Variable-Length Link-Spring Model for Kink Formation During Wire Bonding

Kinks have a strong influence on the structural performance of wire bonds. In this study, a variable-length link-spring model has been developed to better understand kink formation. In this model, a gold wire was decomposed into segments that were represented by a link and a torsional spring. One end of the gold wire was fixed, and the other end was free. The friction and air tension forces at the wire ends were considered a function of the capillary position, and the wire segments and moment balance equations were added at the free end as the wire length increased. By using this model, the wire profile, moment, and curvature diagrams at the reverse motion stage were obtained to study the dynamical kink formation and wire-length increasing processes. The analysis result was verified experimentally. Good agreement is obtained between the analytical and the experimental wire profiles. This study indicates that a moment magnitude of several hundred mN·μm is required to form a kink, and the wire profile is the result of the residual curvature and the instantaneous bending moment.