The effect of microstructure on the electromigration lifetime distribution

In this work we analyze the influence of the statistical distribution of copper grain sizes on the electromigration time to failure distribution based on numerical simulations. We have applied a continuum multi-physics electromigration model which incorporates the effects of grain boundaries for stress build-up. It is shown that the lognormal distribution of grain sizes causes a lognormal distribution for the times to failure. Moreover, the increase of the standard deviation of the grain size distribution results in an increase of the electromigration lifetimes standard deviation.