Modeling of Induction Heating in Oxide Czochralski Systems—Advantages and Problems

Two mathematical models of induction heating for oxide Czochralski crystal growth systems are reviewed, and additional results of electromagnetic field and volumetric heat generation have been computed for both models using a finite element method (ENTWIFE package). In the first model, the eddy current in the RF coil (i.e., the self-inductance effect) has been neglected while for the second model, it is taken into account. For the calculations, the electrical current input and total voltage of induction coil are set to be 1000 A and 200 ν, respectively, with a frequency of 10 kHz; the heat generation in all metallic parts, that is, crucible, afterheater, RF coil, and chamber, has been calculated for a real Czochralski setup. It has been found that by including the self-inductance effect in the RF coil the results change dramatically. Also, it was shown that the spatial distribution of the heat generation in the crucible is more realistic in the second model than in the first model. Concerning the distribution of heat generation in all metallic parts (including the RF coil), the results for the first model are not reasonable, but they are acceptable for the second model.