Hybrid finite-volume/finite-element simulation of heat transfer and melt turbulence in Czochralski crystal growth of silicon

Abstract

Simulation of heat transfer and oxygen incorporation during Czochralski growth of silicon in industrial scale equipment requires coupled simulation of conductive, convective and radial heat transfer throughout the system, with simulation of turbulent convection in the melt. We present a hybrid finite-volume/finite-element method for simulation of heat transfer throughout the Czochralski system and of turbulent convection in the melt. The hybrid method is based on finite-element simulation of the thermal-capillary model of heat transport, and finite-volume solution of the low-Reynolds turbulence model of Jones–Launder. Prototypical calculations demonstrate the robustness of the numerical methods and the influence of crystal and crucible rotation on heat transfer and the turbulent flow.