Crystal Growth Modeling

For some materials crystal growth processes such as Bridgman and Czochralski processes produce crystalline materials with a large number of defects such as dislocations and twining. Since some of these processes operate under very high pressures and temperatures, modeling becomes an important tool to understand and control them. In realistic situations buoyancy effects become important and cause strong convections in the melt flow. Furthermore, they are characterized by large Grashof numbers causing boundary layers and unstable flows. Further, since the melt flow and the crystal quality depend on the temperature distribution, modeling accurately the energy transfer including radiation becomes very important. Modeling and solving the radiation-conduction-convection problem is a very challenging and require large memory and computing power resources. New and innovative techniques are needed to solve these Three dimensional problems and control crystal growth system. Again large Grashof numbers lead to three-dimensional flow unsteady problems which boundary layers coupled with convection-conduction and radiant energy equation. Obtaining numerical solutions to these problems requires the use of adaptive and parallel algorithms. We use parallel and distributed algorithms based on domain decomposition with dynamic load balancing.