Estimating residual stresses of silicon wafer from measured full-field deflection distribution

This paper proposes an experimental-numerical hybrid method for estimating the residual stresses in a silicon wafer from the full-field deflection measurement. In the proposed method, the measured deflection distribution is approximated using regularized least-squares based on the superposition principle. Simultaneously, the residual stresses induced with the deflection are estimated. By applying the proposed method to a deflection distribution by finite element simulation, the basic principle of the proposed method is verified. Then, the proposed method is applied to the steel plate specimens mimicking a silicon wafer. The residual stresses obtained using the proposed method are compared with the results obtained using the X-ray diffraction method, and the appropriate regularization parameter is determined. Finally, the proposed method is successfully applied to the residual stress estimation of an actual silicon wafer. Because the deflection of a silicon is often measured during the inspection process, the proposed method of using the deflection to estimate the residual stresses is useful. Therefore, the proposed method is expected to be applied to the inspection process of silicon wafers.

Automated summary

This paper proposes an experimental-numerical hybrid method for estimating residual stresses in silicon wafers, which is validated through experiments and compared with traditional X-ray diffraction method. The results demonstrate the successful application of this method in estimating residual stresses in silicon wafers.