It was pointed out that a paradox arose when the 2-parameter log-normal distribution was used to predict the early electromigration failure of a 2-level structure with Ti-AlCu-Ti stripes and inter-level W studs. The paradox was a direct result of the observed increase in the log-normal  which occurred as the current density decreased and/or the maximum allowed resistance change increased. The increase in  implied that the first failures from equal and large sample sizes were expected to occur at low, rather than at high, current densities. In the same way, samples at relatively low cumulative failure were expected to fail at high levels of resistance change before failing at low levels of resistance change. The apparent paradox was resolved by testing a large set of samples, and fitting the failure data to the 3-parameter log-normal distribution. The third parameter (incubation or minimum time before failure could occur) was shown to increase as the maximum allowed resistance change increased.

R.G.Filippi, G.A.Biery, R.A.Wachnik: Applied Physics Letters, 1995, 66[15], 1897-9