THE ELECTROMIGRATION FAILURE DISTRIBUTION - THE FINE-LINE CASE

The electromigration failure distribution for fine-line interconnects is unknown, but expected to be strongly affected by microstructure. Results from tests on lines with controlled grain sizes and distributions of grain sizes argue for a series model of failure elements in fine lines. A new statistical model of electromigration is developed based on an extension of the failure model of Shatzkes and Lloyd [J. Appl. Phys. 59 (1986)] incorporating the statistics of microstructure and concomittant variations in the activation energy for grain-boundary diffusion. The resulting electromigration failure distribution is well-approximated by a multilognormal distribution in the fine-line case. This approach results in a failure distribution calculated from first principles which, unlike the lognormal distribution, is scalable.