Effect of crucible and crystal rotations on the solute distribution in large size sapphire crystals during Czochralski growth

Abstract

In this study, the flow, temperature and solute concentration fields in the melt during the CZ growth process are numerically investigated. The results show that the magnitude and distribution of the solute concentration in the melt is strongly affected by the convective flow and thermal distribution. The maximum solute concentration always occurs at the crucible sidewall where the maximum temperature in the melt is found and the solute concentration at the crystal-melt interface increases from the triple point to the centerline. Heat transport from the side crucible wall towards the crystal-melt interface is enhanced by the crucible rotation. The level of the solute concentration inside the melt is reduced due to the lowering of the maximum temperature at the crucible wall. As a consequence, the distribution of the solute concentration along the crystal-melt interface becomes smaller and more uniform as the crucible rotation rate increases. However, after the crucible rotation rate becomes large enough, the maximum solute concentration and the solute concentration along the crystal-melt interface start to increase. Heat transport inside the melt is also affected by the crystal rotation. The centrifugal force induced by the crystal rotation generates a vortex below the crystal-melt interface. This vortex gets larger and stronger as the crystal rotation rate increases. In the smaller crystal rotation rate regime, this vortex is very small, suppressing the solute concentration at the crystal-melt interface. Therefore, the solute concentration along the crystal-melt interface becomes less when the crystal rotation rate is higher, although there is an increase in the maximum solute concentration in the melt due to the higher maximum temperature. In the higher crystal rotation rate regime, there is a reduction in the convexity of the crystal-melt interface due to enhancement of heat transport from the bottom wall of the crucible by vortex motion under the crystal-melt interface. Therefore, there is a switch to an increase in the transport of solute impurities into the crystal-melt interface. Hence, the solute concentration along the crystal-melt interface increases as the crystal rotation rate increases. However, with a further increase in the crystal rotation rate, as the shape of the crystal-melt interface changes becoming concave towards the melt, the solute concentration along the crystal-melt interface decreases because the maximum temperature is significantly reduced. In this study, both counter- and iso-rotations are considered. The results of a comparison of the cases of iso- and counter- crystal rotation show that the lowest and most uniform solute distribution along the crystal-melt interface is achieved when there is no crystal rotation and the crucible rotation rate is fixed at 1 rpm. In other words, the lowest and most uniform solute concentration can be achieved with the only crucible rotation.