Probabilistic immortality of Cu damascene interconnects

Abstract

We have studied electromigration short-line effects in Cu damascene interconnects through experiments on lines of various lengths L, stressed at a variety of current densities j, and embedded in different dielectric materials. We observed two modes of resistance evolution: Either the resistance of the lines remains constant for the duration of the test, so that the lines are considered immortal, or the lines fail due to abrupt open-circuit failure. The resistance was not observed to gradually increase and then saturate, as commonly observed in Al-based interconnects, because the barrier is too thin and resistive to serve as a redundant current path should voiding occur. The critical stress for void nucleation was found to be smaller than 41 MPa, since voiding occurred even under the mildest test conditions of j=2 MA/cm2 and L=10.5 μm at 300 °C. A small fraction of short Cu lines failed even at low current densities, which deems necessary a concept of probabilistic immortality rather than deterministic immortality. Experiments and modeling suggest that the probability of immortality is described by (jL2/B), where B is the effective elastic modulus of the metallization scheme. By contrast, the immortality of Al-based interconnects with shunt layers is described by (jL) if no voids nucleate, and (jL/B) if voids do nucleate. Even though the phenomenology of short-line effects differs for Al- and Cu-based interconnects, the immortality of interconnects of either materials system can be explained by the phenomena of nucleation barriers for void formation and void-growth saturation. The differences are due solely to the absence of a shunt layer and the low critical stress for void nucleation in the case of Cu.