We examine here the global (axisymmetric) heat transfer in Czochralski silicon crystal growth environment. We present here a simplified geometry of a growth furnace in which a heater, crucible filled with molten silicon, the growing crystal and several layers of different shielding materials are placed. The whole furnace is contained in a chamber with low pressure argon atmosphere.

All the surfaces adjacent to the argon gas, most notably the heater, radiate heat. Radiation dominates the heat transfer in the system, but model includes also conduction. The argon gas also conducts heat, but convection is here ignored.

The equations are discretized by using the finite element method. The nonlinearities due to the radiation boundary condition are solved with Newton iteration.

The figure below shows the global temperature distribution with the elements modelling the gas removed from the picture