A statistical method for the characterization of bimodal electromigration distributions

Abstract

We have developed a statistical method for analyzing bimodal electromigration distributions based on experiment and failure analysis. This method assesses whether a distribution is bimodal, and if so, determines the mode of each individual fail through a least-squares method, so that the best lognormal fit is determined for each mode. Once the modes have been separated, the electromigration performance for each mode can be explicitly determined in the usual manner. Unlike methods based on maximum likelihood estimation, this method is robust for small samples sizes, in which random subsets of a large dataset lead to statistically similar results. Further, since this method has been verified through failure analysis for multiple distributions, extensive failure analysis work can be bypassed in order to separate the entire distribution into two modes.