A Numerical Study of Stress Controlled Surface Diffusion During Epitaxial Film Growth

Abstract

A two-dimensional numerical simulation is performed to model the morphological evolution of a strained film growing heteroepitaxially on a substrate under simultaneous action of vapor deposition and surface diffusion. To facilitate numerical implementation, a continuum boundary layer model is proposed to account for the influence of film/substrate interface on the film growth pattern. Discussions are focused on the Stranski-Krastanow growth mode, although our model is capable of explaining Frank-van der Merwe and Volmer-Weber growth modes as well. Both first-order perturbation and numerical results are developed to demonstrate that the film surface tends to remain flat during the initial stage of growth and that surface roughening occurs once the film thickness exceeds a critical value, in consistency with experimentally observed patterns of S-K growth. Numerical results further show that, depending on the deposition rate, the surface evolution could lead to a steady state morphology, unstable cusp formation, or growing islands with flattened valleys.