Showing papers by "Andreas Münch published in 2012"
TL;DR: The direct numerical simulation allows new insight into the conduction mechanisms for different frequency regimes, and numerically computed values for the degree of dissociation are of the same order of magnitude as the values obtained with classical formulas, but still differ by a factor of about 1/3.
22 citations
TL;DR: In this article, a framework for the derivation of surface diffusion models for the self-assembly of quantum dots during Stranski-Krastanov growth is proposed. But the model is not suitable for the modeling of anisotropic surface energies.
Abstract: In this paper 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 2010 Mathematics Subject Classification: Primary 35G20; Secondary 74S25
14 citations