A two-scale model for liquid phase epitaxy
speaker: Christof Eck (University of Bielefeld, Faculty of Mathematics)abstract: Liquid phase epitaxy is a special technique to grow thin solid layers from a liquid solution. The main mechanism is the deposition of atoms in monoatomar layers. Often epitaxy leads to microstructures of the phase interface that may be of technical relevance. We study a model for liquid phase epitaxy that consists of differential equations for the transport of fluid and solute in the liquid phase and a Burton Cabrera Frank (BCF) model for the growth of the solid layer. In order to derive a model that is suitable for a very small scale of the microstructures, we apply homogenization techniques and construct a two-scale model that couples macroscopic equations for the transport processes in the fluid to microscopic evolution equations for the solid phase. For a phase field approximation of the BCF model, the solvability of the two-scale model is analyzed and an estimate for the model error is derived. Numerical examples will be presented and a possible extension of the model that incorporates the effect of elastic deformations in the solid phase will be given.
timetable:
Sat 17 Nov, 15:15 - 16:00, Sala Conferenze Centro De Giorgi
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