Characterization of residual stresses in birefringent materials applied to multicrystalline silicon wafers

Abstract

Birefringence has been used to study transparent materials since 1815, and is based on the decomposition of a polarized ray of light into two distinct rays when passing through an optically anisotropic material. This thesis uses this phenomenon in a study of phase retardation in crystalline materials. Single and multicrystalline silicon was chosen as the model material. Silicon is an interesting and important material in its own right, and the use of photoelasticity to determine stresses at linear and planar defects can have important consequences in the electrical performance of devices such as electronics and photovoltaic cells. This thesis presents the results of an experimental investigation of residual stresses in multicrystalline silicon wafers using near-infrared (NIR) transmission photoelasticity. NIR transmission through multicrystalline silicon is found to vary with crystallographic orientation and relate to planar atomic density, enabling the assignment of appropriate stress-optic coefficients to different grains. Noise in the data is reduced with the Ramji and Ramesh 10-step phase shifting algorithm when compared to the Patterson and Wang process. Normal stresses at points of zero maximum shear stress can be characterized based on isoclinic behavior around the point. Points at which all normal stresses are zero serve as boundary conditions for shear difference integration and allow for stress separation from a point that is not a free boundary. The second part of this work focuses on residual stresses in silicon wafers subjected to known physical damage such as indentations. Residual stress fields around Vickers indentations in silicon are found to be larger in size than predicted by contact mechanics. Placing Vickers indentations in close proximity creates a secondary stress field surrounding the entire indentation array, and a relationship is developed to explain this behavior. High residual stresses measured at grain boundaries are found to be consistent with models of atomic displacement. Placement of Vickers indentations near grain boundaries results in a change in stress state at the grain boundaries. The results of this study demonstrate the capacity of birefringence as a non-destructive evaluation tool and describe the effects of residual stress concentrations in silicon wafers.