Electronic Energy Levels in Group-III Nitrides

4.12 Electronic Energy Levels in Group-III Nitrides D W Palmer, University of Exeter, Exeter, UK ª 2011 Elsevier B.V. All rights reserved.

4.12.1 4.12.1.1 4.12.1.2 4.12.2 4.12.2.1 4.12.2.2 4.12.3 4.12.3.1 4.12.3.2 4.12.3.3 4.12.4 4.12.4.1 4.12.4.2 4.12.4.3 4.12.5 4.12.5.1 4.12.5.2 4.12.5.2.1 4.12.5.2.2 4.12.5.3 4.12.5.3.1 4.12.5.3.2 4.12.5.4 4.12.6 4.12.6.1 4.12.6.2 4.12.6.2.1 4.12.6.2.2 4.12.6.3 4.12.6.3.1 4.12.6.3.2 4.12.6.4 4.12.7 4.12.7.1 4.12.7.2 4.12.7.2.1 4.12.7.2.2 4.12.7.2.3 4.12.7.3 4.12.7.3.1 4.12.7.3.2 4.12.7.3.3 4.12.7.3.4 4.12.7.4

390

Introduction Aims of This Chapter Crystal Structures and Energy Band Gaps Basic Concepts of Electronic Levels Introduction Electrical and Optical Levels Experimental Methods for Investigating Electronic Energy Levels Electrical Methods Optical Methods Irradiation Damage Theoretical Treatment of Electronic Levels Introduction The Hydrogenic Effective-Mass Model Calculations by Density Functional Theory Electronic Levels in Boron Nitride Structural and Electronic Properties of BN Intrinsic Defects in BN Theoretical studies of intrinsic defects in BN Experimental studies of intrinsic defects in BN Impurity Dopants in BN Theoretical studies of impurity dopants in BN Experimental studies of impurity dopants in BN Conclusions on Electronic Levels and Their Identities in BN Electronic Levels in Aluminum Nitride Structural, Electronic, and Luminescence Properties of AlN Intrinsic Defects in AlN Theoretical studies of intrinsic defects in AlN Experimental studies of intrinsic defects in AlN Impurity Dopants in AlN Theoretical studies of impurity dopants in AlN Experimental studies of impurity dopants in AlN Conclusions on Electronic Levels and Their Identities in AlN Electronic Levels in Gallium Nitride Structural, Electronic, and Luminescence Properties of GaN Intrinsic Defects in GaN Theoretical studies of the formation energies of intrinsic defects in GaN Theoretical studies of the thermal-excitation energies of the electronic levels of vacancies in GaN Experimental studies of intrinsic defects in GaN Impurity Dopants in GaN Theoretical studies of the electronic levels of impurity atoms in GaN Experimental studies of acceptor impurities in GaN Experimental studies of carbon in GaN Experimental studies of impurity donors in GaN Conclusions on Electronic Levels in GaN

391 391 392 392 392 393 393 393 394 394 395 395 395 396 398 398 398 398 399 399 399 400 401 401 401 401 401 404 404 404 406 409 410 410 410 410 412 414 419 419 422 427 430 436

Electronic Energy Levels in Group-III Nitrides 4.12.8 4.12.8.1 4.12.8.2 4.12.8.3 4.12.8.4 4.12.9 4.12.9.1 4.12.9.2 4.12.10 References

Electronic Levels in Indium Nitride Structural, Electronic, and Luminescence Properties of InN Theoretical Studies of Intrinsic Defects and Impurities in InN Experimental Studies of Intrinsic Defects and Impurities in InN Conclusions on Electronic Levels and Their Identities in InN Electronic Levels of Transition and Rare-Earth Metals in III-Nitrides Transition Metals in III-Nitrides Rare-Earth Metals in III-Nitrides Summary

4.12.1 Introduction 4.12.1.1

Aims of This Chapter

The semiconductors formed by the combination of the group III elements of the periodic table with nitrogen, that is, the III-nitrides, BN, AlN, GaN, and InN, are, in their crystalline forms, of increasing technological importance for room-temperature and high-temperature electronics, and for light-emitting diodes (LEDs) and lasers. Controlled chemical doping to produce p-type and n-type conductivities is required, and, for fabrication of useful electronic devices, at least a moderate fraction of the doping atoms must be ionized at room temperature. The implication is that the ionization energies of the acceptor and donor elements need to be not larger than about 0.05 eV, that is, that the corresponding electronic levels, in the energy gap between the valence band (VB) and conduction band (CB), need to be within about 0.05 eV of the edges of the VB and CB, respectively. Making effective use of these compound semiconductors requires an understanding of the electronic and optical processes that can occur in them, and many of these processes are strongly affected, not only by the doping elements, but also by the presence of other impurities and by lattice defects, which introduce additional electronic energy levels into the band gap. Many of these electronic levels can add or remove conduction electrons or holes, and thus strongly change the semiconductor’s electrical conductivity. In addition, by acting as scattering centers, especially if positively or negatively charged, the defects decrease the electron and hole mobilities. The essential luminescence by electron– hole combination in III-nitride LEDs is very often due to transitions of electrons in donor levels to holes in acceptor levels; therefore, understanding and then enhancement of the luminescence requires knowledge of the energy levels involved and the

391 437 437 438 438 439 439 439 440 441 441

identification of the defects or impurities that induce these levels. This chapter aims to review the information concerning the electronic energy levels in III-nitride semiconductors, where possible, to state the likely defect or impurity sources of the levels. In an endeavor to know these sources, the chapter focuses on investigations that lead explicitly to likely identification of the origin of the levels, for example, by comparison of the levels found before and after irradiation or without and with doping by a specific element. This review needs to refer to various calculational, measurement, and crystal-growth techniques that have particular acronyms, and, to help the reader, a list of these is given in Table 1. The III-nitride semiconductors in crystalline form can be obtained by bulk growth, but are now mostly produced by epitaxial growth, and the nature of the chemical reactions involved and of the growth temperature are of crucial importance in the incorporation of specific defects, doping elements, and other impurities in the grown layers. The major epitaxial growth methods include molecular-beam epitaxy (MBE, typically at 750–800  C for GaN, with the flux of gallium higher than that of nitrogen), metal-organic MBE (MOMBE, using trimethylgallium as the gallium source or trimethylaluminum for AlN), hydride vapor-phase epitaxy (HVPE), and metal-organic vapor-phase epitaxy/chemical-vapor deposition (MOVPE/MOCVD, at 1000–1150  C, usually with high nitrogen overpressure). Ammonia is usually employed to provide the nitrogen. It is clear that these growth procedures are likely to lead to introduction of carbon, oxygen, and hydrogen as impurities. Detailed information concerning the methods for bulk and epitaxial growth of III-nitrides can be found in several publications (Chapters 3.06, 3.07, and 3.09; Pashkova and Monemar, 2002; MRS, 2009).

392 Electronic Energy Levels in Group-III Nitrides Table 1 Major acronyms used in this chapter ABE Acceptor-bound exciton BL Blue luminescence CB Conduction band CL Cathodo luminescence C–V Capacitance–Voltage DAP Donor–Acceptor pair DFT Density functional theory DLOS Deep-level optical spectroscopy DLTS Deep-level transient spectroscopy EC Energy minimum of the conduction band EV Energy maximum of the valence band EM Effective mass EPR Electron paramagnetic resonance FC Franck–Condon HVPE Hydride vapor-phase epitaxy LCAO Linear combination of atomic orbitals LDA Local-density approximation LDLTS Laplace DLTS

LMTO Linear muffin-tin orbital MBE Molecular-beam epitaxy MOCVD Metal-organic chemical-vapor deposition PAMBE Plasma-assisted MBE PAS Positron annihilation spectroscopy PC Photoconductivity PL Photoluminescence PLE Photoluminescence excitation PPC Persistent photo conductivity SI Semi-insulating SIMS Secondary ion mass spectrometry SSPC Steady-state photo capacitance TL Thermoluminescence UVL Ultraviolet luminescence VB Valence band VL Violet luminescence YL Yellow luminescence ZPL Zero-phonon line

4.12.1.2 Crystal Structures and Energy Band Gaps

4.12.2 Basic Concepts of Electronic Levels

The binary compounds, BN, AlN, GaN, InN, and their alloys, can exist stably or metastably as crystal structures of hexagonal or cubic symmetries. The lattice parameters of these compounds have been reviewed in detail by Moram and Vickers (2009). Of the hexagonal structures, the wurtzite form (the a-phase) is the one that usually results during crystal growth, and the cubic form is the zincblende (sphalerite) structure (the -phase). The atomic arrangements in the wz and zb structures are very similar, differing only in the relative positions of the third-nearest neighbors. In this chapter, the wurtzite forms are denoted by wz-XN and the zincblende forms by zb-XN, where X ¼ B, Al, Ga, or In. The magnitude Eg of the energy gap between the top EV of the VB and the bottom EC of the CB depends on the nature of the atoms of the crystal and on the details of the crystal structure, and, typically, is larger for crystals which have greater ionicity in their interatomic bonds. The Eg values for the III-nitrides range from about 6.2 eV for zb-BN (boron nitride being the most ionic of the III-nitrides) to about 0.7 eV for wz-InN. The location of the electronic level of a defect or impurity in the band gap is conveniently stated in terms of the difference between its energy and the nearest band edge, EV or EC.

4.12.2.1

Introduction

The energy levels created in the energy gap by doping elements, other impurities, or defects are due to the disruption of the perfect crystal structure, and those atoms or defects can usually capture electrons or holes. The change of a level from being electron-unoccupied to being electron-occupied corresponds to making the impurity atom or defect more negative by one electron charge. However, the impurity or defect center may be able to hold more than one electron, which means that it can provide successive levels in the energy gap, one for each change of charge state. For a normal, positive-U center (U denotes energy), levels higher in the gap, that is, of larger electron energy, are due to charge states that are more negative. The notation being used in this chapter for electronic levels is that the symbol (a/b) for a level indicates that the level is electron-occupied in the electric charge state a and is electron-unoccupied in the charge state b; for impurities and defects that behave normally, which means that a ¼ (b  1). For example, the level of a simple acceptor is indicated by the symbol (/0). At thermal equilibrium, the defect or impurity is in state a if the Fermi energy EF of the semiconductor is above the level (a/b) and in the state b if EF is below (a/b). In other words, the charge state of the defect or impurity changes when EF passes through the electronic level. It will be seen in

Electronic Energy Levels in Group-III Nitrides

Section 4.12.4.3 that the energy Ef (the formation energy) to place a lattice defect or impurity into a crystal depends on the charge state of that imperfection. Readers should note that some papers quoted in this chapter express the electronic level in the alternative way, in which the first part of the symbol represents the unoccupied state and the second, the filled state. The notation used here has the advantage, in the opinion of the author, that it is consistent with the appearance of the charge-state information for electronic levels in diagrams in this chapter that show the location of electronic levels in the band gap of a semiconductor (e.g., Figures 10, 11, etc.).

4.12.2.2

Electrical and Optical Levels

The location in a semiconductor’s band gap of an electronic level of a defect or impurity is usually expressed in terms of the thermal energy Eth needed to change the electric charge of the defect or impurity by 1, and can be considered as the thermal energy needed to excite an electron from the level upward to the bottom EC of the CB or of a hole from the level downward to the top EV of the VB. If the defect or impurity is initially electrically neutral, then Eth is the thermal ionization energy of the defect or impurity and is equal, respectively, to the thermal binding energy ED of an electron in a neutral donor or the thermal binding energy EA of a hole in a neutral acceptor. As shown in Figure 1, the consequential

Energy

A0 + e

EPL Eg – EA A–

dFC EA q–

q0

Configuration coordinate

Figure 1 Schematic configuration-coordinate diagram for an acceptor A to show why the thermal and optical ionization energies of a defect or impurity may be different. The arrow marked dFC indicates the Franck–Condon energy difference. Reprinted with permission from Van de Walle CG and Neugebauer J (2004) First-principles calculations for defects and impurities; applications to III-nitrides. Journal of Applied Physics 95: 3851. Copyright 2010, American Institute of Physics.

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change of the charge state of the defect or impurity may cause a positional rearrangement of the atom involved and of its neighboring atoms, and Eth is the electronic energy difference between the initial state and the final, atom-relaxed state. However, the change of charge state can often be caused also by optical excitation, which is a process that occurs in a time much smaller than that, 1012 s, needed for atomic relaxation. The effect is (Figure 1) that the optical ionization energy Eopt differs from Eth if the excitation produces atomic relaxation. The value of (Eth  Eopt) is called the Franck–Condon energy shift dFC. A considerable difficulty is that, although values of Eth and Eopt can often be measured for semiconductors containing defects and/or impurities, lack of knowledge of the respective associated dFC values can prevent their mutual correlation.

4.12.3 Experimental Methods for Investigating Electronic Energy Levels 4.12.3.1

Electrical Methods

Excitation, from the electronic level of a defect or impurity, of electrons into the CB or of holes into the VB increases the electrical conductivity,  ¼ nee or of  ¼ peh, of the semiconductor, where n and p are, respectively, the free-electron concentration in the CB and the free-hole concentration in the VB, and e and h are the respective mobilities. For levels close to the band edges EC or EV, that is, shallow levels, the measured Hall effect of the semiconductor as a function of temperature T, allows determination of the thermal excitation energy Eth from the slope of an Arrhenius plot of n(T) or p(T). The energy locations of levels that are not close to EC or EV can often be measured by deep-level transient spectroscopy (DLTS). In this technique, the time constant of the transient electronic signal due to thermal excitation of an electron into the CB or of a hole into the VB is measured as a function of temperature, with repetitive emptying and refilling of the level so as to provide a good signal-to-noise ratio. The semiconductor sample is usually a pþ–n, nþ–p, or Schottky diode, and the signal measured is typically the transient change in the diode capacitance. The sourceto-drain current of a field-effect transistor (FET) structure can similarly be used, but usually with lower sensitivity to the presence of electronic levels. However, in contrast to the information from n(T) or p(T) studies, the excitation energy obtained from DLTS measurements is that needed for the electron

394 Electronic Energy Levels in Group-III Nitrides

or hole to escape from the defect or impurity and so is equal to (Eth þ Ecapt), where Ecapt is the magnitude of the energy barrier that the electron or hole needs to overcome to fall back into the defect or impurity. Most investigations by DLTS experiments do not include measurements of Ecapt, and so they are not automatically able to provide values of Eth for the defects or impurities being studied. It is often assumed that Ecapt is zero or small, but that may not be a valid assumption. In addition, because Eg is temperature dependent, Eth may also change with temperature. A review of electrical techniques for the investigation of defects and nondoping impurities in semiconductors has been given by Palmer (2001). 4.12.3.2

Optical Methods

The main optical methods for investigating the electronic levels of defects and impurities in semiconductors include optical absorption (OA), photoluminescence (PL), steady-state photoconductivity (SSPC), and deep-level optical spectroscopy (DLOS). In all of these, illumination of the semiconductor sample by photons of wavelength  causes transition of an electron or hole between two energy states (two electronic levels or an electronic level and the VB or CB) whose energy difference is given by Ephoton ¼ 1:23985  10 – 6 eV=ðmÞ

ð1Þ

Table 2 shows the Ephoton values for wavelength ranges of the optical spectrum. Thus, for example, the yellow luminescence (YL) that is a frequent property of as-grown gallium nitride (GaN) is an emission band centered at about 2.15 eV. The OA method is less sensitive than the other techniques to the presence of electronic levels because the illumination intensity transmitted through the sample is usually only slightly decreased by the optically induced electronic transitions. In the other techniques, a new detectable signal is produced Table 2 Relationships between the colors, wavelengths, and photon energies of the visible optical spectrum Colors of Light

Wavelengths

Photon energies

Red Orange Yellow Green Blue Violet

620–750 nm 590–620 nm 570–590 nm 495–570 nm 450–495 nm 380–450 nm

2.00–1.65 eV 2.10–2.00 eV 2.18–2.10 eV 2.50–2.18 eV 2.75–2.50 eV 3.26–2.75 eV

whose magnitude is usually proportional to the number of electronic transitions per second. The DLOS method is similar to DLTS outlined in Section 4.12.3.1: in both the methods, an electrical capacitance transient output signal is measured following a pulsed input, but in DLOS this input is a pulse of photons whose wavelength is progressively changed so as to find possible hole transitions to the VB or electron transitions to the CB. The very good wavelength resolution of optical techniques allows precision measurement of the transition energies, especially when PL is used. A PL emission is often due to a transition from an electronic level to a band edge, but sometimes the emission is due to electron–hole combination from a donor D to a nearby acceptor A, that being called a donor–acceptor pair (DAP) transition. Then the transition energy EDAP is usually stated (e.g., Teisseyre et al., 2005) as being given by EDAP ¼ Eg – ED – EA þ ECoul

ð2Þ

ECoul ¼ e 2 =4KS "0 r

ð3Þ

where

In these formulae, Eg is the band-gap energy, ECoul is the Coulomb interaction energy, KS is the static dielectric constant and r is the distance between the donor and the acceptor. However, the value of r is generally unknown, and that adds uncertainty in the determination of ED and EA; in addition, a spread of r-values leads to a broadening of the PL emission energy. Furthermore, ED and EA should be considered here as the optical binding energies of the donor and acceptor, respectively, rather than the thermal binding energies.

4.12.3.3

Irradiation Damage

During irradiation of a crystalline solid by energetic electrons, collisions of the electrons with lattice atoms can displace those atoms from their sites, so creating vacancies and interstitials, and very possibly antisite defects also. Because such irradiation does not introduce impurity atoms and, if the solid is a semiconductor, measurement of electroniclevel-dependent properties of the solid before and after the irradiation may then allow identification of the nature of the irradiation-induced defects. A special additional feature of electron irradiation of chemical compounds is that, due to the differing masses of the constituent atoms of the solid, there is

Electronic Energy Levels in Group-III Nitrides

a different electron threshold irradiation energy for displacement of each kind of atom. Thus, for GaN, in optimum experiments and conditions, the creation of the vacancy VGa and the interstitial GaI should be easily distinguishable from the creation of corresponding nitrogen defects VN and NI. Irradiation by gamma rays, which causes atomic displacements due to gamma-created energetic electrons in the solid, can be employed to some extent in the same way. If the irradiations are performed at low temperatures, subsequent heat treatments can determine the temperatures at which the irradiation-induced defect levels disappear and thus provide additional valuable information. Ion bombardment can also be used for the creation and subsequent study of intrinsic defects, especially if the ions used are inert gas ions (which are not likely themselves to produce electronic levels) or if the irradiation is by protons of highenough energy that they come to rest at a distance into the solid that is beyond the nearer-surface region in which the irradiation-induced defects are being investigated. Thus, investigation of irradiation effects in III-nitrides gives the possibility of distinguishing the electronic levels of intrinsic defects from those of impurities.

4.12.4 Theoretical Treatment of Electronic Levels 4.12.4.1

Introduction

Theoretical investigations of the properties of lattice defects and impurities in III-nitride semiconductors have been carried out for more than 20 years, including of their structures, their thermodynamic formation energies and their electronic energy levels. Most of such studies have concerned GaN, and the intrinsic defects considered have been mainly the simplest ones, that is, the vacancies VGa and VN, the interstitials GaI and NI, and the antisite defects GaN and NGa. In respect of impurities, the elements expected to produce chemical doping have of course been of great importance. Atoms of group II of the periodic table, such as beryllium and magnesium, which most likely can replace the cation in BN, AlN, GaN, and InN and so be acceptors, and the group-VI atom, oxygen, which is expected to be able to take the site of a nitrogen atom and so be a donor, have therefore been of most interest. However, the properties of the group-IV elements, carbon and silicon, which perhaps may be able to occupy either a

395

cation site as a donor or a nitrogen site as an acceptor, have also been the subject of much theoretical study.

4.12.4.2 Model

The Hydrogenic Effective-Mass

The simplest kind of theoretical consideration of the ground-state electronic level of a defect or impurity in the III-nitride semiconductors is the well-known hydrogenic, effective-mass model. This treatment uses the formula for the ground-state ionization energy of a hydrogen atom including a simple Coulomb potential, but in which the vacuum permittivity 0 is replaced by KS0, where KS is the dielectric constant of the semiconductor and the fundamental electron mass m0 is replaced by the effective mass (EM) m of an electron or hole in the semiconductor. For germanium and gallium arsenide, that model gives values for the ionization energies of the chemical dopant atoms that act as shallow donors and acceptors that are in very good agreement with the experimental values found for those semiconductors. Application of this theoretical method to the III-nitride semiconductors allows valuable comparisons of those calculated ionization energies with values obtained in the more sophisticated theoretical treatments outlined below, and with experimentally obtained ionization energies for the III-nitrides. Knowledge concerning to what extent donors and acceptors in the III-nitrides behave as effectivemass centers is of particular interest. The hydrogenic, effective-mass model gives the following values for the ground-state ionization energy (Eioniz)Dopant of a dopant element and for the corresponding Bohr radius (rBohr)Dopant: ðEioniz ÞDopant ¼ 13:6 eVðm =m0 Þ=KS2

ð4Þ

ðrBohr ÞDopant ¼ 0:053 nmðm0 =m ÞKS

ð5Þ

and

where 13.6 eV and 0.053 nm are respectively the ionization energy (the Rydberg energy) and the Bohr radius of the ground electronic state of a hydrogen atom, m is the electron EM me (for a donor dopant) or the hole EM mh (for an acceptor dopant) in the semiconductor, m0 is the free-electron mass and KS is the dielectric constant of the semiconductor. In semiconductor notation, (Eioniz)Dopant is the energy ED by which the (0/þ) electronic level of a donor element lies below the bottom EC of the CB and (Eioniz)Acceptor is the energy EA by which the

396 Electronic Energy Levels in Group-III Nitrides

(/0) level of an acceptor element lies above the top EV of the VB. For calculating the hydrogenic-model effectivemass ionization energies for donors in III-nitride semiconductors, Tansley and Egan (1992) stated values of (me /m0) and KS, respectively, as follows: AlN, 0.33 and 4.7; GaN, 0.2 and 5.5; InN, 0.12 and 8.4. Use of these values of (me /m0) and KS in (4) and (5) produces the following values for the ionization energies and Bohr radii of donors in those materials (AlN, 0.203 eV, 0.755 nm; GaN, 0.090 eV, 1.46 nm; InN, 0.023 eV, 3.71 nm) as given in Table 1 of their paper. Thus, an effective-mass donor in wz-GaN would be expected to have its thermal ionization (0/þ) level at [EC  0.090 eV]. As the concepts of EM and dielectric constant are properly relevant only if large numbers of lattice atoms are being considered, the hydrogenic model is more likely to give a valid value for (Eioniz)Dopant if (rBohr)Dopant is much larger than the interatomic separation in the semiconductor. This suggests that the hydrogenicmodel donor ionization energy is likely to be closer to the real value for InN than for GaN or for AlN. Concerning (me /m0) and KS for wz-GaN, Look et al. (2005) noted that later, more accurate values for these are 0.22 (Moore et al., 2002) and 9.4 (Zhang et al., 2003), respectively, and that the use of these values in expression (4) above puts the effective-mass donor level in wz-GaN at [EC  0.0339 eV]. The corresponding Bohr radius rBohr for such a donor in wz-GaN is then 2.26 nm. Since rBohr is larger than the value from Tansley and Egan (1992), it seems probable that the actual (0/þ) electronic level of a simple shallow donor in wz-GaN is closer to [EC  0.0339 eV] than to [EC  0.090 eV]. Indeed, Look et al. (2005) reported a measured ionization energy of close to 0.0339 eV for oxygen acting as a donor in wz-GaN. An EM calculation for a shallow acceptor in zb-GaN was given by As et al. (2002). Due to the fact that GaN has both light and heavy holes, the value of the EM m in (4) above needs to be an appropriate average of the two hole masses. They noted the two hole masses in zb-GaN as 0.18m0 and 0.75m0, and, using data from other work, used a value of 0.45m0 for m. For the dielectric constant KS, they stated that the high-frequency value should be used for zb-GaN, and they quoted that as 5.35. From expression (4), the effective-mass acceptor ionization energy for zb-GaN is obtained as 0.214 eV (stated as 0.213 eV in their paper). Wang and Chen (2001) calculated the hydrogenic (Coulomb-potential)

acceptor ionization energies for wz-GaN and zb-GaN using theoretically obtained values for the hole EMs in the two crystal structures. The ionization energies given by their calculations were 0.150 and 0.137 eV for wz-GaN and zb-GaN, respectively. Returning to considering wz-AlN, if the static (zero-frequency) value of 9.14 (Collins et al., 1967) is used instead of the high-frequency value of 4.7 employed by Tansley and Egan (1992), as stated above, then, from expression (4) for (me/m0) again set at 0.33, the hydrogenic ionization energy of a donor in wz-AlN is 0.054 eV. So one may expect the (0/þ) level of a hydrogenic effective-mass donor in wz-AlN to be somewhere within the energy region [EC  0.054 eV] to [EC  0.203 eV].

4.12.4.3 Theory

Calculations by Density Functional

The properties of donors and acceptors are more complicated than assumed in the hydrogenic model above, and more sophisticated theoretical treatments have therefore been used. The main current theoretical method is the computer-based solving of the quantum-mechanical equations that describe the properties of the defects, by application of densityfunctional theory (DFT) with use of the local-density approximation (LDA) for the electrons of the atoms of the semiconductor. The general principles of the method and its strengths and limitations have been described and discussed in various papers, including those of Jones and Briddon (1997), Elstner et al. (1998), and Estreicher (2003). Other papers have also provided valuable descriptions of the DFT method (Van de Walle and Neugebauer, 2004; Ganchenkova and Nieminen, 2006; Sharmar et al., 2009). The details of the particular calculation and the name of the computer program are usually presented in each individual paper. For a system containing nGa atoms of gallium and nN atoms of nitrogen, the energy of formation Ef of a defect or dissolved impurity in charge state q in GaN is given (Neugebauer and Van de Walle, 1994a) by Ef ðqÞ ¼ Etot ðqÞ – nGa ?Ga – nN N – qEF

ð6Þ

where Ga and N are the chemical potentials of gallium and nitrogen, respectively (which depend on the experimental conditions in which the GaN is grown, e.g., Ga-rich or N-rich conditions, and where Ga þ N ¼ GaN), and EF is the Fermi energy in the semiconductor. The important implication of the expression (6) is that, when Ef(q) is plotted as a

Electronic Energy Levels in Group-III Nitrides

397

7 0.43

Formation energy (eV)

6

VGa0

0.5 0.91

1.0

wz-GaN 1.41 1.47

VGa–1 VGa–2

5

4 VGa–3

3

P=0 2 P = 10 GPa

1

0 0.0

0.5

1.0

2.0 1.5 Fermi energy (eV)

2.5

3.0

Figure 2 Calculated formation energies Ef of the gallium vacancy VGa in nitrogen-rich growth of wz-GaN under hydrostatic pressures of 0 and 10 GPa as a function of the Fermi energy EF in the GaN. The zero of the EF scale is the top of the valence band. The values of Ef at which there are changes of slope in the Ef(EF) function indicate the VGa energy levels that correspond to changes of the charge state of the VGa. Reprinted figure with permission from Gorczyca I, Christensen NE, and Svane A (2002) Influence of hydrostatic pressure on cation vacancies in GaN, AlN and GaAs. Physical Review B 66: 075210. Copyright 2010 by the American Physical Society. For information, see: http://publish.aps.org/linkfaq.html

function of EF, there is a sharp change of slope where the q value changes, and the EF value there is the electronic energy level of the defect corresponding to that change of its charge state. Calculations, such as those by using DFT, aim to obtain the function Ef(q) for each kind of lattice defect of interest, and therefore to find the formation energies and energy levels of the defect in each charge state. Figure 2 (Gorczyca et al., 2002) illustrates that kind of calculation, in this case for gallium vacancies in wz-GaN. In almost all DFT/LDA calculations, the electronic levels are found by that procedure, and the results of such calculations can give valuable guidance in the interpretation of experimental data toward the identification of the defects that produce the observed electronic levels. However, the calculations do not have the possibility of giving accurate information. First, there is limitation upon the accuracy of the data due to the LDA method itself and other approximations that have to be made in the calculations, including the fact that the calculated VB-to-CB band gap is typically significantly smaller than the experimental value. The reason for the error in the calculated band gap is that the DFT method is not able to deal well with electronic states associated with the CB. As a result, the energy of any electronic levels that contain

substantial contributions from CB states is difficult to evaluate accurately. Impurity and defect levels calculated with respect to EC, the bottom of the CB, can, however, be calculated to some extent, and various theoretical procedures can be used to ease the problem. There is also the significant difficulty that the number of lattice atoms that can be considered in the calculations is always constrained by the computing speed available, the time for each calculation being approximately proportional to the cube of that number. The intrinsic lattice defect or impurity being considered and the atoms around it mutually interact by electrical and mechanical forces, and a computational cell containing a large number of atoms is required to try to allow the system to behave as a bulk solid. The supercell method simulates a large solid by the use of adjacent crystal cells, each containing the defect or impurity at its center; however, unless each individual cell itself is large, there can be interactions between these, especially by Coulomb interactions if the defect or impurity has a nonzero electric charge. Of important technological interest are defects or impurities that are likely to be ionized, and so produce electrical conductivity, at room temperature. Such defects and impurities have shallow acceptor or donor levels associated

398 Electronic Energy Levels in Group-III Nitrides

with spatially large electron orbitals, which implies that the radius of the computational cell needs to be significantly greater than the electron-orbital radius. Over the years, the development of progressively faster computers has allowed the number of atoms to be increased from several tens to several hundreds, and that has certainly led to calculated data of improved validity. The outcome is, however, still that the calculated energy levels of lattice defects and impurities usually cannot be obtained more accurately than about 0.2 eV. Since in experimental studies that use electrical and optical methods the electronic levels can often be measured to precisions of the order of 0.01 eV and that the experiments often show the presence of many electronic levels due to defects and/or impurities, it is usually not easy to use the DFT-calculated data to make definite identifications of the defects responsible for the observed energy levels. However, the thermodynamic formation energies Ef and stabilities of lattice defects can be obtained with reasonable accuracy from the DFT calculations, to the extent that the results are usually likely at least to show correctly whether the Ef values are large or small. Many of the theoretical investigations have therefore included calculations of the formation energies of the intrinsic defects for the purpose, especially, of knowing which defects are expected to be formed during the crystalline growth of III-nitride semiconductors, a large calculated Ef value for a defect indicating that that defect is not likely to be created at an observable concentration during the crystal growth. The value of Ef of each particular defect depends on its charge state, such that the Ef values of acceptor defects are lower when they can easily capture electrons, that is, in n-type semiconductor material, and, correspondingly, the Ef values of donors are lower in p-type than in n-type material. In addition, as can be expected, if the III-nitride semiconductor is being grown in conditions in which there is an excess of cation atoms, such as gallium-rich conditions in the growth of GaN, cation interstitials and nitrogen vacancies are likely to have lower formation energies than during growth in nitrogen-rich conditions. Correspondingly, nitrogen interstitials and cation vacancies tend to be more easily formed during growth in an excess of nitrogen. The theoretical work therefore provides valuable information concerning which lattice defects are likely to be found in p-type and n-type III-nitrides grown by different methods.

4.12.5 Electronic Levels in Boron Nitride 4.12.5.1 Structural and Electronic Properties of BN Boron nitride, BN, can exist in a variety of crystal structures, including hexagonal (h-BN) similar to the graphite structure, rhombohedral, hexagonal wurtzite (wz-BN), and cubic zincblende (zb-BN). The boron–nitrogen bond in BN is very strong, and that contributes in a major way to the large VB-to-CB energy gap Eg. Cubic zincblende BN is the most thermodynamically stable of the crystal structures. It can be produced in bulk form by a process that includes heating at 2000–3000  C at high pressure, and thin films of zb-BN can be made by various processes. The bandgap of zb-BN has been measured as 6.4  0.5 eV (Chrenko, 1974) and as 6.1  0.2 eV (Miyata et al., 1989). The less stable wz-BN is more difficult to produce and has an Eg value reported to be in the range 4.5–5.5 eV. The electronic levels of intrinsic defects and of impurities in BN have been investigated in a few theoretical studies, but there has been rather little experimental investigation of such levels.

4.12.5.2

Intrinsic Defects in BN

4.12.5.2.1 Theoretical studies of intrinsic defects in BN

Using several full-potential, tight-binding procedures within a LDA, Gubanov et al. (1996) undertook theoretical investigations of the properties of boron vacancies VB and of nitrogen vacancies VN in zb-BN. Their calculations used 64-atom supercells, with the VB or VN at the center of the supercell, and with no positional relaxation of the atoms allowed. Their calculations indicated that the VB created, in the BN band gap, a well-defined band of electronic levels centered above the VB at about [EV þ 0.6 eV] and partially electron-occupied. Their results gave VN as producing two well-defined energy bands, one being somewhat above EV and fully occupied, and the other being a partially occupied band just below the bottom, EC, of the CB. They concluded that VB would act as an acceptor and that VN would be a shallow donor. Their paper attributed the formation of energy bands rather than energy levels to the approximations of the theoretical method, including the low number of atoms in the supercell. Mota et al. (1997) and Piquini et al. (1997)

Electronic Energy Levels in Group-III Nitrides

used an all-electron Hartree–Fock linear combination of atomic orbitals (LCAO) method in calculations, including atomic relaxations, of the electron density distributions and electronic properties of the nitrogen vacancy in a (N19B16H36)3þ cluster of Td symmetry for the zb-BN and in a (N16B14H34)2þ cluster of C3v symmetry for the wz-BN. The paper specified the 3þ and 2þ charges as being needed to produce a neutral charge condition in the clusters, and the hydrogen atoms indicated were at the surfaces of the clusters to saturate dangling bonds. Additional details for zb-BN concerning VN and also for the boron antisite defect BN in that structure were given by Piquini et al. For zb-BN, these calculations showed VN as producing a fully occupied electronic level at about [EV þ 1.76 eV] and a half-occupied level at about [EV þ 4.90 eV], that is, in the upper half of the band gap toward EC, the data for VN being similar to the data of Gubanov et al. (1996) reported above. The calculations by Mota et al. predicted the BN as having a fully electron-occupied, deep donor level at about [EV þ 4.8 eV]. DFT calculations on the formation energies of vacancies VB and VN and of self-interstitials in graphite-like hexagonal-BN (h-BN) and in zb-BN, as functions of the Fermi energy EF, were reported by Orellana and Chacham (1999, 2001). For h-BN, the calculations indicated VB as a triple acceptor, having a single-electron level at [EV þ 0.31 eV] and a doublet at [EV þ 1.29 eV]. The nitrogen vacancy VN was predicted to have two single-electron levels, one at [EV þ 0.1 eV] and the other, as a donor level, just below EC (at [EV þ 3.86 eV] in the situation that the calculated value of the band gap, Eg ¼ [EC  EV], was 4.0 eV). The levels calculated for VB and VN in zb-BN were somewhat different. The VB vacancy was indicated as having a (/0) acceptor level at about [EV þ 0.5 eV], and the VN vacancy as having a filled acceptor level just above EV and a half-filled donor level very close to or essentially at EC. The calculated Eg value for the zb-BN was 4.8 eV. The formation energies of VB were indicated as being very low, toward zero, for nitrogen-rich growth of n-type h-BN and of zb-BN, and those of VN were indicated as being quite low, about 2 eV, in the formation of p-type material, even during nitrogen-rich growth. The calculations for zb-BN suggested that boron interstitial BI 0 has filled levels just above EV and a half-filled level at about mid-gap, and that the nitrogen interstitial NI 0 has partially occupied levels in the lower half of the band gap and an unoccupied level a

399

little below EC. The formation energies of both BI and NI during nitrogen-rich growth of zb-BN were indicated as being large, at least 5 eV, for all EF values. 4.12.5.2.2 Experimental studies of intrinsic defects in BN

Fanciulli and Moustakas (1993) made electron paramagnetic resonance (EPR) measurements on crystalline films of zb-BN grown by radiofrequency (RF) sputtering of a BN target in argon/nitrogen-gas mixtures having differing proportions of nitrogen in order to change the concentration of nitrogen vacancies in the grown films. A single EPR line was detected, and the observed increase of its intensity with decreasing nitrogen gas pressure was interpreted as indicating that the signal was due to nitrogen vacancies. As explained in Section 4.12.3.3, intrinsic defects (lattice vacancies, self-interstitial atoms, and perhaps antisite defects) can be created by particle or gamma-ray irradiation of a crystalline solid by displacement of the component atoms from their lattice sites. Appropriate measurement techniques applied to the irradiated solid can show the presence of the irradiation-induced intrinsic defects and allow them to be distinguished from impurities present in the solid before the irradiation. Nistor (2005) made EPR measurements on zb-BN before and after 1.0 MeV electron irradiation and reported two EPR lines, IR1 and IR2, whose intensities increased linearly with irradiation dose and so were concluded to be due to irradiation-induced intrinsic defects. The IR1 line was suggested to be associated with singly charged vacancies, but the work did not include any electrical measurements that might have indicated its energy level or that of IR2. It is clear that temperaturedependent Hall effect and DLTS investigations of irradiated BN would be of fundamental and technological interest.

4.12.5.3

Impurity Dopants in BN

4.12.5.3.1 Theoretical studies of impurity dopants in BN

Piquini et al. (1997) investigated the properties of nitrogen-site oxygen in zb-BN using a Hartree–Fock LCAO treatment, with atom relaxation, of a cluster of 71 atoms, including 36 hydrogen atoms at the cluster surface to saturate dangling bonds, as in their calculations outlined above on intrinsic defects in zb-BN. Their calculations indicated that the ON would be expected to give rise to a half-occupied level located

400 Electronic Energy Levels in Group-III Nitrides

4.12.5.3.2 Experimental studies of impurity dopants in BN

An early investigation of semiconducting BN was that of Wentorf (1962). He found that he could grow p-type zb-BN by high-temperature, high-pressure treatment of hexagonal BN powder containing beryllium as an impurity, and that the resultant BN:Be was blue in color, presumably due to optical absorption by an electronic transition of about 2 eV between electronic levels or between a level and the VB or CB. Electrical conductivity measurements on the p-type BN:Be showed the ionization energy of beryllium, probably as BeB, to be about 0.2 eV. Wentorf reported that use of silicon, sulfur, or KCN as the impurity instead of beryllium produced n-type BN, with impurity ionization energies of between 0.05 and 0.20 eV.

1000 15

500

Temperature (°C) 200 100

50

20 106

zb-BN

10

103 5

R (ohm)

n-type In (R)

at about the middle of the upper half of the BN band gap. Park and Chadi (1997) reported briefly upon their DFT/LDA investigations of the electronic properties of beryllium, carbon, silicon, germanium, and sulfur dopants in zb-BN. They stated that their calculations suggested that BeB and CB are thermodynamically stable, on-site, acceptor centers, and that SiB, GeB, and SN are shallow donors, that also are stable on their respective lattice sites. Calculations on the electronic states of beryllium as BeB, BeN, and the interstitial BeI in zb-BN were made by Castineira et al. (1998a, 1998b), using a full-potential augmented-plane-wave/LDA method. Their results predicted that BeB would have a low formation energy and would put a shallow acceptor level into the band gap at about [EV þ 0.4e V], and that BeN would create partially occupied levels near the middle of the band gap. The calculations suggested that tetrahedral BeI would produce levels in the upper half of the gap. The results of a theoretical study of the properties of carbon as the acceptor CN in zb-BN were reported by Ramos et al. (2002). They employed DFT/LDA procedures on supercells containing increased numbers of atoms, from 64 to 2744, in order to check for convergence of the output data. For the 2744-atom supercell, they obtained 293 meV for the thermal activation energy for the ionization of CN 0 to CN – , thus putting the (/0) level of CN at [EV þ 0.293 eV]. Their graph of that ionization energy as a function of supercell-edge size suggested that it probably would have been slightly larger for bulk theoretical zb-BN.

p-type

0

1

1

2 3 103/ Temperature (K)

Figure 3 The measured temperature dependence of the resistivity of doped and undoped zb-BN samples. The p-type and n-type samples were BN:Be and BN:Si, respectively, and the upper line shows the data from the high-resistance part of the BN:Si sample and from an undoped sample. From Mishima O, Tanaka J, Yamaoka S, and Fukunaga O (1987) High-temperature cubic boron nitride p-n junction diode made at high pressure. Science 238: 181. Reprinted with permission from AAAS.

Production in zb-BN, at high pressure (55 kbar) and high temperature (1700  C), of p-type conductivity by beryllium doping (giving blue or dark blue BN) and of n-type conductivity by silicon doping was reported also by Mishima et al. (1987) and thence the fabrication in that work of BN p–n junctions of good rectification quality. Their Arrhenius plots of the measured temperature dependence of the electrical resistance of their doped and undoped BN samples are shown in Figure 3. The slopes of the lines in the Arrhenius plots for the p-type and n-type BN gave the ionization energies of beryllium as 0.23  0.02 eV and of silicon as 0.24  0.03 eV. Thus, assuming the expected latticesite locations of the atoms of those elements, the investigation indicated the (/0) acceptor level of BeB to be at about [EV þ 0.23 eV] and the (0/þ) donor level of SiB to be at about [EC  0.24 eV]. The uppermost line in Figure 3 shows the Arrhenius-plot data of Mishima et al. for undoped (yellow) zb-BN, and indicated a conductivity activation energy of 1.11  0.15 eV. The paper does not make it clear whether the undoped BN was p-type or n-type, and so it is not known whether its conductivity was due to

Electronic Energy Levels in Group-III Nitrides

an acceptor level at about [EV þ 1.11 eV] or to a donor level at about [EC  1.11 eV]. Polycrystalline zb-BN, prepared by sintering at high pressure and temperature, and doped with beryllium, was investigated by Taniguchi et al. (1993). They found the BN to be p-type, with a conductivity-activation energy of approximately 0.3 eV in the temperature region 25–700  C. The use of zinc as an acceptor element in zb-BN and in h-BN was studied by Nose et al. (2006). Their electrical conductivity-temperature measurements on the p-type layers showed that the conductivity-activation energy in the zb-BN was decreased from 0.30 eV for very low zinc concentration to less than 0.1 eV for a zinc concentration of about 25  103, and that the activation energies for the h-BN decreased correspondingly from about 0.4 eV to about 0.15 eV. They reported that the higher zinc concentrations caused strong room-temperature conductivity. The data seem to show that the (/0) acceptor level of zinc in zb-BN is at [EV þ 0.3 eV]. 4.12.5.4 Conclusions on Electronic Levels and Their Identities in BN The information concerning electronic levels in BN can be summarized as follows. The theoretical investigations have predicted that the boron vacancy VB has a (/0) acceptor level in the energy region of [EV þ 0.5 eV] to [EV þ 0.6 eV] in both zb-BN and wz-BN. Experimental study has shown the presence of nitrogen vacancies in asgrown zb-BN, and irradiation has been found to create vacancies that are stable at 300 K. For VN in zb-BN, a fully occupied acceptor level at [EV þ 1.76 eV] and a half-full donor level at [EV þ 4.90 eV] have been suggested by theoretical work. Similar levels have been predicted for VN in wz-BN. The boron antisite defect BN is theoretically suggested to have a fully occupied donor level at [EV þ 4.8 eV] in zb-BN. The acceptor level of beryllium as BeB has been measured as being at [EV þ 0.23  0.02 eV] (but at about [EV þ 0.3 eV] in other work) in zb-BN and at about [EV þ 0.4 eV] in wz-BN. Other experimental studies on zb-BN have indicated that the acceptor level of ZnB is at [EV þ 0.3 eV] and that the donor level of SiB is at [EC  0.24  0.03 eV]. A theoretical study has suggested that oxygen as ON in zb-BN has its donor level in the top half of the band gap.

401

4.12.6 Electronic Levels in Aluminum Nitride 4.12.6.1 Structural, Electronic, and Luminescence Properties of AlN Aluminum nitride, AlN, is a mechanically hard material of high melting point and excellent thermal conductivity. It has a strong tendency to absorb oxygen, that being considered as due to the aluminum. Its thermodynamically stable crystalline form is wz-AlN (a-AlN), and that is the structure formed during typical epitaxial growth of AlN on c-face sapphire or SiC substrates. The wz-AlN structure has a direct energy gap of magnitude reported as 6.20 eV (Yamashita et al., 1979) or 6.28 eV (Roskovcova´ and Pastrn˜a´k, 1980) at 300 K. When a specific band-gap value needs to be used in this chapter, a value of 6.24 eV will be used. The zincblende (b-AlN) cubic crystal structure, zb-AlN, is metastable, but it can be epitaxially produced in carefully controlled growth conditions on cubic substrate surfaces such as (100) silicon. The energy gap of zb-AlN is reported as indirect, with an experimentally obtained magnitude at 300 K of close to 5.34 eV (Thompson et al., 2001), that is, considerably lower than the direct band gap of wz-AlN. Especially because of their large band gaps that correspond to the deep ultraviolet (UV) region of photon energies, both wz-AlN and zb-AlN have considerable potential as materials for opto-electronic devices, including LEDs, laser diodes, and photodetectors, and also for high-temperature and/or high-power electronic devices. However, doping of AlN to produce low resistivity p-type and n-type material is found to be difficult. Incorporation of magnesium usually allows formation of p-type AlN, but its quite large ionization energy leads to its being little activated at room temperature. Although n-type AlN can be formed by silicon doping, it is also usually of low conductivity, often due to the electronic levels of intrinsic defects or contaminant impurities.

4.12.6.2

Intrinsic Defects in AlN

4.12.6.2.1 Theoretical studies of intrinsic defects in AlN

Just as for BN discussed in Section 4.12.5, theoretical investigations of the electronic levels of defects in AlN can provide valuable guidance in the interpretation of experimental data. As has been stated in Section 4.12.4.2, use for AlN of the electron

402 Electronic Energy Levels in Group-III Nitrides

effective-mass ratio (me/m0) of 0.33 and dielectric constant of 4.7 stated by Tansley and Egan (1992) leads to a ground-state ionization energy of 0.203 eV for a hydrogenic, effective-mass donor in that semiconductor, and, therefore, if any intrinsic donor in AlN behaves in that way, it would have its (0/þ) level at about [EC  0.20 eV]. Mattila and Nieminen (1997) reported DFT/ LDA calculations using 32-atom supercells for zb-AlN. Their results on the formation energy Ef of aluminum vacancies VAl as a function of Fermi energy suggested that VAl is an acceptor center in zb-AlN, with its (/0), (2/), and (3/2) levels at about [EV þ 0.6 eV], [EV þ 1.2 eV], and [EV þ 1.8 eV] (those values being deduced here from Fig. 2 of their paper). Their calculations gave a low value of Ef, in the range 1 eV to 0, for VGa (an acceptor) in n-type AlN, and a low formation energy approaching zero for VN (a donor) in p-type AlN. The VN vacancy was indicated as having its (/þ) level at about [EV þ 1.5 eV]. They concluded that the deepness below the CB of that donor level can explain why as-grown non-intentionally-doped AlN is usually found to have high resistivity at room temperature. It seems from Fig. 2 of their paper that there is no range of Fermi energies close to 1.5 eV above EV at which the neutral nitrogen vacancy, VN0 , is stable. It is clear that the calculations strongly suggested that VN does not behave as a hydrogenic effective-mass donor in AlN. Stampfl and Van de Walle (2002) used the DFT method on supercells containing up to 72 atoms, in conjunction with a generalized-gradient approximation (GGA) for the electron-exchange correlation which they stated was a better approximation for AlN than the usual LDA. Figure 4, from their paper, shows the locations, in the band gap, of the electronic levels for vacancies, antisite defects, and interstitials as obtained in their calculations for zb-AlN. They stated that, as shown in Figure 4, their calculations indicated that VN has a filled level just above EV and a level containing one electron just above EC; despite the latter location within the CB, the paper states that VN acts as a donor (but as a shallow donor). It is seen that their calculation for VAl suggested that the vacancy in its neutral charge state has, somewhat above EV, a level whose six electron states are only half-occupied, and that therefore VAl was indicated to be a triple acceptor. Figure 4 shows also that the nitrogen interstitial and the aluminum interstitial were predicted to be an acceptor and a donor, respectively. Concerning

zb-AIN Vacancies

Antisites

Interstitials

CB

CB

VB

VB VN

VAl

NAl

AlN

Ni

Ali

Figure 4 Calculated levels of neutral-charge-state intrinsic defects in zb-AlN. The filled and open circles indicate electrons and holes, respectively. Reprinted figure with permission from Stampfl C and Van De Walle CG (2002) Theoretical investigation of native defects, impurities and complexes in aluminum nitride. Physical Review B 65: 155212. Copyright 2010 by the American Physical Society. For information, see: http://publish.aps.org/linkfaq.html.

the formation energies of intrinsic defects during growth of AlN, their calculations suggested that positively charged VN donors are likely to be created in p-type AlN, and that, correspondingly, the 3– acceptor VAl would be expected in n-type AlN and that it would act as a center compensating the electrical conductivity effect of any donor impurity. Stampfl and Van de Walle, and also Van de Walle and Neugebauer (2004), stated that the fact that the band-gap energy of wz-AlN is significantly larger than that of zb-AlN is expected to move the upper level of VN in wz-AlN further away from EC, that is, to cause VN to be a deeper donor in wz-AlN than in zb-AlN. DFT calculations by Ye et al. (2007) also indicated VN in AlN as having a filled, doubly occupied, electronic level just above EV, and a partially occupied level just above EC in zb-AlN and well below EC in wz-AlN; they deduced that VN acts as a shallow donor in zb-AlN and as a deep donor in wz-AlN. Gorczyca et al. (1999, 2002) reported their DFT/ LDA 32-atom supercell calculations using a fullpotential linear-muffin-tin-orbital (LMTO) method (including atomic relaxations) to determine the properties of VAl in zb-AlN. It was found that the VAl created a set of six-electron electronic levels in the lower half of the AlN band gap, and that, as had been found by Stampfl and Van de Walle (2002) (see above), three of the six electron states were empty for the neutral vacancy and so the defect was indicated as a triple acceptor. Because of the small number of atoms per supercell, the VAl produced energy bands in the VB-to-CB band gap instead of sharp levels, and, when the energy location of each level in the band gap was defined as the energy of the centers of gravity of the density of electron states of its band, the electronic energy levels of the VAl were

Electronic Energy Levels in Group-III Nitrides

as follows: (/0) at [EV þ 0.4 eV], (2/) at [EV þ 0.9 V], and (3/2) at [EV þ 1.5 eV] (of which the first is the level of VAl shown in Figure 4 here). As usual in the DFT/LDA method, the calculation by Gorczyca et al. gave an energy gap lower (at about 5 eV) than the real value, but since the electron states of the VAl were found to have strongly VB character, it was expected that the calculated energies of the levels were reasonably accurate, especially the level closest to the VB, that is, the (/0) level. The calculation of Ef for VAl 3 – in strongly n-type AlN indicated that it would be formed at high concentration in the growth of chemically nþ-doped AlN. Theoretical investigations of both VAl and VN, in wz-AlN using the DFT method on a 72-atom supercell with application of a full potential linearized augmented plane-wave treatment, were implemented by Zhang et al. (2008). Their calculations suggested, in agreement with other theoretical work, that VAl acts as a triple acceptor, but put its (/0) level at [EV þ 0.95 eV]. The nitrogen vacancy was indicated as a deep donor, as in other work on wz-AlN, but, although VN þ and VN 3þ were found to be stable charge states of the defect, the VN 2þ state was predicted to be unstable. The (0/þ) level of VN was found to be at [EC  1.75 eV], that is, as a very deep donor, and the (þ/3þ) level at about [EC  4.5 eV]. Using a special procedure in their calculations, they were able to obtain a theoretical

403

band-gap value of 5.98 eV, very close to the reported experimental value of 6.12 eV, thus giving confidence in the validity of the energy level locations determined with respect to EC. The calculations suggested the formation energy of VAl to be very low in n-AlN and that of VN to be very low in p-AlN, for both aluminum-rich and nitrogen-rich growth of wz-GaN. The theoretical work of Laaksonen et al. (2009) for wz-GaN used a DFT computational code that they stated as overcoming the usual errors due to noninfinite supercells and the underestimation of the energy band gap. For electronic energy levels of VN not far below EC, the scissor technique was used to correct the calculated energy levels, the technique being the stretching of the initially calculated band gap of 4.4 eV to make it equal to 6.12 eV, and hence stretching proportionately the energy difference between the VB top and the electronic level. However, this correction was considered unnecessary for levels near the VB. The levels of VAl and VN thus obtained in the work are shown in Figure 5. The calculations indicated VN 2þ and possibly also VN – as unstable states of the nitrogen vacancy. The calculated formation energy data suggested strongly that, in both Al-rich and N-rich growth conditions, the concentration of VAl would be large in n-type AlN and that concentration of VN would be large in p-type AlN.

wz-AIN Calculated levels EC = EV + 6.2 eV VN

3–

VN 0 VN 1+

EC = EV + 6.2 eV EV + 6.00 eV EV + 5.56 eV EV + 5.05 eV

3– VAl

EV + 1.37 eV 2–

VAl

EV + 1.14 eV 1–

VAl

EV + 0.82 eV

0

VN 3+

EV + 0.71 eV

Neg. U

EV

EV VN

VAl Not drawn to scale

Figure 5 Calculated levels of aluminum vacancies VAl and of nitrogen vacancies VN in wz-AlN as reported by Laaksonen et al. (2009).

404 Electronic Energy Levels in Group-III Nitrides

4.12.6.2.2 Experimental studies of intrinsic defects in AlN

As explained earlier in this chapter, identification of the origins of observed electronic levels in a semiconductor can be much aided by irradiation-damage studies. Watkins et al. (1997) and Mason et al. (1999) reported investigation by PL-optically detected electron paramagnetic resonance (PL-ODEPR) of lattice defects in vapor-transport-grown wz-AlN crystals before and after 2.5 MeV electron irradiation. Many PL-ODEPR signals were observed, most attributable to impurities in the AlN, but the concentration of one of them, D5, was increased by the irradiation. Analysis of the EPR spectrum of D5 suggested that it was most likely associated with a displaced aluminum atom. Bulk wz-AlN:O grown by vapor transport was studied also by Tuomisto et al. (2008), using the technique of positron-annihilation spectroscopy (PAS). The basis of this technique is that the presence of vacancies in a crystalline solid decreases the rate of annihilation of positrons by electrons (because of the lower electron density at and near a vacancy) and therefore increases the positron lifetime. Measurements of the positron lifetime in irradiated semiconductors, before and after heating, can then show, for comparison with data from electrical measurements, whether vacancies are stable in the semiconductor at the irradiation temperature and, if so, the temperature at which they are removed by thermal annealing. The experimental data indicated the presence of vacancies at a concentration of about 1  1017 cm3, and the theoretical consideration of the expected magnitudes and temperature dependences of positron lifetimes indicated that the observed vacancies were negatively charged VAl. This experimental result is consistent with the outcomes of the theoretical studies outlined in Section 4.12.6.2.1. Investigations of MBE-grown wz-AlN by lowtemperature cathodoluminescence (CL) and by PAS were reported by Koyama et al. (2007) and Hoshi et al. (2008), the intensities of the impurityrelated and defect-related CL and vacancy-related PAS signals being monitored as functions of the relative III–V beam ratios by changing the beamequivalent pressure of the ammonia source that provided the nitrogen for the growth. The CL data showed violet and UV emission bands, comprising a strong, broad (2–5 eV) violet emission band centered at about 3.1 eV, on which were superimposed considerably weaker and narrower UV bands with peaks at about 3.8 and 4.6 eV, and the intensity of each of the three bands was found to be correlated

with the strength of the PAS-measured signal related to the presence of VAl. On the basis of previous other theoretical work (e.g., Mattila and Nieminen, 1997), the CL bands were assigned to DAP transitions from a shallow donor to deep acceptors. Taking account also of the expectation that the raising of the ammonia pressure would increase the concentration of VAl defects and decrease the incorporation of oxygen ON by reducing the formation of nitrogen vacancies, the experimental data were suggested as indicating that the photon emissions at 4.6, 3.8, and 3.1 eV were due to the transitions from the shallow donor down to acceptor levels of VAl , of [(VAl-complex)2–O] and of [VAl 3 – O] respectively, of which the last has the larger concentration. This interpretation has the difficulty, however, that oxygen seems to behave as a deep DX donor in AlN and not as a shallow donor. 4.12.6.3

Impurity Dopants in AlN

4.12.6.3.1 Theoretical studies of impurity dopants in AlN

Theoretical studies of acceptor impurities in AlN. Mireles and Ulloa (1998) used detailed quantum-mechanical effective-mass theory, taking account of degenerate VB states, crystal symmetries, and the electronic structures of the individual dopant elements, to calculate values for the ionization energies of the acceptors, beryllium, magnesium, zinc, calcium, and silicon in wz-AlN and zb-AlN and also of carbon in zb-AlN, including use of crystal-field splitting energies of different magnitudes which had the effect of giving a range of ionization energies for each element. The ionization energy values reported in the paper are shown in Table 3. The energy indicated as the likely best value for each dopant was that obtained by the use of the crystal-field splitting values for AlN taken from the theoretical work whose crystal-field splitting values for GaN gave theoretical ionization energies closest to the measured ionization energies for GaN in the same work by Mireles and Ulloa. Subsequent calculations of the ionization energies of acceptors in AlN have used density functional theory. Wu et al. (2007) reported on their DFT investigations of beryllium in wz-AlN. Their DFT program allowed full atomic relaxation and used the marker method (Resende et al., 1999) to calculate the (/0) level of BeAl relative to the corresponding experimentally measured level of MgAl at [EV þ 0.50 eV] (see below). Their calculation gave the (/0) acceptor level of BeAl at

Electronic Energy Levels in Group-III Nitrides

405

Table 3 Theoretical ionization energies of acceptor elements in wz-AlN and zb-AlN as obtained by use of quantum-mechanical effective-mass theory (Mireles and Ulloa 1998). wz-AlN

zb-AlN

Ionization energy in eV

Ionization energy in eV

Element

Range

Likely best value

Range

Likely best value

BeAl MgAl ZnAl CaAl SiN CN

0.253–0.472 0.514–0.795 0.255–0.464 0.240–0.402 0.250–0.441

0.262 0.514 0.255 0.240 0.250

0.273–0.292 0.330–0.360 0.269–0.288 0.252–0.268 0.264–0.281 0.345–0.380

0.292 0.360 0.288 0.268 0.281 0.380

Reprinted table with permission from Mireles F and Ulloa SE (1998) Acceptor binding energies in GaN and AlN. Physical Review B 58: 3879. Copyright 2010 by the American Physical Society. For information, see: http://publish.aps.org/linkfaq.htm

[EV þ 0.34 eV]. In a further DFT study on wz-AlN, Zhang et al. (2008) found the (/0) level of BeAl at [EV þ 0.48 eV], that of MgAl at [EV þ 0.58 eV], and of CaAl at [EV þ 0.95 eV]. It is seen that each of those calculated ionization energies is significantly larger than the value, shown in Table 3, obtained by the effective-mass calculation used by Mireles and Ulloa (1998). Calculations by Park and Chadi (1997) had predicted that BeAl and MgAl are thermodynamically stable in both wz-AlN and zb-AlN. Theoretical studies of donor impurities in AlN. As has been stated in Section 4.12.4.2 the hydrogenic, effective-mass model for a donor atom in wz-AlN gives the donor’s (0/þ) electronic level at [EC  0.054 eV] or at [EC  0.203 eV], depending on whether the high-frequency or low-frequency value of the dielectric constant is used. DFT/LDA plane-wave pseudopotential calculations using 32-atom supercells of the formation energies of the donors SiAl and ON in zb-AlN were undertaken by Mattila and Nieminen (1997). Their calculations predicted each of those donors as having a (/þ) level (not (/0)) at about [EV þ 4.1 eV], that is, at about [EC  0.9 eV] in terms of their calculated Eg value of 5.0 eV. It is not clear how to take account of the fact that the measured band gap of zb-AlN is about 5.2 eV (Section 4.12.6.1). The result is seen to be very different from that obtained using the hydrogenic model. A matter of importance concerning impurity donor atoms in AlN is whether, as for some donor atoms in AlAs and in AlxGa1xAs if x exceeds a particular value, the donor atom may be thermodynamically unstable in its normal substitutional site at which it is an electronically shallow donor and moves

to a stable site at a small distance from that site and acts as a deep donor there, not ionizable at or near room temperature and so not producing n-type conductivity at the temperature. Such a deep donor is called a DX center, the D denoting donor and the X indicating that initially the reason for the formation of the deep donor in AlAs and AlxGa1–xAs was unknown. That possibility for the donor impurity atoms in AlN and AlxGa1xN was considered in DFT/LDA studies by Park and Chadi (1997) and by the research group of Van de Walle (Stampfl and Van de Walle, 1998; Van de Walle, 1998; Stampfl and Van de Walle, 2002; Van de Walle and Neugebauer, 2004) in relation to the experimental observation that unintentionally doped wz-GaN and low-x-value wz-AlxGa1– xN are typically n-type, that the shallow donor involved is thought to be oxygen as ON and that the n-type conductivity of such AlxGa1– xN having x > 0.4 is always very low. The work of Park and Chadi offered an explanation for those observed electrical properties of as-grown AlN and AlxGa1xN. Their calculations indicated the shallow donor ON to be unstable in aluminum-rich wz-AlxGa1xN and zb-AlxGa1 xN, and that the oxygen atom would form an off-lattice-site, deep-donor DX center in each case, and therefore in both wz-AlN and zb-AlN. Their calculations predicted that silicon as the shallow donor SiAl would be unstable in wz-AlN and probably also on cation sites in wz-AlxGa1 xN having x > 0.24, and instead would become a deep-donor DX center by movement of the silicon atom from its cation-substitutional lattice site. Their result for zb-AlxGa1xN was, however, that silicon would not form a stable DX center in that structure for any

406 Electronic Energy Levels in Group-III Nitrides

value of x including x ¼ 1, or in wurtzite or zincblende GaN. For germanium and sulfur, the calculation suggested that neither of those impurities would form a stable DX defect in either the wz or the zb structure of AlxGa1xN for any x value, so giving the expectation that germanium on the cation lattice site and sulfur on the nitrogen site are stable as shallow donors in those materials. The theoretical work by the Van de Walle group gave results that agreed qualitatively with those of Park and Chadi concerning oxygen in wz-AlN, indicating the expectation that oxygen exactly on the nitrogen lattice site is not stable and, moving off-site, – would form a DX-type center, ODX , having a donor level well below EC. Their results indicated that that would be expected to occur also in wz-AlxGa1xN for x larger than about 0.4 (and also for wz-GaN subject to hydrostatic pressure larger than approximately 20 GPa), but that, in contrast to the finding by Park and Chadi (1997), that would not occur in zb-AlxGa1xN for any value of x, even for x ¼ 1, or for zb-GaN or zb-AlxGa1xN at high pressure. Also in contrast to the results of Park and Chadi, the calculations by the Van de Walle group gave the result that silicon is stable as a shallow donor on the cation site in both wz-AlxGa1xN and zb-AlxGa1xN for all values of x, including therefore for wz-AlN and zb-AlN, and thus would not form a deep donor, DX center in those materials. The implication is that the calculations by Van de Walle et al. suggest that silicon acts as an effective shallow donor in both wz-AlN and zb-AlN. Theoretical studies of carbon in AlN. Carbon is an element that is likely to be easily incorporated as an impurity during growth of AlN, and so it is important to have information on the acceptor or donor electronic levels that it may create in the AlN band gap. As described earlier, the thermodynamically stable lattice sites of the group-IV atoms silicon and germanium in AlN are indicated as the aluminum lattice sites, and there they give rise to shallow donor levels. However, DFT calculations reported by Ramos et al. (2002), for zb-AlN, have given the strong expectation that the optimum location of the atoms of carbon, also a group-IV element, in that material is the nitrogen lattice site, that is, as the acceptor CN, the stability of that lattice site being understood qualitatively in terms of the close similarity of the radii of the carbon and nitrogen atoms. The study by Ramos et al. used a DFT method in the local density or local spin-density approximations including exchangecorrelation effects, and large supercells extending up to 2744 atoms. The calculations indicated that

carbon in both its neutral and single-negative charge states would stay stably on the nitrogen site without the occurrence of energy-lowering Jahn–Teller lattice distortions. It was found that the electronic levels of the C0N and CN– attained convergence in their energies for supercells of 1728 atoms, thus indicating reliability in the output energy-level data. The calculation gave the (/0) acceptor level of CN at approximately [EV þ 0.87 eV] (thus indicating it as a deep acceptor in zb-AlN), and its optical Franck– Condon energy shift dFC (see Figure 1) as 0.69 eV. 4.12.6.3.2 Experimental studies of impurity dopants in AlN

Experimental studies of acceptor impurity dopants in AlN. Detailed experimental investigations of the electronic levels of beryllium, magnesium, and zinc acceptors in MOCVD-grown wz-AlN epilayers have been undertaken by the research group of H.X. Jiang, mainly by the technique of time-resolved UV PL spectroscopy, and also by electrical conductivity measurements for AlN:Mg. The results of these studies are now summarized. From the work of that research group on beryllium in wz-AlN, Sedhain et al. (2008) reported experimental data showing the binding energy of an exciton to BeAl 0 in wz-AlN as 0.033 eV. Thence, by use of Haynes’s rule (Haynes, 1960) which suggested, from experimental data, that the binding energy of an exciton to a neutral impurity is about 10% of the ionization energy of the impurity, they deduced the (/0) level of BeAl as being at about [EV þ 0.33 eV], and they noted that that agreed with the theoretical ionization energy of 0.34 eV as calculated by Wu et al. (2007). They pointed out that this beryllium ionization energy was usefully lower than the ionization energy of MgAl of about 0.5 eV that they found in their associated investigation described below. The investigations on MgAl in wz-AlN:Mg by researchers of the Jiang laboratory were reported in several papers (Li et al., 2002; Nam et al., 2003; Nepal et al., 2004; Nakarmi et al., 2006). Measurement of the temperature dependence of the electrical conductivity of the AlN:Mg indicated a thermal activation energy of 0.40 eV. By taking account of the variation of the hole mobility with temperature, the thermal ionization energy of MgAl was deduced as 0.50 eV, thus indicating its (/0) acceptor level to be at [EV þ 0.50 eV]. The PL spectra at 10 K of undoped wz-AlN showed a strong free-exciton-associated band-to-band emission line at 6.06 eV, and in the wz-AlN:Mg that emission was replaced by a strong

Electronic Energy Levels in Group-III Nitrides

0.26 eV

1.0

wz-AIN:Mg

wz-Alx Ga1–x N:Mg

CB VNl+

0.86 eV

407

0.8

VN3+

EA = 0.17 + 0.5x

5.55 eV 0.6

Guide to the eyes

EA (eV)

5.29 eV 4.70 eV

0.4

0.50 eV

Mg0

0.2

VB

Figure 6 The levels of nitrogen vacancies as proposed on the basis of photoluminescence and electrical measurements on wz-AlN:Mg. Reprinted with permission from Nakarmi ML, Nepal N, Ugolini C, Altahtamouni TM, Lin JY, and Jiang HX (2006) Correlation between optical and electrical properties of Mg-doped AlN epilayers. Applied Physics Letters 89: 2120. Copyright 2010, American Institute of Physics.

line at 6.02 eV (interpreted as emission involving a MgAl 0 -trapped exciton of binding energy 40 meV), together with additional PL lines at 5.54, 5.36, and 4.70 eV. The intensity of the 4.70-eV emission was found to have a temperature dependence corresponding to a thermal activation energy of 0.50 eV, and it was concluded that the increase with temperature of the 4.70-eV emission was associated with the progressive ionization of MgAl 0 to MgAl – . This emission was therefore interpreted as being due to the electron transition from MgAl – up to a deepdonor level at [EC  0.86 eV]. Figure 6 (Nakarmi et al., 2006) shows the electronic energy levels deduced in the work. On the basis of the variation of the 5.36 eV and 4.70 eV line intensities with different aluminum-to-nitrogen ratios during the AlN:Mg growth and of other experimental information, the donor levels at [EC  0.26 eV] and [EC  0.86 eV] were interpreted as being due to nitrogen vacancies, as indicated in Figure 6. The 5.29-eV transition there was identified with the observed 5.36-eV PL line by considering the likely effect of the donor–acceptor Coulomb field on the transition energy. Similar PL measurements were made by the Jiang researchers also on wz-AlxGa1xN for values of x between 0 (i.e., GaN) and 0.25. Figure 7 taken from their work (Li et al., 2002; Nam et al., 2003) shows their data for the variation of the ionization energy of Mg in that material as a function of the aluminum content x.

0.0 0.0

0.2

0.4 0.6 Al content (x)

0.8

1.0

Figure 7 Measured dependence of the acceptor ionization energy EA of magnesium in wz-AlxGa 1–xN:Mg on the aluminum content x. Reprinted with permission from Nakarmi ML, Nepal N, Ugolini C, Altahtamouni TM, Lin JY, and Jiang HX (2006) Correlation between optical and electrical properties of Mgdoped AlN epilayers. Applied Physics Letters 89: 2120. Copyright 2010, American Institute of Physics.

Further work in the Jiang laboratory concerned AlN doped by zinc, which, as another divalent element, is also expected to take up gallium lattice sites, as an acceptor. PL data on wz-AlN:Zn, reported by Nepal et al. (2006), showed an emission line at 5.40 eV interpreted as due to the electronic transition between EC and the acceptor level of ZnGa somewhat above EV. From the observed band-gap energy of 6.14 eV at the measurement temperature of 10 K, the (/0) acceptor level of ZnGa was deduced as being at [EV þ 0.74 eV]. Experimental studies of donor impurity dopants in AlN. Detailed experimental investigations of the electronic levels of donor dopants in AlN, for comparison with the theoretical data summarized in Section 4.12.6.3.1, are rather few in number. An early study (Lee et al., 1991) of AlxGa1xN considered the experimental observation that the electron carrier density in as-grown n-type wz-AlxGa1xN was always very low in alloys having x larger than about 0.4, and, using UV PL as the investigative tool, found that such material showed the presence of several deep levels that were absent in material having low x values. It seems likely that the n-type conductivity of the AlN being investigated was due to the presence of oxygen, and that the observations by Lee et al. can be

408 Electronic Energy Levels in Group-III Nitrides

understood by the transformation for x > 0.4, of the shallow donor ON to the deep donor ODX, as has been described in Section 4.12.6.3.1. Experimental observation of the formation of an oxygen deep-level donor, that is, an oxygen DX center, in wz-GaN:O, when subject to hydrostatic pressure greater than approximately 20 GPa, was obtained by Wetzel et al. (1997) in a study that used Raman spectroscopy to monitor the free-electron concentration. By noting that the difference between the band-gap energy of GaN and AlN includes a CB offset of 2.0 eV, that a pressure of 1.0 GPa increases the GaN band gap by an amount equivalent to replacing 2.1% of the gallium by aluminum, they deduced that it would be expected that ON in wz-AlxGa1xN would be unstable and would become ODX for x > 0.4, the result being in agreement with the experimental data on the n-type conductivity of wz-AlxGa1xN, and with the theoretical data of Van de Walle et al. (Section 4.12.6.3.1). Wetzel et al. (1997) also found that they could not produce a sharp drop in the electron carrier concentration in wz-GaN:Si by application of hydrostatic pressure, and that concords also with the results by Van de Walle et al that silicon in wz-AlxGa1xN does not form a DX center for any x value. Measurements of the temperature dependence of the n-type electrical conductivity of epitaxial wz-AlN films grown by plasma-assisted MBE were used by Ive et al. (2005) to investigate the energy level of SiGa in the AlN. They stated that, although epitaxial AlN is very often of high resistivity, they believed that their growth of low-resistivity n-type films was made possible by ensuring a very low concentration of carbon, oxygen, and other contaminating impurities. From their analysis of their electrical conductivity data they concluded that SiGa is a comparatively shallow donor, its (0/þ) level being somewhere in the range 0.060–0.180 eV below EC. It is to be noted that a donor level within that energy range is consistent with the result from the hydrogenic, effective-mass model for a donor atom in wz-AlN (Sections 4.12.4.2 and 4.12.6.3.1), which gives the (0/þ) level in the range 0.054–0.20 EV, depending on whether a low-, intermediate-, or high-frequency value of the dielectric constant is used in the calculation. The general consensus is indeed that silicon situated on a gallium site in AlN behaves as a hydrogenic, effective-mass, shallow or shallowish donor. Furthermore, the theoretical work of the Van de Walle group has suggested that SiGa is stable in both wz-AlN and zb-AlN, not forming a

deep-donor DX center in either of those structures. However, this view has to be considered in the context of the striking experimental result (Zeisel et al., 2000) that wz-AlN:Si shows the property of persistent photoconductivity (PPC) after illumination at 20 K by photons of energy larger than 1.5 eV, such behavior being understandable in terms of the formation of a silicon DX center. A proposal, based on additional experimental data on wz-AlN:Si, which seems to provide valuable clarification of the electrical-conductivity properties of that material, including that silicon is a shallow donor in that material and does not form SiDX, has been made by Irmscher et al. (2007) and Schultz et al. (2007). Their investigation employed measurements of thermoluminescence (TL) and of electrical admittance as a function of temperature on bulk crystals of wz-AlN:Si grown by vapor-phase deposition at 2000–2200  C. Secondary ion mass spectrometry (SIMS) analysis indicated the silicon concentration to be (1–3)  1020 cm3 and that the carbon and oxygen concentrations were each about a factor of 10 smaller. The electrical data, including by C-V study, showed that the AlN was n-type, but with a low free-electron concentration, of the order of only 1017 cm3, which suggested that almost all of the silicon SiAl donors were compensated by acceptor centers. The samples were found to have the property of PPC reported earlier for wz-AlN:Si by Zeisel et al. (2000) (see previous paragraph). The TL experiments showed photon-emission peaks at various temperatures between 60 and 400 K, which were quantitatively interpreted as due to several emission energies including near 0.12 eV (definitely related to silicon in the AlN), 0.52, 0.63, and 0.86 eV, of which the last two were obtained also from analysis of the admittance data Figure 8, from Irmscher et al. (2007), shows the electronic energy levels that were deduced from the experimental data. The interpretation of the experimental data in terms of Figure 8 is that the conductivity that would be caused by the presence of the SiAl donors is strongly reduced by electron trapping onto the acceptor-like electron traps at energies of 0.5–1.0 eV below EC, and that the electrical conductivity then shows those 0.5–1.0 eV activation energies because of excitation of those electrons back to the CB. These energies were therefore not considered to be ionization energies of SiAl in wz-AlN; instead, the ionization energy of SiAl was proposed to be that of the first TL peak, that is, about 0.1 eV. The paper suggested the PPC to be due to the presence of

Electronic Energy Levels in Group-III Nitrides

409

wz-AIN:Si EC = EV + 6.2 eV 0 Si donor band

EC –c a 0.1 eV +

Acceptor-like electron traps

EC – 0.5–1.0 eV

Midgap

Negatively charged acceptors, perhaps V A3–l , which compensate most of the Si+ donors EV Not drawn to scale Figure 8 Proposed level of the silicon donor in relation to deep and shallow acceptor levels in wz-AlN:Si from electrical and thermoluminescence measurements. Adapted from Irmscher K, Schulz T, Albrecht M, Hartmann C, Wollweber J, and Fornari R (2007) Compensating defects in Si-doped aln bulk crystals. Physica B 401–402: 323–326. Copyright Elsevier 2010.

the acceptor-like electron traps at 0.5–1.0 eV; illumination at temperatures above about 60 K would excite electrons from those levels to the SiAl donor band, where there would be electron hopping conductivity, and it was suggested that the persistence of that conductivity could be understood if the 0.5 to 1.0-eV traps are assumed to have a capture barrier against electron capture, which would prevent speedy return of the free electrons to them. That interpretation of the PPC therefore avoided the need to postulate silicon as a DX center in wz-AlN:Si. The data and interpretation are then consistent with silicon as a stable, effective-mass donor, SiAl, having its (0/þ) center as about [EC  0.10 eV]. That ionization energy value of about 0.10 eV for SiAl is consistent with the values of 0.054–0.20 eV from the hydrogenic model and of 0.060–0.180 eV from the experimental investigation of Ive et al. (2005) described above. 4.12.6.4 Conclusions on Electronic Levels and Their Identities in AlN The calculations by DFT all predict that the aluminum vacancy VAl behaves as a triple acceptor in both wz-AlN and zb-AlN. For wz-AlN, the indicated values of the (/0) level lie in the interval [EV þ 0.82 eV] to [EV þ 0.95 eV], with the (2/) and (3/2) levels at energies up to about

[EV þ 1.4 eV]. Measurements on wz-AlN indeed show that VAl has acceptor levels below midgap. Calculations for zb-AlN predict the three acceptor levels of VAl to be above EV by 1.5–1.8 eV. Complexes of VAl with oxygen are observed also to create levels in the lower half of the band gap of wz-AlN. The nitrogen vacancy VN is theoretically assessed as a deep donor in wz-AlN, its (0/þ) level being indicated as [EC  1.15 eV] or as [EC  1.75 eV] according to different calculations; experimental studies have found donor levels of VN closer to EC, at [EC  0.26 eV] and at [EC  0.86 eV] in wz-AlN. One calculation has suggested that VN0 is not stable in zb-AlN and that the defect has its (/þ) level at about [EV þ 1.5 eV]. Experimental studies show the (/0) acceptor levels of BeAl and MgAl to be at [EV þ 0.33 eV] and [EV þ 0.58 eV], respectively, in wz-AlN, in reasonable agreement with the results of theoretical work. For zinc in wz-AlN, the (/0) acceptor level of ZnAl is measured as being at [EV þ 0.74 eV]. The calculated dominant location of carbon in zb-AlN is the nitrogen lattice site as the acceptor CN, with thermal and optical hole-ionization energies of 0.87 and 1.56 eV, respectively. Silicon is calculated to be a shallow donor as SiAl in both wurtzite and zincblende AlN. Experimental data from wz-AlN show the (0/þ) level of SiAl at about [EC  0.1 eV], consistent with that calculated by hydrogenic effective-mass theory for

410 Electronic Energy Levels in Group-III Nitrides

an acceptable assumed value of the AlN dielectric constant. It is found that SiAl is thermodynamically stable and does not convert to a deep donor DX center. Experimental and theoretical indications are that oxygen is not stable as a shallow donor on the nitrogen lattice site in wz-AlN, and, instead, moves off-site and forms a deep donor DX center. It seems, however, that ON is stable as a shallow donor in zb-AlN.

4.12.7 Electronic Levels in Gallium Nitride 4.12.7.1 Structural, Electronic, and Luminescence Properties of GaN The wurtzite and zincblende structures of GaN have similar band-gap energies, that of wz-GaN having been measured as 3.44–3.457 eV at 300 K (Monemar, 1974; Koide et al., 1987; Su et al., 2002) and that of zb-GaN as 3.23–3.25 eV at 300 K (Logothetidis et al., 1994; Ramirez-Flores et al., 1994). Of the two structures, wz-GaN has the lower total energy and is therefore the thermodynamically stable form; but the metastable zb-GaN can also be formed under appropriate growth conditions and is long lasting at 300 K. In terms of optical wavelengths, the band-gap energy of wz-GaN corresponds to 360 nm and that of zb-GaN to 383 nm, the first of those being in the UV region and the second being at the UV/violet border. It is found that, even without intentional incorporation of chemical impurities, GaN very often has n-type conductivity (Go¨tz et al., 1994; Hacke et al., 1994; Lee et al., 1995; Haase et al., 1996; Wang et al., 1998), and the reason for this conductivity has been much considered, both theoretically and experimentally. The experimental measurements on as-grown wz-GaN in those studies have shown many electronic levels in the band gap over the wide energy range from [EC  0.18 eV] to [EC  0.96 eV], and the origins of these levels in terms of defects or impurities have been sought. Electron-trapping levels at 0.20, 0.27, 0.47, 0.59, and 0.83 eV have been observed by Gassoumi et al. (2006, 2009) in current-transient spectroscopy investigations on wz-AlGaN/GaN high electron mobility transistor (HEMT) structures, with the likelihood that those levels were due to defects or impurities in the GaN substrate. Hole traps at emission energies of 0.40 and 0.84 eV were also seen in those studies. In n-GaN, all donor centers within about 0.05 eV of EC are likely to be ionized near and above room temperature and so produce n-type conductivity.

Furthermore, the luminescence properties of as-grown GaN show strong indication of electronic energy levels within the band gap. As-grown wz-GaN shows UV luminescence at 3.42 eV, as expected due to CB/VB electronic transitions, but almost always exhibits strong YL (Suski et al., 1995; Sa´nchez et al., 1996). The luminescence spectrum is typically a band extending from about 1.7 to about 2.5 eV, with its peak near 2.15 eV in the yellow region of the photon spectrum. It is clear that this YL band has its origin in one or more electronic levels in the GaN band gap, such levels being due to the presence of lattice defects and/or impurity atoms. This YL is usually considered as a deleterious property of as-grown GaN, and there have been many investigations to try to find its cause and to try to eliminate it. A fairly recent review, by Reshchikov and Morkoc¸ (2005), has given a comprehensive description and discussion of the luminescence properties of GaN. A paper by Look (2001) provided a tabulated list of more than 40 electronic levels that had been experimentally observed in GaN by that date, using various electrical and optical measurement techniques; only a few of the levels were indicated by him as being due to identified defects or impurities. 4.12.7.2

Intrinsic Defects in GaN

4.12.7.2.1 Theoretical studies of the formation energies of intrinsic defects in GaN

The theoretical values of the formation energies Ef obtained for defects by DFT computations are valuable toward knowing which defects can be expected to be formed during GaN growth and which are unlikely, and in understanding the n-type conductivity almost always found in unintentionally doped GaN. Most theoretical investigations of electronic levels in GaN have considered defects and/or impurities in the wurtzite structure, but several studies have indicated that the defect formation energies and electronic levels are fairly similar in the wurtzite and cubic structures, except for some splitting of levels in wz-GaN due to its noncubic symmetry. From calculations using 32-atom supercells for VGa wz-GaN, Gorczyca et al. (1999, 2002) reported results for the formation of gallium vacancies VGa during N-rich growth. They found VGa to be an acceptor defect with near-complete VB character; their results for its formation energy Ef(VGa) in different charge states have been shown in Figure 2. Neugebauer and Van de Walle (1994a,1994b,1994c) and Van de Walle

Electronic Energy Levels in Group-III Nitrides

and Neugebauer (2004) used supercells containing up to 96 atoms in their DFT calculations. They also found VGa to be an acceptor, and their results for Ef(VGa) suggested that that defect would be easily formed in strongly n-type GaN for both Ga-rich and N-rich growth conditions. Their calculations indicated VN as a shallow donor, likely to be formed, in either growth condition, at measurable concentration in strongly ptype GaN and at low concentration in n-type GaN. Ganchenkova and Nieminen (2006) used supercells containing up to 300 atoms in their DFT calculations for wz-GaN, and gave results for Ga-rich growth conditions (Figure 9). It is seen that their calculations suggest that Ef(VN) < Ef(VGa) for all Fermi energies. As explained in Section 4.12.4.3, the values of the Fermi energy EF at which changes of slope occur in the Ef(EF) functions are the electronic energy levels of the respective defects; for example, the (/0) level of VGa is at [EV þ 0.3 eV] according to their calculations. It can also be seen in Figure 9 that their Ef(EF) data for VN contain no sections of slopes 0 or 2. Ganchenkova and Nieminen therefore concluded that the nitrogen vacancy in GaN is not thermodynamically stable in its 0 and 2 charge states. DFT calculations reported by Laaksonen et al. (2009) also used supercells containing up to 300 atoms. Their results suggested easy formation of VGa during both Ga-rich and N-rich growth of n-type GaN, and also easy creation of VN during Garich growth of either p-type or n-type GaN, and a somewhat lower concentration of VN in N-rich growth of either conductivity type.

411

In summary, although the results of the various calculations are different in detail, they agree qualitatively in respect of how the magnitudes of the formation energies of VGa and VN depend on the Fermi energy in the growing GaN and on whether the growth takes place in Ga-rich or N-rich conditions. It can therefore be expected that VGa will not be observably present in as-grown p-type GaN after either Ga-rich or N-rich growth, but that it should be present at significant concentration in n-GaN grown in N-rich conditions and probably also for Ga-rich growth. Correspondingly, nitrogen vacancies are likely to be present in strongly p-type GaN produced by Ga-rich reactants, and perhaps, depending on the growth temperature and postgrowth cooling procedures, also in p-GaN grown in N-rich conditions. As described in the following, these conclusions have been very helpful in understanding the experimentally observed defectrelated properties of GaN. Aid in interpreting experimental data has also been provided by investigations of the formation energies, in GaN, of the interstitial defects GaI and NI, and of the antisite defects GaN and NGa. Neugebauer and Van de Walle (1994) and Van de Walle and Neugebauer (2004) have reported in detail on their DFT calculations (using supercells containing up to 96 atoms) for those defects in GaN grown in Ga-rich conditions. Their results suggested that, of those defects, only GaN (of Ef about 1.0 eV) in p-GaN and possibly GaI (of Ef about 2.4 eV) in p-GaN

10 0

–

9 8 Formation energy (eV)

wz-GaN

2– 0

3–

–

7

2–

VGa

6 5

VGa – VN

3– 3–

4

3– 3

VN

2

– 3–

+

1 0 0

0.5

1

1.5 2 Fermi level (eV)

2.5

3

Figure 9 Calculated formation energies of gallium vacancies, VGa, and nitrogen vacancies, VN, in gallium-rich growth of wz-GaN. Reprinted figure with permission from Ganchenkova MG and Nieminen RM (2006) Nitrogen vacancies as major point defects in gallium nitride. Physical Review Letters 96: 196402. Copyright 2010 by the American Physical Society. For information, see: http://publish.aps.org/linkfaq.htm.

412 Electronic Energy Levels in Group-III Nitrides

have formation energies small enough to allow them to be formed at sufficient concentrations for their effects to be experimentally observable. Their calculations suggested that the other defects have formation energies of at least 3 eV in p-type GaN, and even larger, 5–7.5 eV, in n-type GaN. 4.12.7.2.2 Theoretical studies of the thermal-excitation energies of the electronic levels of vacancies in GaN

Initial overview. As explained in Section 4.12.7.2.1, the vacancies VGa and VN are theoretically assessed to have sufficiently low formation energies Ef in wz-GaN in particular growth conditions that their effects may be observable by electrical and/or optical measurements in bulk-grown or epitaxially grown material. It is therefore important to know the electronic energy levels, within the GaN band gap, that those defects are predicted to have in the different possible charge states. Figure 10 shows a summary of

the energy levels of vacancies and of vacancy-related defects in wz-GaN as given by DFT-based theoretical studies. In accordance with expression (6), the calculated energy levels are the values of the Fermi energy EF at which there are changes of slope in the calculated curve of Ef as a function of EF for each defect. Calculated electronic levels of VGa in GaN. All the major calculations indicate that the neutral gallium vacancy VGa 0 has three outer, valence electrons (as can be expected since gallium is a group-III element) and that it is an acceptor center, able to trap one, two, or three additional electrons, with the associated electronic levels (/0), (2/), and (3/2) being at energies up to about 1.0 eV above EV. The calculations of Boguslawski et al. (1995), for wz-GaN, used 72-atom supercells and suggested that the (/0) level of VGa is at [EV þ 0.3 eV] but with a threefold splitting of 0.1 eV due to the hexagonal symmetry of the wurtzite structure. Gorczyca et al. (2002)

wz-GaN EC

EV + 3.44 eV

VN

Van de Walle and Neugebauer (2004) “a shallow donor level”

EV + 3.0 eV Laaksonen et al. (2009)

Laaksonen et al. (2009)

EV + 2.0 eV

VGa in bulk 3– 2– VGa

3– 2– 2–

EV + 1.0 eV VGa

1– 1– VGa 0

3– VN 1– 3– VN 2– 1– VN 1+

Ganchenkova and Nieminen (2006) Ganchenkova and Nieminen (2006)

1– VN 1+

Elsner et al. (1998)

Ganchenkova and Nieminen (2006) Van de Walle and Neugebauer (2004) Laaksonen et al. (2009) Ganchenkova and Nieminen (2006) Laaksonen et al. (2009)

Gorczya et al. (2002) Laaksonen et al. (2009)

[VGa – ON] in bulk Elsner et al. (1998) Elsner et al. (1998)

2– 1–

[VGa – (ON)2] in bulk 1– 1+ 0 VN Van de Walle and Neugebauer (2004) 3+

Ganchenkova and Nieminen (2006) Boguslawski et al. (1995)

EV Figure 10 Examples of the calculated energy levels of vacancies and vacancy-related defects in wz-GaN.

Electronic Energy Levels in Group-III Nitrides

reported DFT calculations using 32-atom supercells. Their results gave VGa 0 as being occupied by three electrons, as in other previous theoretical investigations, and produced the (0/þ) level of the defect at [EV þ 0.3 eV]. Again, as previously, the defect was found to be a triple acceptor, and the work showed the successive electron-trapping (/0), (2/), and (3/2) levels at 0.5, 1.0, and 1.5 eV, respectively above EV. Their paper states that the lowish number atoms per supercell caused each of the levels to appear as an energy band, and that each energy level value, as quoted above, was obtained by finding the densityof-states center-of-gravity of the respective band. The DFT/LDA calculations in zb-GaN by Mattila and Nieminen (1997), also using supercells of 32 atoms, indicated the (/0), (2/), and (3/2) levels of VGa as also being at about 0.5, 1.0, and 1.5 eV, respectively, above EV (these energies being deduced by this author from Fig. 1 of their paper). The series of papers by Neugebauer and Van de Walle (1994a, 1994b, 1994c) and Van de Walle and Neugebauer (2004) produced DFT results of probably increasing accuracy using supercells of progressively larger numbers of atoms. Their calculations using 96-atom supercells (Van de Walle and Neugebauer, 2004) showed the (3/2) level of the gallium vacancy to be at about [EV þ 1.1 eV], consistent with the result of Boguslawski et al. (1995). The results of their calculations for the gallium and nitrogen vacancies and for the respective interstitial defects are shown in Figure 11. Closely similar results for VGa were found in very detailed DFT calculations by Ganchenkova wz-GaN Calculated levels CB + 3+

– 0

3–

+

2– – 0

2+

VGa

3+

+ 3+ VB

Gai

Ni

VN

Figure 11 Calculated levels of intrinsic defects in wzGaN. Reprinted with permission from Van de Walle CG and Neugebauer J (2004) First-principles calculations for defects and impurities; applications to III-nitrides. Journal of Applied Physics 95: 3851. Copyright 2010, American Institute of Physics.

413

and Nieminen (2006), using supercells of 300 atoms. As can be seen in Figure 9, their graphical plot of Ef(EF) for VGa showed changes of slope that gave its electronic levels as follows: (3/2) at [EV þ 4.27 eV], (2/1) at [EV þ 0.86 eV], and (1/0) at [EV þ 0.34 eV]. These energy levels are consistent with the values calculated by Van de Walle and Neugebauer (2004) (Figure 11). The most recent DFT calculations known are those reported by Laaksonen et al. (2009) in which they also used supercells containing up to 300 atoms. The electronic levels for VGa given by their calculations were: (3/2) at [EV þ 1.07 eV], (2/) at [EV þ 0.77 eV], and (/0) at [EV þ 0.43 eV], all of which are very similar to those of 2006, stated above, from the same research group. It is noteworthy that all recent DFT calculations give the result that VGa can be a single, double, or triple acceptor, and, taking account of the expected possible inaccuracies of the current DFT methodology, mutually consistent energy levels. Calculated electronic levels of VN in GaN. In contrast to the expectations concerning the electronic levels of the gallium vacancy VGa, whose electron wave functions are strongly related to those of electrons near the top of the VB and can therefore be reasonably well treated by DFT, the accuracies of the calculated data for the nitrogen vacancy VN, which is considered to be able to act as a shallow donor having electronic levels high in the GaN band gap, are much more uncertain. A considerable contribution to the difficulties in the calculations for VN is that, as stated in Section 4.12.4.3, the DFT method always significantly underestimates the band-gap value of any semiconductor to which it is applied. The calculations of Boguslawski et al. (1995), for VN defects in wz-GaN, used 72-atom supercells, and produced a band-gap value of 2.5 eV, that is, about 1.0 eV less than the experimentally observed value of 3.4–3.5 eV. On the basis that their calculated energy levels for VN were therefore not far enough above the top of the VB EV, their procedure for correcting each initially calculated in-gap electronic level was to move the level upward from EV by an energy equal to 1.0 eV multiplied by their calculated value of the CB content of the relevant wave functions of the level. Their results for the nitrogen vacancy VN showed electronic levels in the CB, extending down just into the band gap, so making that defect a shallow donor. Mattila and Nieminen (1997) also found VN to be a shallow donor in their DFT/LDA calculations on zb-GaN.

414 Electronic Energy Levels in Group-III Nitrides

The review by Van de Walle and Neugebauer (2004), following previous studies (Neugebauer and Van de Walle, 1994a), described the principles of the DFT/LDA method for semiconductors and presented their results to that date for III-nitrides, obtained now by use of 96-atom supercells. For VN in wz-GaN, their calculations of 2004, the results of which differed considerably from those that they had previously obtained using smaller supercells, predicted the doubly positive state VN2þ as thermodynamically unstable, but the singly positive and triply positive states to be stable with a (þ/3þ) level in the band gap at [EV þ 0.59 eV], as shown in Figure 11. Their papers of both 2004 and earlier stated that VN has also the properties of a shallow donor with its level close to EC. The further detailed DFT calculations by Ganchenkova and Nieminen (2006), for wz-GaN using supercells containing up to 300 atoms, produced results for VN that were significantly different from those of Van de Walle and Neugebauer (2004) summarized above. Their calculations suggested that VN is a negative-U center that forbids the stability of the neutral charge state and that the (3/2), (2/), and (/þ) levels of VN are closely spaced at 2.60–2.63, 2.58–2.61, and 2.43–2.46 eV, respectively, above EV, where, for each level, the first energy was obtained using the Zhang–Northrup formalism method (Zhang and Northrup, 1991) and the second by the marker method (Jones and Briddon, 1997). However, subsequent calculations (Laaksonen et al., 2009) from the same group, again employing the DFT method with supercells containing up to 300 atoms and the Zhang–Northrup procedure, produced different results for VN, suggesting that its double negative state is not thermodynamically stable and that it has levels at [EV þ 2.80 eV] for (3/) and at [EV þ 2.09 eV] for (/þ). Calculated electronic levels of the interstitial defects GaI and NI in GaN. Boguslawski et al. (1995) undertook DFT calculations for the interstitial defects GaI and NI in wz-GaN, and, to try to overcome the problem of the relative smallness of the calculated band-gap value, they applied the procedure that they had used in their calculations for nitrogen vacancies (Section 4.12.2.3). They found then that their calculations indicated two high-symmetry crystallographic locations for the gallium interstitial GaI, with electronic levels at [EC  0.8 eV] and at [EC  1.8 eV] for the neutral charge states. For NI they found two levels near [EV þ 1.0 eV], separated by 0.1 eV. The DFT results of Van de Walle and Neugebauer

(2004) suggested that the gallium interstitial GaI has a (þ/3þ) level in the upper half of the band gap at about [EV þ 2.5 eV], and that the nitrogen interstitial NI has five electronic levels from (2þ/3þ) to (/0) in normal energy order in the band gap from about 0.8 to about 2.0 eV above EV. Calculated electronic levels of the antisite defects GaN and NGa in GaN. The calculations of Boguslawski et al. (1995), for antisite defects in 72-atom supercells of wz-GaN, predicted electronic levels near midgap, at [EV þ 1.4 eV] and [EV þ 2.1 eV] for GaN, and somewhat above EV, at [EV þ 0.4 eV], and just below EC, at [EC  0.2 eV], for NGa. The 96-atom supercell calculations by Van de Walle and Neugebauer (2004) suggested electronic levels from about 0.9 to 2.7 eV above EV for each of GaN and NGa. 4.12.7.2.3 Experimental studies of intrinsic defects in GaN

Initial overview. Major experimental data for electronic levels proposed by the respective researchers to be due to intrinsic defects in wz-GaN, and the identities suggested by them, are shown in Figure 12. The studies involved as well as the results are discussed in the following. Experimentally observed levels of irradiation-damageinduced intrinsic defects in GaN. Valuable work using electron irradiation of GaN to investigate intrinsic defects in GaN has been accomplished by Look et al. (1997, 2003; Look, 2001). They investigated, by temperature-dependent Hall effect and PL, the electronic energy levels of defects created in wz-GaN by electron irradiations of energies up to 1.0 MeV at room temperature. In particular experiments, Look et al. (2003) irradiated the GaN along the [0001] direction, and they stated that although the minimum knock-on energy Ed for displacement of gallium atoms had been calculated as 22 eV and that for displacement of nitrogen atoms as 25 eV, the effective Ed values for atomic displacements for irradiation along [0001] would be 38 and 66 eV, respectively, for gallium and nitrogen displacements. However, because the mass of the nitrogen atom is much smaller than that of the gallium atom, the minimum electron-irradiation energy for displacement of nitrogen atoms is significantly lower at 0.32 MeV than that for displacement of gallium atoms (the latter being 0.706 MeV: Palmer, 2005). Look et al. found that electron irradiations at 0.42 MeV, that is, irradiations that would cause direct displacement of nitrogen atoms (creating nitrogen interstitials NI and nitrogen vacancies VN) but not

Electronic Energy Levels in Group-III Nitrides

415

wz-GaN Measured levels proposed to be due to the intrinsic and intrinsic-defect complexes indicated EC Donor

EC – 0.070 eV Look et al. (1997, 2001, 2003) VN Castaldini et al. (2000)

EV + 3.44 eV

EC – 0.24 eV Arehart et al. (2008a, 2008b) VN EC – 0.25 eV Cho et al. (2008)

EV + 3.0 eV

EC – 0.52 eV Castaldini et al. (2000) NI or [VGa – NI] EC – 0.59 eV Castaldini et al. (2000) EC – 0.62 eV Cho et al. (2008) [VGa – (ON)3] EC – 0.80 eV Umano-Membrane et al. (2008)

Acceptor

EC – 0.90 eV Castaldini et al. (2000) NI or [VGa – NI] EC – 1.0 eV Polyakov et al. (2008) Ni - related EC – 1.01 to 1.08 eV Ito et al. (2008a, 2008b) NGa

EV + 2.0 eV

EV + 1.0 eV

EC – 0.025 eV Yang et al. (2003, 2006) VN

Acceptor

EC – 2.4 eV

Quoted from 3– Arehart et al. (2008a) VGa

E – 2.62 eV Arehart et al. (2008a) [VGa – (HI)n] Acceptor EC + 0.87 eV Hierro et al. (2000a) V Polyakov et al. (2002) Soh et al. (2004) VGa Levels near Emiroglu et al. (2007, 2008) [V – (O ) ] Ga N n EV + 0.87 eV n = 0–3

EV Figure 12 Examples of measured levels in wz-GaN that have been proposed to be due to the stated intrinsic defects.

of gallium atoms, produced a defect donor level at [EC  0.070 eV]. On the basis of the previous theoretical work (see above) that had suggested that VN is a shallow donor but that NI is a deep acceptor, they proposed the observed electronic level at [EC  0.070 eV] to be due to VN. The later theoretical study by Van de Walle and Neugebauer (2004) also indicated VN as a shallow donor. An electron trap having a very similar ionization energy, 0.06 eV, was found by DLTS measurements on gamma-irradiated GaN, together with other electron traps having ionization energies 0.10, 0.20, and 0.27 eV (Goodman et al., 2001). It seems likely therefore that the donor level close to [EC  0.070 eV] in GaN is indeed due to the

nitrogen vacancy VN. Look et al. found also that the irradiation produced acceptor levels (whose energies were not determinable by the experimental method used) and caused a decrease in the concentration of donor levels of energies near [EC  0.025 eV] that were present in the n-GaN before irradiation. Because NI is believed to be an acceptor (and therefore is N I in the n-GaN) and is likely to be mobile at room temperature, and assuming that the pre-irradiationobserved [EC  0.025 eV] level to due to ONþ donors, they suggested that the irradiationinduced acceptor levels were due to the complex (ON–NI)0 formed as a result of Coulomb attraction of mobile NI – to ON þ .

416 Electronic Energy Levels in Group-III Nitrides

Previously, Castaldini et al. (2000) had reported upon their investigations, including by DLTS, of the lattice defects produced in HVPE-grown wz-GaN by 20 GeV proton irradiation near room temperature. Although that irradiation energy is very high, it is likely that many of the irradiation-induced defects are the same simple defects that are created by electron and proton irradiations at 0.5–2 MeV. The DLTS measurements before irradiation showed a strong peak due to an electron trapping level at [EC  0.20 eV], but the DLTS peak height was not changed by the irradiation; the defect causing the peak was considered to be the same as reported in other measurements on as-grown GaN as having its electronic level at [EC  0.25 eV]. It was found, however, that the irradiation produced additional DLTS peaks, and an electronic level at [EC  0.08 eV] was deduced by shape-fitting analysis of a prominent irradiation-induced peak. This peak was considered to be the same as reported at [EC  0.064 eV] by Look et al. (1997) and similarly proposed to be due to VN, and that identity is strengthened by the data of Look et al. (2003), which reported the ionization energy as 0.070 eV. The DLTS measurements by Castaldini et al. indicated that the irradiation also created electron traps having levels at [EC  0.52 eV], [EC  0.59 eV], and [EC  0.90 eV], of which possible identities of NI or [VGa–NI] were suggested. In an informative investigation of irradiationinduced defects in n-type wz-GaN, Polyakov et al. (2008a) used 10 MeV electrons to irradiate MBEgrown AlGaN/GaN and AlN/GaN HEMT structures and made electrical conductivity, capacitance–voltage, and DLTS measurements to study the effects of the irradiation. They found that the n-GaN became resistive due to compensation by irradiationinduced acceptor defects having energy levels near [EC  1.0 eV], and they proposed that those defects involved irradiation-induced nitrogen interstitials. There is thus the reasonable possibility that those [EC  1.0 eV] acceptors are due to the (ON–NI)0 defects proposed by Look et al. (2003). Cho et al. (2008) used DLTS and PL in a study of the effects of plasma-ion damage of n-GaN grown by MOCVD. They reported that the as-grown GaN showed the presence of two electron traps E1 and E2, located in the band gap at [Ec  0.25 eV] and [Ec  0.62 eV] respectively, and, on the basis of the proportionality that they observed of the DLTS signal strength to the logarithm of the DLTS trapfilling pulse, they suggested that both traps were

spatially associated with dislocations. They also found that the concentration of each trap was changed by the plasma irradiation, that the E1 concentration was strongly enhanced for both low and higher plasma bias voltages and that the E2 concentration and also the YL were increased during plasma damage at low bias voltages and decreased at higher bias voltages. They suggested that E1, at [EC  0.25 eV] and probably a donor defect, is an electronic level of the nitrogen vacancy VN; if this is a correct assignment, then the VN defect has electronic levels at both [EC  0.070 eV] (see above) and at [EC  0.25 eV]. Concerning their observed electronic level E2, they proposed that to be the complex [VGa–(ON)3], on the basis of the general consensus that the YL involves gallium vacancies and oxygen impurity atoms, and that the theoretical work by Elsner et al. (1998) has suggested that [VGa–(ON)3] can be formed near dislocation cores. Measurement of the electronic properties of irradiated semiconductors, as described above, can provide information about the energy levels of the irradiation-induced defects, but do not, by themselves, completely indicate the identities of the defects producing those levels. It is therefore valuable to be able to obtain experimental information that can distinguish different kinds of irradiationinduced defects. Studies by Tuomisto et al. (2007a, 2007b) used the PAS technique (Section 4.12.6.2.2) on unintentionally doped n-type wz-GaN grown by HVPE to investigate the effects of irradiation at room temperature by electrons of energy 0.45 MeV (in which, as has been explained above, the irradiation damage is due to the displacement only of nitrogen atoms) and of energy 2.0 MeV (which produces both nitrogen and gallium displacements). Their PAS data showed vacancies present as VN0 and stable at room temperature in the GaN irradiated by 0.45 MeV electrons and that those vacancies were removed by heating near 600 K. They suggested that that annealing was due to VN–NI recombination by mobile nitrogen interstitials NI. The implication is that nitrogen interstitials are also stable at room temperature in wz-GaN. In addition, they found that the 2.0 MeV electron irradiation created defects related to gallium vacancies, and their thermal annealing investigations suggested that about half of those defects were isolated VGa– , which also disappeared near 600 K, and that the rest, suggested to be defect complexes involving VGa, were removed by heating at 800–1100 K.

Electronic Energy Levels in Group-III Nitrides

Irradiation of free-standing nominally undoped (but probably containing ON and SiGa) n-type HVPE wz-GaN by 0.42 MeV electrons in studies by Yang et al. (2003, 2006) gave data interpreted as also providing information about the nitrogen vacancy in wz-GaN. Their PL data from the irradiated GaN showed bound exciton lines assessed as arising from an irradiation-induced shallow hydrogenic shallow donor having an optical ionization energy of 24.9  0.4 meV. On the basis that 0.42 MeV electrons are able to displace only nitrogen atoms and that VN is expected to be a shallow donor, they attributed the level located near [EC  0.025 eV] to the donor level of VN. Laser-illumination increases of the intensities of ON-bound and SiGa-bound exciton PL lines in the irradiated GaN were interpreted as being due to release of nitrogen interstitials NI from [NI–ON] and [NI–SiGa] complexes formed by trapping of negatively charged irradiation-induced NI by ON þ and SiGa þ . Although Look et al. (1997, 2001, 2003) had proposed (see above) that the VN has its donor level at [Ec  0.070 eV], Yang et al. (2006) suggested that that level might instead be due to [NI–ON] or [NI–SiGa]. The effects of electron irradiation at 0.546 and 2.28 MeV (the two energies simultaneously employing a 90Sr radioactive source) on n-type GaN were studied using DLTS by Goodman et al. (2001). They found that an electron-trapping level at [EC – 0.22 eV] was produced by the irradiation at a large introduction rate that suggested that it resulted from primary displacements of gallium or nitrogen atoms. Earlier electrical property investigations of the effects of 60Co gamma-ray irradiation of n-type wz-GaN had shown irradiation-induced creation of various deep-level electron traps; however, because, as in the investigation by Goodman et al. (2001), such irradiation certainly causes displacement of both gallium and nitrogen from their respective lattice sites, valid identification of the levels with particular defects is difficult. Shmidt et al. (1999) reported that their irradiations increased the concentration of an electron-trapping level at [EC  0.59 eV] present before irradiation, and also produced new electron traps at [EC  0.115 eV] and [EC – 0.95 eV]. Subsequent work by Umana-Membreno et al. (2002, 2003) showed gamma-irradiation-induced electron traps at energies of [EC  0.089 eV] and [EC  0.132 eV], which they suggested to be due to VN-related defects. Clear identification of defects created in GaN by electron irradiation was achieved in the

417

investigations of Watkins et al. (1997; Linde et al., 1997; Chow et al., 2000, 2004; Johannesen et al., 2004). That was possible because the measurement technique used optical detection of electronparamagnetic resonance (ODEPR) and allowed determination of the nature and local environments of observed lattice defects. The electronic levels of several irradiation-induced defects could then also be determined. In these studies, electron irradiation at 2.0 MeV at 4.2 K of HVPE-grown n-type GaN was found to produce, without heating above 4.2 K, an ODEPR signal due to a shallow, EM donor level and another ODEPR signal labeled L5. The latter was evaluated as involving (see Figures 13(a) and 13(b)) electron transfer from the EM level down to a level at [EV þ 0.8 eV] identified as being due to gallium tetrahedral-site (T-site) interstitials in their doubly positive charge state, i.e., GaI 2þ . In addition, also without heating above 4.2 K, the irradiation produced a PL band centered at 0.95 eV. Heating at 60–300 K caused a reduction in the L5 signal and formation of new ODEPR signals L6 and L1. Detailed consideration in that work of the ODEPR signal L6 indicated it to be also due to gallium interstitials GaI 2þ , but in a lattice configuration different from that of L5. The 0.95 eV PL emission was assessed as being due to an electron transition down to the VB from a gallium vacancy level at [EV þ 0.95 eV], and it was proposed that the L1 signal was due to a transition from a level of the L6 interstitial down to that [EV þ 0.95 eV] level of the VGa. Both L5 and L6, the EM signal, and most (about 85%) of the 0.95 eV PL band were progressively removed by heating at 250–300 K, and heating above about 500 K caused disappearance of the L1 signal and the remainder of the 0.95 eV PL emission. The ODEPR, PL, and annealing data were interpreted as suggesting that L5 and subsequently L6 were gallium interstitials somewhat spatially separated from their gallium vacancies, and that the disappearance of L5 and L6 at 60–300 K resulted from GaI–VGa recombination, but leaving some isolated gallium vacancies as the cause of the residual fraction, about 15%, of the original magnitude of the 0.95 eV PL band. The paper of Chow et al. (2004) presented two alternative tentative models for the electronic energy levels and transitions producing the ODEPR and PL signals, and those are shown here in Figures 13(a) and 13(b). Important implications concerning the energy levels of lattice defects in wz-GaN, from the Watkins et al. investigations and proposals, are that

418 Electronic Energy Levels in Group-III Nitrides

(a)

wz-GaN Gai(T)

EM 0 +

(b)

VGa

Gai(O) 0 +

0 + ++ +++ EM L5

EV + 0.8 eV

EM

Gai(T)

0 +

0 +

VGa

++ EV + 2.6 eV +++

EV + 2.6 eV L6 L1

+ ++

EC

wz-GaN

+ ++ EV + 1.7 eV +++

EV + 1.1 eV

EM L5

EV + 0.8 eV

PL 0.95 eV EV

Gai(T*)

EM

0 +

0 +

EC

++ +++

L6 L1 + ++

+ PL 0.95 eV ++ EV

Figure 13 Two alternative models, (a) and (b), for the levels of irradiation-induced defects in wz-GaN, proposed using data from PL and ODEPR measurements. EM means an effective-mass donor level, Gai(T), Gai(T), and Gai(O) refer to gallium interstitials in different crystallographic locations near the gallium vacancy VGa. Reprinted with permission from Nakarmi ML, Nepal N, Ugolini C, Altahtamouni TM, Lin JY, and Jiang HX (2006) Correlation between optical and electrical properties of Mgdoped AlN epilayers. Applied Physics Letters 89: 2120. Copyright 2010, American Institute of Physics.

any defect-related electronic levels observed to be present in wz-GaN at room temperature cannot be those of isolated gallium interstitials, but that defectrelated levels found in measurements made at temperatures below 500 K may be due to isolated gallium vacancies. Experimentally observed levels of intrinsic defects in as-grown GaN. The theoretical investigations outlined in Section 4.12.7.2.1 predict both the defects that are likely to be formed during the different methods for growing GaN and their electronic levels. However, although the various theoretical studies agree fairly well about the defects expected to be created during ideal growth of pure GaN, the actual conditions for growth of GaN can never be ideal and the GaN can never be 100% pure. Furthermore, the theoretical studies often differ significantly in their calculated energy levels of the defects. In trying to identify electronic levels observed in as-grown III-nitrides including GaN, it is therefore valuable to know by other means which defects are present in the grown GaN. PAS-technique studies (Section 4.12.6.2.2) were carried out on GaN by the research group in Helsinki that included Hautoja¨rvi and Saarinen (Saarinen et al., 1997, 1998, 1999, 2001, 2006; Armitage et al., 2003; Oila et al., 2003). Their measurements showed the presence of negatively charged defects containing gallium vacancies at high concentrations (of the order of 1017 cm3 or larger) in wz-GaN that had been grown as bulk samples and

as epitaxial layers by MOCVD (Saarinen et al., 1997) and by HVPE (Oila et al., 2003). Although grown without intentional chemical doping, the GaN samples had n-type conductivity, considered to be due to oxygen incorporated as ON. Where Hall-effect measurements were performed on the same GaN material, those measurements showed acceptor defects in the GaN at the same concentrations as found for the defects containing gallium vacancies. In addition, the latter defects had almost the same spatial dependence (from the GaN final surface) as oxygen atoms, and, for a set of GaN epitaxial-layer samples, the intensity of the YL was proportional to the gallium-vacancy concentration as determined by the PAS experiments. The conclusions of those PAS investigations were 1. the acceptor defects that act as compensating centers in as-grown n-type GaN are complexes of VGa with another defect or impurity, suggested to be ON; 2. that complex could be [VGa–ON]2 formed during growth of the GaN by the Coulomb-attraction-aided diffusion to ON þ of theoretically predicted VGa 3 – ; 3. the concentration of the acceptor VGa is less than that of ON and therefore the GaN remains n-type; 4. all of the VGa are captured by ON; 5. the YL band centered at about 2.15 eV (believed to be due to an electron transition from a shallow donor to a deep acceptor) results from the presence of ON as the shallow donor and [VGa–ON]2 as the deep acceptor.

Electronic Energy Levels in Group-III Nitrides

It seems therefore that the [VGa–ON]2 has its energy level at [EC(donor ionization energy of ON)  2.15 eV]. If the ON optical donor level is at [EC  0.035 eV] (Soh et al., 2004), then the [VGa–ON]2 optical level is at [EC  2.185 eV], that is, at about [EV þ 1.255 eV]. Look et al. (2005) reported and reviewed the results of their electrical (Hall effect and DLTS) and optical (PL) investigations of the electronic levels of lattice defects and impurities in HVPE-grown n-type wz-GaN. Their data concerning silicon and oxygen are summarized in Section 4.12.7.3.4, below; their data and suggestions relating to intrinsic defects are outlined here. Their paper stated that it is clear that the nitrogen vacancy VN is a donor, that its ionization energy to the CB is approximately 0.070 eV, and that ionization energy value means that VN does not contribute to the observed room-temperature n-type conductivity in unintentionally doped GaN. Their DLTS measurements showed electron traps at [EC  0.16 eV], [EC  0.60 eV], and [EC  1.0 eV], and their paper stated that the first of those has been definitely identified with the nitrogen vacancy VN. They also stated that the second of those levels is the most common electron trap in GaN grown by any method (and that its typical DLTS characteristics indicate it to be an isolated defect), and that they have found a correlation between the presence of that trap and the blue luminescence (BL) of GaN. Concerning the [EC  1.0 eV] level, they suggested that that and also a DLTS-observed acceptor at [EV þ 1.2 eV] may be related to interstitial nitrogen. Referring specifically to HVPE-grown GaN, Look et al. stated that VGa is the dominant acceptor in such material. Valuable information was given by Arehart et al. (2008a, 2008b) from their DLTS, DLOS, and SSPC measurements on n-type wz-GaN grown by gallium/ammonia MBE. The combination of measurement techniques used in that work allowed defect and impurity levels in almost the whole of the GaN energy gap to be studied, and varying the Ga-to-NH3 flux ratio during the GaN growth aided them toward being able to identify the origins of the observed levels. Their DLTS data showed the presence of an electron trap at [EC  0.25 eV] in the GaN, and their finding that a doubling of the NH3/Ga ratio led to a reduction of its concentration by a factor of 6 strongly suggested to them that it was due to a VN-related defect. The concentrations of other DLTS-observed levels at [EC  0.40 eV], [EC  0.62 eV], and [EC  0.72 eV] also depended on the NH3/Ga flux ratio, but no clear origins of

419

these levels could be proposed. The SSPC data obtained in the studies showed a capacitance increase at an incident photon energy of 2.62 eV, i.e., due to a level at [EC  2.62 eV]. They noted that other work had suggested that the level of VGa 3 – in wz-GaN is close to [EC  2.4 eV], but that the level is moved to about [EC  2.6 eV] by hydrogen saturation of the VGa 3 bonds (Van de Walle, 1997b). They therefore attributed the level that they observed at [EC  2.62 eV] to hydrogen-saturated VGa 3. However, they found that changing the Ga/NH3 ratio in the MBE growth process produced no observed effect on the concentration of that electronic level, and they surmised that that might be due to the opposing gallium and hydrogen effects of altering that flux ratio. DLTS investigations by Ito et al. (2008a, 2008b) on n-type MOVPE-grown GaN showed electron traps at [EC – 0.49 eV], [EC  (0.72–0.92 eV)], and [EC  (1.01–1.08 eV)]. The filling-pulse-duration dependence of the second of those indicated it as a point defect, not a dislocation-related defect. The third level, at [EC  (1.01–1.08 eV)] was suggested, following Polenta et al. (2007), to be due to the antisite defect NGa. From DLTS investigations on MOVPE material, Umana-Membreno et al. (2008) reported levels at [EC  0.53 eV] and [EC  0.80 eV], which seem likely to be the same, respectively, as the first and second levels specified above as seen by Ito et al. They observed a level also at [EC  0.21 eV], and it seems reasonable to assume that that was the level found at [EC  0.25 eV] by Arehart et al. (2008a, 2008b) (see above) and attributed by them to VN. By use of minority-carrier DLTS, Umana-Membreno et al. (2008) observed the presence of a level at about [EV þ 0.65 eV] in their MOVPE-grown GaN. In studies employing DLTS and Laplace DLTS (LDLTS) on MOVPE n-type wz-GaN, Emiroglu et al. (2007, 2008) reported electronic levels attributed to [VGa–ON ] complexes, and those results are summarized Section 4.12.7.3.4 below concerning oxygen in GaN.

4.12.7.3

Impurity Dopants in GaN

4.12.7.3.1 Theoretical studies of the electronic levels of impurity atoms in GaN

The hydrogenic, effective-mass model for calculating the ionization energies of dopants in semiconductors has been outlined in Section 4.12.4.2. For zb-GaN,

420 Electronic Energy Levels in Group-III Nitrides

the model gives the (/0) acceptor level at [EV þ 0.214 eV] when the average hole EM and the dielectric constant stated by As et al. (2002) are used. That value would apply to group-II elements, such as magnesium, on gallium lattice sites, and to group-IV elements such as carbon on nitrogen sites. Calculated hydrogenic ionization energies for acceptors in wz-GaN and zb-GaN were also reported by Wang and Chen (2001), as 150.4 meV for wz-GaN and 137.2 meV for zb-GaN; but their paper did not state what values of KS and mh  they had used. Concerning donors, if values of 0.2 and 5.5, respectively, for (me/m0) and the dielectric constant KS of wz-GaN are used (Tansley and Egan 1992), the model gives the (0/þ) donor level at [EC  0.090 eV]. However, if the values are 0.2 and 9.4 (Look et al., 2005), then the level would be at [EC  0.0339 eV]. These are therefore estimates for wz-GaN of the donor level of an atom of a group-IV element

occupying a gallium lattice site and an atom of a group-VI element on a nitrogen lattice site. In order to improve the estimates of the acceptor and donor ionization energies, several research groups have, in the hydrogenic model, used hole and electron properties calculated specifically for the particular III-nitride semiconductor and impurity atom under consideration. Tables 4 and 5 show values for the ionization energies of acceptor elements in wz-GaN and zb-GaN, as calculated by Mireles and Ulloa (1998) and by Wang and Chen (2001). The work of Mireles and Ulloa used an EM treatment, with detailed parameter calculations including of the pseudo-potentials applicable to the holes (instead of the simple Coulomb potential of a hydrogenic model) for each impurity atom in the two crystal structures. The ionization energies shown in the Tables 4 and 5 are their tabulated values that took polaron corrections into account, and the ranges

Table 4 Theoretical ionization energies for acceptor elements in wz-GaN obtained using calculated effective-masses and pseudopotentials, as reported in the papers stated. wz-GaN

Element BeGa MgGa CaGa ZnGa CdGa CN SiN GeN

Ionization energy in eV (Mireles and Ulloa, 1998)

Ionization energy in eV (Wang and Chen, 2001)

0.193–0.241 0.204–0.253 0.255–0.305 0.331–0.419

0.186–0.190 0.224 0.295–0.301 0.355–0.367 0.597–0.621 0.142–0.161 0.225 0.278–0.284

0.223–0.272 0.191–0.239

Table 5 Theoretical ionization energies for acceptor elements in zb-GaN obtained using calculated effective-masses and pseudopotentials, as reported in the papers stated zb-GaN

Element BeGa MgGa CaGa ZnGa CdGa CN SiN GeN

Ionization energy in eV (Mireles and Ulloa, 1998)

Ionization energy in eV (Wang and Chen, 2001)

0.125–0.133 0.130–0.140 0.151–0.164 0.162–0.184

0.183 0.220 0.296–0.298 0.355–0.356 0.604–0.622 0.142–0.143 0.220 0.276

0.138–0.148 0.125–0.132

Electronic Energy Levels in Group-III Nitrides

of values indicated arose from differing assumed VB properties. The theoretical method employed by Wang and Chen was also an EM treatment, but was different in detail from that of Mireles and Ulloa in respect of the hole masses and the potentials. It is seen that the ionization values obtained in the two calculations are not very different from each other, except for CN in wz-GaN and for ZnGa and SiN in zb-GaN. A different theoretical method was employed by Boguslawski and Bernhole (1997) to calculate the properties of substitutional carbon, silicon, and germanium atoms in wz-GaN. They used quantum molecular dynamics in the LDA, with 72-atom supercells, and the calculation allowed locationrelaxation of the atoms. Their paper stated that their treatment of the gallium d-electrons as part of the atomic core potential instead of as outer electrons produced an error of about 0.2 eV in the GaN energy-gap value, in addition to errors due to other approximations such as the LDA. They noted that the noncubic symmetry of the wz-GaN would cause twofold energy splitting. Their calculations gave the result that CGa, SiGa, and GeGa would each behave as a shallow EM donor, and that the formation energy of SiGa would be low in both gallium-rich growth (0.9 eV) and nitrogenrich growth (1.4 eV) and that that of GeGa would be 2.3 and 2.2 Ev, respectively for those growth conditions. However, the Ef values for CGa were indicated as being large, 5.7 and 4.0 eV, respectively. Their calculations suggested that a deep donor state, a DX center (Section 4.12.6.3.1), could be formed by movement of the carbon atom from the gallium lattice site, but that such a deep state would not be stable for a silicon or germanium atom. Concerning the respective atoms as acceptors on nitrogen lattice sites, the calculations showed each as having two symmetrysplit electronic energy levels. The two levels of CN 0 were obtained as about 0 eV and 0.2 eV above EV, those of SiN 0 as about 0.6 and 1.2 eV above EV, and those of GeN 0 as about 0.75 and 1.35 eV above EV. Of the formation energies of those impurities on nitrogen sites, only that of CN 0 in Ga-rich growth (Ef indicated as 1.1 eV) was low enough to suggest that high concentrations could be formed in the practical growth of wz-GaN. It is seen that the calculations of Boguslawski and Bernhole (1997) suggested that silicon would be incorporated in wz-GaN as SiGa and therefore would produce n-type conductivity (as indeed is found), and that carbon, by forming CN, might produce p-type conductivity. The fact

421

that their calculated formation energy of the acceptor SiN was large (except perhaps for very-Ga-rich conditions) suggested that GaN:Si would always be n-type due to SiGa, and not of high resistivity due to the presence of both SiGa and SiN. Calculations of the (/0) electronic energy levels of the acceptors MgGa and CN in wz-GaN were made by Chisholm and Bristowe (2001), using a DFT/LDA treatment applied to computational cells of 108 atoms, with the gallium d-electrons being taken into account properly as valence electrons. Their calculations gave the (/0) level of MgGa at [EV þ 0.14 eV] and that of CN at [EV þ 0.37 eV]. The ionization energy of CN in wz-GaN was also calculated by Wright (2002), using the DFT/LDA method on 72-atom supercells, with the gallium d-electrons set also as valence electrons. His study put the (/0) level of CN at [EV þ 0.3 eV], but he emphasized that ionization energies given by such calculations are expected to be accurate only within 0.2 eV. The calculations of formation energies indicated that carbon would be expected to be easily incorporated as CN during both Ga-rich and N-rich growth of wz-GaN. Wright (2002) also considered carbon on gallium sites and his calculations indicated that defect, CGa, to be a donor with its (0/þ) level likely to be at about [EC  0.2 eV]. For the formation energy of CGa, his calculations indicated values of about 3.0 to 6.5 eV for gallium-rich growth and of 1.5 to 4.5 eV for nitrogen-rich growth, where the lower values were for p-type GaN (the latter being of course encouraging for the creation of the donor defect CGa). These theoretical results therefore suggested that, if carbon is available during growth of GaN, the carbon atoms will easily go onto nitrogen sites as the acceptor CN and so produce p-type GaN, but that that is likely to lead to the incorporation of the carbon also on gallium sites as the donor CGa; in other words, both CN and CGa would be formed, thus leading to highresistivity GaN. As described in Section 4.12.7.3.3, experimental measurements show that that is indeed so, at least for wz-GaN. For zb-GaN, calculated, DFT/LDA properties of carbon as the acceptor CN were reported by Ramos et al. (2002) for supercells containing from 64 to 1000 atoms. For that largest supercell, they obtained the (/0) level of CN at [EV þ 0.182 eV], but their paper stated that increasing the number of atoms per supercell upward from 1000 might cause the level to be slightly higher in the band gap. Their investigation also suggested that the formation energy of CN in zb-GaN is small enough to allow its creation during many typical growth situations. They, however,

422 Electronic Energy Levels in Group-III Nitrides

reported no information concerning the donor CGa in zb-GaN. The results of a series of theoretical studies of several important impurity atoms in GaN by Van de Walle and Neugebauer (Neugebauer and Van de Walle, 1994b, 1996, 1999; Van de Walle and Neugebauer, 1997, 2004) can be summarized as follows. Their work used the DFT/LDA computational method on wz-GaN supercells containing up to 96 atoms, and the gallium d-electrons were typically considered as valence electrons. As other theoretical investigations had also indicated, their results showed both SiGa and ON to be shallow donors, and their formation energies to be very low in p-GaN, rising to only about 1 eV in n-GaN (thus strongly suggesting that wz-GaN should be able to be easily made n-type by incorporation of silicon or oxygen). Concerning acceptor dopants, their calculations gave MgGa as having its (/0) electronic level at about [EV þ 0.20 eV], (Neugebauer and Van de Walle, 1996; Van de Walle and Neugebauer, 2004), its formation energy being fairly low, about 2 eV in strongly p-type GaN and about 0.5 eV in n-type GaN, even for gallium-rich growth. Their results for magnesium on nitrogen lattice sites and in interstitial positions showed large formation energies such that very few magnesium atoms would be expected to take up such locations. The (/0) acceptor levels of calcium and zinc, that is, CaGa and ZnGa, were indicated by their calculations (Neugebauer and Van de Walle, 1999; Van de Walle and Neugebauer, 2004) as being at about [EV þ 0.64 eV] and [EV þ 0.23 eV], respectively. Latham et al. (2003) reported on their DFT–LDA calculation on beryllium as BeGa in wz-GaN, for which they used supercells of 72 atoms, the gallium d-atoms being included as part of a modified pseudopotential for the core electrons. Because of the limitations of the theoretical method, they were unable to deduce an absolute energy location for the (/0) acceptor level of BeGa, but calculated it to be about 0.09 eV below that of MgGa. Using an experimental result of [EV þ 0.208 eV] for that MgGa level (Go¨tz et al., 1999), they therefore deduced the (/0) level of BeGa to be at about [EV þ 0.12 eV]. Calculations were made by Teisseyre et al. (2005) of the (/0) acceptor level of BeGa in zb-GaN by using a DFT/LDA treatment and the LMTO basis set on 32-atom supercells. From their calculated formation-energy function Ef(EF), they predicted the acceptor level of BeGa to be at [EV þ 0.075 eV].

Popovic et al. (2004) noted the possibly important magnetic properties of GaN:Mn and reported on their DFT calculations concerning respectively MnGa and interstitial MnI in wurtzite-structured Ga15MnGaN16 and Ga16MnIN16 supercells. The calculations predicted MnGa to be a deep acceptor having an electronic level at about [EV þ 1.8 eV], and they pointed out that the result agreed precisely with data reported from optical absorption measurements on GaN:Mn (Graf et al., 2002), which indicated that the manganese had a (2þ/3þ) acceptor level at 1.8 eV above EV. The study by Popovic et al. gave MnI as a deep donor, its electronic level being at about [EV þ 2.4 eV] in the situation that the energy gap Eg of the Ga16MnIN16 compound was obtained as 3.8 eV in their calculations. 4.12.7.3.2 Experimental studies of acceptor impurities in GaN

Introduction. It is expected that acceptor centers will be formed in GaN if atoms of the group-IIa elements, that is, beryllium, magnesium, calcium, strontium, and barium, or atoms of group IIb, that is, zinc, cadmium, and mercury, go into gallium lattice sites, or if atoms of group-IV elements, that is, carbon, silicon, germanium, tin, and lead, occupy nitrogen sites. As summarized in Section 4.12.7.3.1, theoretical studies predict MgGa in wz-GaN to have its (/0) acceptor in the energy region [EV þ 0.2 eV] to [EV þ 0.25 eV], that is, that it is a fairly deep acceptor center. As will be shown below, data from experimental investigations accord with that prediction but indicate a variety of additional important effects of magnesium in GaN. Concerning doping by beryllium, the calculations for GaN:Be suggest (Table 4) that the (/0) level of BeGa might be somewhat lower, perhaps at about [EV þ 0.19 eV], than that of MgGa, and that therefore beryllium in wz-GaN would be more easily activated as an acceptor than magnesium. In addition, the fact that a beryllium atom is considerably lighter than a magnesium atom has the effect that the ion implantation range of beryllium is larger than that of magnesium for the same implantation voltage. However, the severe carcinogenic properties of beryllium and its compounds constitute a considerable deterrent to the technological use of beryllium for doping semiconductors. Additionally, beryllium is much more costly than magnesium. Nevertheless, there have been a few experimental investigations of GaN:Be. Concerning the other group-IIa elements and the group-IIb elements, the calculated ionization energies of their

Electronic Energy Levels in Group-III Nitrides

atoms situated on gallium lattice sites are mostly found, as has been stated in Section 4.12.7.3.1, to be larger than that of magnesium, and so seem likely to be even less activated as acceptor dopants, at room temperature. The outcome is that magnesium is the group-II element whose electronic energy levels have been the subject of most experimental investigations in GaN. In respect of the group-IV elements as acceptors when their atoms occupy nitrogen sites, theoretical work has strongly suggested that only CN has a formation energy in GaN that is low enough to allow it to be present at sufficient concentration to produce p-type conductivity. It is found, however, that in wz-GaN (but perhaps not in zb-GaN) the carbon atoms can go also into gallium sites, as the donor CGa, and so offset the acceptor activity of the CN atoms. The observed electrical and optical properties of carbon in wz-GaN and zb-GaN, and the deduced information about its electronic levels, are described in Section 4.12.7.3.3. Magnesium in GaN. Magnesium is the element that, as MgGa, has been most used to produce chemically doped p-type GaN. Hall-effect studies have shown, however, that even growth conditions for wzGaN:Mg that should be considered as optimum for incorporation of the magnesium produce a resultant hole concentration at room temperature that is only a few percent of the concentration of magnesium atoms. That low activation fraction of the magnesium atoms suggests that MgGa is a deep acceptor, and analysis of the various sets of experimental data indicates the (/0) level to be in the approximate energy region [EV þ 0.15 eV] to [EV þ 0.25 eV]. There is the difficulty, however, that measurements on GaN:Mg grown using different techniques and growth/annealing conditions are found to give different values for the ionization energy of the magnesium atoms. The general belief is that, although magnesium atoms can occupy gallium sites as simple MgGa acceptor centers, they are often in the form of complexes, with lattice defects and impurities, which may or may not be acceptors. It is convincingly believed that hydrogen, easily available during GaN growth, such as by HVPE and MOVPE, can passivate the magnesium acceptor due to the formation of Mg–H complexes by Coulomb-attraction-assisted diffusion of Hþ to MgGa – . Some details of these results are given in the following. In Hall-effect/temperature studies of magnesiumdoped GaN grown by the MOVPE technique, Tanaka et al. (1994) found two acceptor levels, close to [EV þ 0.13 eV] and [EV þ 0.16 eV].

423

Huang et al. (1996) reported on their frequencydependent capacitance and admittance spectroscopy investigations on lightly magnesium-doped and on strongly magnesium-doped MOVPE GaN; their data indicated the presence of two magnesiumrelated acceptors, at [EV þ 0.124 eV] and at [EV þ 0.160 eV] respectively, for the lower magnesium concentration, but a single acceptor level at [EV þ 0.136 eV] for the more strongly doped sample. For MOCVD-grown GaN:Mg, Hall-effect and conductivity measurements by Johnson et al. (1996) indicated an acceptor activation-energy range of 0.17 to 0.18 eV. Studies by Kim et al. (1996, 1997) on GaN:Mg grown by reactive MBE showed activation energies in the range 0.11 to 0.21 eV. Similar data were obtained by Kozodoy et al. (2000) on MOVPE-grown material in investigations by temperature-dependent Hall-effect measurements; they found that progressive increase of the magnesium concentration in the GaN caused the acceptor activation energy to decrease from 0.190 to 0.112 eV. Using the same measurement method, Go¨tz et al. (1999) also noted a magnesium-concentration dependence of the observed magnesium-ionization energy in GaN. By extrapolation to low magnesium concentrations, they proposed the acceptor level of isolated MgGa to be at about [EV þ 0.208 eV] within a precision of 0.006 eV. High-temperature annealing of MOCVD-grown GaN:Mg was found by Seghier and Gislason (2000) to produce progressive increase in p-type conductivity, that the annealed material showed acceptor levels at [EV þ 0.13 eV] and [EV þ 0.17 eV] (the latter being of low concentration) and that the concentration of the 0.13 eV level was proportional to the measured hole concentration. They concluded that the annealing-induced p-type conductivity was produced by dissociation of a magnesium–hydrogen complex, leading to the formation of a simpler magnesium acceptor whose level was that observed at [EV þ 0.13 eV]. Activation of Mg acceptors, as observed by electrical capacitance measurements on a p-GaN:Mg/nþ-GaN junction structure, by heat treatments above 550 C in a nitrogen atmosphere, had previously been found by Pearton et al. (1996); their finding also that, during heating in a hydrogen atmosphere, activation did not occur significantly until 650  C was evidence that the activation of the magnesium acceptor involved dissociation of a magnesium–hydrogen complex. Acceptor activation of as-grown GaN:Mg by heat treatment in nitrogen gas at about 700  C or above is

424 Electronic Energy Levels in Group-III Nitrides

now a well-established procedure in GaN device manufacture. Information on Mg-related electronic levels in GaN has been also sought by optical methods, in particular by photocapacitance measurements, photoluminescence excitation (PLE), and PL emission. However, despite much experimental and theoretical work, the identities of the electronic levels between which the optically induced transitions occur in GaN:Mg are in general still uncertain (Reshchikov and Morkoc¸, 2005). In addition to the full band-to-band transition, there may be a transition between the CB and an acceptor level near to the VB or between a donor level near the CB and such an acceptor, the latter being a DAP transition. This uncertainty denotes that it is not possible to use the observed optical-energy data to deduce with validity the electronic levels involved in the various observed transitions or their identities; however, some indications can be obtained. Yi and Wessels (1996) studied MOVPE-grown n-GaN without and with partial compensation of the n-type conductivity by magnesium incorporation and investigated the electronic levels in the n-GaN by use of photocapacitance measurements on Schottky diode structures. They reported that their optical-threshold capacitance data showed that incorporation of the magnesium created levels at 1.0, 1.2, 1.8, and 3.1 eV below the CB, and that heating the n-GaN:Mg in nitrogen gas at 850  C caused the removal of all the levels except that at 3.1 eV, which might therefore correspond to electron excitation from the MgGa – acceptor level to the CB. MOCVD-grown wz-GaN:Mg was studied by Hierro et al. (2000a), using both standard DLTS and DLOS, and they were thus able to investigate the energy levels of majority and minority carrier traps in much of the whole band gap. Of the various observed levels, they proposed those at 0.58–0.62 eV and at 3.22 eV below EC to be associated with the presence of magnesium, and, in particular, that the latter, at [EC  3.22 eV], was the acceptor level of MgGa. Using 3.44 eV as the band-gap value, they deduced the MgGa acceptor level to be at approximately [EV þ 0.22 eV]. Likely confirmation that as-grown MOCVD-grown GaN:Mg contains complexes of MgGa and hydrogen was shown in a further study by the same research group (Hierro et al., 2000b). They found that postgrowth hydrogenation of the GaN in an RF-plasma reactor produced no change in the electronic level which they observed at [EC  3.22 eV], and which probably involves MgGa

and that the lack of change could be understood if the center responsible for that level already contained hydrogen. That the level at [EC  3.22 eV] is due to magnesium acceptors was stated by Armstrong et al. (2004) as having been established. A slightly different energy location of that level, [EC  3.24 eV], was reported by Armstrong et al. (2008) for the MgGa level from their measurements by SSPC and DLOS on p-type GaN grown by plasma-assisted MBE. Their analysis of their experimental data showed a zero value for the Franck–Condon energy for that level (Armstrong A, 2009, personal communication, the Sandia National Laboratories, USA); that is, its optical and thermal ionization energies were found to be the same. Their DLOS data showed also a level at [EC  2.97 eV] and they stated that it might be the same as that observed by DLTS at [EV þ 0.45 eV] in MOCVD-grown GaN:Mg (Armstrong et al., 2005), and that, if so, the Franck– Condon shift dFC is small, equal to 0.02 eV, for that defect (that deduced dFC value being [3.44 eV– 2.97 eV–0.45 eV] in which 3.44 eV is the assumed band-gap energy). Still concerning here the acceptor level of MgGa, Reshchikov and Morkoc¸ (2005) discussed the energy levels of defects and impurities that may provide the electronic transition that produces the UV luminescence band (named by them the UVL band) in GaN:Mg. This band has its zero-phonon line at 3.27 eV and they stated that it is well established that it is due to a transition from a shallow donor down to the acceptor level of MgGa. If then one assumes that the MgGa acceptor level is at [EV þ 0.22 eV] (see above) and small Franck–Condon energy shifts, then that shallow donor level lies at about [EC  0.05 eV]. A very important property of Mg-doped GaN is the PL band in the blue region of the spectrum, with its maximum close to 2.8 eV, that is usually strong even at room temperature. Kaufmann et al. (1999) reported that they observed that blueluminescence (BL) band in MOCVD GaN having magnesium concentrations of greater than about 1  1019 cm3 and, by investigation of the dependence of the BL emission upon the intensity of the laser excitation source, they concluded that the BL is due to a DAP electronic transition. Their paper presented convincing arguments that the shallow acceptor was the acceptor of MgGa, and, on the basis of that latter level being at about [EV þ 0.20 eV] and the band gap being 3.43 eV, they deduced that the donor level lay at about [EC  0.43 eV], that is, a deep donor. They

Electronic Energy Levels in Group-III Nitrides

wz-GaN:Mg

wz-GaN EC

Ev + 3.44 eV Deep donor perhaps [MgGa – VN]

Ev + 3.0 eV

Blue luminescence at about 2.8 eV

Ev + 2.0 eV

Ev + 1.0 eV

Normalized PL intensity (lin. scale)

0.43 eV

[Mg] = 1 × 1019 cm–3

0.2 eV

MgGa

Figure 14 The levels and transitions associated with the blue-luminescence property of wz-GaN:Mg as proposed by Kaufmann et al. (1999).

suggested that that deep donor was a [MgGa–VN] complex, spatially close enough to a MgGa to allow the electronic transition to occur. The paper by Reshchikov and Morkoc¸ (2005) discussed the BL band in detail and also concluded that it is due to transitions from deep donors down to the MgGa acceptor level, not to transitions from the CB or from a shallow donor down to a Mg level further above EV than that of MgGa. The energy levels and transition producing the BL proposed by Kaufmann et al. are illustrated in Figure 14. On the basis of their DLOS and DLTS data, Armstrong et al. (2008) suggested that either or both of the [EV þ 3.05 eV] and [EV þ 3.22 eV] near-CB levels that they observed might be the shallow donor involved in the DAP transition that produces the BL band. In detailed PL studies of MOCVD-grown magnesium-doped p-type wz-GaN before and after thermal annealing at 800  C, Monemar et al. (2006, 2009) found that the as-grown GaN:Mg showed at low temperature (at which the GaN band gap was about 3.47 eV) an acceptor-bound exciton (ABE) PL band, ABE1, with its zero-phonon line at 3.466 eV, and that the annealing treatment removed that band and produced a new ABE band, ABE2, having its peak at 3.454 eV (Figure 15).

ABE2 ABE1

Annealed

DBE

As-grown

3.38 Ev

425

3.40

3.46 3.42 3.44 Photon energy (eV)

3.48

3.50

Figure 15 Low-temperature photoluminescence spectra from wz-GaN:Mg, as-grown and after annealing at 800  C for 1 min. (Monemar, 2009, personal communication). Reprinted figure with permission from Monemar B, Paskov PP, Pozina G, et al. (2009) Evidence for two Mg-related acceptors in GaN. Physical Review Letters 102: 235501. Copyright 2010 by the American Physical Society. For information, see: http://publish.aps.org/linkfaq.htm.

Their conclusion was that magnesium in wz-GaN creates two close acceptor levels, A1 corresponding to ABE1 and A2 corresponding to ABE2. The paper states that other work by them has shown the ABE1 luminescence to be correlated with the UVL band in GaN that has its zero-phonon line at 3.27 eV and is well established (see above) as a transition down to a level associated with MgGa. They found also that the intensity of the ABE1 band was progressively decreased during the process of luminescence excitation (using 4.65 eV photon energy, i.e., above band-gap energy), which they stated as characteristic of a defect that includes hydrogen. Monemar et al. proposed therefore that the acceptor A1 that produces the ABE1 band is a complex of MgGa, perhaps with hydrogen, and that the A2 is the MgGa itself, formed by heating-induced removal of the hydrogen from the complex A1. The paper also stated that, since the energy difference between the stated ABE1 and ABE2 energies is small (only 0.012 eV), it is very difficult for thermal excitation measurements, such as by DLTS, to distinguish between the A1 and A2 electronic levels. It is worth noting that DFT calculations by Wright et al. (2003), for wz-GaN, produced a value of 1.76 eV for the sum of the binding energy of Hþ to MgGa– and the diffusion activation energy of Hþ.

426 Electronic Energy Levels in Group-III Nitrides

That is, 1.76 eV would be the thermal activation energy for the dissociation of [MgGa–H], and it seems that that dissociation would take place at a temperature considerably lower than 800  C. Perhaps therefore the A1 acceptor of Monemar et al. is a defect that is more complicated than [MgGa–H]. An additional energy level at [EC – (0.580.62 eV)] was proposed by Hierro et al. (2000a, 2000b) to be associated with the presence of magnesium in GaN on the basis of their data from DLTS, DLOS, and SIMS measurements, which indicated that that level and the magnesium impurity had similar spatialconcentration profiles. From the information quoted above it seems very clear that unannealed magnesium-doped wz-GaN grown by MOCVD and HVPE contains much or all of the magnesium as complexes of MgGa with hydrogen, formed by the Coulomb-enhanced capture of þ Mg ions, and that heating in an Ga by mobile H inert non-hydrogen atmosphere at temperatures of about 700  C or higher can dissociate the complex so as to produce simple MgGa acceptor centers. However, it is not clear that the exact energy location of the acceptor level of the MgGa is yet known. Experimental studies such as DLOS that relate the level to the CB have produced the result that it is close to [EC  3.23  0.01 eV]. On the basis of 3.44 eV as the wz-GaN band gap, that puts the level at [EV þ 0.21  0.01 eV]. However, the Hall-effect/ temperature, thermal-equilibrium measurements give the level at close to [EV þ 0.13 eV]. It may be that the difference is due to the existence of a carrier-capture energy barrier, of about 0.08 eV, which contributes to the energy found in the nonequilibrium transient measurements, or to a nonzero Franck–Condon energy relevant in the optical excitation experiments. Also however, the PL work by Monemar et al. (2009) has suggested that Mg-related acceptor level comprises two very close levels, separated by only about 0.01 eV, with the possibility that one of them is due to MgGa itself and the other due to [MgGa–H]. In addition, various previous investigations on as-grown GaN:Mg before high-temperature annealing have indicated that the Mg is present there as a complex, also suggested as being a [MgGa–H] complex, having a hole-trapping level at about [EV þ 0.17 eV], which can be distinguished from the one at about [EV þ 0.13 eV] even by electrical measurements. Aliev et al. (2005) also experimentally investigated the acceptor levels that are found to be created in GaN by magnesium doping and proposed that isolated MgGa creates not only its expected

shallow acceptor level, but also deep acceptor levels that are not due to magnesium-defect complexes. Their investigations employed the PL and ODMR techniques applied to wz-GaN:Mg (grown by VPE and then annealed at 850  C in nitrogen gas for 20 min), and allowed measurement of the g values of the magnetic resonance microwave transition energies of the donor and acceptor levels involved in the blue-emission PL band at 2.5–3.1 eV. On the basis of their detailed analysis of the experimental data, they proposed that MgGa atoms can produce deep acceptor levels due to the trapping of a hole in a strongly localized p-orbital on an adjacent nitrogen atom, and in particular on each of the three nitrogen atoms for which the MgGa–N bond is inclined to the c-axis of the wz-GaN. The importance of the proposal is that it implies that the deep acceptors found in magnesium-doped wz-GaN are not necessarily due or not all due to magnesiumdefect complexes. Other acceptor elements in GaN. In addition to magnesium as the most commonly used acceptor dopant in wz-GaN, a few other group-II elements have been investigated for that purpose. Ronning et al. (1998) reported upon their PL investigations of wz-GaN after beryllium-ion implantation followed by thermal annealing in vacuum at temperatures up to 900  C to remove the implantation-induced irradiation-induced defects. Various PL lines were observed, and they correlated the emission at 3.35 eV to the presence of the implanted beryllium. They assumed the transition involved to be from the CB down to the acceptor level of the beryllium, and, on the basis of a band-gap value of 3.5 eV for the GaN, deduced the acceptor level of BGa to be at [EV þ 0.150  0.010 eV]. The electrical thermal-admittance method was used by Nakano and Jimbo (2002) to study berylliumimplanted GaN, and their data indicated a beryllium acceptor level at a very different energy of about [EV þ 0.231 eV]. Yu et al. (2002) implanted beryllium into GaN:Mg grown by MOCVD. They found that their temperature-dependent PL measurements on the GaN:Mg:Be samples showed an acceptor-activation energy of 0.17 eV, whereas the corresponding energy of the non-beryllium-implanted GaN:Mg had been 0.25 eV; the suggestion was that the 0.17 eV value might be the acceptor-activation energy of BeGa. Teisseyre et al. (2005) investigated, in wz-GaN:Be grown by plasma-assisted MBE, the hydrostaticpressure dependence of a PL line at 3.39 eV considered

Electronic Energy Levels in Group-III Nitrides

to be due to an electronic transition of a DAP involving a shallow donor and BeGa as the acceptor and compared their data with those obtained by them previously (Teisseyre et al., 2000) for a PL line at 3.27 eV due to the corresponding DAP transition involving MgGa in wz-GaN:Mg. With the assumption of the same donor and the same donor–acceptor separation in the GaN:Be as they had obtained for GaN:Mg, viz 2.6 nm, and taking account of the slightly different observed band-gap values of 3.47 and 3.49 eV respectively for their GaN:Be and GaN:Mg samples, they deduced the (/0) acceptor level of BeGa to be lower by 0.140 eV than that of MgGa. On the basis that their previous work had indicated [EV þ 0.247 eV] as the acceptor level of MgGa, they deduced the acceptor level of BeGa to be at about [EV þ 0.11 eV]. The rate of change of the BeGa acceptor-level energy with pressure was measured to be small, 0.8  0.5 meV GPa1, compared to about 4.8 meV GPa1 for the MgGa acceptor level. For zb-GaN, experimental data on the electronic levels of zinc as ZnGa and of cadmium as CdGa were reported by As et al. (2002), in comparison, as shown in Figure 16, with the corresponding levels in (cubic) GaAs and GaP. Their presented data indicate the acceptor level of ZnGa to be at [EV þ 0.34 eV] and that of CdGa to be at [EV þ 0.55 eV].

EA in meV of (zb) GaP and (zb) GaAs

100 Cd

90 80

GaP Zn

70 Mg

60 C 50

Cd

40 Mg 30 20 100

Zn

C

200

GaAs 300 400 EA (zb-GaN) in meV

500

600

Figure 16 The measured thermal ionization energies of acceptors in zb-GaN compared to the corresponding energies in the zb structure semiconductors GaAs and GaP. Adapted from As DJ, Ko¨hler U, and Lischka K (2002) Optical properties of carbon-doped cubic GaN grown on GaAs (001) substrates by molecular beam epitaxy. Materials Research Society Symposium Proceedings 693: 12.3.

4.12.7.3.3 in GaN

427

Experimental studies of carbon

As the free-electron concentration at room temperature in GaN:Mg is only a few percent of the magnesium concentration, there has been consideration of other possible p-type doping elements, in addition to beryllium, that might be easily ionized at room temperature, and carbon has been investigated for that purpose on the basis that CN would act as an acceptor. Although theoretical work (Section 4.12.7.3.1) does not clearly indicate whether the acceptor ionization energy of CN is smaller than that of MgGa, significant effort has been made in experimental investigations since 2000 to know and understand the behavior of carbon in GaN. However, the strong possibility that carbon can go into the GaN also as the donor CGa has seemed likely to lead to doping uncertainty, and the experimental data quoted below shows that that is indeed so, at least for wz-GaN. Most of the understanding of carbon in GaN has been obtained by the experimental studies of Ringel et al. (Armstrong et al., 2004, 2005, 2006, 2007; Arehart et al., 2008a, 2008b) employing electrical conductivity, DLTS, SSPC, and transient photo-capacitance (also called DLOS) on MOCVD-grown and MBEgrown wz-GaN containing various concentrations of silicon and carbon. By means of these electrical and optical methods, they were able to investigate the presence of electronic levels of defects and impurities in almost all of the GaN band gap. In addition, by detailed analysis (using the method described by Chantre et al. (1981)) of the DLOS spectra, they were able to determine, for each of many levels, the optical-excitation energy Eopt of the level with respect to the relevant energy-band edge and the Franck–Condon energy difference dFC. They were thus able to deduce the thermal excitation energy Eth from the relationship Eth ¼ (Eopt  dFC). An important finding from the Ringel et al. studies on the GaN:C:Si was that, when the carbon concentration exceeded that of silicon, the GaN became semi-insulating, indicating a Fermi energy near midgap, and they interpreted that effect in terms of the presence of both CGa and CN at similar concentrations, with CGa having its donor level somewhat below EC and CN having its acceptor level near EV. In their investigation, they found no growth conditions that allowed carbon doping to produce p-type GaN. Conductivity of n-type was, however, produced for silicon concentrations significantly larger than those of carbon, which enabled study of the presence of carbon-related acceptor levels, including

428 Electronic Energy Levels in Group-III Nitrides

of CN, in n-GaN. Their analysis of the DLOS data indicated the presence of an acceptor level at an optical-excitation energy Eopt ¼ 3.28 eV with respect to the CB, with a dFC value measured as zero, thus indicating (using 3.44 eV as the energy gap for wz-GaN) its thermal-excitation acceptor level to be at [EV þ 0.16 eV]. Their investigations showed that the concentrations of the center producing that level was correlated with the carbon concentrations in their GaN samples, and they therefore attributed that [EV þ 0.16 eV] level to the (/0) acceptor level of CN. It is considered that a zero or near-zero value of dFC is to be expected for electronic states whose ionization energies can be treated reasonably accurately by hole or electron effective-mass theory, because lattice vibrations have little influence on such states. The thermal ionization energy of 0.16 eV for CN, as experimentally determined in the Ringel et al. work, is very consistent with the theoretical value of 0.152 eV found by Wang and Chen (2001) (Section 4.12.7.3.1), but different from the value, 0.23–0.27 eV, given by the calculations of Mireles and Ulloa (1998). Other levels whose concentrations tracked the carbon concentrations were found by Ringel et al. at optical excitation energies Eopt to the CB of 1.35, 2.05, and of about 3.0 eV. Particular information about the near-3.0-eV level was found by comparing GaN:C:Si samples grown by MBE at 650 and 720  C. Analysis of their DLOS spectra for that level showed that its Eopt and dFC energies were 3.00 and 0.40 eV, respectively, for the samples grown at 650  C, but were 3.19 and 0.56 eV for the samples grown at 720  C. They therefore deduced the almost identical thermal ionization energies Eth (equal to Eopt  dFC) of 2.60 and 2.63 eV, respectively, for the 650 C-grown and 720 C-grown GaN, and concluded that the same carbon-related center, having a thermal-excitationdefined level at about [EC  2.6 eV], had been formed at the two growth temperatures, but with differing atomic environments affecting the local lattice vibrations. This information on carbon-related energy levels in GaN:C allowed Ringel et al. (Armstrong et al., 2005) to consider the observation made in other work (Green et al., 2004) that a YL band, centered near 2.2 eV, of GaN is produced by the presence of carbon. Their suggestion was that, although, if carbon is not present, the YL very often observed from GaN can be understood in terms of an electronic transition involving the gallium vacancy (see Section 4.12.7.2.3), there is an additional process involving electronic transitions in the carbon-related

defect having Eopt ¼ 3.00–3.19 eV that causes YL in n-GaN and SI–GaN when they contain carbon. An additional important result from Ringel et al. should be noted (Armstrong et al., 2005). Their DLTS measurements showed the presence, in GaN:C:Si containing a high carbon concentration, of a carbonrelated level of thermal ionization energy equal to 0.11 eV, which they attributed to the presence of CGa, having its donor level, presumably (0/þ), at [EC  0.11 eV]. The absence of the 0.11 eV level in samples containing a carbon concentration lower than the silicon concentration was explained by them as due to the low probability for the formation of a donor defect in a semiconductor that was n-type due to chemical doping. The effects of carbon in GaN:C:Si grown by plasma-assisted MBE were studied by Seager et al. (2002), using C–V measurements and DLTS on p–n junctions and by CL. As in the studies of Ringel et al., the work of Seager et al. showed that GaN that had been grown with a carbon concentration larger than that of silicon was semi-insulating, that observation being interpreted also in terms of the simultaneous presence of CGa as a donor and CN as an acceptor. The results of DFT calculations on CGa and CN in wz-GaN, also presented in the paper, predicted that CGa as a shallow donor has its (0/þ) level at about [EC  0.2 eV] and that CN as a shallow acceptor has its (/0) level at about [EV þ 0.3 eV]. The CL measurements showed that the presence of carbon produced a strong, broad BL band with its peak at about 2.86 eV, and it was suggested that this BL was due to transitions between the donor level of CGa and the acceptor level of CN, the transition energy therefore being equal to (Eg  0.20.3 eV), that is, equal to about 2.94 eV, essentially in agreement with the photon energy of the carbon-associated BL. The paper notes, however, that the energy levels of impurities and defects calculated by current DFT methods can be in error by up to 0.2 eV, and so the near-agreement of the theoretical CGa to CN transition energy with the experimentally observed BL energy may be fortuitous. Seager et al. (2002) also reported that their measurements on their MOCVD-grown n-type GaN:C:Si showed the presence of two electron-trap levels, giving DLTS peaks near 140 and 290 K, that were identical to those at [EC  0.26 eV] and [EC  0.58 eV] previously observed by Hacke et al. (1994), but at considerably larger concentrations, in studies on unintentionally doped n-type HVPE GaN which would be expected to contain very little

Electronic Energy Levels in Group-III Nitrides

carbon. They therefore concluded that it seemed very likely that these electron traps having levels at 0.26 and 0.58 eV below EC were not associated with carbon in the GaN, but they had no additional information to allow them to suggest the origins of these levels. The formation of a BL band, having its peak near 2.86 eV, in GaN also grown by plasma-assisted MBE and carbon doped by use of carbon tetrabromide during the growth, was also subsequently reported by Green et al. (2004), but the paper made no suggestions concerning the nature of the electronic levels involved. A carbon-related BL band, with its maximum height near 2.86 eV, was observed also in the experimental investigations of Armitage et al. (2005) on wz-GaN:C:Si samples grown by plasma-assisted MBE, and in a semi-insulating GaN sample grown by MOVPE and containing carbon at a concentration lower than that in their MBE samples. They found that their MBE GaN samples grown without intentional carbon doping did not show the BL band, but that the BL property was always found in the MBE GaN samples having carbon-doping concentrations greater than 1018 cm3 whether the GaN was n-type (i.e., when the silicon concentrations were significantly greater than the carbon concentrations) or semi-insulating. They thus observed the BL, not only when the Fermi energy was near the CB, but also when it was anywhere above about midgap. On the basis of their detailed investigations of the BL emission, they concluded that its properties could be well understood as being due to transitions between the electronic levels of CGa and CN, as had been previously proposed by Seager et al. (2002). They noted that it is thought (from experimental data of Fischer et al. (1995)) that the optical ionization energy of the CN acceptor is 0.23 eV, and they stated that this indicates that the hole-ionization energy of CGa is about 0.40 eV. One may think, however, that (Eg  2.860.23 eV), that is, 0.35 eV (by using Eg ¼ 3.44 eV), would be a better estimate for that ionization energy. An additional important point from the investigation by Armitage et al. (2005) is that they found that, whereas the peak energy of the BL band in their carbon-doped MBE GaN was temperature independent, the peak energy of the BL band in their carbon-containing MOVPE GaN changed with temperature from 3.0 eV at 12 K to 2.86 eV at 150 K. They concluded that the blue-emission property of the MOVPE GaN at low temperature cannot be due to transitions between the same two

429

electronic levels as in the blue emission from GaN:C grown by MBE: either one or both of the levels causing the low-temperature blue emission from the MOVPE GaN must be different from those in their MBE GaN:C and may not involve carbon at all. There has also been experimental information on carbon in zb-GaN. In particular, As et al. (2002; As and Ko¨hler, 2001; Ko¨hler et al., 2001; Fernandez et al., 2004) have reported that carbon doping of zb-GaN can, in strong contrast to carbon doping of wz-GaN, lead to effective p-type conductivity. Their investigations were made on zb-GaN grown by plasma-assisted MBE (with carbon doping by electron-beam evaporation of a graphite rod) on a {001} surface of semiinsulating GaAs, with measurements by Hall effect and PL. Their electrical data indicated that the p-type conductivity in their samples was due to the presence of a carbon-associated shallow acceptor and they suggested that to be CN. The low-temperature (2 K) PL spectra of the zb-GaN:C showed photon emission at two sharp energies, separated by 0.025 eV, close to 3.08 eV. They further found that the PL spectrum measured at temperatures higher than 100 K showed only the PL line of higher energy. On the basis of these data they proposed that the emission line having the lower energy, observed in the low-temperature PL spectra, was due to electron– hole recombination via an electronic transition between a shallow donor and a shallow acceptor, and that the PL line, higher in energy by 0.025 eV, occurred by the electronic transition between the CB minimum EC and the same shallow carbon-related acceptor (electrons being able to be thermally excited from the shallow donor level at [EC  0.025 eV] into the CB at temperatures above about 100 K). By detailed analysis of the spectral shape of the 3.08 eV PL emission, they deduced a value of 0.215 eV for the activation energy of the shallow acceptor, assigned by them as CN, and that energy value was also given by their electrical-measurement data. These electronic transitions proposed by them are shown in Figure 17. The CN acceptor energy has been indicated also in Figure 16. Concerning the donor of ionization energy 0.025 eV, they noted that that energy was the same as found by them (As et al., 1997) for a donor in zb-GaN grown also by plasma-assisted MBE but without intentional carbon or other chemical doping. It is therefore possible that, although CGa would be expected to be a donor center, the 0.025 eV donor that they observed in the zb-GaN is not due to CGa. It seems to the present author that, if CGa is not

430 Electronic Energy Levels in Group-III Nitrides

zb-GaN:C Ec

ED = 25 meV

EDeep = 1185 meV (D0

Deep

Eg (D0 A0)C (e A0)

A0)C

(D

Deep

h)

(D0

Deep

A0)

(e A0)C

(D0 A0)

EA = 129 meV

EAC = 215 meV

EA = 129 meV

Ev

Figure 17 Proposed energy levels and observed transitions in zb-GaN:C. From As DJ, Ko¨hler U, and Lischka K (2002) Optical properties of carbon-doped cubic GaN grown on GaAs (001) substrates by molecular beam epitaxy. Materials Research Society Symposium Proceedings 693: 12.3.

formed during growth of carbon-doped zb-GaN, then that would explain why carbon-doped zb-GaN becomes p-type, whereas, as has been described above, due to the formation of CGa in addition to CN, carbon-doped wz-GaN cannot be grown to have p-type conductivity. As et al. (2002) described also a red PL emission band, having its peak at 2.1 eV, in highly carbondoped zb-GaN. The production of that PL band was accompanied by a strong reduction of the 3.08 eV luminescence, and they therefore suggested the possibility that carbon at large concentrations might be preferentially in the form of carbon atom clusters, instead of the isolated carbon atoms CN in samples containing less carbon. Their analysis of the 2.1 eV band showed that it could be understood as containing three components whose energies were consistent, as shown in Figure 17, with electronic transitions from a single deep donor level at [EC  1.185 eV] down, respectively, to the VB, to an acceptor level (of unknown identity, previously observed by them (As et al., 1997) in zb-GaN grown without intentional doping, and stated by them as being omnipresent) at [EV þ 0.129 eV] or [EV þ 0.130 eV] and to the acceptor level at [EV þ 0.215 eV], proposed by them to be due to CN. Their suggestion for the identity of the donor having its level at [EC  1.185 eV] was that it might be a di-carbon split-interstitial defect. In summary, concerning carbon in GaN, although it is certain that carbon dissolved in GaN causes donor and acceptor electronic levels in the GaN energy gap, the information about such levels is far

being from complete. What seems to be clear is that, in wz-GaN, carbon has the possibility of occupying both gallium and nitrogen lattice sites, that carbon, as CGa, produces a (0/þ) donor level at about [EC  0.11 eV] and, as CN, produces its (/0) acceptor level at or close to [EV þ 0.16 eV]; however, the presence of both CGa and CN causes wz-GaN to have high resistivity. In contrast, carbon-doped zb-GaN has been found to be p-type, with an acceptor level at [EV þ 0.215 eV] presumably due to CN.

4.12.7.3.4 Experimental studies of impurity donors in GaN

Introduction. Gallium nitride grown by various bulk and epitaxial techniques without intentional chemical doping is almost always found to be electrically conducting due to the presence of free electrons, and the origin of that n-type conductivity in terms of the donor or donors involved has been the subject of many experimental and theoretical investigations. A significant early proposal was that that conductivity was due to the presence of nitrogen vacancies VN, since they are securely believed to act as donors in GaN, and it was thought that they could be formed at the high temperatures at which crystalline GaN is grown. However, successive DFT calculations (Section 4.12.7.2.1) strongly indicated that, except possibly for GaN grown in Ga-rich conditions and strongly p-type by chemical-acceptor doping, the formation energy of VN is too high to permit formation of VN at concentrations that would produce observable electrical conductivity.

Electronic Energy Levels in Group-III Nitrides

It therefore became accepted that the nearubiquitous n-type conductivity of unintentionally doped GaN must be due to impurities. Temperature-dependent Hall-effect investigations on such GaN allowed the electronic energy level or levels of the grown-in donor impurity or impurities to be measured, and these data were then compared with the energy levels determined by experimental investigations on GaN intentionally doped with specific impurities and with values obtained by theoretical studies. Detailed PL studies have also given very pertinent information. Complementary measurements, by SIMS and other methods, of the impurity concentrations in unintentionally doped GaN samples provided additional data for the purpose of identifying the cause of their n-type conductivity. It is now generally accepted that that cause is the presence of oxygen. As oxygen is in group VI of the periodic table of elements, ON is certainly expected to be a donor center in GaN. The information concerning oxygen in GaN, including its likely involvement in the YL band, is now reviewed. Other elements that are potential donors in GaN are then considered. Oxygen in GaN. It was always clear that the methods for growing GaN led to the possibility that oxygen would be incorporated as an impurity, and that, on the basis of atomic radii, the oxygen atoms would probably be in the form of ON which would be a donor center. DFT calculations in the 1990s (e.g., Neugebauer and Van de Walle, 1994b, 1994c; Van de Walle and Neugebauer, 1997) showed that the formation energy of ON in wz-GaN would be expected to be low enough to allow it to be created at the usual GaN-growth temperatures and that it should be a shallow donor. Early experimental investigations, in the 1990s, of the electrical properties of GaN gave indication that oxygen indeed produces a shallow donor level in wz-GaN. Electrical and optical experimental studies by Niebuhr et al. (1997) on MOVPE-grown wz-GaN, with oxygen doping by N20 gas, showed n-type conductivity that increased with enhanced concentration of N2O in the growth gas mixture, and the results of the work were interpreted as indicating that oxygen in GaN behaves as a shallow donor. Studies by Go¨tz et al. (1996, 1999), using temperature-dependent Hall-effect measurements, found two shallow donors, of which one was definitely assignable to silicon and of which the other, at about [EC  0.034 eV] (Go¨tz et al., 1996) or [EC  0.029 eV] (Go¨tz et al., 1999), was suggested to be due to ON.

431

Wetzel et al. (1997) investigated the effects of applied hydrostatic pressure up to 38 GPa on the electrical conduction properties of oxygen-doped GaN and silicondoped GaN as monitored by Raman spectroscopy. They found that, for GaN:O but not for GaN:Si, the effect of the pressure was to change a shallow donor state to a deep DX state (Section 4.12.6.3.1), analogous to the well-known pressure-induced conversion of shallow donors to DX centers in GaAs and to the corresponding DX centers in AlxGa1–xAs for sufficiently large value of x. On the basis that both GaN and AlxGa1–xN of low x value, grown in mutually similar conditions without intentional doping, show significant n-type conductivity, they suggested that oxygen in GaN and low-x AlxGa1–xN is the cause of the n-type conductivity in those materials. This conclusion for AlxGa1–xN and AlN has been also given in Section 4.12.6.3.2 of this chapter. Valuable detailed information concerning the electronic levels of oxygen as ON in wz-GaN was obtained by Moore et al. (2001, 2002) by measurements of the infrared photon transmittance spectra, without and with applied magnetic field up to 10 T, of free-standing n-type HVPE-grown GaN films. Their experimental data allowed them to identify the 1s2p and 1s3p optical transitions, and the magnetic-field-induced splitting of each of those to form the transitions to 2p and 2pþ and to 3p and 3pþ, respectively, as shown in Figure 18 from their paper of 2002. Their data showed that the transition energies corresponded well to those expected for a hydrogenic-like effective-mass donor, and they then deduced the optical ground state of the ON center to be at 33.20  0.1 meV below EC. A similar value for the ground-state electronic energy of ON was found by Reshchikov et al. (2001) by PL measurements on freestanding GaN grown by MBE on HVPE GaN. From the energies of identifiable PL lines involving donorbound excitons, Reshchikov et al. were able to deduce the optical ionization energy of ON as 32.6 meV. Information on both the electrical and the optical effects of ON in unintentionally doped and silicondoped n-type wz-GaN as-grown on (0001) sapphire by MOCVD, and after thermal annealing treatments of the samples at 750 and 850  C, was obtained by Soh et al. (2004), by X-ray diffraction, temperaturedependent Hall-effect measurements, PL, and DLTS. Analysis of X-ray rocking data for several crystal planes indicated lowish dislocation densities of about 1  109 cm2 for the unintentionally doped GaN and about 2  108 cm2 for the silicon-doped samples. The presence of oxygen in all the GaN

432 Electronic Energy Levels in Group-III Nitrides

wz-GaN:O

wz-GaN

40 Ec

1s-3p+

DD Ec – (0.2 to 0.24) eV

1s-3p–

2.27 eV YL band

Oxygen

Transition energy (meV)

35

ON complexes at dislocations

30 1s-2p+ AD Ev + 0.87 eV 25

1s-2p–

20

15

Ev Figure 19 A proposed model for the origin of the very frequently observed, yellow-luminescence property of as-grown wz-GaN. Reprinted with permission from Soh CB, Chua SJ, Lim HF, Chi DZ, Tripathy S, and Liu W (2004) Assignment of deep levels causing yellow luminescence in GaN. Journal of Applied Physics 96: 1341. Copyright 2010, American Institute of Physics.

?

0

2

8 10 4 6 Magnetic field (T)

VGa

12

14

Figure 18 Magnetic-field dependence of observed PL transitions associated with oxygen as ON in wz-GaN. Reprinted figure with permission from Moore WJ, Freitas JA, Jr., Lee SK, Park SS, and Han JY (2002) Magnetooptical studies of free-standing hydride-vaporphase epitaxial GaN. Physical Review B 65: 081201. Copyright 2010 by the American Physical Society. For information, see: http://publish.aps.org/linkfaq.htm

samples was shown by X-ray photoelectron spectroscopy, and that also indicated that some silicon was present in the samples that had not been intentionally silicon-doped; it was considered that the source of that silicon contamination was SiH4 impurity in the NH3 used as the nitrogen source in the MOCVD gases and/or SiO2 from the quartz tube of the MOCVD reactor. The Arrhenius plots of the Hall-effect data showed shallow donor levels in the GaN, and the comparison of the unintentionally doped and silicondoped samples allowed the energy levels of oxygen and silicon to be distinguished. Their data indicated a donor level at 35 meV below EC, which they attributed to isolated ON in the samples both before and after the thermal annealing, the concentrations of the ON being always of the order of 1016 cm3. From their DLTS measurements on those wz-GaN samples, Soh et al. deduced the presence of deep levels at [EC  (0.20–0.24 eV)] and also a deep level at [EV þ 0.87 eV]. They proposed that the first of

those was a band of levels due to ON-associated centers at dislocations and that the latter was a level of the gallium vacancy VGa. The dislocation-related nature of the [EC  (0.20–0.24 eV)] band was indicated by their observation that the intensity of the DLTS signals from those levels was proportional to the logarithm of the duration of the DLTS filling pulse. Their PL data from the samples showed the wellknown YL band with its peak near 2.27 eV (about 550 nm), and they found that the YL was strongly decreased by thermal annealing treatments; they suggested that that reduction was due to decrease in the impurity/defect complexes producing that luminescence. Taking account of their DLTS and PL data, they proposed, as shown in Figure 19, that the YL is due to transitions from the [EC  (0.2–0.24 eV)] deepdonor band of levels, due to ON at or near dislocations, down to the [EV þ 0.87 eV] deep acceptor level of VGa. Using 3.44 eV as the band-gap energy of wz-GaN gives transitions energies of approximately 2.35 eV, which, noting the possible differences between thermal and optical transition energies, can be considered as corresponding to the energy of about 2.15 eV of the peak of the YL band. It is to be noted that the DFT calculations of Mattila and Nieminen (1997) had given the result that, when VGa 3 – and ON þ are present in GaN, thermodynamic energy lowering is achieved by their associating to form the defect complex [{VGa–(ON )}2].

Electronic Energy Levels in Group-III Nitrides

EPL;n ¼ 3:472 25 eV – Rexpt ð1 – 1=n2 Þ

wz-GaN 1016

1015 n (cm–3)

Additional information relating to the electronic level of ON was given by Look et al. (2005). In studies on unintentionally doped n-GaN grown by HVPE, using detailed low-temperature (4 K) spectroscopy, they analyzed four sharp PL lines, labeled n ¼ 1–4, observed in the spectral region 3.44–3.46 eV, due to the presence of a donor center present in the GaN, and reported that the observed PL emission energies EPL,n had the hydrogenic-atom relationship:

ND1 = 7.8 × 1015 cm–3 ED1 = 28.1 meV ND2 = 1.1 × 1015 cm–3 ED2 = 53.2 meV

1014

NA = 7.2 × 1014 cm–3

ð7Þ

in which they found, Rexpt, their experimental value for the Rydberg energy of the donor, to have the value 0.0339 eV. Their interpretation of that result was that the PL lines were due to (D0  XA) transitions, that is, transitions from the ground electronic state and excited states of a neutral effectivemass donor to an acceptor-bound exciton, in which the donor had a ground-state optical ionization energy of 0.0339 eV. They then noted, as stated in Section 4.12.4.2, that the use of the effective-mass Bohr-hydrogen formula for electronic levels, given as (4) in this chapter, with (me /m0) ¼ 0.22 and KS ¼ 9.4 for wz-GaN, gives the theoretical value, Rtheo, of the Rydberg energy of an effective mass donor in GaN as also equal to 0.0339 eV. They stated as fortuitous the fact that that theoretical value was exactly the same as their experimental value, but they indicated that they believed that the data strongly suggested that they were observing PL involving a shallow effective-mass donor present as an impurity in the HVPE GaN. From SIMS measurements, Look et al. knew that their samples contained both oxygen and silicon at concentrations amply large enough to allow the PL emissions that they were studying. On the basis that oxygen has nearly the same atomic radius as nitrogen, whereas the radius of a silicon atom is much smaller than that of gallium, they proposed that ON seemed more likely than SiGa to behave as an effective-mass donor center in GaN. They therefore suggested, in agreement with proposals from other work, that the dominant donor in their HVPE GaN was oxygen as ON, acting as a shallow donor of optically measured ionization energy equal to 0.0339 eV. In the same paper of 2005, Look et al. reported the results, from Hall-effect measurements, of the electron carrier concentration as a function of temperature in the HVPE n-GaN. Figure 20, from their paper, shows the Arrhenius plot of their experimental data and their fitted theoretical curve.

433

1013

0

10

20 103/T (K–1)

30

Figure 20 The observed temperature dependence of the Hall-effect-measured free-electron concentration of an HVPE-grown wz-GaN sample, together with the fitted line corresponding to the donor ionization energies and concentrations stated. From Look DC, Fang Z-Q, and Claflin B (2005) Identification of donors, acceptors and traps in bulk-like HVPE GaN. Journal of Crystal Growth 281: 143. Copyright Elsevier 2010.

As indicated, the data are consistent with the presence of two donors having thermal levels at [EC  0.0281 eV] and [EC  0.0532 eV], respectively, at the concentrations stated, and also of acceptors of concentration indicated by the symbol NA (the energy level or levels of the acceptor not being obtainable from the experimental data). Of the two donors, they proposed that the one of thermal ionization energy equal to 0.0281 eV was the oxygen donor, ON. Although accepting that the YL band in GaN involves the ON and VGa defects, Polenta et al. (2007) made a somewhat different proposal concerning the details of the origin of that luminescence, that proposal arising from their DLTS and spectral PC investigations on free-standing n-type wz-GaN of low dislocation density grown by HVPE. Their DLTS data showed four electron trapping levels, at thermal energies of 0.25, 0.52, 0.63, and 1.04 eV, respectively, below EC, and, of those and in agreement with other previous work, they attributed the level at [EC  0.25 eV] to the presence of ON complexes near or at dislocations. Their PC spectra at 300 K showed peaks at photon energies near 2.25 eV (yellow region), 2.4 eV (green region), 2.8 eV (blue region), and 3.4 eV (the band-gap energy), and they concluded that the 2.25 and 2.4 eV peaks covered the photon spectrum region that had been usually considered as the broad YL band. They therefore proposed that broad YL band to be due to two distinct electronic transitions that involve, respectively,

434 Electronic Energy Levels in Group-III Nitrides

different configurations of the gallium-vacancy/ oxygen complex, and, from their observation that the relative intensities of the two components could be changed by heat treatment, they deduced that one configuration could be changed to the other. In particular, their suggestion was that the 2.25 eV YL is due to the presence of the acceptor complex [VGa– (ON)2] near dislocations (for which they referred to the DFT calculations of Elsner et al. (1998)), and that that complex can be thermally dissociated (with an activation energy that they measured as 0.3 eV) into ON and [VGa–(ON)] of which the latter has its energy level slightly farther down in the band gap and allows production of the green luminescence near 2.4 eV. Further support for the existence of defect complexes of VGa with ON defects was provided by the DLTS investigations of Emiroglu et al. (2007, 2008) on n-type wz-GaN grown by MOVPE. Their data on the as-grown GaN showed three electron traps whose energy levels were measured as [EC  (0.25–0.35 eV)], [EC  (0.50–0.62 eV)], and [EC  1.5 eV)]. The first and second of these electron-trapping levels had also been reported from DLTS studies on wz-GaN, by Hacke et al. (1994) on HVPE GaN, by Cho et al. (2003) (the first being measured as being at [EC  0.23 eV]) on MOCVD GaN, and by Zhan and Kang (2004) on wz-GaN grown by plasma-assisted MBE. They were observed similarly by Umana-Membreno et al. (2008) on MOCVD-grown wz-GaN. It is clear that the defects producing these levels are very commonly formed during growth of GaN. From the dependences of the DLTS peak heights on the DLTS filling-pulse duration, Emiroglu et al. deduced that the first two levels were due to defects associated with dislocations (the spread of the energies of each level being suggested as due to a range of distances of the defect from the dislocation line), and that the third behaved as a point defect. Cho et al. (2003) had similarly reported the dislocation-related property of the first of the three electron traps. In their investigations, Emiroglu et al. found also that successive DLTS scans up to 480, 500, and 520 K progressively removed the electron-trap peaks and gradually produced a broad negative DLTS peak centered at 470 K corresponding to hole emission to the VB. They then employed, for the latter peak, the LDLTS method, which, by analysis of the shape of the capacitance-time transient signal produced by the thermally induced carrier emission, allows the thermal ionization energies of lattice defects and impurities to be measured with considerably greater precision than in the standard

DLTS method. The LDLTS investigation of the hole-emitting level showed four emission peaks, of different heights, of which the tallest was that corresponding to the greatest emission rate, that is, to the level closest to the VB maximum EV. None of those four hole-emission levels showed a fill-pulse-duration dependence of its peak height, thus suggesting that each of them to be a simple point defect (but perhaps at different distances from dislocations). Emiroglu et al. noted that a hole trap in the same region of the energy gap had been reported by Hierro et al. (2000a) by DLOS and DLTS measurements on n-type MOCVD GaN (that trap level being found to be at [EC  (2.57 to 2.64 eV)] when detected by optical excitation, and, very similarly, at [EV þ 0.87 eV] when detected by thermal excitation). The same band of hole-emission levels near [EV þ 0.9 eV] had also been seen by Polyakov et al. (2002), by DLTS with optically induced injection of minority carriers, in n-type HVPE GaN, and they had suggested that they were due to defects near dislocations. The proposal by Emiroglu et al. was that the three hole traps having electronic levels near [EV þ 0.87 eV], that they found to be formed as a result of their DLTS scans up to about 500 K, were due to individual kinds of point-defect associations of gallium vacancies and oxygen atoms of the form [VGa–(ON)n], with n being 1, 2, and 3, respectively. They pointed out that Saarinen et al. (2001) had interpreted their positronannihilation spectroscopy data from GaN containing oxygen in terms of the trapping of VGa at one, two, or three ON. Returning now, to complete this section, to ON as a shallow donor, it is seen that the experimental data indicate that its thermal ionization level is at or near [EC  0.028 eV] and that its optical ionization level is at about [EC  0.034 eV]. The difference between these two values is the Franck–Condon energy shift dFC, equal to [Eopt – Eth], as represented in Figure 1 of this chapter, that is, apparently about 6 meV for ON. The dFC value is quite small, and, if one takes account of the likely uncertainties in the measured values of the thermal and optical ionization energies, it is not certain that the dFC value of ON is different from zero. Silicon in GaN. As silicon is in group IV of the periodic table of elements, it might be thought that there would be the possibility of its occupying the lattice sites of both gallium and nitrogen in GaN, of which the first would be a donor and the second an acceptor, as has been found for the group-IV element carbon in GaN:C. Instead, probably related to the

Electronic Energy Levels in Group-III Nitrides

wz-GaN:Si 40 Silicon 35 1s3p+ Transition energy (meV)

fact that the atomic size of carbon is not very different from that of nitrogen, whereas silicon is significantly larger, it seems that the two elements usually behave differently when dissolved in GaN, and that, as has been found by DFT calculations (Section 4.12.7.3.1), the strongly or completely dominant location of silicon in GaN is on gallium sites as the donor SiGa. Experimental investigations by Go¨tz et al. (1996, 1999), of silicon-doped MOCVD-grown wz-GaN, showed that the GaN was strongly n-type, and they proposed that conductivity to be due to the presence of SiGa. By Hall-effect measurements as a function of temperature and also by low-temperature PL, they determined the values of the thermal ionization energy and the optical ionization energy, respectively, of the donor, proposed to be SiGa, and found the first to be 12–17 meV and the second to be 22  4 meV. The second of those energies was deduced by attributing a particular observed PL emission to an electron–hole recombination via a DAP transition, in which the donor level was assumed to be that of the donor producing the n-type conductivity. Essentially, the same PL and data analysis method were used by Jayapalan et al. (1998) on HVPE GaN containing various concentrations of silicon; the value that they found for the SiGa optical ionization energy was again 22 meV. However, similar PL investigations by Reshchikov et al. (2001) produced a value of 28.8 meV for that energy. From Hall-effect measurements on silicondoped wz-GaN grown by MOCVD, Soh et al. (2004) reported the thermal-excitation level of SiGa to be at [EC  0.018 eV] in the as-grown GaN and to be still present following heating at 750 and 850  C. Information concerning the optical level of the shallow SiGa donor was also obtained by Moore et al. (2001) from analysis of PL spectra from samples of HVPE wz-GaN containing different concentrations of silicon (as measured by SIMS). This work indicated the optical ionization energy of the silicon donor as 31.23  0.1 meV. However, in a subsequent, more detailed study using magneto-PL spectral measurements on a free-standing wafer of HVPEgrown n-type GaN, the research group found (Moore et al., 2002) that optical ionization energy to be slightly smaller, at 30.18  0.1 meV. This value was obtained, as in their associated studies on the shallow donor level of ON (Section 4.12.7.3.4), by analysis of the energies of the nonsplit 1s to 2p and nonsplit 1s to 3p optical transitions at zero magnetic field and of the transitions when the 2p and 3p levels were split by

435

30

1s3p–

1s2p+

25 1s2p0 /2s

1s2p– 20 ? 15

0

2

8 10 4 6 Magnetic field (T)

12

14

Figure 21 Magnetic-field dependence of observed PL transitions associated with silicon as SiGa in wz-GaN. Reprinted figure with permission from Moore WJ, Freitas JA, Jr., Lee SK, Park SS, and Han JY (2002) Magnetooptical studies of free-standing hydride-vaporphase epitaxial GaN. Physical Review B 65: 081201. Copyright 2010 by the American Physical Society. For information, see: http://publish.aps.org/linkfaq.htm.

applied magnetic fields up to about 12 T. Their data from their paper are shown in Figure 21. In summary, the experimental data show the shallow donor level of SiGa in wz-GaN to be at about [EC  0.018 eV] when measured by thermal excitation and at about [EC  0.030 eV] when measured by optical excitation. The Franck–Condon energy shift dFC, the difference between the two energies, is therefore about 12 meV, which seems, taking account of the probable measurement inaccuracies of about 1 or 2 meV in each of the ionization energy values, to be significantly different from zero, and also larger than the magnitude of dFC for ON (Section 4.12.7.3.4). The optical-excitation energies of the SiGa and ON donor centers in wz-GaN were considered by Reshchikov and Morkoc¸ (2005) in their discussion of the cause of a strong UVL band, from GaN, that has its zero-phonon line at about 3.27 eV. Their paper stated that both nominally undoped (i.e., n-type) and magnesium-doped p-type doped GaN almost always

436 Electronic Energy Levels in Group-III Nitrides

show that UVL band and that it is considered to be due to transitions from a shallow donor level such as that of SiGa or ON to acceptor level or levels somewhat above EV, but that the identity or identities of those latter levels are not known for certain. They argued that the presence of MgGa enhances the UVL band because MgGa is itself a deep acceptor, that is, it is a deep acceptor additional to those in the nominally undoped GaN. They also stated that, at low temperatures, the transition down to the deep acceptor can be from the shallow donor itself, as a DAP transition, but that at higher temperatures it can become a transition from electrons near the bottom of the CB down to the deep acceptor, that is, an eCB-A transition, because at the higher temperatures the donor-atom electron has been thermally excited into the CB. Other donor impurities in GaN. The doping of GaN by the group-IV element germanium has been the subject of a few investigations, one such being temperature-dependent Hall-effect measurements by Go¨tz et al. (1999). They reported the (0/þ) donor level of GeGa to be at [EC  0.019 eV] and noted that that was very similar to the corresponding level of SiGa which they found to be at [EC  0.017 eV]. It seems that sulfur as SN and selenium at SeN would also be donors, but no detailed studies of these elements in GaN have been reported.

4.12.7.4 in GaN

Conclusions on Electronic Levels

Electrical and optical investigations have indicated that the band gaps of wz-GaN and of zb-GaN grown by different techniques and in differing conditions contain, in addition to electronic levels of impurities, a variety of levels believed to be associated with the presence of lattice defects. However, despite many experimental and theoretical studies, the valid linking of these levels to specific defects or defect– impurity complexes is far from certain, and it is possible to draw only very general conclusions. There is, however, much better understanding of the chemical doping of GaN to produce p-type and n-type conductivities, and the electronic levels of important impurities are now reasonably well established. This section summarizes the main proposals presented in Sections 4.12.7.2 and 4.12.7.3 about the electronic levels of defects and impurities in GaN. Unless otherwise stated the information is for the wurtzite structure.

Concerning intrinsic defects, electron irradiation expected to displace only nitrogen atoms in wz-GaN has been found to introduce a donor level in the region of [EC  0.07 eV] to [EC  0.08 eV]. As all theoretical studies have predicted the nitrogen vacancy VN to be a shallow donor, the observed level has been proposed to be the (0/þ) level of that defect. But a level at [EC  0.025 eV], observed after similar irradiation, has also been attributed to that VN donor level, together with the suggestion that the level at 0.07–0.08 eV below EC is due to a complex of a nitrogen interstitial NI with an impurity. An irradiation-induced electron-trapping level at [EC  0.25 eV] and other such levels between EC and about [EC  1.0 eV] have also been attributed to VN-related or NI-related defects. Since DFT/LDA calculations are not able to deal well with electronic levels associated with the CB, they cannot provide good guidance in the interpretation of levels observed in the upper half of the band gap. In contrast, there is clearer understanding of levels associated mostly with the VB and therefore likely to be in the lower half of the band gap. The theoretical studies all predict that the gallium vacancy VGa in GaN is a triple acceptor that gives levels at successive energies somewhat above EV. Because as-grown GaN is usually n-type due to donor impurity atoms, the acceptor nature of VGa is expected to cause easy formation of VGa during GaN growth, especially of negatively charged VGa. Several acceptor levels observed between EV and [EV þ 1.0 eV] are therefore very likely to be due to VGa or to VGa-related complexes, and data from PAS measurements indeed indicate the presence of such defects in as-grown n-type GaN. The theoretical investigations for the VGa acceptor suggest that its (3/2), (2/), and (/0) levels are at about 1.1–1.2, 0.8–0.9, and 0.3–0.4 eV, respectively, above EV, and experimental studies have shown levels, due to lattice defects, which seem to correspond to two of those, at [EV þ 1.0 eV] and at [EV þ 0.87 eV]. Some information about intrinsic interstitial defects in GaN is also available. Interpretation of the ODEPR data obtained from GaN irradiated by high-energy electrons at low temperature indicated the presence of a tetrahedral-site gallium interstitial that had an electronic level at [EV þ 0.8 eV] but was removed by annealing to 300 K. Electrical measurements in other work showed irradiation-induced electronic levels near [EC  1.0 eV] suggested to be due to defects involving nitrogen interstitials which might be (ON–NI) complexes.

Electronic Energy Levels in Group-III Nitrides

As stated above, there is now quite reliable information on the acceptor and donor levels of various impurities in GaN. Theoretical studies give the clear prediction that atoms of group-II elements occupy gallium sites and are therefore acceptors. Magnesium is the element that is most employed to produce p-type GaN, but it is very likely that as-grown GaN:Mg contains the magnesium in the form of one or more magnesium–hydrogen complexes which are acceptors having electronic levels at [EV þ 0.20  0.01 eV]. High-temperature heating in nitrogen is able to dissociate the Mg–H complexes, and the MgGa then formed has its (/0) acceptor level at [EV þ 0.12  0.01 eV]. However, there are additional data suggesting that the acceptor level of Mg–H or of MgGa may comprise two levels separated by only 0.012 eV. Other levels associated with magnesium have also been reported. Beryllium as BeGa is also a p-type dopant in GaN; experimental studies indicate its acceptor level to be in the region of [EV þ 0.11 eV] to [EV þ 0.17 eV], but a location of [EV þ 0.23 eV] has also been suggested. Acceptor levels at [EV þ 0.34 eV] and [EV þ 0.55 eV] have been reported for ZnGa and CdGa, respectively in zb-GaN. Considering now the atoms of the group-IV elements, carbon, silicon, and germanium, these may perhaps be expected to occupy both gallium and nitrogen sites. This is indeed so for carbon in wzGaN, the (0/þ) donor level of CGa being at about [EC  0.11 eV] and the (/0) acceptor level of CN being at or near [EV þ 0.16 eV], but the presence of both renders the wz-GaN highly resistive. However, zb-GaN:C has been observed to have p-type conductivity, the acceptor level of CN being reported as [EV þ 0.215 eV]. Silicon-doped wz-GaN is found to be a good n-type conductor, presumably because all or most of the silicon occupies gallium sites; the experimental evidence is that the (0/þ) donor level of SiGa has its thermal excitation level at about [EC  0.018 eV] and its optical excitation level at about [EC  0.030 eV]. GaN:Ge is found to be n-type, with its GeGa donor level at [EC  0.019 eV]. The atoms of the group-VI element oxygen are expected to go into nitrogen lattice sites in GaN as the donor ON. Electrical and optical measurements suggest that the thermal and optical (0/þ) donor levels of ON are near [EC  0.028 eV] and [EC  0.034 eV], respectively. It has been securely concluded that the very common n-type conductivity of GaN grown without intentional doping is due to the presence of oxygen as a contaminant. Large hydrostatic pressure

437

applied to wz-GaN:O causes a change from low to high resistivity, and it is concluded that that is caused by the transformation of the shallow ON donor to a deep donor DX center. It is now strongly believed that the YL property of wz-GaN is due to the presence of oxygen, and the electronic transition involved has been proposed to be from levels near [EC  0.22 eV], perhaps due to ON complexes at dislocations, down to a level or levels near [EV þ 0.87 eV] due to VGa or to [VGa–ON] complexes.

4.12.8 Electronic Levels in Indium Nitride 4.12.8.1 Structural, Electronic, and Luminescence Properties of InN Of the III-nitride semiconductors, indium nitride, InN, is the least ionic, and both the wurtzite and zincblende crystal structures have smaller VB-to-CB energy gaps than any of the other such nitrides. For a long time, the experimental data on wz-InN seemed to show a band gap Eg of 1.9 eV, but, since about 2003, an Eg value of approximately 0.7 eV has been progressively accepted as correct for the InN structure. PL measurements by Arnaudov et al. (2004) have indicated a value of 0.692  0.002 eV for the band gap of wz-InN at 2 K. Measurements, employing various optical techniques and soft X-ray spectroscopy, by Walukiewicz et al. (2006) have indicated a band-gap value of 0.67  0.05 eV for wz-InN at room temperature. The band gap of zb-InN has been observed to be significantly smaller, at 0.48 eV (Inoue et al., 2008). Because of its high electron mobility, InN gives the possibility of its use for fabrication of terahertz FETs, and the small band gaps of InN and its alloys InxGa1xN leads to potential new LED and solarcell applications. There have been various theoretical studies of the electronic levels of intrinsic defects and impurities in InN, but the realization that the band gaps of wz-InN and of zb-InN are much smaller than 1.9 eV renders such earlier studies less useful. The number of experimental investigations of electronic levels in InN is so far small. Present-day as-grown InN is always strongly n-type, but the cause of that conductivity is not yet clear. It has been suggested that much of the n-type property, at least near the InN surface, is not due to defects or impurities, but to surface donor states (Mahboob et al., 2004; King et al., 2009) or to nitrogen vacancies at dislocations (Piper et al., 2006). Growth of p-type InN has been reported, but is not easy to achieve.

438 Electronic Energy Levels in Group-III Nitrides

4.12.8.2 Theoretical Studies of Intrinsic Defects and Impurities in InN As for other III-nitrides considered above, it is useful to refer first to the ionization energy of a simple donor as calculated using the hydrogenic, effectivemass model. As stated in Section 4.12.4.2, Tansley and Egan (1992) used 0.12 for the value of (me /m0) and 8.4 for the dielectric constant, and that gives the donor ionization energy as 0.023 eV. If, however, one uses the more recent value (me /m0) band-edge value of 0.05 (Fu and Chen, 2004), and the high-frequency dielectric constant value of 6.7 (Kasic et al., 2002), the calculated hydrogenic donor ionization energy is 0.015 eV. Jenkins and Dow (1989) used a nearest-neighbor tight-binding model to calculate the electronic levels of intrinsic defects and likely doping impurities in wz-InN. They reported that their calculations predicted that the indium vacancy VIn has an acceptor level very slightly above EV, and that the nitrogen vacancy VN produces a (0/þ) donor level somewhat below EC. Noting that InN shows optical absorption at 0.2 eV, they suggested the VN donor level to be at [EC  0.2 eV] and nitrogen vacancies to be the cause of the always-found n-conductivity of as-grown InN. The antisite defects InN and NIn were indicated as creating levels respectively above and below midgap. Their calculations showed group-II atoms on indium sites as being shallow acceptors, and group-IV atoms on nitrogen sites as producing deep levels that would trap both electrons and holes. Oxygen substituting for nitrogen was predicted to be a shallow donor; sulfur, selenium, and tellurium were indicated as producing additional levels in the bandgap. DFT/LDA total-energy calculations for InN were made by Stampfl et al. (2000) and by Van de Walle and Neugebauer (2004). Stampfl et al., studying zb-InN, also found that nitrogen vacancies VN should be donors and they were indicated as having a low formation energy Ef, of about 0.5 eV, in p-type InN. Their calculations predicted, however, in contrast to the predictions of Jenkins and Dow (1989), that the Ef value for VN in n-InN would be too high, at greater than 2 eV, to allow nitrogen-vacancy formation at sufficient concentration to account for the large free-electron density in as-grown InN. Their work indicated VN as having a (þ/3þ) level at about [EV þ 0.2 eV], the defect, being unstable in its 2þ charge state. Concerning dopant impurities, MgIn was suggested to be an acceptor center having its (/0) at about [EV þ 0.2 eV], and that SiIn and ON,

would be shallow donors, with formation energies much lower than that of VN in n-type InN. The Stampfl et al. calculations produced a theoretical band-gap value of approximately 1.3 eV for zb-InN, and, since the measured band-gap value is much smaller than that (Section 4.12.8.1), it is not clear how the Stampfl et al. data for the energy locations of the electronic levels should now be assessed. The theoretical investigations of Van de Walle and Neugebauer also predicted SiIn and ON, and interstitial hydrogen, to be shallow donors, with formation energies considerably lower than that of VN. They proposed therefore that nitrogen vacancies could not be the cause of the strong n-type conductivity of as-grown InN, but that impurities might be. The properties of carbon located on a nitrogen site in zb-InN were studied by Ramos et al. (2002) in a DFT calculation, using supercells containing up to 512 atoms, that included explicit treatment of the indium d-electrons and atomic relaxation. Their calculations produced a band-gap value of 0.52 eV, that is, very close to the experimental value of 0.48 eV (Section 4.12.8.1) and indicated the CN as a shallow acceptor, having its (/0) level at [EV þ 0.012 eV]. The investigation predicted, however, that, in all growth conditions, CN was much less likely to be formed in InN than in other III-nitrides of zincblende structure. 4.12.8.3 Experimental Studies of Intrinsic Defects and Impurities in InN In a review of experimental data concerning electronic levels in wz-InN, Tansley and Egan (1992) suggested that the low-photon-energy optical absorption spectra indicated the presence of donor levels at [EC  0.150 eV] and [EC  0.040 eV], which they suggested to be due to nitrogen vacancies VN, and of other levels at about 1.0 and 1.5 eV below EC, suggested as possibly due to indium interstitials InI. Since the experimental data indicated energies with respect to EC, the VN level locations stated may still be valid, despite the fact that the band-gap energy of InN is now known to be lower than was thought in 1992. Concerning intrinsic defects, irradiation (Section 4.12.3.3) has been found to cause very considerable increase in the free-electron concentration of as-grown n-type wz-InN (Li et al., 2005; Plesiewicz et al., 2007), thus indicating that many of the irradiation-induced defects, InI, VIn, NI, and VN, are donors having electronic levels high in the band gap. As

Electronic Energy Levels in Group-III Nitrides

stated in Section 4.12.8.2, theoretical work predicts that nitrogen vacancies act as donors in InN. Measurements of the pressure dependence of the electron mobility in low-conductivity n-type InN have been interpreted as showing the presence of a donor level resonant with the CB, at 0.08–0.09 eV above EC, probably due to an impurity, since irradiation did not increase its concentration (Dmowski et al., 2005; Plesiewicz et al., 2007). Experimental information concerning hydrogen as a shallow donor in wz-InN was obtained by Davis et al. (2003), by measurements of the temperature-dependence of the frequency spectrum of the spin-precession of muons implanted into the InN where the muons behave like hydrogen. The thermally induced signal change above approximately 60 K was found to indicate an activation energy of 12 meV, so suggesting the donor level of interstitial hydrogen to be at [EC  0.012 eV]. It is seen that that ionization energy is very close to the simple effective-mass result of 0.015 eV stated in Section 4.12.8.2. The shape of the PL emission band extending from about 0.70 to 0.92 eV produced by MBE-grown non-intentionally-doped n-type wz-InN at room temperature was reported by Wang et al. (2004) as comprising a main peak centered at 0.74 eV, suggested to be due to the fundamental CB-to-VB transition, together with a superimposed smaller band at 0.72 eV, interpreted by them as the transition down to EV from a shallow donor at [EC  0.020 eV], the origin of which they did not suggest. Nonintentionally-doped n-type layers grown by MBE and by MOVPE were investigated by Arnaudov et al. (2004), using PL at 2 K. Their analysis of their data also indicated transitions involving shallow levels, but their proposal was that they were acceptor levels at [EV þ 0.018 eV] and at [EV þ 0.085 eV]. The achievement of p-type wz-InN was reported by Jones et al. (2006) in studies using electrical measurements on layers grown by MBE with magnesium as the dopant. Samples without magnesium doping showed the usual n-type conductivity, with n  1021–1020 cm3 close to the surface (electron accumulation), decreasing to about 1019 cm3 at a depth of a few micrometers. The InN:Mg layers showed p-type conductivity beyond about 1 mm into the InN, with hole concentrations (equal to [NA  ND]), of a few 1019 cm3 at room temperature. It is clear that magnesium acts as a reasonably shallow acceptor in InN, presumably as MgIn.

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4.12.8.4 Conclusions on Electronic Levels and Their Identities in InN There have been some theoretical studies of electronic levels in wz-InN and zb-InN, and a small number of experimental studies, mainly on wz-InN. The theoretical work has predicted the indium vacancy VIn to be an acceptor with its (/0) level slightly above EV and that the nitrogen vacancy VN is a donor with its (0/þ) level just below EC, these results being qualitatively the same as the expectations for cation and nitrogen vacancies in the other III-nitride semiconductors. Magnesium as MgIn is predicted to be an acceptor with its (/0) level at about [EV þ 0.2 eV], and indeed as-grown InN:Mg has been found to be p-type. Silicon as SiIn and oxygen as ON are expected to be shallow donors, and it may be that the usual n-type conductivity of as-grown, non-intentionallydoped InN is due to the presence of oxygen. PL data from such InN have been interpreted as indicating the presence of a shallow donor at about [EC  0.020 eV], which is an energy similar to that of [EV  0.015 eV] calculated from a hydrogenic, effective-mass model. An experimental investigation of muons implanted into wz-InN has indicated a shallow donor level of interstitial hydrogen at [EC  0.012 eV].

4.12.9 Electronic Levels of Transition and Rare-Earth Metals in IIINitrides 4.12.9.1

Transition Metals in III-Nitrides

Transition metals in solids, including in III-nitride semiconductors, have important luminescence applications because electronic transitions within their unfilled d-electron subshells allow them to produce sharp emission lines. Correspondingly, their common, filled 4s outer subshells have the effect that their properties are rather similar in all the III-nitrides. Of these elements, iron and manganese have been the most investigated in III-nitride semiconductors, partly because of their magnetic properties in connection with spintronics, and also because their incorporation is found to create deep trapping levels that can compensate donor and acceptor centers in as-grown material and so form high-resistivity substrates for electronic-device applications. From theory and EPR data, it is expected that iron and manganese atoms dissolved

440 Electronic Energy Levels in Group-III Nitrides

in GaN occupy gallium sites, that is, of the group-III element. The electron configuration of iron is [ ]3d64s2 as an isolated atom, but therefore, as FeGa in GaN, it becomes [ ]3d54s0, that being called the 3þ (ferric) oxidation state. It is energetically possible, however, for an iron atom to change to the 2þ (ferrous) oxidation state [ ]3d64s0 by capturing an electron. The result is that, depending on the Fermi-level location in the GaN band gap, an iron atom can produce a (/0) acceptor level corresponding to the notation (2þ/3þ) in terms of its oxidation states. Although a similar process is expected to occur also in the other III-nitrides, the main investigations have been on GaN:Fe. From PL studies on wz-GaN/AlN structures, Baur et al. (1994) deduced the respective FeGa (/0) acceptor levels, that is, the change from the 2þ to 3þ oxidation state, to be high in the band gap, at [EV þ 2.5 eV] in GaN and at [EV þ 3.0 eV] in AlN. Malguth et al. (2006) used optical absorption, PL, and EPR in a study of HVPE-grown wz-GaN:Fe that was n-type at low iron concentration. They also deduced from their data that iron as FeGa acts as a very deep acceptor, its (/0) semiconductor level being at [EV þ 2.863  0.005 eV], corresponding to [EC  0.68  0.06 eV]. They reported that, as the iron concentration was increased beyond 1  1019 cm3, the Fermi level moved progressively down from near EC and became pinned at that energy level. The PL spectra showed, below the (/0) level, additional levels due to its splitting by the crystal field, and also a shallow acceptor level at about [EV þ 0.05 eV], interpreted as an effective-mass state of FeGa – . Fermi-energy pinning somewhat below EC in GaN:Fe for large iron concentrations was also found by Polyakov et al. (2008b), using electrical-conductivity/temperature and C–V measurements; their result gave the pinning at about [EC  0.57 eV]. Their C–V data indicated the presence of an electron trap near [EC  0.25 eV], which they suggested to be due to silicon in the GaN, and also of electron traps at [EC  0.55 eV] to [EC  0.60 eV]. They found, however, that the spatial location of the latter traps was not indicative of their being due to FeGa acceptors and suggested that the energy level of FeGa might be closer to midgap. They had previously (Polyakov et al., 2003) reported also electron traps at [EC  0.9 eV] and hole traps at [EV þ 0.9 eV]. Electronic levels at [EC  0.56–0.60 eV] and at [EC  0.94 eV] were found in HVPE-grown GaN:Fe by Fang et al. (2008), using Hall-effect and thermally stimulated current (TSC) measurements. A different EF pinning energy in

GaN:Fe, at approximately [EC  1.4 eV], was found by Muret et al. (2007), using photo-induced and thermally induced DLTS on MOVPE-grown layers. Their data indicated a high concentration of donor traps at [EC  1.39 eV], that is, corresponding to the observed EF pinning, and also an acceptor level at [EV þ 0.75 eV]. They proposed these to be due to FeGa, as, respectively, the (0/þ) level of the 3þ oxidation state and the (/0) level of the 2þ oxidation state. They suggested that the pinning of EF closer to EC reported in other work might be due to surface conductivity effects. Manganese has an electron configuration [ ]3d54s2 as an isolated atom, and its properties in the III-nitrides are expected to be similar to those of iron. From optical absorption and PL measurements, Korotkov et al. (2001) proposed that manganese in wz-GaN:Mn has a deep acceptor level at [EV þ 1.4 eV] and also possibly at [EV þ 2.06 eV]. Optical absorption and PC measurements by Graf et al. (2002) on wz-GaN:Mn grown by plasma-assisted MBE suggested that manganese has its (/0) acceptor level (oxidation state change 2þ to 3þ) at [EV þ 1.8 eV], in exact agreement with DFT calculations by Popovic et al. (2004) for MnGa. That manganese in GaN produces several deep levels, corresponding to different charge states, was reported by Malguth et al. (2008), from the changes produced in the optical absorption and PL spectra when the Fermi energy was moved down by magnesium doping or up by silicon doping. The same group had reported that heavy Mn-doping of GaN caused formation of deep donors, which they attributed to Mn-related defect complexes, possibly involving hydrogen and/ or nitrogen vacancies (Gelhausen et al., 2004). 4.12.9.2

Rare-Earth Metals in III-Nitrides

The rare-earth (RE) elements have filled outer 4s or 5s subshells (scandium or yttrium) or filled outer 6s subshells, erbium being of much technological importance because of its intra-4f luminescence at 1.54 mm, a wavelength at which silica fiberoptic glass is very transparent. In a study of erbium in GaN, Wilson et al. (1994) reported such strong luminescence from GaN:Er provided that the samples were also oxygen doped; since the oxygen must have made the GaN n-type, the observation suggests that the erbium acceptor level in GaN is near to EC. Moreover, a Rutherford backscattering/channeling investigation (Alves et al., 2001; Monteiro et al., 2001) on wz-GaN containing dissolved erbium, cerium, praseodymium, dysprosium, and lutetium showed that the atoms of these elements occupied

Electronic Energy Levels in Group-III Nitrides

gallium lattice sites, but that dissolved europium atoms were slightly displaced from gallium sites. DLTS measurements by Song et al. (2007) on GaN, after erbium implantation followed by anneal at 900  C, showed extra gap levels at [EC  0.19 eV], [EC  0.30 eV], [EC  0.41 eV], and [EC  0.60 eV]. The electronic levels resulting from europium implantation into wz-GaN were investigated by Marnor et al. (2004). Their experiments showed a strong DLTS peak near 170 K due to a level, measured to be at [EC  0.36 eV], after randomdirection implantation (expected to produce a high damage concentration) but not after channelingdirection implantation, but which had not been reported in undoped GaN after irradiation by electrons, protons, helium ions, or nitrogen ions. They concluded therefore that the [EC  0.36 eV] level was europium-related, but might be due to a Eu-defect complex. It seems that that would be consistent with the europium-location result stated above. Experimentally known optical-emission properties of RE elements in GaN were used by Dorenbos and van der Kolk (2006) to deduce that europium and ytterbium each produce an electron-trapping level in the band gap close to EC, and that cerium, praseodymium, and terbium produce in-gap hole trapping levels, of which that of praseodymium is close to EV. However, DFT calculations have predicted (Petit et al., 2005; Jones, 2006) that atoms of RE elements occupying cation sites in wurtzite GaN and AlN create no levels within the band gap of GaN, but produce deep donor levels at about [EV þ 0.5 eV] in AlN. Their calculations for GaN suggested that [RE–VN] complexes could be formed, having electron-trapping levels near [EC  0.2 eV], and that such levels might explain the experimental data for GaN.

4.12.10 Summary This chapter has reviewed the information concerning the electronic energy levels of lattice defects and impurities in the III-nitride semiconductors, BN, AlN, GaN, and InN in their wurtzite and zincblende crystalline structures, which has been obtained by theoretical and experimental (electrical, optical, and EPR) investigations. BN and InN have been the subjects of rather few studies, but AlN has been much investigated and there have been many studies of GaN. The information from each of the nitrides

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has been summarized above at the end of the relevant section. For each of the four III-nitrides considered, theoretical expectations are that cation vacancies are acceptor centers and nitrogen vacancies are rather shallow donors. The experimental data seem to confirm the predictions. It is found both theoretically and experimentally that the elements of group-II of the periodic table preferentially occupy cation lattice sites as fairly deep acceptors. However, magnesium atoms seem often to be in the form of magnesium– hydrogen complexes. Carbon atoms may occupy both cation sites as donors and nitrogen sites as acceptors, so producing high resistivity. Silicon and germanium atoms preferentially occupy cation sites as fairly shallow donors. Oxygen is a frequent unintentional impurity in the III-nitrides, producing n-type conductivity due to its occupancy of nitrogen lattice sites as a rather shallow donor. However, in AlxGa1–xN of x larger than about 0.4, and therefore in AlN itself, oxygen becomes a deep donor, as a DX center, by moving away from the exact nitrogen site. It is very likely that oxygen is involved in the YL frequently exhibited by GaN. To fulfill the potential of III-nitrides as electronic and optoelectronic devices, much remains to be investigated and understood concerning the electronic levels of lattice defects, impurities, and their complexes. In particular, because of its likely excellent electronic and optoelectronic properties, the thermodynamically stable form of BN, the cubic, zincblende crystal structure, deserves much detailed study. (See Chapters 3.06, 3.07, 5.06 and 6.02).

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Further Reading Estreicher SK and Boucher DE (1997) Theoretical studies in GaN. In: Pearson SJ (ed.) Gallium Nitride and Related Materials, pp. 171–199. New York, NY: Gordon and Breach. Fall CJ, Jones R, Briddon PR, and O¨berg S (2001) Electronic and vibrational properties of Mg- and O-related complexes in GaN. Materials Science and Engineering B 82: 88. Gwo S, Ager JW, Ren F, Ambacher O, and Schowalter L (eds.) (2009) III-Nitride Materials for Sensing, Energy Conversion and Controlled Light–Matter Interactions, 2009 Fall Meeting, Symposium I, MRS Proceedings, vol. 1202. Warrendale, PA: Materials Research Society. Harima H, Inoue T, Nakashima S, Ishida M, and Taneya M (1999) Local vibrational modes as a probe of activation process in p-type GaN. Applied Physics Letters 75: 1383. Henini M and Razeghi M (2005) Optoelectronic Devices: III Nitrides. ISBN: 978-0-08-044426-0. Oxford: Elsevier. Karch K, Bechstedt F, and Platl T (1997) Lattice dynamics of GaN: Effects of 3d electrons. Physical Review B 56: 3560. Kuball M, Myers TH, Redwing JM, and Mukai T (eds.) (2005) GaN, AlN, InN and Related Materials, 2005 Fall Meeting, Symposium FF, MRS Proceedings, vol. 892. Warrendale, PA: Materials Research Society.

Electronic Energy Levels in Group-III Nitrides Madelung O, Schulz M, and Weiss H (eds.) (1987) Intrinsic Properties of Group IV Elements and III–V, II–VI, and I–VII Compounds, Landolt–Bo¨rnstein New Series Group III vol. 22. Berlin: Springer. Myers SM, Wright AF, Petersen GA, et al. (2001) Diffusion, release and uptake of hydrogen in magnesium-doped gallium nitride: theory and experiment. Journal of Applied Physics 89: 3195. Myoung JM, Shim KH, Kim C, Kim K, Kim S, and Bishop SG (1996) Optical characterization of p-type GaN films grown by plasma-assisted molecular beam epitaxy. Applied Physics Letters 69: 2722. Nakamura S and Chichibu SF (eds.) (2000) Introduction to Nitride Semiconductor Blue Lasers and Light Emitting Diodes. ISBN: 978-0-74840-836-8. Boca Raton, FL: CRC Press. Nakamura S, Pearton S, and Fasol G (2000) The Blue Laser Diode – The Complete Story, 2nd edn., ISBN: 978-3-54066-505-2. Berlin, Heidelberg: Springer. Neugebauer J and Van de Walle CG (1996) Gallium vacancies and the yellow luminescence in GaN. Applied Physics Letters 69: 503. Palmer DW (2010) Semiconductors-Information Web site, http://www.semiconductors.co.uk (accessed March 2010). Pearton SJ, Abernathy CR, and Ren F (2006) Gallium Nitride Processing for Electronics, Sensors and Spintronics, Springer Series in Engineering and Processes, ISBN: 978-85233-935-7. Berlin, Heidelberg: Springer.

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¨ berg S Pinho NMC, Torres VJB, Jones R, Briddon PR, and O (2001) Mg-H and Be-H complexes in cubic boron nitride. Journal of Physics: Condensed Matter 13: 8951. Quay R (2008) Gallium Nitride Electronics, Springer Series in Materials Science, vol. 96, ISBN: 978-3-540-71890-1. Berlin, Heidelberg: Springer. Robertson MA, Estreicher SK, and Chu CH (1993) Interstitial oxygen in elemental and compound semiconductors: Fundamental properties and trends. Journal of Physics: Condensed Matter 5: 8943. Schubert EF (2006) Light Emitting Diodes, 2nd edn., ISBN: 139780521865388. Cambridge: Cambridge University Press. Sheu JK and Chi GC (2002) The doping process and dopant characteristics of GaN. Journal of Physics: Condensed Matter 14: R657. Wetzel C, Gil B, Kuzuhara M, and Manfra M (eds.) (2004) GaN, AlN, InN and Their Alloys, 2004 Fall Meeting, Symposium E, MRS Proceedings, vol. 831. Warrendale, PA: Materials Research Society. Veal TD, McConville CF, and Schaff WJ (eds.) (2009) Indium Nitride and Related Alloys, ISBN: 978-4200-1. Boca Raton, FL: CRC Press. Wilson RR and Wright AF (2005) Binding of the N interstitial with neutral MgH in p-type GaN investigated by density functional theory. Physical Review B 72: 024114. Wright AF (2001) Interaction of hydrogen with gallium vacancies in wurtzite GaN. Journal of Applied Physics 90: 1164.