Three-dimensional modelling of 300 mm Czochralski silicon crystal growth with a transverse magnetic field

A local three-dimensional model of heat and mass transfer for 300 mm Czochralski silicon crystal growth with a transverse magnetic field was presented. The model implemented a PID control system and main physical effects including release of crystallization latent heat, crystallization interface correction, Marangoni effects, oxygen transport, and electromagnetic effects. A method including an additional data processing step was developed for crystallization interface correction. This method is particularly suitable for obtaining an axisymmetric interface under a non-axisymmetric flow when the crystal rotates. The simulation results show that the inhomogeneity of temperature, growth-rate and oxygen concentration on the crystallization interface is caused by melt convection. This phenomenon may provide theoretical support for controlling oxygen content. Furthermore, the model is validated at different solidified fractions, and the simulation results of oxygen concentration are in good agreement with the experimental results.

Automated summary

A local three-dimensional model of heat and mass transfer is proposed for 300 mm Czochralski silicon crystal growth with a transverse magnetic field. The model includes a PID control system and main physical effects such as release of crystallization latent heat, crystallization interface correction, Marangoni effects, oxygen transport, and electromagnetic effects. A method for crystallization interface correction is developed, particularly suitable for non-axisymmetric flow when the crystal rotates. Simulation results show that temperature, growth-rate, and oxygen concentration on the crystallization interface are influenced by melt convection. The model is validated at different solidified fractions, and the simulation results of oxygen concentration are in good agreement with experimental results.