Browsing by Subject "Fluid flows"
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Item Modeling of Particle Engulfment during the Growth of Crystalline Silicon for Solar Cells(2016-12) Tao, YutaoA major challenge for the growth of multi-crystalline silicon is the formation of carbide and nitride precipitates in the melt that are engulfed by the solidification front to form inclusions. These lower cell efficiency and can lead to wafer breakage and sawing defects. Minimizing the number of these engulfed particles will promote lower cost and higher quality silicon and will advance progress in commercial solar cell production. To better understand the physical mechanisms responsible for such inclusions during crystal growth, we have developed finite-element, moving-boundary analyses to assess particle dynamics during engulfment via solidification fronts. Two-dimensional, steady-state and dynamic models are developed using the Galerkin finite element method and elliptic mesh generation techniques in an arbitrary Eulerian-Lagrangian (ALE) implementation. This numerical approach allows for an accurate representation of forces and dynamics previously inaccessible by approaches using analytical approximations. We reinterpret the significance of premelting via the definition of an unambiguous critical velocity for engulfment from steady-state analysis and bifurcation theory. Parametric studies are then performed to uncover the dependence of critical growth velocity upon some important physical properties. We also explore the complicated transient behaviors due to oscillating crystal growth conditions as well as the nonlinear nature related with temperature gradients and solute effects in the system. When compared with results for the SiC-Si system measured during ParSiWal experiments conducted by our collaborators, our model predicts a more realistic scaling of critical velocity with particle size than that predicted by prior theories. However, the engulfment growth velocity observed in the subsequent experiment onboard the TEXUS sounding rocket mission turned out to be unexpectedly higher. To explain this model discrepancy, a macroscopic model is developed in order to account for the natural convection in the terrestrial experiments. We demonstrate that the convective flows are able to keep most small particles suspended in the melt, so that the observed critical velocities and their variance are enhanced in the experiments conducted on earth. According to simulation results, some solutions, which are applicable in photovoltaic industry, to the inclusion problem are also discussed and studied.Item Thermal-capillary analysis of the horizontal ribbon growth of solar silicon(2013-12) Daggolu, ParthivHorizontal ribbon growth (HRG) promises the growth of crystalline silicon at rates that are orders of magnitude greater than vertical ribbon growth technologies. If successful, this process would enable the production of higher-quality, near-single-crystalline silicon wafers at fraction of the cost of current production techniques. This fascinating process was first conceived by Shockley in late 1950's for silicon growth and was practiced by Bleil in the late 1960's for germanium growth. Large-scale development efforts were sub- sequently carried out by Kudo in Japan in the late 1970's and by the Energy Materials Corporation in the US in the early 1980's. However, after encouraging early results, experimental advances and process development efforts stalled, and this technique was abandoned in favor of growth methods that were easier to develop.Unlike vertical meniscus-defined crystal growth processes, such as edge-defined film- fed growth (EFG), which are inherently stable, there are many failure modes that must be avoided in the HRG process. We argue that its successful operation will rely on a thorough understanding of system design and control-issues that are perhaps only feasibly addressed via computational modeling of the system. Towards these ends, we present a comprehensive thermal-capillary model based on finite-element methods to study the coupled phenomena of heat transfer, fluid mechanics and interfacial phenom- ena (solidification and capillarity) in the HRG process. Bifurcation analysis coupled with transient computations using this model reveals process limitations that manifest as failure mechanisms, such as bridging of crystal onto crucible, spilling of melt from the crucible, and undercooling of melt at the ribbon tip, that are consistent with prior experimental observations and suggests operating windows that may allow for stable process operation. Further, coupled impurity transport calculations reveal interesting and potentially beneficial redistribution mechanisms at the solidification interface that lead to an inherent purification of the majority of the growing crystal ribbon.