A Real‐Time Simulation of Point Defect Reactions Near the Solid and Melt Interface of a 200 mm Diameter Czochralski Silicon Crystal

Abstract

A real-time simulation of the point-defect reactions near the solid and melt interface of a 200 mm diam Czochralski silicon crystal was performed. The results from the thermal stress calculation accounting for the temperature dependence of the elastic modulus of silicon indicate that the thermal stresses in the vicinity near the solid and melt interface are far above the silicon yield strength. Therefore, it is suggested that the effect of thermal stresses on the point defect reactions in a growing crystal is negligible. In this work, the crystal cooling conditions are found to have a significant impact on the point defect reactions. Under fast cooling conditions, the simulator predicts a supersaturation of vacancies in the vicinity near the solid and melt interface while the silicon interstitial concentration retained in the crystal grown under slow cooling conditions could increase significantly. The present results also indicate that the point defect reactions near the solid-melt interface as well as at the crystal periphery are governed predominantly by a short-range pair recombination which is driven by the chemical potential of point defect saturation. The contribution of a long-range or up-hill diffusion, on the other hand, is considered to be negligible.

Solid mechanics and material strength studies on the melt growth of bulk single crystals

“…In this study, the extrapolated values were used as the material properties near the melting point. Wijaranakula [26] used Young's modulus of the Si single crystal calculated from the critical resolved shear stress in his thermal stress analysis, and reached the conclusion that dislocation-free Si bulk single crystals can be obtained by the CZ growth. Young's modulus used by him is much lower than that of the Miyazaki et al's analysis [25].…”

Transient wafer deflection in Si epitaxy

“…Assuming a process temperature of 1085 1C and considering the temperature dependence of the modulus [8], Eq. (1) is reduced to w ¼ À4:89 Â 10 À5 ða 2 À r 2 Þ 2 where w is in micrometers and a is in centimeters.…”

Dislocation density simulations for bulk single crystal growth process

“…The Young's modulus of the latter is much smaller than the former at around the melting point. The temperature variation of the latter Young's modulus would be considered as more realistic at elevated temperatures than that of the former because the Young's modulus at the melting point, where the crystal cannot exist as a solid, should be virtually zero as mentioned by Wijaranakula [4].…”

“…One po~ sible reason for the disagreement is the unreliability of the estimated material constants at around the melting point. Wijaranakula [4] performed a thermal stress analysis of the 8-inch diameter CZ silicon crystal, using the Young's modulus estimated from the experimental data of the critical resolved shear stress given in the literature. His analysis indicates that the themaal stress is below the critical resolved shear stress.…”

“…In these simulations, both the Young's modulus cited from the INSPEC data handbook [3] and that used by Wijaranalatla [4] were used in order to examine the effect of the Young's modulus on the dislocation density.…”