealing may be important. If strain is in fact an issue then use of thicker GaN layers might reduce the effects of lattice mismatch with the substrate. It is useful to recall (Section 4.4) that various surface-sensitive spectroscopies have been shown to be capable of detecting strain in GaN [258,310–314] It is also noted [698] that GaN films on sapphire are more highly strained when grown by hydride VPE than by MOCVD. (8) Electron-stimulated desorption of chemisorbed H and O. Section 7.3 discusses experimental results that document the very efficient ESD of H from the GaN (0001) surface. No explanation for this effect has yet been provided. A critical step in identifying the mechanism would be to determine the charge state and kinetic energy of the desorbing species and also the threshold incident electron energy necessary for desorption. Different excitation processes [864] lead to ejection of anions, cations or neutrals, which are characterized by different threshold energies and desorption kinetic energies. Observation of the angular distribution of desorbed species in an electron-stimulated desorption ion angular distribution (ESDIAD) experiment would be very helpful. It might be, for example, that the high ESD cross-section is due to adsorption at facets or step edges, and this should be evident in the ESDIAD pattern. Comparison of results for different surfaces and/ or correlation with HREELS data would also be very useful in determining if the effect is specific to either Ga-H or N-H bonding. There is the further suggestion, discussed in Section 7.8, that a very facile ESD process might also affect a particular species of adsorbed O. This could be investigated by the same procedure discussed for the ESD of H. If this effect is occurring, it should be relatively easy to determine whether the desorbed species is an OH ion or an O ion, which would provide valuable insight. (9) Dependence of Schottky-barrier height on surface preparation. The dependence of barrier heights on the method of clean-surface preparation and metal contact formation has been well documented but is not well understood and is difficult to study systematically. A useful approach to this important issue might be to focus on the non-polar (101̄0) surface, which can be prepared by cleaving in UHV (Section 4.6.3). It has been found [676] that a nearly-ideal Schottky contact is obtained when Au is deposited on such a surface if it is "good", i.e., smooth and well-cleaved (Section 5.20). This is consistent with the low density of Ga DB surface states below the bulk CBM on this surface (Section 4.7.1.3). Although reproducible cleaving can be difficult, it may be possible to circumvent this problem by in-situ homoepitaxial growth [132,139], which could potentially convert a "bad" to a "good" surface and also permit reuse of the substrate. It has also been shown by Walker et al. [676] that SBHs can be deduced from electron-excited AES data. Since the focused primary electron

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beam in AES is typically ∼100 μm in diameter, only a small wellcleaved area is required. By this means one avoids the requirement for in-situ cleaning and also eliminates the surface bound polarization charge as another variable in establishing the SBH [574]. With such an ideal (101̄0) contact as a baseline, it would be possible to investigate systematically the different in-situ cleaning procedures with the goal of understanding the effect of each on Fermi-level pinning and on the SBH. In this study, well-prepared clean (101̄0) surfaces would be subjected to a range of different in-situ treatments (IBA, Ga flux-annealing, etc.). After each, a Au contact would be formed and the SBH measured. It is noteworthy that for Al and Au deposited in situ on a (0001) surface grown by MBE [564], the SBHs are much smaller than the ideal Mott-Schottky values (Table 5), which suggests that factors other than defects introduced by in-situ cleaning are impeding ideal behavior. One such factor might be damage caused by the metal deposition itself. A useful approach, which was mentioned in Section 6, would be to use the "soft-landing" method [816,817] to deposit metal contacts in UHV while avoiding the damage done by the impact of translationally-hot metal atoms from a thermal evaporation source. Eliminating this effect should make it easier to interpret the dependence of the SBH on surface treatment, and other results [815] indicate that less-energetic methods for metal deposition can yield better contacts on GaN. (10) Identification of surface-state features near the band edges. In work on the electronic structure of clean GaN (0001) and (0001̄ ) surfaces, as well as in many studies of adsorption on such surfaces, it is commonplace in UPS (and also ELS) to find evidence for one or more filled surface-state bands near the VBM. Conventional angleintegrated UPS data typically show a narrow band lying within ~0.5 eV of the bulk VBM that is very sensitive to the adsorption of reactive species such as O2, H2O, etc. In the case of (0001) surfaces grown by MBE and studied in situ, the nature of these states is well understood in both theory and experiment [459]. The situation is much less clear for surfaces that have been cleaned in situ. For surfaces prepared using IBA or Ga-cleaning, the filled surface state agrees at least qualitatively with theoretical results for 0.25 ML of Ga adatoms in a (2x2) SUC (Section 4.7.1.1). However, theory (Fig. 25) shows the filled states lying farther into the gap than is seen experimentally, which suggests that something may be missing from the simple model. A closely-related and as yet unresolved issue concerns surface states following cleaning by in-situ annealing in NH3 vapor. As discussed in Section 4.7.1.1, it is unclear what type of surface state forms in this case and to what extent it differs from that seen after IBA. In this case there is the added complication of readsorption of NH3 from the UHV background, which has been shown to eliminate surface-state emission in UPS. Insight into the electronic structure of (0001) and (0001̄ ) surfaces after in-situ cleaning could be gained by comparing the surface-state features in UPS and ELS for different cleaning methods with theoretical results for different adatom and vacancy structures, as was done by Himmerlich et al. [459] for MBE growth. Here ELS can be useful as a means for detecting empty surface states near the CBM. The ELS data are relatively easy to obtain but can be difficult to interpret since it is often not clear whether the initial state, the final state or both lie in the gap. Furthermore, in common with optical spectroscopy, excitonic effects (i.e., attractive electron-hole interaction) can lead to an underestimation of the separation between filled and empty states in the electronic ground state. Hence, STS or IPES (which has been reported for GaN in only one study [450]) would be more useful than ELS for direct comparison with theoretical results. (11) The effect of Ga and N adatoms and vacancies on adsorption. Many of the surface cleaning methods used for GaN quite probably result in Ga or N adatoms and/or vacancies. In-situ cleaning by IBA,

for example, is believed to produce a surface stabilized in a semiconducting state by the presence of Ga adatoms. There appears to be less evidence for N adatoms as a consequence of in-situ cleaning, but it is not clear that such species have been searched for systematically. With some exceptions (Refs. [94,433,472,607,738,826,827,870–872,883]), theoretical studies of adsorption on GaN begin with an ideally-terminated surface or one that is covered with a Ga mono- or bilayer or in some cases with pre-adsorbed H. Theoretical work focusing on the effects of Ga and N adatoms and vacancies on adsorption of O2, H2O, NH3, etc. as well as on the interfaces with various metals would be very useful in interpreting experimental data. This is an important issue since a surface that is passivated by the appropriate coverage of adatoms is expected to be less reactive than one that is ideally terminated. This is seen, for example, in the theoretical work of Uhlrich et al. [94], which shows the effect of 0.25 ML of adsorbed N on the reaction of GaN (0001) with HCl, and of Zywietz et al. [883] that discusses the effect of 0.25 ML of Ga adatoms on ΔEads for the adsorption of O. Hence conclusions based on theoretical descriptions of reactions on ideal surfaces might not apply directly to data obtained for samples cleaned in situ. For the adsorption of an electronegative species on a passivated (0001)(2x2) surface with empty Ga DBs, it is necessary to promote an electron from a filled surface state near the VBM into the empty DB surface state near the CBM in order to facilitate the reaction. This reduces the theoretical ΔEads by an amount comparable to the theoretical Eg, which for GaN is typically 1.7-2.0 eV in a standard DFT calculation using LDA or GGA. This idea has been developed and described by Kempisty et al. (Ref. [840] and works cited). Another aspect to this problem is that the adatoms or vacancies themselves might, in some cases, be reactive centers. This is suggested by the many studies of metal (e.g., Al) interfaces that indicate an enhanced reactivity for GaN surfaces cleaned in situ. Further evidence takes the form of the high degree of sensitivity to adsorption that is exhibited by surface states, some of which are thought to be associated with Ga adatom back-bonds. A reasonable starting point for this type of study would be 0.25 ML of Ga or N adatoms or vacancies, all of which correspond to semiconducting surfaces according to the ECR, in a (2x2) or larger SUC. (12) Structural studies of semi-polar surfaces. Sections 4.6.4 and 4.7.1.4 describe several theoretical studies of the physical and electronic structures of semi-polar GaN surfaces. To our knowledge, there is little in the way of experimental data other than a few studies of surfaces prepared by in-situ cleaning. It may be possible to investigate such surfaces, and in particular to evaluate theoretical predictions regarding surface reconstruction, by means of homoepitaxial MBE growth on well-oriented single-crystal surfaces of GaN. (13) Interaction of Cs with n-GaN polar surfaces. In Section 5.10, two significantly-different interpretations are described, based on experimental data, for the effect of Cs adsorption in reducing the work function of n-GaN polar surfaces (δϕs = δχ + δϕBB). One study concludes that the effect arises mainly from the production of a Gaδ−-Csδ+ dipole layer that lowers the electron affinity (δχ). The other proposes a large negative (downward) band bending (δϕBB) that leads to an inversion layer (i.e., a 2DEG). It is tentatively suggested that both are correct for the respective experimental conditions and that the difference arises from some factor having to do with material growth, surface orientation or preparation or perhaps sample temperature. This would be a very worthwhile topic for further study. (14) Infrared spectroscopy of surface reactions. It is clear, in Sections 7 and 8, that extracting information about chemical bonding in studies of molecular adsorption and reaction can be difficult using techniques such as UPS that probe mainly electronic structure. Vibrational spectroscopy affords a more direct approach,

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and HREELS is often used for this purpose. However, the energy resolution in a typical HREELS experiment is at best only a few meV (∼20-40 cm-1), and, for non-metals, multiple FK-phonon losses can obscure the much weaker adsorbate features even when reduced by numerical data processing (e.g., Ref. [556]). These problems can sometimes be severe when studying a larger organic molecule, one with many closely-spaced normal modes. Infrared spectroscopy, in which the resolution is typically 4 cm-1 or better, can be useful if the sensitivity limitations can be overcome, and there are demonstrated methods for accomplishing this [980] that are applicable to GaN. Wurtzite GaN can be grown epitaxially on certain materials (e.g., ZrB2 [981–984]) with metallic optical properties in the mid- and far-IR (hν o 4000 cm-1). An ultra-thin GaN layer can also be grown [985] by reacting a clean CoGa (100) surface with NH3. CoGa is a cubic crystalline metal compound for which the (100) surface is Ga-rich. The use of a thin (o 100 nm-thick) non-metallic (GaN) layer on a metal substrate in a grazing-incidence IR reflection-absorption experiment can provide a sensitivity to sub-ML coverages of adsorbate molecules on the non-metal that is comparable to that obtained for the same species on the bare metal (Ref. [986] and works cited). This type of sample configuration is termed a "buried metal layer", and the thin layer of non-metallic material is described as being "chemically thick but optically thin". The so-called "metal surface selection rule" [987] applies in this case; hence, only p-polarized adsorbate modes are detectable. This can be used to advantage since it is then possible to employ polarization modulation [988] to detect weak but polarized absorption due to surface species in the presence of much stronger but isotropic absorption by gas-phase reagents. Surface reactions on metals under steady-state conditions have been studied by this means. Another approach would be to grow a thin GaN layer on a Si (111) substrate of the appropriate configuration and perform multiple internal reflection spectroscopy [987]. This offers the advantage that both s- and ppolarized adsorbate modes are observable. One topic that might be especially suitable for further study using IR spectroscopy is the finding by Li et al. [917,918] that GaN surfaces are catalytically active in the aromatization of light alkanes (Section 8.2). This would use to full advantage the ability of such techniques to obtain detailed chemical information under conditions that are not necessarily UHV. Another very useful application of this technique would be in the identification of the NHx (x≤3) and Ga-H species that form when NH3 chemisorbs on various GaN surfaces. This is an important issue in MOCVD and is difficult to address using, for example, UPS or XPS alone.

Acknowledgments All my work on GaN was supported by the Office of Naval Research, and the computational work was performed using facilities provided by the Department of Defense High-Performance Computing Modernization Program (HPCMP). During the course of these studies I have benefited greatly from interactions with many outstanding colleagues. My earliest work was with Ray Kaplan (Naval Research Lab. (NRL), retired) using samples provided by M. Asif Khan (Univ. of South Carolina). Subsequently Dan Koleske (now at Sandia National Lab.) and Alma Wickenden (now at the Army Research Lab.) generously provided a large quantity of high-quality samples together with much helpful advice and discussion. Some work, especially that performed at the Brookhaven National Synchrotron Light Source, would have been impossible without the expertise of Jim Long (NRL, retired). The work of Antoine Kahn (Princeton Univ.), Kevin Smith (Boston Univ.) and their respective research groups has been a continuing source of inspiration and

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guidance during my own efforts with GaN. Stan Krukowski (Institute of High-Pressure Physics / Polish Academy of Sciences) has been a valuable source of theoretical insights concerning GaN surface reactions and electronic structure, and I have also benefited from discussions with Vic Bellitto (now at Naval Surface Warfare Center), Brian Thoms (Georgia State Univ.) and John Russell (NRL). The late Charles Hor (NRL) provided valuable technical advice during the whole course of my GaN experimental work, and Pehr Pehrsson (NRL) was instrumental in obtaining several literature references that would have otherwise been unavailable. Not least, I am grateful to my wife Catherine for her patience, support and encouragement during the long and sometimes-difficult process of writing this review.

Note Added in Proof Several important publications appeared while the present review was in the final editorial stages. There may be others of which the author is unaware. Winnerl et al. [989] have reported an electrochemical study of surface states appearing on the n-GaN (0001) surface after exposure to aqueous HCl solution and their removal by wet-chemical oxidation. Kempisty et al. [990] have performed a comprehensive thermodynamic analysis of the interaction of GaN (0001) with a gasphase mixture of NH3, N2 and H2 based on ab-initio results for the structure and composition of the adsorbate-covered surface. Lymperakis et al. [991] have presented a detailed experimental and theoretical study of the adsorption of H on the (101̄0) surface. Kollmannsberger et al. [992] have used TPD to study the adsorption and photo-stimulated desorption of CO on n-type GaN (0001) as a function of doping. Winnerl et al. [993] have reported a comprehensive study of the effects of doping, growth technique and polarity on SPV for GaN (0001). Irkha et al. [994] have reported a study of the effects of K adsorption and K+H2O coadsorption on the chemical and electronic properties of n-GaN (0001). This work may provide insight regarding the different experimental results for Cs on n-GaN (0001) discussed in Section 5.10.

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