From bell shapes to pyramids: A reduced continuum model for self-assembled quantum dot growth |
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Authors: | MD Korzec PL Evans |
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Institution: | a Weierstrass Institute for Applied Analysis and Stochastics (WIAS), D-10117 Berlin, Germany b Institute for Mathematics, Humboldt University of Berlin, D-10099 Berlin, Germany |
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Abstract: | 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 faceted 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 simulations are carried out. These clearly show faceting of the growing islands and a power law coarsening behavior. |
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Keywords: | Anisotropic surface energy Self-assembly of quantum dots Small slope approximation Stationary solutions Coarsening Linear stability analysis |
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