The nonlinear Czochralski growing process of crystals with variable thermal properties

The nonlinear dynamic process of Czochralski crystal growth with variable thermal properties is studied by the perturbation method. After evaluating the order of magnitude of these thermal properties, it is found that the temperature-dependent thermal conductivity is the dominant parameter in this problem. Comparing the results with that of the constant thermal conductivity model, we find that at the initial transient stage the difference between these models is insignificant, while the model difference is enlarged gradually, and at the final steady stage the model difference is the largest. Moreover, during the process, the higher the temperature difference between the crystal melting point and the surroundings is, the lar er is the model difference. Finally, to avoid the computational burden, in this article, an optimal constant value of thermal conductivity is recommended. Copyright (C) 1996 Elsevier Science Ltd.