The zinc blende (110) surface: GaAs(110)
______________________________________________________________________
Alastair McLean
Dpt Physics, Queen's University, Kingston, Ontario, K7L 3N6
mclean@mnbsun.phy.queensu.ca
12 February 1992

Copyright 1992. Permission is granted to modify and/or make copies of this file for any purpose other than direct profit, or as part of a commercial product, provided this copyright notice together with the header containing the author's name and address is left intact.

Introduction

This notebook was written because I wanted to generate some pictures of Bi overlayers on GaAs(110), and some of the pictures that are contained within this notebook have been incorporated in papers our group have written on the electronic structure of these systems. The process of generating these models can be quite time consuming, so I hope that by distributing this notebook and the associated packages (GaAs1.m through GaAs2.m) they will give you some ideas and hopefully save you some time ! I would be particularly interested in any comments you may have and any packages that you may develop using this as a starting point. It would be convenient for example to have a library of the common crystallographic bulk and surface structures available. Although I have generated these models by brute force I'm sure that it would be possible to write some code to generate them automatically. I will leave that up to someone else for the moment. 

The notebook explores the GaAs(110) surface crystal structure and the epitaxial adlayer structure formed by depositing one monolayer of either Sb or Bi onto the (110) surface. The initial part of the notebook applies to all zinc blende lattices. The latter part is specific to the compound semiconductor GaAs.

The zinc blende structure

The zinc blende structure can be generated from the diamond structure
by substituting equal numbers of anions and cations in the diamond lattice 
positions so that each anion has four cation nearest neighbours and each cation 
has four anion nearest neighbours (the diamond structure has been rendered
already in CrystalStructure.m which I received this with the first release of 
Mathematica.).  Each atom then has four nearest neighbours and twelve next
nearest neighbours. The diamond structure can be regarded to be two face
centred cubic lattices displaced from each other by one quarter of the body
diagonal (Kittel, Introduction to Solid State Physics, John Wiley and Sons,
5th Edition, p29 (1976)). The zinc blende (zinc sulphide) structure arises when zinc atoms are placed on one of the face centred cubic lattices and sulphur atoms are placed on the other. 

We start with the observation that a section through a zinc blende lattice, 
taken parallel to the (110) plane, will contain a zigzag chain of anions and cations.  The following compounds crystallise in the zinc blende crystal structure: CuF, CuCl, CuBr, CuI, AgI, BeS, BeSe, BeTe, MnS(red), MnSe, ZnS, ZnSe, ZnTe, CdS, CdTe, HgS, HgSe, HgTe, AlP, AlAs, AlSb, GaP, GaAs, GaSb, InP, InAs, InSb, SiC (e.g. see  Solid State Physics, by Ashcroft and Mermin, Holt, Rinehart and Winston, p81, table 4.7). For GaAs the anion is As (rendered black in the following views) and the cation is Ga (rendered gray). GaAs1.m renders a section through a zinc blende lattice taken parallel to the (110) plane.

<<GaAs1.m

Show[Picture, 
	ViewPoint->{-1.643, -2.718, 1.168},
	BoxRatios->{1, 1, 0.5}]

We will build up a lattice gradually, layer-by-layer, by adding another (110) section displaced by the vector

	T = 0.5a + 0.5b + c

where a, b and c are the cubic lattice vectors.  This process, which is repeated here only once in GaAs2.m, can be repeated, as many times as you want,  to generate a crystal, as large as you want.  For the zince blende lattice the interlayer spacing along the [110] direction is 0.364 times the cubic lattice constant.

Ex. Generate an infinite crystal by displacing an infinite number of (110) planes by integer multiples of T.

<<GaAs2.m

Show[Picture, 
	ViewPoint->{1.75, 0, 0.9},
	BoxRatios->{1, 1, 0.4}]

In GaAs3.m I have added the interplanar bonds between the first layer
and the second layer. Note that each of the anions in the top layer bonds
to a cation in the second layer and eachof the cation in the top layer
bonds to an anion in the second layer.

<<GaAs3.m

Show[Picture, 
	ViewPoint->{1.75, 0, 0.9},
	BoxRatios->{1, 1, 0.35}]

The nice thing about these models is that you can view them from
different angles in the same way that you would rotate a real ball and stick model. So far, I have basically generated a model of the unrelaxed GaAs(110) surface that is two atoms deep. The structure assumes that the bulk atomic positions are preserved to the surface. This is not what happens in reality. Although the atoms at the surface do not rebond (reconstruct) the atoms do move. This displacement of the surface atoms is called a reconstruction. Before we go on to reconstructed surfaces,  I have shown GaAs3.m again from the side to illustrate that the Ga and As atoms are planar in the bulk terminated model.

Show[Picture, 
	ViewPoint->{1.0, 0.1, 0.25},
	BoxRatios->{1, 1, 0.40}]

Relaxed (110) surfaces

Now we explore the relaxed surface (GaAs4.m). I have generated a model of the relaxed surface using atomic positions that have been obtained from a recent low energy electron diffraction (LEED) study. The study was performed by Wayne Ford and coworkers at Montana State University and their work, Dynamical low-energy electron-diffraction analysis of bismuth and antimony on GaAs(110) is published in Physical Review B, 42, 8592 (1990). For more details I suggest you read their paper. To cut a long story short, each of the Ga and the As atoms in the surface layer have an unsaturated dangling bond. The free energy of the surface is reduced if the Ga bonding configuration (sp3) flattens and becomes more sp2-like. This causes the surface to buckle and the buckling is accompanied by a transfer of charge from the Ga to the As atoms.
The As atoms move out of the surface plane and the Ga atome move in towards the bulk. This is often discussed in terms of a bond angle rotation. There is a counter rotation in the second layer but its magnitude is small compared with the relaxation of the top layer. The electronic states associated with the two bonds have been studied by angle resolved and inverse photoemission. Both states lie outside the fundamental energy gap of GaAs. The Ga dangling bond is unoccupied and lies above the conduction band minimum and the As dangling band state is occupied and lies below the valence band maximum (for a review see Hansson and Uhrberg, Photolectron spectroscopy of surface states on semiconductor surfaces, Surface Science Reports, 9, 197 (1988)).

So the As atoms in the top layer move up and the Ga atoms in the top layer move down.  In the second layer the movements with respect to the unperturbed second layer are in the opposite sense and the magnitude of the perturbation is smaller.

<<GaAs4.m

Show[Picture, 
	ViewPoint->{1.0, 0.1, 0.25},
	BoxRatios->{1, 1, 0.40}]

In preperation for rendering an epitaxial overlayer on the GaAs(110) surface, I have added another GaAs(110) plane with the associated  interplanar bonds. The atomic positions are unrelaxed.

<<GaAs5.m

Show[Picture, 
	ViewPoint->{2.0, 0.1, 0.50},
	BoxRatios->{1, 1, 0.40}]

Epitaxial (1x1) overlayers on (110) surfaces

Now by altering the shading of the top layer I have a model of either Bi or Sb overlayers on GaAs(110) (Ford et al. Physical Review B, 42, 8592 (1990)). However the model is not complete until I add the relaxation of the top and second layers. The relaxation that occurs when Bi or Sb is bonded to the GaAs(110) surface is very small compared to that of the clean GaAs(110) surface.

<<GaAs6.m

Show[Picture, 
	ViewPoint->{2.0, 0.1, 0.50},
	BoxRatios->{1, 1, 0.40}]

Now I include the relaxation of the first and second layers in the model using the parameters from Wayne's paper. Note that all thesse models are scale models using real parameters. The relaxation is greatly reduced by the epitaxial overlayer, and there not a great difference between the relaxed and the unrelaxed geometries. To emphasise the relaxation the model has to be viewed form the side.

<<GaAs7.m

Show[Picture, 
	ViewPoint->{2.0, 0.15, 0.05},
	BoxRatios->{1, 1, 0.50}]

The electronic structure of both the GaAs(110)(1x1)Sb and the GaAs(110)(1x1)Bi monolayer epitaxial structures have been studied by angle resolved photoemission. For the former see the references in Hansson and Uhrberg's review article. For the latter, refer to some of our own papers:

References

[1] Electronic and structural properties of a discommensurate monolayer system: GaAs(110)(1x1)Bi, A. B. McLean, R. M. Feenstra, A. Taleb-Ibrahimi and R. Ludeke, Phys. Rev B, 39, 12925 (1989).
[2] Two-dimensional electronic structure of the GaAs(110)-Bi system, A. B. McLean, R. Ludeke, M. Prietsch, D. Heskett, D. Tang, T. Maeda Wong, Phys. Rev. B, 43, 7243 (1991). 
[3] Resonant inverse photoemission study of layer dependent surface states at the epitaxial GaAs(110)-Bi interface, A. B. McLean and F. J. Himpsel, Phys. Rev. B, 40, 8425 (1989).
[4] The polarisation dependence of Bi-induced surface states on GaAs(110), A. B. McLean, R. Ludeke, M. Prietsch, D. Heskett, D. Tang, T. Maeda Wong, J. Vac. Sci. Technol, A9, 1836 (1991).
[5] Metal-induced states on the GaAs(110) surface probed by angle resolved photoemission spectroscopy, D. Heskett, D. Tang, A. B. McLean, R. Ludeke, M. Prietsch,  T. Maeda Wong, E. W. Plummer and N. J. DiNardo, Applied Surface Science, 48/49, 260 (1991).