Combined 3D and 2.5D modeling of the floating zone process with Comsol Multiphysics

• 3D calculation of HF induction coil.
• 2.5D calculation of the global temperature field for the FZ process.
• Model validation with experiment and former simulation.
• Application example for melt flow computation and axial magnetic field.
• Application example for stress reduction by pull speed or reflector.

The floating zone (FZ) technique is an industrially used method to crystallize silicon and make use of induction heating. The shape of the single-turn coil can be optimised with the help of numerical simulation of the electric current. The next step in process design is to discern the consequences on the temperature field, for what our axisymmetric model includes all important features like movement of silicon parts, temperature-dependent heat conductivity, view factor approximation for radiation heat transport, latent heat production and consumption along the phase boundaries as well as interface tracking. The simulations are conducted in Comsol Multiphysics and Matlab, assuming steady-state conditions. To verify the results, the calculated deflection of the crystallization interface is compared to results obtained from other numerical calculation software as well as to measurements, both showing a good agreement.The calculated temperature field is used as input to other physical models in Comsol. We calculated the thermal stress field of the crystal and the melt flow under the influence of a static magnetic field in axial direction. Model for other physical quantities like the doping distribution could be added with relatively low development effort.