Homogenization of liquid phase epitaxy

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The project focuses on new two-scale models for liquid phase epitaxy that are capable to simultaneously describe the evolution of epitaxial microstructures and the macroscopic transport of solute, heat and fluid. The model is derived by homogenization from a microscopic model that is given by a Burton-Cabrera-Frank model for the growth of the epitaxial solid layer on a part of the boundary of a given threedimensional domain, and by convection-diffusion equations for the transport of solute, heat and matter. The working plan contains a mathematical analysis of the two-scale model that addresses the solvability of the model and its approximation of a given situation with small scale, the numerical approximation of the model and extensive parameter studies including comparisons with experiments in order to verify the model and evaluate its range of applicability. These tasks shall be carried out for a phase field version of the epitaxial growth model. It is planned to proceed in several steps, starting from a simple model that only describes diffusion of adatoms in the solid and the growth of the epitaxial solid layer. Then this model shall be gradually extended to finally describe the full physics including heat transfer in the fluid and fluid flow.