Nonlinear evolution of a morphological instability in a strained epitaxial film

A strained epitaxial film deposited on a deformable substrate undergoes a morphological instability, relaxing the elastic energy by surface diffusion. The nonlinear dynamical equation of such films with wetting interactions are derived and solved numerically in two and three dimensions. Nonlocal nonlinearities together with wetting effects are crucial to regularize the instability, leading to an island morphology. The island chemical potential decreases with its volume, and the system consistently experiences a noninterrupted coarsening evolution described by power laws with a marked dimension dependence.