Numerical optimization of czochralski sapphire single crystal growth using orthogonal design method

Abstract

Crystal quality during Czochralski (Cz) growth is influenced significantly by the convexity of solid/liquid (S/L) interface, which is related to operating conditions, such as Radio-Frequency (RF) coil position, crystal rotation and crucible rotation. Generally, a flat interface shape is preferred for high-quality crystal growth. It is difficult to achieve the optimized conditions even from numerical modeling due to the large computational load from examining all of the affecting factors. Orthogonal design/test method, fortunately, provides an efficient way to organize the study of multiple factors with the minimization of computational load. In the paper, this method is adopted to investigate the affecting factors of Cz-sapphire single crystal growth based on the coupled calculation of thermal field and melt flows. The orthogonal analysis clearly reveals the optimized growth conditions to achieve a relative flat S/L interface under the current ranges of the parameters. Crystal quality during Czochralski (Cz) growth is influenced significantly by the convexity of solid/liquid (S/L) interface, which is related to operating conditions, such as Radio-Frequency (RF) coil position, crystal rotation and crucible rotation. Generally, a flat interface shape is preferred for high-quality crystal growth. It is difficult to achieve the optimized conditions even from numerical modeling due to the large computational load from examining all of the affecting factors. Orthogonal design/test method, fortunately, provides an efficient way to organize the study of multiple factors with the minimization of computational load. In the paper, this method is adopted to investigate the affecting factors of Cz-sapphire single crystal growth based on the coupled calculation of thermal field and melt flows. The orthogonal analysis clearly reveals the optimized growth conditions to achieve a relative flat S/L interface under the current ranges of the parameters. © 2014 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.