Development and validation of a thermal simulation for the Czochralski crystal growth process using model experiments

Abstract

The Czochralski (CZ) process is one of the most important techniques for the production of bulk single crystals. Various numerical models for CZ growth furnaces exist, however, a review of the recent literature demonstrates that their validation is often questionable due to missing in-situ measurement data. In this work, a new 2D open-source thermal CZ growth model is introduced, verified with analytical solutions, and validated using dedicated model experiments with tin and hence easy access for the required measurements. A three-step procedure is applied to identify critical modeling parameters, make adjustments of these parameters, and evaluate the resulting modeling accuracy. Gas and melt convection, modeled with heat transfer coefficients and an effective heat conductivity, are found to be crucial and are adjusted using experimental data. Comparison of measured temperatures in the crucible shows good agreement, with deviations of max. 0.3 / 1.3 K under natural / forced convection. The model is able to predict the influence of crystal pull velocity and melt temperature on crystal diameter qualitatively.