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A three-dimensional simulation model is used to study the oxygen concentration distribution in silicon crystal during the Czochralski growth process under a transverse uniform magnetic field. The flow, temperature, and oxygen concentration distributions inside the furnace are calculated for different crystal lengths. There is significant variation in the flow structure in the melt with the growth length. The results show that in the initial stages, there is a decrease in the oxygen concentration at the crystal-melt interface as the length of the growing crystal increases. As the crystal lengthens further, a minimum value is reached after which the oxygen concentration increases continuously. This trend is consistent with that shown in the experimental results. The variation of the oxygen concentration with the growth length is strongly related to the depth of the melt in the crucible and the flow structure inside the melt. Better uniformity of the axial oxygen concentration can be achieved by proper adjustment of the crucible rotation rate during the growth process.

A numerical simulation has been performed to investigate the effect of a cusp magnetic field on the melt flow, thermal field and oxygen concentration during the Czochralski silicon crystal growth process. The results show a decrease in the oxygen concentration due to the reduction in size of the secondary flow cell that formed between the Taylor–Proudman vortex and the buoyancy-driven one. There is a significant reduction in the size of the secondary flow cell when the magnetic field is applied. As a consequence of the higher strength of the magnetic field there is a significant decrease in the oxygen concentration along the melt-crystal surface. The oxygen concentration is also very sensitive to the crucible rotation rate. There is an optimum crucible rotation rate for obtaining the lowest oxygen concentration. The oxygen concentration is lower for higher argon flow rate. The oxygen concentration decreases as the zero-Gauss plane (ZGP) moves from the free surface towards crucible bottom. When the ZGP is far from the free surface, the secondary flow cell appears and then the oxygen concentration increases. There is an optimum position of the ZGP to obtain the lowest the oxygen concentration.