A one-dimensional diffusion model was used to analyze electromigration-induced edge drift in a finite thin-film conductor. The edge drift was caused by the accumulation of vacancies at the negative (upstream) terminal of the conductor as Al diffused under the electrical current. When the Cu content exceeded its solubility limit, the grain boundaries became decorated with Al2Cu precipitates. These had to dissolve before significant Al diffusion could occur. By assuming 1-dimensional flow in an homogeneous polygranular film, the rate of growth of the precipitate-free zone at the upstream terminal was calculated. Estimates were made of the incubation time for the onset of edge drift. The results predicted an incubation time that increased with the grain size and the initial Cu content, and decreased with the square of the current density. The incubation time was inversely proportional to the so-called electromigration diffusivity: that is, the product of the grain-boundary Cu diffusivity, the effective grain boundary thickness, and the effective valence of the Cu ion. The results were used to compare a number of prior experimental studies, which were shown (with one exception) to produce consistent values of the electromigration diffusivity. An analysis of the experimental results suggested that edge drift began almost as soon as the precipitate-free zone length exceeds the "Blech length" for the line. It was concluded that the presence of Al2Cu precipitates in the grain boundaries was essential in order to retard Al electromigration.

Kinetics of Electromigration-Induced Edge Drift in Al-Cu Thin-Film Interconnects C.U.Kim, J.W.Morris, H.M.Lee: Journal of Applied Physics, 1997, 82[4], 1592-6