Electromigration behavior under a unidirectional time-dependent stress

The problem of current induced electromigration in VLSI interconnects, under an arbitrary time-dependent stress, is considered within the drift/diffusion model. It is shown that, by transforming into the convected frame and solving the resulting moving boundary problem, the vacancy build-up may be followed by solving two coupled integral equations. The important large-time behavior is obtained using standard asymptotic techniques. A series solution and an approximate small-time solution are also derived. It is found that, for a unidirectional periodic stress, the equivalent dc current, appropriate to EM reliability tests is the periodic average value. In addition a design rule for arbitrary time-dependent stress is suggested.