For the seeding process of the Czochralski crystal growth of sapphire, the flow and temperature field with a nonflat melt-gas interface have been studied numerically using the finite element method. The configuration usually used initially in a real Czochralski crystal growth process consists of a crucible, active afterheater, induction coil with two parts, insulation, melt, and gas. At first, the electromagnetic field produced by the radio frequency (RF) coil in the whole system and the volumetric distribution of heat inside the metal crucible and afterheater were calculated. Using this heat distribution as a source, the fluid flow and temperature field were determined in the whole system. 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 our lab. It was shown that an active afterheater and its location with respect to the crucible influences markedly the temperature and flow field of the gas in the chamber and partly also in the melt.

For the seeding process of oxide Czochralski crystal growth, the flow and temperature field of the system as well as the seed-melt interface shape have been studied numerically using the finite element method. The configuration usually used initially in a real Czochralski crystal growth process consists of a crucible, active afterheater, induction coil with two parts, insulation, melt, gas and non-rotating seed crystal. At first the volumetric distribution of heat inside the metal crucible and afterheater inducted by the RF coil was calculated. Using this heat source the fluid flow and temperature field were determined in the whole system. We have considered two cases with respect to the seed position: (1) before and (2) after seed touch with the melt. It was observed that in the case of no seed rotation (ω seed = 0), the flow pattern in the bulk melt consists of a single circulation of a slow moving fluid. In the gas domain, there are different types of flow motion related to different positions of the seed crystal. In the case of touched seed, the seed-melt interface has a deep conic shape towards the melt. It was shown that an active afterheater and its location with respect to the crucible, influences markedly the temperature and flow field of the gas phase in the system and partly in the melt.

Different shapes and orientations of an active afterheater for oxide Czochralski crystal growth systems are considered and corresponding results of electromagnetic field and volumetric heat generation have been computed using a finite element method (Flex-PDE package). For the calculations, the eddy current in the induction coil (i.e. the self-inductance effect) has been taken into account. The calculation results show the importance of an active afterheater, its shape as well as its geometry and position with respect to the crucible on the heat generation distribution in a CZ growth system.

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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.