Computation of strained epitaxial growth in three dimensions by kinetic Monte Carlo

A numerical method for computation of heteroepitaxial growth in the presence of strain is presented. The model used is based on a solid-on-solid model with a cubic lattice. Elastic effects are incorporated using a ball and spring type model. The growing film is evolved using kinetic Monte Carlo (KMC) and it is assumed that the film is in mechanical equilibrium. The force field in the substrate is computed by an exact solution which is efficiently evaluated using the fast Fourier transform, whereas in the growing film it is computed directly. The system of equations for the displacement field is then solved iteratively using the conjugate gradient method. Finally, we introduce various approximations in the implementation of KMC to improve the computation speed. Numerical results show that layer-by-layer growth is unstable if the misfit is large enough resulting in the formation of three dimensional islands.