Anisotropy Driven Interrupted Coarsening of the Asaro-Tiller-Grinfeld Instability

Abstract

We investigate the effects of surface energy anisotropy on the coarsening dynamics of the Asaro-Tiller-Grinfeld instability at stake in thin semiconductor films. We consider a continuum model which accounts for wetting interactions between the film and its substrate, elasticity driven mass currents and surface energy anisotropy. We derive an explicit non-linear, non-local evolution equation for the film height that we solve numerically. Anisotropy, which dictates the island shapes, impacts the growth kinetics by weakening the possible elastic relaxation, which can lead during annealing to an interruption of Ostwald ripening. The resulting stationary state is characterized by square-based pyramids separated by a wetting layer. It is found that the instability onset is delayed when the film thickness decreases above the critical thickness for the instability to occur. We characterize the influence of the growing flux used for the film deposition on the stationary state reached during subsequent annealing, and find that the density of the resulting self-organized islands increases with the flux.