Monte Carlo simulation of epitaxial growth in MBE and ALE mode

Abstract

A Monte Carlo based method for simulation of epitaxial crystal growth is reported. The improvement of our concept in comparison to the simulations based on the solid on solid model is the possibility to simulate crystal growth without the assumption of a discrete crystal lattice structure. Our model requires only an assessment for the Hamiltonian. The method is used for studying growth in a two-dimensional cross section through the substrate and the epilayer with a width of up to 80 atoms. Two different potentials can be chosen for the simulations: (a) Lennard-Jones and (b) directional Lennard-Jones to describe covalent systems. In addition to the selection of the potential, we can set the following parameters for different kinds of atoms: radii of the potential minimum, binding energies between the atoms for all possible pairings, growth temperature and substrate structure. The epitaxial growth of strained layers was simulated to study the incorporation of dislocations at the interface. Island and layer growth in the nucleation stage were investigated by selecting different binding energies of the epilayer atoms to the substrate atoms. As further extension of our MC calculations we allowed the reevaporation of particles which is essential for the simulation of atomic-layer epitaxy.