An empirical equation for prediction of silicon wafer deformation

作者:Zhu, Xianglong; Chen, Xiuyi; Liu, Haijun; Kang, Renke; Zhang, Bi; Dong, Zhigang*
来源:Materials Research Express, 2017, 4(6): 065904.
DOI:10.1088/2053-1591/aa71ed

摘要

A thin subsurface damage layer is often formed in the ground layer of a silicon wafer. Compressive stresses exist in the damage layer of the wafer and cause the wafer to deflect when it is unloaded from the vacuum chuck. The residual stresses play an important role in evaluating the machining quality of a wafer. A concise yet accurate stress-deflection relationship is desired so that the residual stresses can be calculated from the wafer deflection. The theoretical equation based on minimizing the total strain energy is often used. However, the anisotropic effects of silicon are neglected and would incur errors when it is applied on silicon wafers. This study establishes an empirical equation via a finite element (FE) model. Both equations are verified in experiments. It is found that FE model is more accurate than the theoretical equation.