Modeling of Fluid Dynamics in the Czochralski Growth of Semiconductor Crystals

This chapter discusses the problems related to the melt flow during the crystal growth from the melt. It focuses on an analytical approach for determining the effects of the external forces based on the gravitational acceleration and on rotations of a crystal, and does an analysis of the effects of the electric, magnetic, and electromagnetic forces on the melt convection. One of the key points for controlling the vacancy flux in crystals, especially that near a solid-liquid interface, is control of the convection of melt, by which the shape of the solid-liquid interface can be controlled. Crystal growth industries have mainly focused on quantitative prediction of a solid-liquid interface, point defect distribution, oxygen concentration, and dislocation free growth. Since molten silicon, like molten steel or metal, has many free electrons, electromagnetic hydrodynamics can be used to control convection in metallically conducting melt of molten silicon when magnetic or electric fields are applied to the metallically conducting melt. The effects of magnetic fields such as vertical and transverse magnetic fields applied to the Czochralski (CZ) method on convection of the melt are also discussed.