THERMAL-ANALYSIS OF THE DOUBLE-CRUCIBLE METHOD IN CONTINUOUS SILICON CZOCHRALSKI PROCESSING .2. NUMERICAL-ANALYSIS

Numerical simulations were performed for the melt temperature and convection in a double-crucible method. The k-epsilon turbulent flow model was applied and its results were compared to the experimental data. The calculation using the k-epsilon model converged successfully to a stable solution, while that with the laminar flow model did not. By the application of the k-epsilon mode, we could simulate the temperature gradient in the thickness of the inner quartz crucible and the forced convection under the crystal. Moreover, the conclusion that the time-averaged isotherms were not much deformed was investigated from the model.