Simulation of the organization of heteroepitaxial monolayer islands under anisotropic conditions

This paper addresses the effect of anisotropy on the organization of epitaxial islands deposited on a substrate. Focus is on in-plane anisotropies in surface stress and lattice mismatch between the film and substrate materials. Starting from a configuration where island sizes and position are random, evolution towards equilibrium through mass transport via condensation/ evaporation is simulated. The effect of the degree of anisotropy is investigated. An efficient numerical method is obtained by reducing a model of square monolayer islands of finite size to point defects that interact through their elastic fields. Models for both the kinetics and energetics of the system are obtained by this reduction. It is found that the point source model is accurate for island separations larger than about 3 times the width of an island. Under isotropic conditions islands tend to form into hexagonal arrays, and as there is no preferred orientation of these arrays, defects analogous to grain boundaries in a crystalline material tend to arise. With anisotropy islands tend to align in particular directions. This is found to enhance organization in cases of modest anisotropy and cause islands to form into zigzagged lines in cases of high anisotropy.