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Greg Hildeman, Sc.D., SPI's Vice President of Engineering, stated, "To design, fabricate and test the minicaster, Dr. Wang worked as a member of an SPI project team that included Dr. Daniel Meier and Mr. Vinodh Chandrasekaran." Part of the PEDA funding was used by SPI to purchase ALGOR multiphysics software for analysis of the minicaster design. Wang explained, "The reason we chose ALGOR was due to its cost-effective performance and local service and training program." Wang attended a one-day training course at ALGOR's headquarters in Pittsburgh, Pennsylvania. "The training was very helpful," he said. "While modeling the minicaster, I used ALGOR's technical support service to discuss particular issues such as mesh generation and transient phase modeling." Inside the minicaster, silicon feedstock is loaded in a vitreous quartz crucible. Graphite plates surround the crucible -- providing mechanical support. Surrounding the crucible is a bank of resistive heaters that uniformly heats the charge. A movable insulation cage serves as the primary means by which the desired cooling rate and directional solidification growth is achieved. Wang explained, "In order to assess the design of the minicaster 'hot zone' prior to fabricating the components, finite element modeling and analysis was first carried out for the melting phase and then the solidification phase." Multiphysics Analysis of the Melting Phase "We created a 3-D model of the minicaster in Autodesk Inventor," said Wang. "Then, we modeled the cross-sectional geometry in ALGOR." Custom-defined, temperature-dependent orthotropic material properties were specified for the silicon feedstock, quartz crucible, graphite heaters and insulation. Thermal loads were defined for internal heat generation, surface radiation at the outside surfaces and body-to-body radiation between exposed internal surfaces. Fluid velocities were specified for surfaces that surrounded the silicon. "Natural convection due to buoyancy plays an important role for transport phenomena inside the silicon melt," said Wang. "The strong velocity field inside the silicon melt cannot be neglected. Therefore, we used ALGOR multiphysics analysis to couple the calculation of the silicon melt flow field and temperature field, which accounted for the effect of natural convection." Wang performed a steady coupled fluid flow and thermal analysis to obtain the convective fluid flow and temperature results for the melting phase. Transient Heat Transfer Analysis of the Solidification Phase For the solidification phase, a lower internal heat generation value was used to simulate lower temperatures while cooling. ALGOR transient heat transfer analysis results allowed SPI to better understand the minicaster's solidification process. Upon examining the first silicon ingot produced by the minicaster, SPI noticed some concerns. "Most of the ingot's surface was flat and smooth, but there were some regions at the top of the ingot where the solidification proceeded erratically," explained Wang. "This was thought to be associated with an undesired solidification at the top of the melt, which initiated while solidification was occurring from the bottom upward. Such solidification was predicted by the thermal finite-element model of the growth." In order to maximize ingot quality, multiple transient heat transfer analyses of the solidification phase were conducted to determine the best placement and output power for the minicaster’s heaters. "By adjusting the heater position and increasing the heater power level by 25 percent, surface solidification was prevented during the growth process," said Wang. "Another effective way to modify the thermal environment was by adjusting the insulation lift distance. The resulting solidification interface was flat and slightly convex to the silicon melt, which is beneficial for high-quality silicon crystal growth."
Future Plans for ALGOR FEA "The PEDA-funded research project was finished in 2006," said Wang, "but research using the minicaster is still ongoing. Additionally, I am using ALGOR to simulate other crystal growth furnaces." To read a technical white paper about SPI's work, see "'Minicaster' - A Research-scale Directional Solidification Furnace". Dr. Chenlei Wang is a Senior Engineer for Casting Technology. He joined Solar Power Industries in May 2006 and is responsible for optimization of the silicon crystal growth process, thermal system design of DSS furnaces, testing and investigation of new silicon raw material and quality control of wafer production. He is currently conducting studies on silicon crystal growth with different feedstock materials. Dr. Wang earned a Ph.D. degree from the Department of Mechanical Engineering, State University of New York at Stony Brook and has authored 15 journal and conference papers in the area of solar-grade silicon crystal growth. He has more than 8 years of experience in numerical modeling with finite-element, finite-volume and finite-difference methods of heat and mass transfer as well as fluid flow of silicon crystal growth systems for solar applications. For more information about SPI, visit solarpowerindustries.com. Sources:
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