The Effect of Copper Grain Size Statistics on the Electromigration Lifetime Distribution

We investigate the influence of the statistical distribution of copper grain sizes on the electromigration time-to-failure distribution. We have applied a continuum multiphysics electromigration model which incorporates the effects of grain boundaries for stress build-up. The peak of tensile stress develops at the intersection of copper grain boundaries with the capping layer. It is shown that the electromigration lifetimes follow lognormal distributions. Moreover, the increase of the standard deviation of the grain size distribution results in an increase of the electromigration lifetimes standard deviation. The results strongly imply that the lognormal distribution of the grain sizes is a primary cause for the lognormal distribution of electromigration lifetimes.