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

TL;DR

This paper investigates the simultaneous occurrence of step bunching and meandering in surface growth, using both a cellular automaton model and a continuum PDE approach to unify understanding of these phenomena.

Contribution

It introduces a combined modeling framework that captures both step bunching and meandering within a single growth process, bridging two traditionally separate approaches.

Findings

Both models produce similar surface patterns under comparable parameters.

The continuum model enables long-time scale evolution analysis.

The cellular automaton model links to the continuum description through potential energy landscape.

Abstract

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.