Bifurcation and Hysteresis of Flow Pattern Transition in a Shallow Molten Silicon Pool with Cz Configuration

Abstract

Three-dimensional numerical simulations of transient thermal convection in a shallow molten silicon pool with Czochralski configuration (depth d = 3 mm) have been conducted to understand the transition mechanism of the flow patterns on silicon melt in Czochralski furnaces. The crucible side wall is maintained at constant temperature. Bottom and free surfaces are either adiabatic or allow heat transfer in the vertical direction. The simulation results indicate that two flow transitions occur when the radial temperature difference along the free surface increases. First, the steady two-dimensional flow becomes steady three-dimensional flow, and then it evolves to three-dimensional oscillatory flow when the temperature difference is further increased. This oscillatory flow is characterized by spoke patterns traveling in either the clockwise or counterclockwise direction. It is observed that a transition hysteresis exists from oscillatory three-dimensional flow to steady three-dimensional flow when the radial temperature difference decreases. The critical conditions for the flow pattern transition are determined. Characteristics of the bifurcation and hysteresis of flow pattern transition are discussed.

This work was partly supported by the NSFC (grant number 50476042) and partly by the Scientific Research Foundation for the Returned Overseas Chinese Scholars, State Education Ministry of China. Dr. Tien-Chien Jen and Mr. Qinghua Chen would also like to acknowledge the partial financial support of National Science Foundation through DMI 9908324.