Morphological instability in epitaxially strained dislocation-free solid films: Nonlinear evolution

B. J. Spencer*, S. H. Davis, P. W. Voorhees

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

97 Scopus citations


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.

Original languageEnglish (US)
Pages (from-to)9760-9777
Number of pages18
JournalPhysical Review B
Issue number15
StatePublished - 1993

ASJC Scopus subject areas

  • Condensed Matter Physics

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