Numerical Simulation of Thermal History for Czochralski Growth of Silicon Single Crystals

Numerical simulation was conducted to study the thermal history of Czochralski growth of large silicon single crystals. The computations were performed for various crystal diameters and emissivities of the crucible inner wall. The analysis gives the change of temperature distribution in the crystal and the shape of the solid-melt interface. The computed results show the importance of the effects of radiation from the crucible inner wall and the melt free surface on crystal growth. Also, increasing crystal diameter decreases the pull speed and increases the concavity of the solid-melt interface into the crystal. The result of this analysis is in good agreement with measurement of the pull rate on production apparatus, and the shape of the crystal-melt interface showed a tendency to qualitatively agree with the observations of X-ray diffraction.