We consider a continuum model for the evolution of an epitaxially strained dislocation-free solid film on a rigid substrate in the absence of vapor deposition. In the context of this model a planar film is unstable for film thicknesses greater than a critical thickness and the instability is characterized by long waves at the critical thickness. By exploiting the long-wave nature of the instability we are able to derive a nonlinear evolution equation for the film surface. We examine the nonlinear evolution equation for two-dimensional steady states and find subcritical spatially periodic finite-amplitude rounded-cusp steady solutions as well as near-critical spatially periodic small-amplitude steady solutions. We analyze these solutions for stability and find them all to be unstable. Our analysis suggests that there are no stable two-dimensional steady states that can be described by long-wave theory. Thus, the evolution of the film may be to a steady state outside the realm of long-wave theory or to a transient state characterized by coarsening.

• Received 19 August 1992

DOI:https://doi.org/10.1103/PhysRevB.47.9760