Evaluation of Three-Point Bending Strength of Thin Silicon Die with a Consideration of Geometric Nonlinearity

With the trends of electronic packaging development toward small size, low-profile features, high-pin count, and high performance, the 3D IC (Three-dimensional Integrated Circuits) or stacked-die packages have been gaining popularity. For such package applications, IC silicon wafers have to be ground and processed to be relatively thin and then the thin silicon dies cut from these wafers have to gain sufficient strength in order to bear high stresses resulting from process handling, reliability testing, and operations. Hence, the strength of the thin dies has to be determined to ensure the good reliability of the packages. Three-point bending test is commonly used for measuring die strength; however, the feasibility of the test is still questionable for determining the strength of relatively thin dies. Therefore, the feasibility of the linear beam theory is evaluated by a nonlinear finite element method (NFEM) with taking into account geometric nonlinearity in this study. The results show that this nonlinearity would cause errors of the strength of thin dies if calculated by the linear beam theory. The fitting equations of the correction factors ( \eta ) to linear solutions, extracted from the NFEM simulation, are proposed and proved to be workable with very good accuracy. It is also found that the correction factor highly depends on the deflection ( \delta ), span length (L) and radius of roller support (r), but not elastic modulus (E) and thickness (t) of test specimens. After the nonlinearity has to be taken into account for the relatively thin silicon dies, the consistent statistical strength data have been obtained for various thicknesses of the test die specimens.