Three-dimensional thermocapillary-buoyancy flow in a shallow molten silicon pool with Cz configuration

In order to understand the characteristics of surface patterns on silicon melt in Czochralski furnaces, we conducted a series of unsteady three-dimensional numerical simulations of thermocapillary-buoyancy flow of a shallow molten silicon pool with Czochralski configuration (depth d = 3 mm). The crucible sidewall is maintained at constant temperature. Bottom and free surfaces are adiabatic or allow heat transfer in the vertical direction. The simulation results indicate that two flow transitions occur with increasing the radial temperature difference along the free surface. At first, the steady two-dimensional flow becomes steady three-dimensional flow and then oscillatory three-dimensional flow. The critical conditions for the onset of the instability were determined. Characteristics of the steady and the oscillatory three-dimensional flows were discussed.