Diffusion-induced islanding in heteroepitaxial systems

A microscopic lattice gas model for ultra-thin film dynamics is developed and applied to the case of heteroepitaxial growth. A set of non-linear kinetic equations for average occupations of adsorption sites in 3D lattice is studied analytically in a continual limit. It is found that within a range of parameters of heteroepitaxial system space-uniform state becomes unstable in critical thickness range and system undergoes spontaneous islanding. Space-ordered quasistationary solutions to the model equations describe the dynamics of 3D islanding induced by the uphill diffusion in the field of deposit–deposit and deposit–substrate interactions. Lateral size of islands depends on material constants of the system, surface temperature and deposition rate. Initial discrete system of non-linear kinetic equations is studied numerically; results for surface morphology describe dense arrays of 3D nanoislands.