Strength characterization of ultrathin chips by using large deflection theory of multi-layer plate for three-point bending tests

Abstract

This study developed mathematical formulas for a two-layer structure, specifically an ultrathin memory die with a film, which accounted for large deflection effects with Legendre-Jacobi’s elliptic integrals and frictional forces on the supports. The formulas were used to calculate die strength using three-point bending tests and were verified through comparisons with simulated and measured load-deflection curves. The study found that the Poisson's effect cannot be neglected for plate-like structures, and the slip effect was also significant, with accounting for friction improving accuracy. Additionally, the span between supports was found to increase nonlinearity. The study concluded that stress-deflection curves derived in the study can be used to determine die strength, with calculated strengths of 745 MPa and 1296 MPa for film-up and film-down configurations, respectively.