Microstructure based statistical model of electromigration damage in confined line metallizations in the presence of thermally induced stresses

Probability distributions are evaluated for electromigration induced open failures in narrow, passivated interconnects with a near-bamboo grain structure. Void formation is initiated at the cathode ends of the polycrystalline line segments or ‘‘grain clusters.’’ If these clusters are longer than a critical size Lc, they can accommodate enough atoms for voids to reach the critical size to fail the line. Obviously, the critical size Lc depends on the thermal stress: a cluster under a tensile stress is able to incorporate more atoms from the void than an unstressed cluster. In the case the clusters are shorter than Lc, atoms from the voids must be distributed also to bamboo sections, outside the clusters, in order for the voids to induce open failures. Based on this physical picture, failure probabilities are evaluated as a function of time. The predicted failure distributions and parametric dependencies compare well with the experiments.