The effects of pulling rates on the shape of crystal/melt interface in Si single crystal growth by the Czochralski method

The temperature profile and the shape of the crystal/melt interface in a Czochralski (CZ) furnace for large Si single crystal growth was simulated taking into consideration the fluid flow and surface radiational heat transfer. The view factors of the surface elements were calculated for radiation heat transfer. Two phases (crystal and melt) were treated as a continuous phase by assigning artificially large viscosity to the solid phase and the latent heat was accounted for by iterative heat evolution method, This simulation model of a CZ system was applied to the growth process of a 6 inch Si single crystal to study the effects of pulling rates on the interface shape. It was found that the interface becomes more concave to the melt as the crystal grows or as the pulling speeds become higher, and that the interface height is linearly dependent upon the pulling rate.