Real-time prediction of crystal/melt interface shape during Czochralski crystal growth

Abstract

The shape of the crystal/melt interface during Czochralski crystal growth strongly influences the crystal quality. In this paper, a novel method for real-time detection of the varied interface shape is proposed for engineering applications. Variations of the interface shape caused by the crystal cooling intensity, growth rate and crystal length in iso-diameter processes were investigated numerically. The varied interface shapes can be predicted by the dimensionless parameter φ = (T_m − T₁)/(T_m − T₂), according to the temperatures (T₁ and T₂) of two monitoring points (P₁ and P₂) and the melting temperature (T_m). The two monitoring points (P₁ and P₂) were distributed on the crystal side wall in the axial direction, and P₁ is located equidistantly between P₂ and the tri-junction point. As the monitoring points become closer to the tri-junction point, the variation of the interface shape is more easily observed.