Impact of parameter variability on electromigration lifetime distribution

The interconnect scaling and the introduction of new processes and materials raise an issue of justifiability and applicability of phenomenological continuum-level models. The parameters of continuum-level electromigration models are averages over values which generally vary on microscopic and atomistic scale. Therefore it is necessary to investigate under which conditions these microscopic or atomistic spatial variations influence the validity of continuum models. Regarding both important parameters of continuum-level electromigration models, effective valence Z* and vacancy diffusivity, their variations depend on crystal orientation and the variations between bulk, grain boundaries, and interfaces. We apply the results of quantum mechanical calculations of the effective valence in order to parameterize the continuum electromigration model and subsequently investigate the impact of parameter variation on the variability of the electromigration behavior.