Temperature Distribution and Gradient during CZ Silicon Crystal Growth

Abstract

  Temperature distribution in the growing crystal is the most important parameter that determines the grown-in-defects, growth rate, etc. In general understanding, and some experiments showed that higher growth rate leads to the larger thermal gradient. But other reports showed that temperature gradient in growing crystal decreases as increasing the growth rate. In order to make clear the reason of this discrepancy, the effects of growth rate on the temperature distribution in growing crystal were analyzed by numerical modeling. As increasing the growth rate, the shape of melt/crystal interface becomes more convex toward the crystal. Along the center axis, conductive heat transfer is dominant. Then convex interface shape and larger thermal gradient were obtained. In the growing crystal near the triple points, because of convex interface shape, heat transfer in radial direction, and radiative heat transfer from growing crystal surface becomes important. Then smaller thermal gradient along surface was obtained..