Shape dynamics in anisotropically strained two-dimensional self-assembling systems

Abstract

We analyze the evolution of equilibrium and growth shapes of anisotropically strained two-dimensional self-assembled structures using a dynamic growth model. As examples of such structures, we study the shapes of nanowires grown heteroepitaxially on cubic (001) surfaces and monolayer islands or stress domains grown homoepitaxially on Si(001) surface. In the former case, the anisotropy in the mismatch strain in the two principal directions is large, while in the latter case, the principal components of the strain are equal in magnitude and opposite in sign. In the case of nanowires, we find that the slow kinetics of growth limits the formation of wirelike shapes with constant widths as predicted by equilibrium models. In particular, the aspect ratios of nanowires during growth are considerably smaller than the equilibrium aspect ratios. For monolayer islands on Si(001), we show that the anisotropy in strain gives rise to a novel fourfold symmetry in their equilibrium shapes. This strain-induced symmetry, coupled with the kinetics of growth, is shown to result in rich shape dynamics of monolayer islands on Si(001) as seen in recent experiments.