Mathematical modeling of the multi-run process of crystal pulling from the melt by EFG (Stepanov) technique in dependence on the angle of inclination of the working edges of the dies

摘要

A mathematical model for the determination of melt hydrodynamics, impurity concentrations and thermal stresses in the multi-run process of the growth of sapphire ribbons by EFG (Stepanov) technique with inclinated working surfaces of the dies is considered. The mathematical model deals with thermal conductivity equation, Navier-Stokes equation, diffusion equation, capillary Laplace equation. This problem has been solved by the finite-element method. (c) 2007 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.