(Dr. Steven Danyluk, advisor)

"Analysis of the Residual Stresses in Silicon Wafers using Shadow Moirè Technique"

Abstract

Many problems of defective device in silicon integrated circuits can be traced ultimately to stresses that develop in various stages of processing. Initial stresses which act on a plate when no other forces or constraints are applied are called residual stresses. The in-plane residual stresses do not affect the shape of a silicon wafer, which remains flat even though these stresses are present, but they can lead to crack growth and fast fracture.

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. The measured out-of-plane displacement of the plate will be affected by the in-plane residual stress which exist on the plate (a drumhead, which gains lateral stiffness as it is tightened, would be a good example).

This thesis concerns extracting in-plane 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 cubic single crystal plates the generalized Hooke's law simplifies to an isotropic-like Hooke's law for which equivalent material properties can be defined. Then, the full anisotropic material properties are considered in conjunction to 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 von Kármán plate theory (large deflections approach). Both the isotropic-like and anisotropic cases will be considered. In small deflection approach, the central deflection of a simply supported plate transversally loaded is measured. Deflection-load data is used to extract an uniform equivalent residual stress. Shadow moiré interferometry is used to measure the deformed surface shape of the silicon wafers. A full field phase information is used to obtain the large 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.