
69Different Techniques for Growing Single-Crystal Silicon
and the vertical turbulent heat ux at the crystal-melt interface. Buoyantly driven ow of
the molten silicon is the highlight of this simulation study.
Järvinen et al. [32] have developed a detailed mathematical model and numerical simula-
tion tools for time-dependent silicon crystal growth and the crystal growth environment.
All three heat transfer mechanisms—conduction, convection, and radiation—were applied
to study the case, and the information regarding the temperature and velocity elds were
evaluated. Modern supercomputers were used to solve the results to effectively assist t