Comparison of measurements and numerical simulations of melt convection in Czochralski crystal growth of silicon

This paper is concerned with a direct comparison of measured and predicted temperature readings in an industrial silicon Czochralski melt during real crystal growth conditions. The temperature was measured at three reading points under the crystal using a thermocouple. The predictions are based on three-dimensional time-dependent simulations of the flow and heat transfer in an identical crucible geometry. The simulations were performed using a fine grid with 1,945, 600 control volumes and six geometric blocks. To improve the convergence rate and reduce the simulation time, the multigrid method was applied. Two different crucible rotation rates were considered. Minimum, maximum. and average temperature and standard deviation from numerical simulations were found to agree well with experimental data. In order to discuss overall flow mechanisms in the melt, the sampled temperatures were analyzed by performing fast Fourier transformation and comparing frequency spectra. The analysis of the transformed data showed that by applying a high resolution in space and time it is possible to predict the impact of growth parameters on the flow field. From experiments and numerical simulations it is shown that a higher crucible rotation damps the temperature fluctuations under the crystal. (C) 2001 Elsevier Science B.V. All rights reserved.