Computer simulation studies of the growth of strained layers by molecular-beam epitaxy

Two new types of discrete-space Monte Carlo computer simulation are presented for the modeling of the early stages of strained-layer growth by molecular-beam epitaxy. The simulations are more economical on computer resources than continuous-space Monte Carlo or molecular dynamics. Each model is applied to the study of growth onto a substrate in two dimensions with use of Lennard-Jones interatomic potentials. Up to seven layers are deposited for a variety of lattice mismatches, temperatures, and growth rates. Both simulations give similar results. At small lattice mismatches ({}4%) the growth is in registry with the substrate, while at high mismatches ({}6%) the growth is incommensurate with the substrate. At intermediate mismatches, a transition from registered to incommensurate growth is observed which commences at the top of the crystal and propagates down to the first layer. Faster growth rates are seen to inhibit this transition. The growth mode is van der Merwe (layer-by-layer) at 2% lattice mismatch, but at larger mismatches Volmer-Weber (island) growth is preferred. The Monte Carlo simulations are assessed in the light of these results and the ease at which they can be extended to three dimensions and to more sophisticated potentials is discussed.