Kinetic Ising model of site-correlated adsorption and surface diffusion in molecular-beam epitaxy

Abstract

Atom-adsorption process and diffusion process in molecular-beam epitaxy (MBE) are modeled in the framework of the dynamic three-dimensional Ising model. The growth system considered here was a pseudobinary system described as A x III B 1− x C V grown on a B III C V (001) compound substrate. A Fokker-Planck equation has been derived to couple the adsorption and surface diffusion processes on the basis of an effective Ising Hamiltonian of the growing pseudobinary system. The effective Ising Hamiltonian is an extension of the usual Ising-model description of crystal growth within the lattice-gas model to the pseudobinary growth system, which takes into account the intralayer interatomic interaction and the interlayer interatomic interaction. The intralayer (in-plane) interatomic interaction is essentially anisotropic in a zincblende lattice which has geometrical anisotropy in the [110] and [ 110 ] directions of the growing surface. Using the effective Hamiltonian, site-correlated adsorption (SCA) probability which describes the effects of local atomic configuration on the adsorption probability of an impinging atom and the site-exchange probability are formulated assuming the local equilibrium approximation. It has been found that the formation processes of recently observed sublattice long-range ordering (LRO) in an A x III B 1−x III C V pseudobinary system is well described within the MBE-growth model. It is also found that the type of LRO, such as L1 0 (CuAu-I), L1 1 (CuPt) and E1 1 (chalcopyrite), is classified and predictable by the types of interatomic interactions of the adsorbed (A, B) atoms.