Iterative method for obtaining nonuniform grinding-induced residual stress distribution of silicon wafers based on global deformation

Abstract

Grinding as the main thinning process for silicon wafers is widely used in chip manufacturing. The residual stress distribution is desired to be known to optimize the grinding process. In this paper, an iterative method for obtaining the nonuniform residual stress of ground silicon wafers was proposed. The deformation of ground silicon wafers was divided into two parts in which one part was large spherical deformation and the other was a small out-of-sphere deformation. The spherical deformation which was in the nonlinear range corresponded to an average stress which was obtained using the bisection method. The small out-of-sphere deformation corresponded to the stress variation which was obtained using the regularization method with continuity constraints. An iterative successive approximation process was conducted to address the nonlinear problem which was transformed into a local linear problem. The residual stress distribution of a ground silicon wafer was obtained successfully using the proposed method. Although the overall shape of the wafer deformation was approximately spherical, the residual stress value varied a lot with the crystal orientation of the silicon wafer. The stress values in the <110> orientations were much larger than those in the <100> orientations. The method could be used to evaluate the grinding process independently of the dimension sizes of ground silicon wafers. The proposed method in this paper is non-destructive and could be used to track the residual stress changes in the grinding process and the process parameters could be optimized accordingly.