Shape and coarsening dynamics of strained islands

TL;DR

This paper studies the formation and coarsening of strained islands in thin films, combining analytical and numerical methods to understand equilibrium shapes and dynamics of island interactions.

Contribution

It introduces a two-dimensional continuous model for equilibrium island shapes and describes the two-stage coarsening process of island assemblies.

Findings

Equilibrium island solutions have a maximum height and sit on a wetting layer.

Coarsening involves a quasi-static stage where smaller islands shrink.

The process depends on the distance between islands and leads to mass redistribution.

Abstract

We investigate the formation and the coarsening dynamics of islands in a strained epitaxial semi-conductor film. These islands are commonly observed in thin films undergoing a morphological instability due to the presence of the elasto capillary effect. We first describe both analytically and numerically the formation of an equilibrium island using a two dimensional continuous model. We have found that these equilibrium island-like solutions have a maximum height $h_0$ and they sit on top of a flat wetting layer with a thickness $h_w$. We then consider two islands and we report that they undergo a non-interrupted coarsening that follows a two stage dynamics. The first stage may be depicted by a quasi-static dynamics, where the mass transfers are proportional to the chemical potential difference of the islands. It is associated with a time scale $t_c$ that is function of the distance $d$ between the islands, and leads to the shrinkage of the smallest island. Once its height becomes smaller than a minimal equilibrium height $h_{0}^{*}$, its mass spreads over the entire system. Our results pave the way for a future analysis of coarsening of an assembly of islands.