Minimum Void Size and 3-Parameter Lognormal Distribution for EM Failures in Cu Interconnects

Broad failure time distributions were observed for line depletion electromigration in Cu interconnects for various structures without sufficient liner contact and via redundancy. The root cause for this behavior was identified as the sensitivity of failure times to the void size, shape and location. Application of the traditional 2-parameter lognormal distribution model to corresponding stress data often results in very pessimistic EM lifetime projections. A 3-parameter lognormal distribution was found not only to fit the experimental data better, especially for the early portion of the failure time distributions, but also to generate more accurate lifetime projections for void-size-limited EM. Given the nature of EM wear-out, deeper consideration indicates that a 3-parameter lognormal distribution has a sounder physical basis than a 2-parameter lognormal distribution. The new parameter introduced in the model, the minimum failure time (X₀ ), scales with via size over several technology generations, further validating the minimum void size explanation