Numerical calculation of electromigration under pulse current with Joule heating

Electromigration behavior under pulsed directional current (PDC) was investigated theoretically and experimentally, A vacancy diffusion equation under current stress was derived, and the relationship between vacancy concentration and time to failure was calculated numerically. The results show that if Joule heating is considered, the ratio of lifetime under PDC to that under DC is less than what was reported by other authors. In addition, the dependence of the lifetime on duty ratios and frequencies of PDC is not the same in different regimes of PDC frequencies. The analytical equation describing the relation between MTFPDC and MTFDC in the entire regime of frequencies, including Joule heating, is given. All calculated results are compared to experimental results.