Failure Model for Electromigration

A model is presented for electromigration induced failure following the nucleation of grain boundary voids which lengthen by electromigration transport along neighboring grain boundaries. A grain boundary crevasse growing parallel to the electron currentflow does not accelerate failure. However, a crevasse growing perpendicular to the current has three effects: the electron flux near the crack decreases, and the electron flux and stripe temperature increase near the tip, enhancing the tip growth rate. A consideration of these effects yields a stripe lifetime integral which fits the simple form Pn = 1/2(1+.265¿¿T0), where ¿=¿H/kT2 is the temperature coefficient of the diffusion constant and ¿T0 is the initial stripe temperature rise. Pulsed d. c. operation causes thermal effects that allow extended lifetimes. Lifetimes are proportional to the reciprocal of the duty cycle for long pulse times. Short pulse times and high repetition rates result in lower average stripe temperatures and allow even longer lifetimes.