Modeling electromigration-induced stress evolution in confined metal lines

A model for stress evolution in confined metal interconnects due to electromigration was proposed recently by M. A. Korhonen, P. Borgesen, K. N. Tu, and C.-Y. Li [J. Appl. Phys. 73, 3790 (1993)], in which interconnect failure is associated with the buildup of stress to a critical level. We show that the analytic solution for a semi-infinite line with a blocking boundary given by Korhonen et al. is a good approximation only when the stress buildup is small. This is not usually the case for narrow, encapsulated interconnect lines in which the electromigration-induced stress can be quite high prior to failure. A complete model description and a more accurate analytic solution to the differential equations describing the electromigration-induced stress buildup at a blocking boundary is presented.