The distribution of the normal stress and the mass flux in the plane of each grain boundary of a polycrystalline thin-film conductor during electromigration was calculated by assuming zero grain boundary flux divergence (steady-state) for various boundary conditions and by using the standard boundary-value methods of diffusion theory. A steady state, which represented a balance between the applied electric and induced stress driving forces, developed after a transient period which was expected to be short in the cases which were considered. Continuity of stress and flux was assumed to hold at the intersections of grain boundaries at triple junctions. The intersections of the grain boundaries with the film surfaces were assumed to be of 2 types: open (with free passage of flux) or closed (zero flux). The lower film surface (substrate) was assumed to be closed while the upper surface (bare metal) was open. Grain boundary intersections with the film edges (edge junctions) could be of either type. Several grain boundary configurations, and combinations of boundary conditions, were considered. The results clearly demonstrated the accumulation or depletion of matter at open edge junctions, and the formation of incipient holes and hillocks near to the intersection of the triple junctions with the upper surface. The maximum tensile or compressive stresses occurred at the intersections of triple junctions and closed edge junctions with the lower surface.

M.Scherge, C.L.Bauer, W.W.Mullins: Acta Metallurgica et Materialia, 1995, 43[9], 3525-38