Theoretical Analysis of the Deflection of a Cantilever Plate for Wirebonding on Overhang Applications

Explicit analytic solutions of the deflection of the overhang during the wirebonding process were derived. The wirebonding on overhang were modeled as a cantilever plate subjected to concentrated force at the corner or edge. Depending on the length of the overhang and the position of the bonding pad, the cantilever plate was divided into three types. The first is a rectangular plate whose two adjacent edges are free and the others clamped, which represents the deflection at the corner. The second is a cantilever plate whose three edges are free. And the third is a semi-infinite cantilever plate, which represents the middle of an edge that is sufficiently far from the corner. Ritz´s approximation method employing polynomial function was applied and the deflection was successfully achieved. Critical locations, where the maximum or minimum deflection occurred, were at the corner and at the middle of the edge. The deflections at these locations were obtained in an explicit form where the material properties, chip thickness, overhang length, and applied force are taken into consideration. The solution was expanded to an anisotropic plate to consider the material anisotropy of a silicon wafer, and a multilayered plate to consider several layers on a chip.