3D numerical analysis of the influence of EM and marangoni forces on melt hydrodynamics and mass transport during FZ silicon crystal growth

Three-dimensional numerical modelling is carried out to analyze the influence of EM and Marangoni forces on melt hydrodynamics and mass transport during floating zone crystal growth with the needle-eye technique used for the production of high-quality silicon single crystals with large diameters (> J00 mm). Since the pancake inductor has only one turn, the EM field and the distribution of heat sources and EM forces are only roughly axisymmetric. The nonsymmetry together with crystal rotation is reflected in the hydrodynamic, thermal, and dopant concentration fields in the molten zone and causes variations of resistivity in the grown single crystal, which are known as rotational striations. The nonsymmetric high-frequency electromagnetic field of the pancake inductor is calculated by the boundary element method. The obtained nonsymmetric power distribution on the free melt surface and the corresponding EM forces are used for the calculation of the coupled 3D hydrodynamic and temperature fields in the molten zone on a body-fitted structured 3D grid by a commercial program package (control volume approach). The calculated corresponding 3D dopant concentration field is used to derive the variations of resistivity in the longitudinal cut of the grown crystal. The influence of the nonsymmetric EM, Marangoni, and buoyancy forces on the melt flow and on the resistivity variations is studied.