A Volume Radiation Heat Transfer Model for Czochralski Crystal Growth Processes

Abstract

Thermal modeling of Czochralski (CZ) crystal growth processes is a challenging task owing to the complex interaction of heat conduction, convection, thermal radiation, fluid flow, and other transport phenomena. A highly innovative, general-purpose computer model for phase-change and free-surface problems, utilizing a multi-zone adaptive grid generation and curvilinear finite volume scheme, is linked to a spectral, volume and surface thermal radiation algorithm to predict the temperature distribution within a Czochralski growth furnace. The radiative transfer model, based upon the Discrete Exchange Factor (DEF) method, is capable of addressing the complexities due to irregularly-shaped axisymmetric geometries and shadowing effects. A unified exchange factor model is used to account for multiple reflection/scattering of radiation within the enclosure. Several numerical trials are performed to simulate the CZ growth of yttrium aluminum garnet (YAG). The effect of the top surface boundary condition on temperature profile, crystal/melt interface shape, and process stability is studied to examine the applicability of this model to control the growth conditions and interface shape. The results show that there exists a temperature range for this surface for which the desirable conditions for crystal growth are possible. This limiting temperature range is, however, dynamic and changes as the growth progresses.