Optimization of Multilayer Probe Card Using Strain Energy-Based Analytical Model and Multiobjective Programming Algorithm

Wafer testing in the semiconductor industry is generally performed using a multilayer probe card. In this paper, Castigliano's second theorem is used to derive analytical formulae for the contact force and scrub mark length generated during the probing test. The formulations are then integrated with a multiobjective programming algorithm to optimize the probe needle parameters in such a way as to ensure a uniform contact force and a minimum scrub mark length. The validity of the analytical model is confirmed by comparing the solutions obtained for the contact force and scrub mark length with the equivalent results obtained from finite element simulations. The effectiveness of the analytical model and optimization procedure is demonstrated by optimizing the needle parameters of a commercial four-layer probe card. It is shown that the optimized probe card not only produces a more uniform contact force than the original probe card but also yields a shorter and more uniform scrub mark length.