On the prediction of electromigration voiding using stress-based modeling

Abstract

In modeling electromigration failure, it is common to employ the concept of a critical stress at which interconnect failure occurs. In this report, we illustrate that the atomic flux divergence, obtained directly from the one-dimensional stress-based modeling, is more appropriate in characterizing the formation of void in electromigration. A numerical analysis was carried out, to model the evolution of stress, atomic flux, and flux divergence in an aluminum line containing a fast-diffusion segment. The maximum flux divergence, not the maximum tensile stress, predicts the voiding location which is consistent with microscopic observations in the experiments of Joo et al. [Acta. Mater. 46, 1969 (1998); J. Appl. Phys. 85, 2108 (1999)] utilizing nanoindented single-crystal aluminum lines. This is because the flux divergence directly reflects the extent of matter depletion, and thus the propensity of voiding.