Correction factors to strength of thin silicon die in three- and four-point bending tests due to nonlinear effects

The thin silicon dies have been widely used in the three-dimensional integrated circuits (3DIC), stacked-die or wearable electronic packages to meet the requirements of small size, low-profile features, high-pin count, high performance, low-power consumption or even flexibility. The bending strengths of the thin dies cut from silicon wafers have to be determined to ensure no reliability problems, mostly resulting from packaging process handling, reliability testing, and operations. Three-point bending (3PB) and four-point bending (4PB) tests are commonly used for measuring die bending strength; however, both tests are still problematic for testing the thin silicon dies. Therefore, the mechanics of both tests are reevaluated in this study by a nonlinear finite element method (NFEM) with taking into account geometric nonlinearity (or large deflection), associated with the related theoretical formulations. The nonlinear mechanics of both tests are discussed in detail. NFEM results-based correction factors to the linear beam solutions are further proposed in the form of the polynomial fitting equations in this study. Those polynomial fitting equations of the correction factors are proved to be workable and easy to use with an engineering acceptable accuracy. Those correction factors are also found highly dependent on the deflection (delta), span length (L) and radius of roller support (r), but not on test specimen thickness (t) and elastic modulus (E).