It was recalled that, in multi-level interconnects, current-crowding occurred when the current changed direction. It was proposed here that, in current crowding, the current density-gradient could exert a driving force which was strong enough to cause excess vacancies to migrate from high current-density to low current-density regions. This then led to void formation in the latter. It was noted that a drop from 106 to 103A/cm2, across an 0.5μm-thick strip, implied a gradient which was as high as 1010A/cm3. Under such a large gradient, high-order effects could be expected to occur. Although this analysis assumed a single-crystal strip, it could be applied to strips which had a bamboo-type microstructure. This was because the current-crowding region was typically limited to a short distance from the cathode end. On the other hand, interfacial diffusion or grain-boundary diffusion predominated in a polycrystalline strip at low temperatures. The current-crowding effect still existed. Current-crowding at the anode was also expected to be different.

Effect of Current Crowding on Vacancy Diffusion and Void Formation in Electromigration. K.N.Tu, C.C.Yeh, C.Y.Liu, C.Chen: Applied Physics Letters, 2000, 76[8], 988-1000