Numerical study of induction heating and heat transfer in a real Czochralski system

Abstract

The equations of induction heating and heat transport have been solved for a real Czochralski crystal growth system, using the ENTWIFE package (finite-element method). The configuration usually used in dielectric crystal growth consists of a crucible, afterheater, induction coil with two parts and insulation. At first the electromagnetic field produced by the RF coil in the whole system and the generated heat inside the metal crucible and afterheater was calculated. Using this as a heat source then the temperature field and air convection inside the crucible and afterheater was determined. We have considered two cases: (1) configuration without a gap between crucible and afterheater and (2) with a gap corresponding to an often used growth situation. In both cases it was observed that there are two separate eddies of air convection with approximately equal strength and opposite rotation. Concerning the temperature field, the maximum temperature is in the crucible wall and the minimum is in the bottom corner of the crucible insulation. Along the axis of symmetry, in the first case the temperature is approximately constant and then drops close to the afterheater hole. But in the second case the temperature in the crucible is constant, decreases in the gap and is constant in the afterheater until it drops near its hole. This behavior has been observed during experimental measurements in the lab, too.