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From bell-shapes to pyramids: a continuum model for self-assembled quantum dot growth

Please always quote using this URN:urn:nbn:de:0296-matheon-5873
  • A continuum model for the growth of self-assembled quantum dots that incorporates surface diffusion, an elastically deformable substrate, wetting interactions and anisotropic surface energy is presented. Using a small slope approximation a thin film equation for the surface profile that describes facetted growth is derived. A linear stability analysis shows that anisotropy acts to destabilize the surface. It lowers the critical height of flat films and there exists an anisotropy strength above which all thicknesses are unstable. A numerical algorithm based on spectral differentiation is presented and simulation are carried out. These clearly show faceting of the growing islands and a logarithmically slow coarsening behavior.

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Metadaten
Author:Maciek Korzec, Peter L. Evans
URN:urn:nbn:de:0296-matheon-5873
Referee:Barbara Wagner
Document Type:Preprint, Research Center Matheon
Language:English
Date of first Publication:2009/07/15
Release Date:2009/07/15
Tag:
Institute:Humboldt-Universität zu Berlin
Weierstraß-Institut für Angewandte Analysis und Stochastik (WIAS)
MSC-Classification:41-XX APPROXIMATIONS AND EXPANSIONS (For all approximation theory in the complex domain, see 30E05 and 30E10; for all trigonometric approximation and interpolation, see 42A10 and 42A15; for numerical approximation, see 65Dxx) / 41Axx Approximations and expansions / 41A60 Asymptotic approximations, asymptotic expansions (steepest descent, etc.) [See also 30E15]
74-XX MECHANICS OF DEFORMABLE SOLIDS / 74Axx Generalities, axiomatics, foundations of continuum mechanics of solids / 74A50 Structured surfaces and interfaces, coexistent phases
Preprint Number:583
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