Nonlinear problems in EFG and Dewetted Bridgman crystal growth processes

Dr. Liliana Braescu
Department of Computer Science, Faculty of Mathematics and Computer Science
West University of Timisoara, Romania

Abstract: The major problem with which crystal growth researchers have been confronted was the development of techniques capable to monitor and control the external shape of melt-grown crystals, and simultaneously to improve the crystal structures. These requirements have imposed techniques in which crystals are grown without contact with the container walls: Czochralski, floating-zone, edge-defined film-fed growth (EFG), and Dewetted Bridgman (DW).

The goal of this talk is to prove the great potential of the mathematical and computational modeling in deeper understanding of two growth processes: EFG and DW. Toward this aim, starting from a nonlinear boundary problem of the meniscus surface determined by the Young-Laplace equation, qualitative and numerical studies of the nonlinear systems of ordinary differential equations which allow the prediction of the crystal shape are presented for both crystal growth techniques. Also, using nonlinear partial differential equations, numerical studies on the compositional uniformity for crystals grown by EFG technique are performed.

Numerical results are given and are compared to experimental data.