Morphology evolution during the growth of strained-layer superlattices

We present a linear stability analysis for epitaxial growth of strained-layer superlattices, calculating how a shape perturbation propagates through the whole multilayer stack. We assume that bulk diffusion is negligible, so the morphology is controlled by surface diffusion. Unlike the case of a single strained layer, there are conditions under which the growth of the planar superlattice is stable, i.e., perturbations to the growth surface decay. For the conditions of unstable film growth (where the amplitude of the perturbation increases from layer to layer), we find three different types of resulting film morphology, classified according to the phase of the perturbation in successive layers, which is a function of materials parameters and growth conditions. We also determine the growth rate and wave vector of the propagating perturbation corresponding to the fastest growing instability wave.