Study of island formation in epitaxially strained films on unbounded domains

Peter Bella, Michael Goldman, and Barbara Zwicknagl

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Submission date: 27. Feb. 2014 (revised version: September 2014)
Pages: 48
published in: Archive for rational mechanics and analysis, 218 (2015) 1, p. 163-217 
DOI number (of the published article): 10.1007/s00205-015-0858-x
Bibtex
Keywords and phrases: epitaxial growth, island formation
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Abstract:
We consider a variational model for the formation of islands in heteroepitaxial growth on unbounded domains. We first derive the scaling regimes of the minimal energy in terms of the volume of the film and the amplitude of the crystallographic misfit. For small volumes, non-existence of minimizers is then proven. This corresponds to the experimentally observed wetting effect. On the other hand, we show the existence of minimizers for large volumes. We finally study the asymptotic behavior of the optimal shapes.