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We perform numerical simulations to study effects of alternating current (AC) frequency on thermal stress evolution during the Joule heating process in a 48-rod Siemens reactor. The characteristics of temperature, current density, and stress distributions within the rods located in different rings are analyzed first. A Joule heating model using AC is then proposed for flexible power adjustment. The voltage-current curves are obtained from analysis of rod radius, location, and skin depth, as well as the properties of the polysilicon. The results indicate that, during the Joule heating process, large stresses typically occur in the central regions of the silicon rods. The highest stress occurs at the center of the silicon rods located in the outer ring when a standard power frequency of 50 Hz is utilized. The results further indicate that von Mises stress significantly decreases as AC frequency increases. Additionally, we propose a novel Joule heating method that is useful for producing larger high-purity polycrystalline silicon rods by considering both low frequency and high frequency power. Based on an analysis of energy consumption during the Joule heating process, we recommend optimized power supplies for the 48-rod Siemens reactor.

This paper presents an electrical heating model using alternating current (AC) for the silicon rods located in a 24-rod Siemens reactor. In this model, the combined effects of heat dissipation (radiation, convection, and reaction energy), skin effect, and heat conduction owing to Joule effect are examined. The presence of the skin effect, which yields an important radial temperature profile controlled by the heat conduction equation for the rods, has been considered. The present model is validated using industrial current data, and it is observed that the numerical results are in good agreement with them. The influence of the location of the silicon rods, AC frequency, radius of rod, and wall emissivity on the temperature profile and current density has been studied through the application of the developed model. Tailoring the temperature profile of silicon rods and extending the maximum deposition radius has also been performed. Voltage-current curves, which are applied to generate the required heat during the manufacturing period, have also been studied using different AC frequencies and wall emissivities.

In the Siemens reactor, all the energy is supplied by the heat generation on silicon rods which are heated up by the passage of current, the center of the rods will become hotter than the surface which is maintained ideally at 1373 K. Understanding the thermal and electrical behaviors of silicon rods in electric heating process is crucial for an optimal operation of the Siemens reactor. In the present paper, the electric heating model of silicon rod for the 24-rod Siemens reactor has been developed. In order to verify the present model valid, calculated results by application of the model were compared with industrial data. The results show that comparing to the industrial data obtained using a 24-rod Siemens reactor, the relative error of theoretical calculations are 7.32% and 9.41% for the rods located in the inner ring and outer ring, respectively. Based on the developed model, the influence of the location of silicon rods within Siemens reactor and reactor wall emissivity during electric heating process has been investigated. Interesting results show that the temperature gradient of silicon rods located in the outer ring is larger than the inner ones when the rods are heated up by direct current (DC). The temperature gradient within the rod becomes smaller and the required voltage and current decreases when the emissivity of the reactor wall surface decreases. Two interesting ways to reduce energy consumption can be deduced: increasing radius of the rod at the end of the process and decreasing the wall emissivity by wall surface treatment or/and selecting more appropriate materials.