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Accurate determination of bifurcation points for ground silicon wafers considering anisotropy using FEM method

Silicon wafers warp under residual stress when they are thinned by grinding or plated with a thin layer of a different material. Bifurcation and geometric instability of silicon wafers occur at critical residual stresses that serve as the basis for evaluating the significance of large deformations. Analytical approach based on minimizing the total strain energy is often used to determine the bifurcation points. However, the curvature is assumed uniform across the wafer, which deviates from actual scenarios because of large deformation and anisotropic effects of monocrystalline silicon. In this study, the finite element method considering the anisotropy of silicon was applied to examine the deformation process. Then the surface features of deformed silicon wafer were extracted by employing sphere fitting and removing techniques to the wafer deformation shapes. Based on the variation rule of the deformation features, line fitting technique was applied and the residual stress of the bifurcation point was obtained as the intersection point. The critical value of the stress parameter, which is an important parameter for silicon wafers, was obtained as 650.7 GPa. The bifurcation points of silicon wafers with other dimensions could be obtained easily based on the value with sufficient accuracy, which were verified by FEM results. The proposed method could also be used to determine the bifurcation points of other anisotropic materials.