Numerical Simulation of CZ Crystal Growth of Oxide

In this paper, our recent numerical studies on the Czochralski (CZ) crystal growth of oxide are surveyed. In the first part of the analysis, a "global" heat transfer model for an inductively heated CZ furnace is introduced and depicted in detail. It is emphasized that accounting for the internal radiation within the crystal and/or melt is of crucial importance since they are often semitransparent to infrared radiation. Results coming from such a "global" approach suggest that the melt/crystal interface shape is strongly affected by the optical properties of the crystal, of the melt and by the melt convection. The second part of the article is devoted to illustrate some convective instabilities that can arise in the CZ oxide melt. They are discussed within the framework of a numerical analysis for unsteady, three-dimensional flows. It is demonstrated that "spoke patterns" seen on the melt surface are due to a Marangoni instability, while "wave patterns" are caused by a baroclinic instability.