ILES of melt turbulent convection with conjugated heat transfer in the crucible and gas flow for Czochralski silicon crystal growth system

Abstract

Results of Implicit Large Eddy Simulation (ILES) of buoyancy, rotation, and surface tension driven turbulent melt convection during Czochralski (Cz) silicon crystal growth are presented. Convective and conductive heat transfer in the melt is coupled with heat transfer in surrounding crystal, crucible, and gas flow. Distributions of resolved turbulence kinetic energy (TKE), Reynolds stress tensor, production terms and dissipation rate in the silicon melt are discussed and compared to published results. We have found significant anisotropy of the melt velocity fluctuations along the melt free surface and the crucible. Conjugated heat transfer in the melt flow and in the crucible has provided important results of the temperature fluctuation intensity along the liquid/solid interface. Our ILES results have also shown that there are significant regions in the melt with negative values of the shear production term. To estimate the quality of calculations using a conventional turbulence model for a Cz configuration, we have compared our ILES data to respective results obtained within the Boussinesq eddy viscosity assumption. As well we have evaluated how precise are available approximations of the production terms and dissipation rate of TKE for Si melt turbulent convection.