Numerical Modeling of Czochralski Silicon Crystal Growth

Modeling of heat transfer is presented for the entire Czochralski Si-growth furnace. The axisymmetric steady-state approach with moving computational grids is used. Melt turbulent flow, inert gas flow, heat transfer in solid parts, and radiative heat transfer in the system are considered. The Reynolds-averaged Navier-Stokes equations written with the Boussinesq approximation and the energy equation are used to calculate the melt flow. The eddy viscosity of turbulent melt convection is calculated using the low Reynolds number k-ε model of Chien. The Navier-Stokes conservation equations for slow subsonic laminar motion were used for simulation of steady-state axisymmetric argon mass and heat transfer. The melt-crystal interface shape and the heater power are calculated to provide a desired crystal growth rate. The computational results are discussed to illustrate the melt-crystal interface dependence on the Si crystal growth rate. The crystal rotation effect on the interface and on the melt flow is examined to obtain a desired interface shape. An example of the dynamic interaction between the inert gas and melt turbulent convection is shown for two gas flow rates. V.V. Kalaev, I.Yu. Evstratov, Yu.N. Makarov, E.M. Smirnov, and A.I. Zhmakin.