Numerical study of thermal stress during different stages of silicon Czochralski crystal growth

In this paper, the influence of various crystal heights to the crystal/melt interface shape and thermal stresses distribution in the large diameter (300 mm) of the silicon single crystal growth in a Czochralski process was studied numerically. A tow dimensional fluid flow and heat transfer with solidification model was developed. The Navier-Stoks and energy equations in melt and the heat conduction equation in crystal are solved using the control volume-based finite difference method. The thermal elastic stress fields for different stages are calculated from the temperature field by adopting the plane strain model in an axi-symmetric geometry of a cylindrical crystal. It was found that the melt/crystal interface shape becomes more concave and the maximum value of thermal stress in the crystal reduces as the crystal grows. A good agreement between our numerical simulations and those found in the literature is obtained.