Influence of temperature-dependent thermophysical properties of sapphire on the modeling of Kyropoulos cooling process

Sapphire is widely used as substrates in semiconductor industry. Kyropoulos (Ky) method is the most popular technique to grow large-size and substrate-quality sapphire single crystals. Computational modeling is a powerful tool to analyze the growth conditions for the improvement of this crystal growth. for simulation, thermophysical properties of sapphire are usually set constant, which may increase the deviation between experiments and modeling results. In this paper, temperature-dependent properties of sapphire, i.e., heat capacity, thermal conductivity, and thermal expansion coefficient, are summarized and adopted in the simulation studies. Their effects on the predicted results are discussed for the cooling process, during which large temperature change in the crystal leads to big differences of the material properties. Comparative analysis tells that temperature difference and thermal stress can be more than 200 K and 4 MPa for the cases with or without consideration of the temperature-dependence of the properties. Consequently, it is necessary to consider the impact of material properties on the accuracy of numerical simulation during the sapphire single crystal growth.