Shape and coarsening dynamics of strained islands

We investigate the formation and the coarsening dynamics of islands in a strained epitaxial semiconductor film. These islands are commonly observed in thin films undergoing a morphological instability due to the presence of the elastocapillary 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 noninterrupted coarsening that follows a two stage dynamics. The first stage may be depicted by a quasistatic 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 a 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.