Integration of atomistic and continuum-level electromigration models

Interconnect scaling and the introduction of new processes and materials raise an issue of justifiability and applicability of phenomenological continuum-level electromigration models. The parameters of continuum-level 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-level models. Regarding both important parameters of continuum-level electromigration models, effective valence and vacancy diffusivity, their variations depend on the 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-level electromigration model and subsequently investigate the impact of parameter variation on the variability of the electromigration behavior. With the effective valence and vacancy diffusivity, which depend on the crystal orientation inside the grains as follows from atomistic simulations, we obtain a substantially more accurate electromigration behavior compared to that predicted with previous models. This difference implies the necessity of application of atomistic simulations in order to increase the predictive capability of continuum-level models.