Morphological instability in epitaxially strained dislocation-free solid films

We perform the first analysis of the morphological instability of a growing epitaxially strained dislocation-free olid film. We derive an evolution equation for the film surface based on surface diffusion driven by a stress-dependent chemical potential. From the time-dependent linear stability problem we determine the conditions for which a growing film is unstable. Our results reveal that the critical film thickness for instability depends on the growth rate of the film itself, and that the instability we describe exhibits many of the observed features of the onset of the ``island instability.''