Computational study of formation mechanism of impurity distribution in a silicon crystal during solidification

The mechanism of formation of boron distribution in silicon crystals grown by the Czochralski method was numerically investigated. The diffusion processes in both the crystal and the melt were taken into account. The transient model involves the seed holding process and the crystal growth process. A Lagrangian method was developed for the computation in order to reduce numerical diffusion. A technique of grid cell generation was adopted for the adaptive mesh to track the crystal-melt interface. The results of computational analyses showed that the diffusion processes in the seed and grown crystals play an important role in the formation of the boron distribution in the grown crystals. The effects of concentration difference between the seed and the melt, the annealing treatment, the seed holding time and the crystal growth rate on the formation of impurity distribution during the seeding process were numerically investigated. The computation results are in good agreement with the experimental data.