A Numerical study of the fluctuation behavior of the oxygen concentration and the temperature in the silicon melt of Czochralski crystal growth system

The momentum, heat and mass trasfer phenomena in the silicon melt of the Czochralki crystal growth system are calculated using a three dimensional numerical simulation thechnique. Even though axisymmetrical boundary conditions are imposed to all calculations in a 3cm diameter crucible, several types of non-axisymmetric profiles of velocities, temperature and oxygen concentration appeared in the melt. Because of the non-axisymmetric profiles of velocities, temperature and oxygen concentration appeared in the melt. Because of the non-axisymmetric profiles and rotations of fluid induced by the crucible rotation, temperatures and oxygen concentrations in the silicon melt fluctuate. The rotating velocity of the profile is calculated from the phase shift of the data of temperature or oxygen at two different points which have same radius from center but 90 degree angular difference. From this calculation, it is found that the rotating veolocity of the oxygen and temperature is different from the crucible rotation rates. Therefore the frequencies of the oscillating temperature and oxygen concentrations are not same to the frequencies of the crucible rotations. Futhermore, the components of the frequencies of the temperature and oxygen concentration at the same point are not same. The fluctuation behaviors of the temperature or oxygen themselves are also different when the points are different. The calculation show that the temperature and the oxygen concentration near the interface also fluctuate. The results suggest that the striation pattern found in the grown silicon single crystals may ben generated by the oxygen concentration and the temperature oscillations of the melt occurred near the interface.