Work package number and title:

9. Influence of 3D electromagnetic field of HF-inductor on the shape of molten zone, melt hydrodynamics and crystallisation process during Floating-Zone growth of large single silicon crystals

Objectives:

1. From experimental investigations with Floating-Zone (FZ) silicon growth systems it is well known that the industrially used one turn HF inductor cause partly asymmetric (3D) electromagnetic field and as a consequence the shape of molten zone and corresponding melt hydrodynamics and crystallisation process have unsymmetric features also. The group in mathematical modelling of crystal growth at Latvia University has developed as an approximation a complex axisymmetric model for coupled calculation of temperature and electromagnetic fields to determine the axisymmetric shape of the molten zone. Beside this, the specialized 3D model and software for calculation of 3D HF electromagnetic field in FZ System is developed also. However, in the FZ systems for large crystal growth (up to 200 mm diameter) the 3D effects are more distinct and the development of coupled system of 3D EM and thermal models is necessary. With such a model system the 3D shape of molten zone will be calculated and used afterwards for 3D hydrodynamic, mass transport and crystallisation process calculations. Aim of this package is the development of problem oriented 3D mathematical model system for calculation of asymmetric shape of molten zone, melt hydrodynamics and crystallisation process during Floating-Zone growth of large single silicon crystals.