Development of a global model of heat transfer in the czochralski furnace taking into account specular reflection at the crystal surface

In this study, a global model of heat transfer for the Czochralski crystal growth of oxides is developed by integrating the conventional model and the improved radiation element method by the ray emission model (REM²) in which radiative heat transfer in semitransparent crystals with a specular surface, that is, reflection and refraction at the crystal surface, is considered. The validity of the present model is verified by comparing it with the conventional model. Then, the effects of the optical thickness and the refractive index of the crystal on the temperature distribution in the furnace and on the melt/crystal interface shape are numerically investigated.