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 to (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. Importantly, this framework also captures both step bunching and step meandering. While these behaviors are rarely treated together in earlier approaches, they naturally coexist in real materials. 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.

16 pages, 10 figures