A bimodal three-parameter lognormal mixture distribution for electromigration failure analysis

The electromigration (EM) phenomenon often exhibits two failure mechanisms. The early failures are due to voids developed in the via or at the via-line interface while the wear-out failures are predominantly attributed to voids developed within the interconnect line itself. Presence of these two failure mechanisms necessitates the use of a bimodal mixture distribution for analyzing EM data. Also, due to the presence of incubation time in EM, the three-parameter lognormal distribution should be applied to account for the initial failure-free duration. An efficient global optimization technique called "simulated annealing" is introduced in this work to globally optimize the log-likelihood function of the mixture distribution and determine the values of the lognormal parameters that accurately fit the experimental EM failure data.