Inversion of Residual Stresses in Silicon Wafer from Surface Deflection Measurements

Abstract

This paper describes the evaluation method of residual stress of thin plate from deflection distribution. Using the deflection distribution calculated from the FEM and the deflection distribution of the actual silicon wafer, coefficients used for the principle of superposition are calculated from the least squares method. Residual stress is estimated from the principle of superposition using the stress obtained from FEM and the calculated coefficient. In order to evaluate the validity of the proposed method, residual stress distributions of those obtained by the finite element method and those obtained by the propose method are compared. Also from actual deflection distribution of silicon wafers, Residual stresses are estimated by the proposed method. Results show that the residual stress in silicon wafers can be obtained by the proposed method.