MORPHOLOGICAL INSTABILITY IN EPITAXIALLY STRAINED DISLOCATION-FREE SOLID FILMS - NONLINEAR EVOLUTION

We consider a continuum model for the evolution of an epitaxially stra ined dislocation-free solid film on a rigid substrate in the absence o f vapor deposition. In the context of this model a planar film is unst able for film thicknesses greater than a critical thickness and the in stability is characterized by long waves at the critical thickness. By exploiting the long-wave nature of the instability we are able to der ive a nonlinear evolution equation for the film surface. We examine th e nonlinear evolution equation for two-dimensional steady states and f ind subcritical spatially periodic finite-amplitude rounded-cusp stead y solutions as well as near-critical spatially periodic small-amplitud e steady solutions. We analyze these solutions for stability and find them all to be unstable. Our analysis suggests that there are no stabl e two-dimensional steady states that can be described by long-wave the ory. 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.