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

G. Ratnieks¹ - A. Muiznieks¹ - L. Buligins¹ - G. Raming² - A. A. Muhlbauer²

¹ Department of Physics, University of Latvia, Zellu str. 8, LV-1002, Riga, Latvia
² Institute for Electroheat, University of Hanover, Wilhelm-Busch-Str. 4, D-30167, Hanover, Germany

Abstract
Three-dimensional numerical modelling is carried out to analyse the influence of EM and Marangoni forces on melt hydrodynamics and mass transport during the floating zone crystal growth with the needle-eye technique used for the production of high quality silicon single crystals with large diameters (>100mm). 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 non-symmetry together with crystal rotation reflects itself on 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 so-called rotational striations. The non-symmetric high-frequency electromagnetic field of the pancake inductor is calculated by boundary element method. The obtained non-symmetric 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 afterwards 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 non-symmetric EM, Marangoni and buoyancy forces on the melt flow and on the resistivity variations is studied. Figs 13, Refs 8.