N ov 2 00 2 Surface properties of epitaxially grown crystals

In this PhD thesis, we develop models of surfaces of epitaxially grown crystals. In the introductory chapter 1, we introduce the most important physical processes which occur on crystal surfaces in a molecular beam epitaxy (MBE) environment. In the first part of this work (chapters 2–4) we model the (001) surface of the II-VI semiconductors CdTe and ZnSe, our main focus being on CdTe. In the second part (chapters 5 and 6), we study generic features of epitaxial growth which are not specific to one particular material. These are kinetic roughening and the formation of mounds. Both effects can be investigated only after the deposition of a thick film on the substrate. Therefore, we must restrict ourselves to simple models which can be simulated with moderate computational effort. In chapter 2, we introduce a lattice gas model of flat (001) surfaces of CdTe and ZnSe in thermal equilibrium. Both the arrangement of metal atoms in vacancy structures and the dimerization of nonmetal atoms are considered. The surface is represented by a twodimensional square lattice. We introduce anisotropic interactions between nearest and next nearest neighbour sites which reflect the known properties of the surface. The phase diagram of this model is determined by means of transfer matrix calculations and Monte Carlo simulations. The phases of the model are identified with different reconstructions which have been observed in experiments. In particular, the transition between a Cd terminated c(2×2) reconstruction at low temperature and a Cd terminated (2×1) reconstruction at high temperature which occurs on the CdTe surface can be explained as an encompanying effect of an orderdisorder phase transition. Here, the small energy difference between both reconstructions plays an important role. Crystal surfaces in an MBE environment are not in thermal equilibrium. Instead, nonequilibrium processes like growth and sublimation occur. Are the essential features of our equilibrium model preserved under these conditions or are there completely different, nonequilibrium effects? To answer this question, we need to extend our two-dimensional lattice gas to a model of a three-dimensional crystal which can be used to simulate growth and sublimation. The basic idea is that there is an isotropic attraction between particles in the bulk of the crystal while particles on the surface interact with the anisotropic interactions of the lattice gas. Such a model which, however, contains several simplifications compared to a realistic model of CdTe, is investigated in chapter 3. We neglect the dimerization of surface Te atoms and simulate a simple cubic lattice instead of the zinc-blende lattice of CdTe. In spite of these simplifications, many effects which have been observed on sublimating CdTe(001) surfaces in vacuum and under an external flux of pure Cd or pure Te can be reproduced. Additionally, the behaviour of this model agrees qualitatively with that of a simplified version of our lattice gas where the dimerization of Te atoms is neglected. Thus, we have shown that the investigation of two-dimensional lattice gas models in thermal equilibrium is an appropriate tool to obtain insight into the behaviour of reconstructed surfaces in an MBE environment. On the other hand, the non-equilibrium conditions of sublimation induce characteristic deviations from the behaviour of the equilibrium model which should be considered in precise investigations. Starting from this result, we develop a model of the CdTe(001) surface which is closer to reality. It is introduced in section 4. We simulate a zinc-blende lattice instead of a simple