A statistical model for electromigration failures

The lognormal has been traditionally used to model the failure time distribution of electromigration failures. However, when used to estimate the failure of large metal layers, it leads to a clear disagreement with established empirical data. To resolve this problem, we propose to use a shifted lognormal (SLN) as a better model of the failure time of individual wires. We will show that the SLN is well justified because it matches other more detailed and more physical models, such as the multilognormal. We will also show that the SLN exhibits the right behavior for long wires. Finally, we will provide an estimation methodology by which the parameters of the SLN can be estimated from failure data. Finally, the analysis will be extended to large metal layers where the advantages of using SLN over LN will be clearly demonstrated