The influence of radiative heat transfer on the limit pull rate in Czochralski crystal growth of silicon

Abstract

In this paper the results of an analytical study of the influence of the radiative heat transfer on the limit pull rate in Czochralski process are reported. An analysis of the contribution of the radiative heat transfer components shows that the limit pull rate depends non-monotonically on the effective temperature for radiation and, hence, at some temperature the limit pull rate has a maximum. For Czochralski crystal growth of silicon, the limit pull rate is shown to have the maximum when the effective temperature for radiation is within the 500–650 K range — depending on the convective heat transfer on the crystal surface. For commercially used apparatus, this temperature is evaluated to be about 1300 K. The most considerable contributions to this temperature are made by the radiative flux from the melt and crucible surfaces. The increase of the limit pull rate is possible (up to 50%) if the surface of the growing crystal can be protected from these surfaces, for example, by means of a special cooler installed around the crystal and kept at 500–650 K.