Correction factors to biaxial bending strength of thin silicon die in the ball-on-ring test by considering geometric nonlinearity and material anisotropy

The ball-on-ring test (BoR) is one of the standard tests for biaxial bending, suggested in ASTM F394-78. This test has been applied to determine the biaxial bending strength of silicon dies to avoid the die edge effect of the three-point bending tests. However, from the literature, when the relatively thin silicon dies are tested, this test suffers from a contact-nonlinearity effect, due to a maximum applied stress moving away from the loading pin center before the specimen failure, and thus results in overestimated maximum stress calculated by the theoretical linear solution. This study aims to investigate this mechanical issue experimentally, theoretically and numerically by taking into account the specimen material anisotropy and thickness effects on the maximum stresses and deflections, and then propose new correction factor equations to the theoretical linear solutions, based on the numerical fitting results of the geometric nonlinear finite element solutions. Those correction factor equations proposed in this study are material-property independent, but specimen thickness dependent, which can be estimated by an interpolation function. It has been proved that the BoR test using the conventional theory associated with the proposed correction factor equations can successfully determine the bending strength of the thin silicon dies on untreated surfaces, which mostly fails in the contact-nonlinear region.