Theoretical study of the atomic and electronic structure of the c-4 × 4 reconstructed GaAs(100) surface

Surface Science 120 (1982) L42SL430 North-Holland Publishing Company

SURFACE

SCIENCE

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LETTERS

THEORETICAL STUDY OF THE ATOMIC AND ELECTRONIC STRUCTURE OF THE c-4 X 4 RECONSTRUCTED GaAs(100) SURFACE D.J. CHADI, C. TANNER * and J. IHM ** Xerox Palo Alio Research Center, 3333 Coyote Hill Road Palo Alto, California 94304, USA Received 30 March 1982; accepted for publication

11 May 1982

The c-4X 4 reconstruction of the As( 100) face of GaAs is examined using an energy-minimization approach. Other structures with 1 X 1, c-2X2 and p-2X2 periodicities are also examined in this study. The calculations predict that dimerization of surface As atoms is energetically favorable; however, structures with only one type of dimer per unit cell are found to be unstable. A four atom unit cell with two inequivalent dimers is the minimum size necessary for an adequate description of the surface atomic and electronic properties. The c-4X4 surface is suggested to consist of equal numbers of symmetric and asymmetric As dimers.

The polar Ga.As( 100) surface exhibits a variety of surface reconstructions as a function of surface stoichiometry and temperature [l--7]. The c-2 X 8, 2 X 4 and c-4 X 4 structures are As rich [3,5], the 1 X 6, 4 X 6 are Ga rich [3,5] while the c-8 X 2 seems to be intermediate [5]. The surface electronic structure of a number of these structures have been investigated experimentally via photoemission [&lo], electron loss [ 111, and work function [7] measurements. Theoretical studies of the electronic structure [12-141 of ideal surfaces have been useful in identifying possible mechanics for surface reconstruction. A lack of knowledge of the precise nature of the (100) surface reconstructions of GaAs has hindered a methodical theoretical study of the surface electronic structure. In this paper we concentrate on the As terminated GaAs(100) surface. Experimentally this should correspond to the c-4X 4 structure [5] seen in low-energy-electron-diffraction (LEED). The purpose of this study is to determine the optimal geometry of the surface via energy-minimization calculations, and then to calculate the surface electronic states for this structure. To facilitate the study we have used smaller unit cells with 1 X 1, c-2X 2 and

* Present address: Department USA. ** Present address: Department Massachusetts 02139. USA.

0039-6028/82/0000-0000/$02.75

of Physics, University

of California.

of Physics, Massachusetts

Berkeley, California

Institute of Technology,

0 1982 North-Holland

94720,

Cambridge,

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D.J. Chadi et al. / c-4 X 4 reconstructed GaAs(lO0) surface

p-2 X 2 periodicities

before proceeding with the full c-4X 4 structure. The main results of the calculations and the organization of the paper are as follows: The electronic structure of the 1 X 1 As-terminated GaAs(100) surface is discussed. Simple considerations verified by the calculation show that the surface is metallic with a f filled upper band. A dimer c-2 X 2 model for the surface is also discussed. It is found that dimerization is energetically favorable but that, as expected, it does not remove the metallic behavior of the surface when the unit cell contains only two atoms. Results for larger unit cells with p-2 X 2 and c-4 X 4 periodicities are then discussed. It is shown that energyminimization leads to a prediction of two structurally inequivalent dimer geometries in the unit cell. This is in contrast to the case of the Si( 100) surface where the dimers occurring in 2 X 1 or c-4 X 2 structures are structurally equivalent. In addition, unlike in Si, there is a large energy gain in GaAs in going from small (e.g., 2 X 1 or c-2 X 2) to large unit cells (i.e., p-2 X 2 or c-4 X 4). The extra degrees of freedom available in a large cell are utilized to reduce the total energy in GaAs. The structural and electronic properties of the surface are also described. GaAs( 100): 1 X 1. The 1 X 1 surface is metallic. A simple way for demonstrating this has been given by Appelbaum, Baraff and Hamann [12]. The argument is that, in the bulk or at the surface, every As atom contributes 5/4 electrons to each bond. The two As surface dangling-bonds therefore contain 5/2 electrons which (with two electrons per band) lead to full and f filled bands if there are no degeneracies or band overlap. The calculations of the surface electronic structure give a 0.35 eV wide, partially filled band, in the gap region which at T is 1.28 eV above the v~en~-band-m~mum (VBM). This state is As p, in character where x is along the projection of the dangling-bond on the surface plane. The highest filled surface state extends 0.2 eV above the VBM at r to 1.42 eV below it at the corner K of the 1 X 1 Brillouin zone. The character of this state is primarily As p,-like. Other surface states similar to those in previous tight-binding calculations 113,141are also obtained. To calculate the 1 X 1 surface bands, a 17 layer slab periodic in two dimensions was employed in the calculations. A minimal tight-binding basis set consisting of one s and three p orbitals was used. The tight-binding parameters and the energy-minization approach described in ref. [IS] were used. An odd number of layers was employed in all the calculations so that both ends of the slab consisted of the same type of atoms. Identical relaxations or reconstructions were carried out on each surface to avoid any ambiguities in band ordering or band filling. GaAs( 100): c-2 X 2. Two atom per cell structures are not experimentally

D.J. Chadi et al. / c-4 X 4 reconstructed

GaAs(100) surface

l.427

observed on the GaAs( 100) surface. Nevertheless, useful information on surface atomic properties can be obtained by considering a c-2 X 2 structure [ 161. The most important question to be addressed for this structure is whether a dimer geometry is energetically favorable. Experimental results by: (i) Cho [2] on the direction of unit cell doubling on various GaAs(lQ0) surfaces; (ii) Bachrach et al. [5] on surface As core-level shifts; (iii) Larsen et al. [8] from angle-resolved photoemission; and (iv) Foxon et al. [ 171 on As, molecular chemisorption and desorption from the surface, all provide indirect evidence in favor of a dimerized model. Our calculations indicate that dimerization is in fact energetically very favorable, resulting in a relatively large lowering of the total energy by = 0.95 eV/dimer [ 181. Self-consistent pseudopotential calculations based on the local density functional formalism by Ihm et al. [ 191 on the c-2 X 2 dimer model using coordinates obtained from the tight-binding calculations also predict a similar reduction in the total energy. The optimized dimer geometry is found to be asymmetric as in Si(lO0). The electronic structure of the c-2 X 2 GaAs(100) surface is metallic, independent of the precise dimer geometry unlike the case of the Si(100) surface [20]. This can be shown using an electron and band counting argument, similar to that for the 1 X 1 surface [ 121. An interesting question is whether the dimer geometry obtained for the c-2 X 2 structure is sufficient for building the larger unit cells observed on the GaAs( 100) surface. On the basis of purely one-electron-theory band filling arguments, a minimum of four atoms per cell is required to obtain a non-metallic surface. This suggests that if the dimer geometry is correct, then there are probably two distinct types of dimer at the surface. The results discussed in the following sections confirm this conjecture and show that there is a large energy gain in going from a two atom per cell to a four (or eight) atom per cell geometry. p-2 X 2 and c-4 X 4 unit cells. The essential feature of the energy minimization results for the p-2 X 2 and c-4X 4 cells is the occurrence of both

d

a

b

Ideal Surface

Asymmatric Dimar

(Type

A

AsygricSD~mer

Syy;a;icfi;rer

1

Fig. 1. The side view of four different structural units on the GaAs(lO0) surface is shown. The ideal atomic positions are shown in (a). The asymmetric dimers labeled A and B are structurally equivalent. The c-4X4 surface is proposed to consist of a combination of both asymmetric and symmetric dimers. All Ga-As bond-lengths are calculated to remain within 2.5% of those in the bulk.

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D.J. Chadi et al. / c-4 X 4 reconstructed GaAs(IW)

surface

symmetric and asymmetric dimers at the surface [21] (fig. 1). This results in an appreciable energy gain of 2 0.35 eV/dimer over the c-2 X 2 structure and is accompanied by a change from metallic to semiconducting surface energy bands. The same reduction in total energy is obtained in our self-consistent pseudopotential calculations [ 191 on the p-2 X 2 surface using the atomic coordinates obtained from the tight-binding calculations. Using the A, B and C classification of dimers shown in fig. 1, the p-2 X 2 surface geometry used in the calculations can be represented schematically as BBBB

AAAA CCCC

or

y

cccc

AAAA

BBBB

cccc

cccc

Two of the c-4 X 4 structures

!--

(1)

X

tested can be similarly

represented

by

ABABAB cccccc BABABA

(2)

cccccc ABABAB ccccc B A B’ A B A

(3)

ccccc

The latter structure differs from the one above it by a translation of all covalent dimers by a 1 X 1 lattice constant along the x-direction. The bond angles at the surface are indicative of the bonding rearrangements resulting from the surface reconstruction. In both the p-2 X 2 and c-4X 4 structure one As atom in four (the down atom of the asymmetric dimer) comes close to having an sp* bonding configuration (and contributes 1.4 electrons on the average to each bond). The bond angles involving this atom are given by f?= 115.5“, 115.4O and 122.3’. The strongly p,-like empty surface state = 1.15 eV above the valence-bandmaximum (VBM) is localized almost entirely on this atom. The bonding geometry makes this atom more positively charged than all other bulk or surface As atoms. The charge from this atom is distributed nearly uniformly on the other three As atoms; the underlying Ga substrate is also predicted to become slightly more negatively charged than bulk Ga atoms. The angles around the second atom of the asymmetric dimer are 0 = 93.3”, 93.3’ and 109.7’.

D.J. Chadi et al. / c-4 X 4 reconstructed

GaAs(100) surface

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The states localized on this atom are at = 1 eV below the VBM and are primarily p, in character (mixed with a little s-character). For the two symmetric dimers the bond angles are B = 102.1’,

103.5” and 104.8’.

The states associated with these are located between the VBM and 0.5 eV below it. These states have mixed p, and p, character. Many possible models for the c-4 X 4 structure in addition to those shown schematically in eqs. (2) and (3) were examined. No contraints on the types of dimer were made. Nevertheless, only two types of dimer similar to those occurring in the p-2 X 2 structure were found. An interesting question is whether the c-4 X 4 structure is lower in energy than the p-2 X 2 structure. The calculations show that the p-2 X 2 structure is a strained structure in the sense that the relaxation of surface atoms tends to stress the covalent As-As bond by stretching the bond-length to 2.69 A. By breaking the dimer bonds and rejoining them in the c-4 X 4 configuration of eq. (3), an energy lowering of 0.1 eV/dimer is obtained. The c-4 X 4 structure is a much less strained structure than the p-2 X 2 structure and this probably explains why the latter is not observed at the surface. The electronic structure of the two surfaces are calculated, however, to be very similar. We have examined the atomic and electronic structure of the As-terminated GaAs( 100) surface. Energy-minimization calculations lead to the prediction of two types of As dimer at the surface. The electronic structure of p-2 X 2 and the experimentally observed c-4 X 4 structures constructed from these dimers is predicted to be semiconducting. Calculations of surface electronic charge densities and total energies using the self-consistent pseudopotential method and the local-density-functional approach will be reported elsewhere [ 191. The authors would like to thank Dr. R.Z. Bachrach and Professor J.D. Joannopoulos for useful discussions. This work is supported in part by the Office of Naval Research through Contract No. NOO014-79-C-0704.

References [l] [2] [3] [4] [5]

A.Y. Cho, J. Appl. Phys. 42 (1971) 2074. A.Y. Cho, J. Appl. Phys. 47 (1976) 2841. P. Drathen, W. Ranke and K. Jacobi, Surface Sci. 77 (1978) L162. J.H. Neave and B.A. Joyce, J. Crystal Growth 44 (1978) 387. R.Z. Bachrach, R.S. Bauer, P. Chiaradia and G.V. Hansson, J. Vacuum Sci. Technol. (1981) 797. [a] J. Arthur, Surface Sci. 43 (1974) 449. [7] J. Massies, P. Devoldere and N.T. Linh, J. Vacuum Sci. Technol. 16 (1979) 1244. [8] P.K. Larsen, J.H. Neave and B.A. Joyce, J. Phys. Cl4 (1981) 167; Cl2 (1979) L869.

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[9] R.Z. Bachrach

D.J. Chadi et al. / c-4 X 4 reconstructed GaAs(IW) and R. Bringans,

surface

to be published.

[IO] A.J. van Bommel, J.E. Crombeen and T.G.J. van Girschot, Surface Sci. 72 (1978) 95. [ 111 R. Ludeke and A. Koma, J. Vacuum Sci. Technol. 13 ( 1976) 241. [12] J.A. Appelbaum, G.A. Baraff and D.R. Hamann, Phys. Rev. B14 (1976) 1623; J. Vacuum Sci. Technol. 13 (1976) 750. [13] J. Pollmann and S. Pantelides, Phys. Rev. Bl8 (1978) 5524. [14] J. Ivanov, A. Mazur and J. Pollmann, Surface Sci. 92 (1980) 365. [15] D.J. Chadi, Phys. Rev. B19 (1979) 2074. [ 161 The c-2X 2 structure allows greater freedom for subsurface relaxation than the 2 X 1 structure. This is the primary reason for choosing this structure in our study. [17] CT. Foxon, J.A. Harvey and B.A. Joyce, J. Phys. Chem. Solids 34 (1973) 1693. [ 181 To extend our calculation to the situation where As atoms interact as first neighbors, we have used experimental data on the As, molecular binding energy. The lowering of the electronic energy with dimerization has been corrected by using a nearest-neighbor repulsive ion-ion interaction term of 5 eV/dimer. The Hamiltonian matrix elements between adjacent As orbitals have also been taken to be the same as between Ga and As orbitals. [19] J. Ihm, D.J. Chadi and J.D. Joannopoulos, to be published. [20] D.J. Chadi, Phys. Rev. Letters 43 (1979) 43. [21] Since there are a number of ways of obtaining a c-4 X4 unit cell using the building blocks of the p-2 X2 structure, separate energy-minimization calculations were done on several c-4X4 structures. The atomic positions were determined by minimizing the Hellmann-Feynman forces acting on the atoms. This provides the most efficient way of energy-minimization when the unit cell is large. The forces can be evaluated straightforwardly within the tight-binding approach.