Model of surface instabilities induced by stress

TL;DR

This paper introduces a Ginzburg-Landau based model to analyze surface instabilities caused by stress, specifically focusing on the Grinfeld instability during thin-film growth, highlighting nonlinear effects and coarsening behavior.

Contribution

It presents a novel nonlinear model for the Grinfeld instability and explores coarsening dynamics, providing insights into strain relief mechanisms at stressed interfaces.

Findings

Nonlinearities lead to competitive coarsening of interfacial structures.

The model captures the evolution of surface instabilities in 2D and 3D.

Suggestions for experimental measurement of coarsening are provided.

Abstract

We propose a model based on a Ginzburg-Landau approach to study a strain relief mechanism at a free interface of a non-hydrostatically stressed solid, commonly observed in thin-film growth. The evolving instability, known as the Grinfeld instability, is studied numerically in two and three dimensions. Inherent in the description is the proper treatment of nonlinearities. We find these nonlinearities can lead to competitive coarsening of interfacial structures, corresponding to different wavenumbers, as strain is relieved. We suggest ways to experimentally measure this coarsening.