Thin-film evolution equation for a strained solid film on a deformable substrate: Numerical steady states

We consider the nonlinear behavior of the thin-film evolution equation for a strained solid film on a substrate. The evolution equation describes morphological changes to the film by surface diffusion in response to elastic energy, surface energy, and wetting energy. Due to the thin-film approximation, the elastic response of the film is determined analytically, resulting in a self-contained evolution equation which does not require separate numerical solution of the full three-dimensional elasticity problem. Using a pseudospectral predictor-corrector method we numerically determine the family of steady state solutions to this evolution equation which correspond to quantum dot and quantum ridge morphologies.