Impact of emissivity of a crystal on temperature distribution in a silicon crystal during growth as a function of impurity concentration

The advancement of power devices necessitates silicon wafers with elevated concentrations of impurities to diminish resistivity in the substrate crystal. These devices demand crystals devoid of voids and the meticulous control of temperature distribution during growth to satisfy the annihilation condition between a vacancy and an interstitial atom. This study characterizes the effect of the emissivity of a 300-mm-diameter crystal - grown via the Czochralski method - on the temperature distribution within a crystal during the growth process as a function of impurity concentration. Employing data on the emissivity of the crystal as a function of impurity concentration, we conducted calculations to compare the temperature distributions within crystals with high and slightly doped impurity concentrations. The findings demonstrate that the temperature gradients in crystals with high doping are more pronounced than those in slightly doped crystals. Additionally, in a highly doped crystal, the interface is position lower than that in a slightly doped crystal.