Nonlinearities in thin-silicon die strength tests

While the semiconductor packages are evolving toward smaller package size and higher performance, the 3D IC or stacked-die packages are gaining popular. For these applications, IC wafers have to be ground to be relatively thin and the dies cut from these wafers have to possess sufficient strength against high stresses resulting from process handling, reliability testing, and operation. Hence, the strength of the dies, especially for the thin dies, has to be determined to ensure good reliability of the packages. Three-point bending test is widely used for measuring die strength; however the feasibility of the test is still questionable for determining strength of relatively thin dies. Meanwhile, the pin-on-elastic-foundation (PoEF) test [1] with special feature of bi-axial stress mode and elimination of the die edge effect has been proved more simple and reliable, but not for thin dies. In this study, the three-point bending test (under un-axial stress state) and the PoEF test (under bi-axial stress state) are evaluated for aiming at the thin-die strength determination which may features geometrical and contact nonlinearities. The feasibility of both test methods with their linear theories is evaluated by a nonlinear finite element method (NFEM) with taking into account geometrical and contact nonlinearities. The results show that these nonlinearities would cause an error of strength prediction by the linear beam theory for thin dies. For three-point bending test, the concept of moment equilibrium associated with the fitting equation for F_x extracted from the NFEM simulation is proposed and proved workable with good accuracy. The similar problem is faced in the PoEF test. The fitting equations based on the NFEM results are also proposed for calculating the strength of thin dies with better accuracy than theoretical formulation. Therefore, the nonlinearities has to be taken into account for both tests when the thin silicon dies are tested for strength.