Radial distribution of temperature gradients in growing CZ-Si crystals and its application to the prediction of microdefect distribution

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Experiments were performed to estimate the adequacy of simulation results obtained using global analysis of heat transfer performed using melt convection models. First, we reproduced the shapes of the crystal–melt interface for several crystal lengths using two turbulence models with standard value of the Karman constant. Moreover, axial temperature distributions were measured by imbedding thermocouples into the crystal as it grew from the silicon melt. During the experiment, the crystal and the crucible were rotated to match the simulation conditions. Temperatures were measured at three points located at different distances from the crystal axis. Comparing these results with the simulation results, we found that the distribution predicted by the k− l turbulence model was more realistic and agreed well with the results of the experiments. Finally, computer simulation, based on the parallel model of the void and oxide precipitate formation in silicon crystals is reported. The unusual microdefect pattern observed in the silicon crystal with a diameter of 150 mm, where oxide particles occured in the interstitial-rich region was reproduced by the simulation and explained.