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 = (Tm − T1)/(Tm − T2), according to the temperatures (T1 and T2) of two monitoring points (P1 and P2) and the melting temperature (Tm). 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.