Dynamics of melt-crystal interface and coupled convection-stress predictions for Czochralski crystal growth processes

Abstract

A coupled thermal-elastic model is developed to study the transport phenomena of Czochralski crystal growth and thermal stresses in the grown crystal, both at low- and high-pressures. A multizone adaptive scheme for transport and phase-change processes (MASTRAPP) is used to predict the melt and gas flows as well as the temperature distribution. Using the grid field and temperature distributions generated by MASTRAPP, a finite-element software package, ALGOR calculates the stresses in the crystal. The numerical results demonstrate that the convective flows in both the melt and the gas have significant effects on thermal stresses in the crystal. Indeed, a realistic model for a high-pressure CZ process must account for thermal interaction between the melt and the gas. Also, the novel approach of combined finite-volume/finite-element methods can be successfully used for thermo-mechanical problems.