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Study of Island Formation in Epitaxially Strained Films on Unbounded Domains

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Abstract

We consider a variational model related to 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.

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Authors and Affiliations

  1. Max Planck Institute for Mathematics in the Sciences, Leipzig, Germany

    P. Bella & M. Goldman

  2. Institute for Applied Mathematics, Bonn University, Bonn, Germany

    B. Zwicknagl

Authors
  1. P. Bella
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  2. M. Goldman
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  3. B. Zwicknagl
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Correspondence to M. Goldman.

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Communicated by I. Fonseca

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Bella, P., Goldman, M. & Zwicknagl, B. Study of Island Formation in Epitaxially Strained Films on Unbounded Domains. Arch Rational Mech Anal 218, 163–217 (2015). https://doi.org/10.1007/s00205-015-0858-x

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  • DOI: https://doi.org/10.1007/s00205-015-0858-x

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