Biaxial bending strength of thin silicon dies in the ring-on-ring test by considering geometric nonlinearity and material anisotropy

The ring-on-ring test (RoR) is a standard biaxial bending test specified in ASTM C1499-19 and ISO 17167. This test has been utilized for characterizing the biaxial bending strength of silicon dies or wafers to eliminate the die edge chipping effect in the four-point bending test. However, judging from the literature, when testing thin silicon dies, the test is subject to geometric nonlinear effects. This study aims to investigate this nonlinear mechanics in the RoR test using experimental, theoretical, and numerical methods while considering silicon material anisotropy. A 2D-isotropy model of a nonlinear finite element method (NFEM) simulation with specimen elastic modulus of 130 GPa is utilized and verified by experiments and a 3D-anisotropy model in terms of deformation (or displacement) and stresses. Based on the 2D-isotropy NFEM solutions, the fitting equations of correction factors to the theoretical solution are proposed and implemented on determining the biaxial bending strength of 10 mm × 10 mm silicon dies ranging from 57 μm to 297 μm in thickness. It is found that those proposed fitting equations are independent on the test specimen thickness, radius, and materials but not on the radii of the loading and supporting rings. It has also been successfully demonstrated that the RoR test using the theory associated with the correction factor equations can be easy to use to determine the biaxial bending strength of the thin silicon dies that frequently failed in the nonlinear range.