Development of numerical calculation of electromagnetic fields in FZ silicon crystal growth process

A. Muiżnieks - K. Lācis - A. Rudeviċs - U. Lācis - A. Sabanskis - M. Plāte

Faculty of Physics and Mathematics, University of Latvia, 8 Zellu str., LV-1002 Riga, Latvia

Abstract
The paper describes the development of a calculation of a high-frequency electromagnetic field from a 2D axially symmetric approximation to a full 3D description for the calculation of the molten zone shape in the FZ silicon crystal growth process. The configuration of one inductor used in crystal growth experiments is considered. The used slot parameters of the inductor in a 2D approximation are given. Induced electrical current densities on the melt free surface and the calculated shape of the molten zone are compared for 2D and 3D cases. The paper also analyzes the precision of the calculation results on a low-frequency rotating magnetic field and a corresponding force density distribution in the melt domain of a 4" FZ crystal growth system. Due to technical reasons, magnetic fields in such systems often are extremely inhomogeneous. For calculations, an edge finite element method based specialized self-developed software is used. The influence of the numerical parameters of calculation, such as pre-conditioners, admissible tolerance value and mesh density on the obtained results is examined. An example of the calculated melt flow in the molten zone for the case with a rotating magnetic field is given. Tables 1, Figs 14, Refs 10.