Nonlinear buckling analysis of vertical wafer probe technology

Due to the demand of the industry for an increase of the number of I/Os, while decreasing the die size, the bond pads had to shrink and design restrictions for the active structures underneath had to fall. This leads to new challenges for the electrical probing and the mechanical robustness of the under-pad structures. This paper presents analytical and numerical simulation approaches for predicting the force/travel relation of buckling beam-probes that are used for testing the electrical functionality of back-end-of-line (BEOL) interconnect system underneath a chip pad. For this purpose we investigate, first, in a closed-form manner, the elastic stability of the probe needle according to the large deflection theory of buckled bars. Second, we determine, for a specific geometry of the beam, the probe forces as functions of the probe card overdrive by using the closed-form methods as well as finite-element simulations. The results are finally compared to that obtained in (probe card) experiments.