Numerical Simulation And Application Of Vacuum Directional Solidification Process For Polycrystalline Silicon In Metallurgical Process

The process of directional solidification is a significant component in the current craft of solar-grade multicrystalline silicon preparation. Whereas, directional solidification is an invisible process, proceeding in high temperature and high vacuum conditions, which is accompanied by the complicated phenomena of heat transfer, liquid phase flow, phase change and thermal stress, etc. In-depth study and research from the perspective of theory and craft is essential if this complicated coupled process is to be thoroughly understood. Consequently, it is of great significance to conduct researches revealing the universal heat transfer process of multicrystalline silicon vacuum directional solidification, solving the migration mechanism of phase change, flow and thermal stress with changing temperature field and thus determine the coupling relations during the directional solidification process.In this paper, heat transfer-stress model of transient vacuum directional solidification process with the principal varying factor of radiation heat transfer angular coefficient was established. Pilot and industrial scale models of heat transfer, flow and stress during multicrystalline silicon vacuum directional solidification process were established with the method of numerical simulation, which reveals the temperature distribution in furnace and silicon as well as evolution rule of solidification interface, etc. Furthermore, systematic heat transfer analysis and investigations on the effect of different crafts and different equipment conditions on the temperature, growth orientation of multicrystalline silicon as well as crystal stress were conducted. The optimal craft methods and equipment conditions for the preparation of multicrystalline silicon were obtained by comparing the simulation results with the experimental ones. The specific content includes:1. Transient model for pilot scale test of multicrystalline silicon vacuum directional solidification was established, conducting researches on the problems of heat transfer, flow, interface shape and stress, etc. during the process of solidification, furthermore, the solidification states of multicrystalline silicon obtained under different pulling-down rates were compared with each other. Simulation results demonstrated that temperature gradient of silicon was increased to some extent with increasing pulling-down rate, single vortex flow along upward axial direction was easy to be formed in the melt, and also directly results in the increase of thermal stress. Consequently, an appropriate pulling-down rate should be chosen to form the optimal temperature distribution so as to provide suitable conditions of flow, stress and interface for the solidification process of silicon. It can be found from the multicrystalline silicon ingot prepared according to the same pulling-down rate of simulation narrated above that, silicon ingot obtained at the pulling-down rate of 10 um/s showed fine crystal morphology, which had quite big size columnar grain. Moreover, the average minority carrier lifetime of the middle and upper part silicon reached 3μs, showing quite strong (111) growth crystal plane.2. Heat transfer characteristics of pilot scale test vacuum directional solidification process was analyzed in detail, the formula of angular coefficient for radiation heat transfer was deduced and calculated, putting forward adopting the craft scheme of changing pulling rate and the equipment improvement of broadening the cooling zone to optimize the pilot scale test vacuum directional solidification process of multicrystalline silicon. According to the numerical simulation results, the optimized vacuum directional solidification process and equipment of multicrystalline silicon could provide better thermal field conditions, average the temperature distribution of silicon ingot, declining thermal stress and improving the interface shape. Similarly, it was found that the temperature condition in the furnace could be improved by widening the hot zone at the condition of crucible bottom without the water heat exchange. The temperature difference and thermal stress of silicon ingot was obviously reduced. Moreover, the conical heat preservation device added in the cooling zone could provide a gradually enlarging heat dissipation space for the sidewall of crucible when the crucible was pulled to enter the cooling zone for heat dissipation, which can not only effectively control crosswise heat dissipation but also provide a better temperature field and growth interface for silicon during the solidification process. The temperature of solidified silicon ingot could be declined uniformly so as to reduce the temperature gradient of silicon ingot as well as reduce thermal stress dramatically.3. Investigations on crucibles were performed during the pilot scale test vacuum directional solidification process of multicrystalline silicon. Simulation results indicate that "cylinder type crucible" could concentrate the stress on the extreme upper edge of silicon ingot, the distribution zone of stress was consequently reduced, which is beneficial for improving the whole quality of silicon ingot as well as enlarging the utilization zone of silicon ingot. Similarly, when silicon solidified in the "crucible with V plane bottom", the quantity of nucleation was small, the unbeneficial effect between crystal grains could be reduced. Furthermore, the effect of radial thermal gradient during the initial solidification period was quite small, after nucleation, driven by the axial temperature difference, crystal grains could grow vertically to form column crystals. The multicrystalline silicon solidification process of increasing loading height in pilot scale test vacuum directional solidification furnace was compared with that of increasing loading diameter. Simulation results indicate that when loading was increased along the axial direction, time consumed to heat the silicon to the phase change temperature was unchanged, axial temperature gradient increased during the solidification process, however, flow in the smelt was gradually divided from a vortex into two opposite direction vortexes, the distribution area of the large stress zone tended to increase. While, when loading was increased along the radial direction, heat time was obviously increased, radial thermal gradient increased during solidification process, contributing to the phenomenon that solid-liquid interface tended to be convex, the vortex formed in the smelt gradually flew near the inner wall of crucible, the maximum value of stress increased, but it was only concentrated in the edge of upper side of silicon.4. For improving the quality of the silicon ingot in the process of practical production and reduce production costs, the transient 3D numerical model of industrial grade vacuum directional solidification equipment for multicrystalline silicon has been established, and simulation and experimental research on this process has also been conducted. Simulation results indicate that when directional solidification was conducted according to purification technology, the axial temperature gradient of silicon was quite big, the edge of solid-liquid interface and its middle part tended to be convex, the solid-liquid interface concentrated from the edge to center when solidification came to an end. After the solidification of silicon ingot, stress was mainly distributed on the bottom and central part of silicon ingot, which decreased along the axial direction with the range of 2.43 Mpa-70.63 Mpa. When directional solidification was performed according to the proposed optimization technology, the temperature gradient of silicon was quite small with the proceeding of solidification and the overall temperature was quite uniform. The solid-liquid interface of the whole solidification process showed slight convex shape, the solid-liquid interface moved gradually from central part to the edge when solidification was about to end. There was almost no difference between the stress distribution in silicon ingot after solidification and that in the silicon ingot obtained by purification craft, however, the stress was only distributed during the range of 1.06 Mpa-30.99 Mpa, which was far less than that of the silicon ingot obtained by purification technology. The conclusions obtained by numerical simulation were also tested and verified by the experimental results of industrial grade directional solidification, the content of impurity Cu and Ti was the minimum in the prism part of the edge of silicon ingot, whereas, the content was quite high in the central zone. It was found through testing that the minority carrier lifetime of silicon ingot obtained by purification technology was quite low, with the average value of 0.61 μs～0.75μs in the central cross section and 0.55μs～0.71μs in side part, the fluctuation of electrical resistivity value was also quite high. The content of impurity Cu was the maximum in the edge and corners of silicon ingot prepared by the optimized technology, the content of Cu was the minimum in the central part. The minority carrier lifetime of silicon ingot prepared by the optimization technology was improved dramatically, with the average minority carrier lifetime of silicon located in the central cross section improved and reaching over 5.85μs, and the average minority carrier lifetime of silicon located in the edge side of silicon ingot was improved to over 2.99μs. The fluctuation of resistivity of silicon ingot was obviously reduced and the homogeneity of electrical resistivity was improved.