| Numerical simulations including the fluid flow, conduction and radiation heat transfer have been performed using the geometry of real furnace for the single-crystal growth by heat exchanger method. The finite difference method based on the control volume approach and SIMPLE algorithm were used to solve the momentum and energy equations. Almost all parts of the furnace including the heater, insulating materials and crucible were considered in the calculation domain and the latent heat was accounted by an iterative heat evolution method. Silicon with low thermal conductivity was selected as a model material in order to compare the results with the previous report on the copper single-crystal growth. The effects of cooling rate of the heater, crucible material, crucible shape and melt weight on single-crystal growth were investigated together with the role of natural convection in melt. The optimum process conditions such as the critical cooling rate and the critical ratio of the height to the radius of crystal for the silicon single-crystal growth by heat exchanger method were determined. According to the simulations, among many parameters crucible shape was a dominant processing parameter to control single crystal growth when a thermal conductivity of the specimen was low. The lower the thermal conductivity of base material of crucible was then that of the specimen, the less the region of poly crystal formed at the edge of the crystal was. |
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