Complex surface patterning in homo- and heteroepitaxial contexts: (simultaneous) step bunching and step meandering

Abstract

We confront a meso-scale continuum model, archetypical for the heteroepitaxial context, with an atomistic Vicinal Cellular Automaton (VicCA), built as a homoepitaxial counterpart, to show that in (2+1)D complex surface instabilities are fundamental growth phenomena rather than context-specific artifacts. Our approach is to first construct a Ginzburg-Landau-type model, designed to extend the previously (1+1)D Tersoff-type models in (2+1)D. We complement the continuum approach with a discrete one - the VicCA, in which we use a novel version of the potential landscape for the diffusing particles - a double-well potential located at each step edge. Notably, this framework also reproduces step bunching and step meandering - which are typically treated as incompatible in the theoretical paradigm, but coexist in real material systems. Thus we establish a cross-context correspondence at the level of obtained morphologies and morphology diagrams and, additionally, a multiscale perspective on the governing parameters, bridging the gap between the mesoscale and atomistic modeling.