The combined effect of heat transfer and skin effect on Joule heating for silicon rod in Siemens reactor

The Maxwell's field equations and Ohm's Law were added to energy equation to account for the electromagnetic contributions to heat transfer phenomena within silicon rod arranged in an industrial Siemens reactor. Based on the combined effect of the heat dissipation (radiation, convection and reaction energy), a Joule heating model using alternating current (AC) has been developed. The analysis accounts for the rod radius, location, skin depth, as well as the properties of the polysilicon. The results indicate that high frequency current sources can generate an even temperature profile, and a higher deposition radius can be obtained. Alternating current, having a fixed or variable high frequency in the range of about 2.4 kHz to 500 kHz, is provided to concentrate at least 70% of the current in an annular region that is the outer 15% of a growing rod due to the skin effect. The voltage-current curves have been predicted based on the present model. Finally, a novel Joule heating method useful for producing the larger high-purity polycrystalline silicon rods by considering the low frequency power and the high frequency power is proposed. It is interesting that the average energy consumption (AE) can be decreased from 55 kWh/kg to about 44 kWh/kg as extending the maximum deposition radius from 7 cm to 10 cm by using a high-frequency current source.