Self-organised growth on strained substrates: the influence of anisotropic strain, surface energy and surface diffusivity

The morphological stability of coherent thin films subjected to unequal in-plane biaxial strains is investigated to determine how non-uniform strain states can be used to influence the growth of self-organised island nanostructures. The evolution via surface diffusion is modelled analytically using a small perturbation approach and allows for anisotropies in the surface energy and the surface diffusivity. It is shown that conventional uniform biaxial epitaxy does not provide a driving force towards a particular wavelength as is popularly assumed. This reduces the potential for highly self-organised growth. It is predicted that improvements in island size, shape and spatial distributions can be obtained under certain conditions of anisotropic strain, surface energy and surface diffusivity. This increase in uniformity would be beneficial to the construction of practical devices. Enhancing surface diffusivity anisotropy via the application of an applied strain could offer the most realistic opportunity for controlling the growth of self-assembled structures this way.