Analysis of the residual stresses in silicon wafers using shadow moire technique

Many problems of defective device in silicon integrated circuits can be traced ultimately to stresses that develop in various stages of processing. This thesis considers the plate theory assumption that the behavior of a plate when transversal loaded at its center is different when the plate is initially in-plane stressed than when it is free of stress (an example is a drumhead, which gains lateral stiffness as it is tightened).; This thesis concerns extracting residual stress from the analysis of the out-of-plane deformation of plates loaded at the center. Material anisotropy is also considered by this thesis. In a first order approximation, it can be shown that for thin circular anisotropic plates the generalized Hooke's law simplifies to an isotropic-like Hooke's law for which equivalent material properties can be defined. The full anisotropic material properties are considered in the plate theory. The thesis seeks determination of the relationship between the initial in-plane tensions and the characteristic strain fields using linear plate theory (small deflections approach) and non-linear plate theory (large deflections approach). Shadow moiré is used to measure the deformed surface shape of the silicon wafers. A full field phase information is used to obtain the deflection displacement of the plate due to a central transversal load. A self-balanced residual stress is calculated using the displacement as an input in the von Kármán elastic plate theory.