Numerical simulation of the oxygen concentration distribution in silicon melt for different crystal lengths during Czochralski growth with a transverse magnetic field

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.