3D Viscoplastic Finite Element Modeling of Dislocation Generation in a Large Size Si Ingot of the Directional Solidification Stage

Growing very large size silicon ingots with low dislocation density is a critical issue for the photovoltaic industry to reduce the production cost of the high-efficiency solar cell for affordable green energy. The thermal stresses, which are produced as the result of the non-uniform temperature field, would generate dislocation in the ingot. This is a complicated thermal viscoplasticity process during the cooling process of crystal growth. A nonlinear three-dimensional transient formulation derived from the Hassen-Sumino model (HAS) was applied to predict the number of dislocation densities, which couples the macroscopic viscoplastic deformation with the microscopic dislocation dynamics. A typical cooling process during the growth of very large size (G5 size: 0.84 m × 0.84 m × 0.3 m) Si ingot is used as an example to validate the developed HAS model and the results are compared with those obtained from qualitatively critical resolved shear stress model (CRSS). The result demonstrates that this finite element model not only predicts a similar pattern of dislocation generation with the CRSS model but also anticipate the dislocation density quantity generated in the Si ingot. A modified cooling process is also employed to study the effect of the cooling process on the generation of the dislocation. It clearly shows that dislocation density is drastically decreased by modifying the cooling process. The results obtained from this model can provide valuable information for engineers to design a better cooling process for reducing the dislocation density produced in the Si ingot under the crystal growth process.