Anisotropic surface energy formulations and their effect on stability of a growing thin film
type: Item
instance of: scholarly article
title: Anisotropic surface energy formulations and their effect on stability of a growing thin film
zbMATH Open document ID: 1263.35068
DOI: 10.4171/IFB/291
author: M. D. Korzec
author: Andreas Münch
author: Barbara Wagner
published in: Interfaces and Free Boundaries
publication date: 2013-04-12T00:00:00Z
review text: Summary: We revisit models for the description of the evolution of crystalline films with anisotropic surface energies.We prove equivalences of symmetry properties of anisotropic surface energy models commonly used in the literature. Then we systematically develop a framework for the derivation of surface diffusion models for the self-assembly of quantum dots during Stranski-Krastanov growth that include surface energies also with large anisotropy as well as the effect of wetting energy, elastic energy and a randomly perturbed atomic deposition flux. A linear stability analysis for the resulting sixth-order semilinear evolution equation for the thin film surface shows that that the new model allows for large anisotropy and gives rise to the formation of anisotropic quantum dots. The nonlinear three-dimensional evolution is investigated via numerical solutions. These suggest that increasing anisotropy stabilizes the faceted surfaces and may lead to a dramatic slow-down of the coarsening of the dots.
Mathematics Subject Classification ID: 35G25
Mathematics Subject Classification ID: 74S25
Mathematics Subject Classification ID: 76A20
Mathematics Subject Classification ID: 35B35
zbMATH DE Number: 6153555
zbMATH Keywords: pseudospectral methods
zbMATH Keywords: surface diffusion
zbMATH Keywords: derivation of surface diffusion models
zbMATH Keywords: Stranski-Krastanov growth
zbMATH Keywords: linear stability analysis
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 6153555