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Numerical Analysis of Velocity, Temperature and Thermal Stress Fields in Czochralski Furnace

Single crystal of oxides, such as Al_2O_3 and LiNbO_3, are prepared by Czochralski method. Melted oxides have larger Prandtl number than the molten semiconducting materials, thus shape of the crystal varies with operating conditions. The shape and temperature distribution give influences on thermal stress, and the quality of the crystal. There was, however, no theoretical background to calculate thermal stress in the growing crystal, because of the complicatedly coupled non-linear phenomena in the CZ furnace. The finite element method is used to develop a computational code and sample computations are carried out for Al_2O_3 system. In this case, the crystal shape, and the thermal stress distribution are found to be dependent on the crystal rotation rate. When crystal rotation rate is increased, with other operating conditions unchanged, the melt/crystal interface changes its shape from convex to concave toward melt, at the critical Reynolds number (Re_s). When Re_s<Re_s, the maximum thermal stress on the melt/crystal interface is small and insensible to Re_s. When Re_s exceeds Re_s, thermal stress on the interface increases very rapidly