3D unsteady modelling of the melt flow in the FZ silicon crystal growth process

A. Muiznieks¹ - K. Lacis¹ - B. Nacke²

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

Abstract
A previously developed system of 3D numerical models made for modelling steady-state melt hydrodynamics and dopant concentration fields in the floating zone silicon single crystal growth process has been modified in order to solve unsteady problems. The asymmetric form of one turn of a high frequency inductor coil, the shift of a polycrystalline feed rod and a single crystal axis are taken into account at calculating the 3D HF electromagnetic field. During transient 3D hydrodynamic calculations, the EM forces, Marangoni and buoyancy forces are considered. The paper presents a 3D unsteady calculation example of a realistic FZ silicon single crystal growth system showing the influence of the crystal rotation rate change on the melt motion and dopant concentration field, which is used to derive variations of normalized resistivity profiles in the grown crystal. Figs 8, Refs 13.