Step Bunching and Meandering as Common Growth Modes: A Discrete Model and a Continuum Description

The coexistence of step bunching and step meandering remains contradictory in the understanding of the unstable step-flow growth. Considered separately, the two instabilities have generated rich but largely independent modeling traditions. Especially, the one-dimensional framework faces a fundamental difficulty once bunching and meandering occur simultaneously -- step bunching is usually associated with an inverted Ehrlich--Schwoebel effect, whereas step meandering is associated with a direct one. The key experiments also focus mainly on the two basic limiting cases. How, then, can both instabilities coexist within the same growth process once the simultaneous occurrence of bunching and meandering cannot be adequately captured as a simple superposition of the two? In this work, we confront results from two substantially different approaches: a (2+1)D Vicinal Cellular Automaton based model (VicCA) and a differential-difference PDE-based description combining a model of step bunching with a relaxation term in the perpendicular direction. The continuous framework enables to explore long-time scales evolution to find large variety of surface patterns. Introducing a proper shape of the potential energy landscape in the VicCA model produces similar patterns and links both models on the level of parameters.