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We have decided to discontinue the publication of preprints on our preprint server as of 1 March 2024. The publication culture within mathematics has changed so much due to the rise of repositories such as ArXiV (www.arxiv.org) that we are encouraging all institute members to make their preprints available there. An institute's repository in its previous form is, therefore, unnecessary. The preprints published to date will remain available here, but we will not add any new preprints here.

MiS Preprint
32/2014

Study of island formation in epitaxially strained films on unbounded domains

Peter Bella, Michael Goldman and Barbara Zwicknagl

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.

Received:
Feb 27, 2014
Published:
Mar 6, 2014
Keywords:
epitaxial growth, island formation

Related publications

inJournal
2015 Repository Open Access
Peter Bella, Michael Goldman and Barbara Zwicknagl

Study of island formation in epitaxially strained films on unbounded domains

In: Archive for rational mechanics and analysis, 218 (2015) 1, pp. 163-217