Geometric Nonlinear Effect on Biaxial Bending Strength of Thin Silicon Die in the PoEF Test

Abstract

The easy-to-use point-load on elastic foundation (PoEF) test, similar (or alternative) to a typical biaxial bending ball-on-ring test, is studied for determining the bending strength of thin silicon dies. The feasibility of this test method with a linear theory is also evaluated using a nonlinear finite element method (NFEM) by taking into account geometric and contact nonlinearities. The mechanics of the PoEF test is discussed in terms of geometric linearity and nonlinearity. The results show that the geometric nonlinearity would cause significant errors of bending strength data, due to the maximum applied stress moving away from the loading pin center, if the linear theory is applied for thin die specimens in this test. The comprehensive fitting equations based on the NFEM results, with better accuracy than the linear theory, are proposed for calculating the thin die strength. Some key parameters, including the head radius of the loading pin ( ${r}$ ), elastic modulus of the foundation ( $E_{EF}$ ), elastic modulus of the test specimen ( ${E}$ ), and test specimen thickness ( ${t}$ ), are also discussed individually by studying their effects on the fitting equations. In an experimental implementation, the thin silicon die specimens with various thicknesses are actually performed in the PoEF test. It is found that the thinner specimen suffers from more severe geometric nonlinearity effect. The statistical strength data converted by the fitting equations are demonstrated and show that the geometric nonlinearity has to be taken into account in the PoEF test when the thin specimens are tested. The ready-to-use fitting equations proposed in this study are proved to be viable solutions for the conversion of those nonlinear test data.