3D modeling of the molten zone shape created by an asymmetric HF EM field during the FZ crystal growth process

A. Rudeviċs¹ - A. Muiżnieks^1,2 - G. Ratnieks³ - H. Riemann⁴

¹ Department of Physics, University of Latvia
² Institute for Electrothermal Processes, University of Hanover, Wilhelm-Bush-Str. 4, D-30167 Hanover, Germany
³ Siltronic AG, Johannes-Hess-Str. 24, D-84489 Burghausen, Germany
⁴ Institute for Crystal Growth, Max-Born-Str. 2, D-12489 Berlin, Germany

Abstract
In the modern industrial floating zone (FZ) silicon crystal growth process by the needle-eye technique, the high frequency (HF) electromagnetic (EM) field plays a crucial role. The EM field melts a rotating poly silicon feed rod and maintains the zone of molten silicon, which is held by the rotating single crystal. To model such a system, the 2D axi-symmetric models can be used, however, due to the system's asymmetry (e.g., the asymmetry of the HF inductor) the applicability of such models is restricted. Therefore, the modeling of FZ process in three dimensions (3D) is necessary. This paper describes a new complex 3D mathematical model of the FZ crystal growth and a correspondingly developed software package {ėxttt{Shape3D}}. A 3D calculation example for the realistic FZ system is also presented. Figs 25, Refs 9.