It was pointed out that the scaling to service conditions, of electromigration results which had been obtained under accelerated test conditions, required an understanding of the microstructural characteristics of the interconnects. An analytical model was developed which permitted the prediction of the average polygranular cluster lengths, and of the number of clusters in a line, given the line-width, the line length and the grain size distribution in the original film. The grain-structure characteristics were also measured for lines that were patterned from computer-generated thin-film microstructures. The large tail of the polygranular cluster-length distribution could be closely fitted by an exponential distribution function that was accurately predictable by using the new analytical model. Polycrystalline clusters which were shorter than a critical length could not fail due to electromigration-induced grain-boundary diffusion alone. Thus, when all of the clusters in a line were shorter than the critical length, there was a transition in failure mechanism. The model could be used to calculate the number of clusters which were longer than the critical length, as a function of the line and grain-structure characteristics, as well as of the current density. The current-density dependence of the median time to failure due to polygranular failure mechanisms in near-bamboo lines, as well as the transition current density at which the transition in failure mechanism occurred, were predicted. This transition current density depended upon the line-width and the line length, as well as upon the grain size and grain size distribution of the film from which the line was patterned.

Y.C.Joo, C.V.Thompson: Journal of Applied Physics, 1994, 76[11], 7339-46