The advance of a fine slit along a planar grain boundary, under the influence of an electric field that was parallel to the slit, was investigated by considering the effect of electromigration along both the grain boundary and the slit surface. Electrically-induced fluxes in the grain boundary (positive towards the slit tip), and electrically-induced and curvature-induced fluxes on the slit surfaces, were considered. It was assumed that the flux (positive away from the slit tip) on each of the parallel slit surfaces, far removed from the tip, was greater than the grain-boundary flux. Steady-state solutions of the transport equations were classified on the basis of the value of a certain parameter. Under normal conditions, this parameter was expected to depend only upon the material properties. For some parameter-values, unique steady-state solutions existed which could be multiple. For other parameter values, no steady-state solutions were possible. In the case of multiple solutions, those which corresponded to the smallest width (and highest velocity) were determined. For all of the steady-state solutions, the slit width and tip velocity scaled as E-1/2 and E3/2, respectively, where E was the electric field strength. The results were also suggested to be applicable to the propagation of a slit within a grain or along a passivating layer. The velocities were expected to approach 1nm/s, and thus to represent a likely failure mechanism in fine-line interconnects.

L.M.Klinger, X.Chu, W.W.Mullins, C.L.Bauer: Journal of Applied Physics, 1996, 80[12], 6670-6