Effects of crystal-crucible iso-rotation and a balanced/unbalanced cusp magnetic field on the heat, flow, and oxygen transport in a Czochralski silicon melt

Abstract

• Melt flow pattern is varied by crystal-crucible rotation rates and magnetic ratios. • CMF insignificantly affects oxygen content at low crystal iso-rotation rates. • Iso-rotating crystal faster than crucible enhances oxygen content under a CMF. • Iso-rotating crystal faster than crucible increases the uniformity of oxygen content under a CMF. The effects of using a balanced/unbalanced cusp magnetic field (CMF) along with crystal-crucible counter-/iso-rotation on the heat, flow, and oxygen distributions during Czochralski (Cz) growth of an 8-inch silicon crystal are numerically investigated. One counter-rotation example is compared to iso-rotation cases. In both rotation modes, the vertical flow in the central melt region is strengthened while the buoyancy-driven melt flow is weakened under a cusp field. The CMF has a stronger effect on the oxygen content when there is a large difference in rotation rate between the crystal and the crucible (n S − n C ). This is because a higher value of (n S − n C ) induces stronger melt convection and hence, the Lorentz force has a more significant effect on a fast melt flow than a slow one. Although diffusion significantly influences oxygen transport in the melt at low crystal iso-rotation rates, different flow patterns and local melt velocities induced by different crystal iso-rotation speeds will modify the oxygen distribution. There is a slight change in the oxygen content at a low ingot iso-rotation rate with a CMF. In cases of iso-rotation, the radial oxygen content is enhanced more by an unbalanced CMF than a balanced one. Greater uniformity of the radial oxygen concentration is achieved applying iso-rotation with n S > n C under a CMF.