Calibration of the Enthalpy-Porosity Based Method for CZ Silicon Growth

Abstract

A global transport model for industrial Czochralski (CZ) silicon growth is reported in the paper. The model quantifies the temperature fields in all components of the growth system. The heat transport by the conduction, convection (melt and argon flows) and radiation are treated along with the momentum balance in the presence of the static magnetic fields. The crystallization process is modeled by an enthalpy-porosity method in which, the phase change occurs across a finite region defined by volumetric sink/source of heat (enthalpy) and momentum. The momentum sink/source is formulated based on the Darcy's law for porous medium, which is simply a numerical treatment for the isothermal solidification. The flow field in the Czochralski melt predicted by the global enthalpy-porosity based model is compared with that predicted by a more accurate simplified local model. Our studies indicate that the intensity of the flow induced by the presence of the crystal/melt interface is underestimated by the enthalpy-porosity based formulation.