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Finite element analysis of the effects of geometry and microstructure on electromigration in confined metal lines Stress evolution due to electromigration in confined metal lines Probability distributions are evaluated for electromigration induced open failures in narrow, passivated interconnects with a near-bamboo grain structure. Void formation is initiated at the cathode ends of the polycrystalline line segments or "grain clusters." If these clusters are longer than a critical size L,, they can accommodate enough atoms for voids to reach the critical size to fail the line. Obviously, the critical size L, depends on the thermal stress: a cluster under a tensile stress is able to incorporate more atoms from the void than an unstressed cluster. In the case the clusters are shorter than L,, atoms from the voids must be distributed also to bamboo sections, outside the clusters, in order for the voids to induce open failures. Based on this physical picture, failure probabilities are evaluated as a function of time. The-predicted failure distributions and parametric dependencies compare well-with the experiments. 4995

Stress-voiding and electromigration have become urgent reliability concerns at the decrease of interconnect dimensions to submicron size. Severe stress voiding may arise in multilevel metallizations, particularly at contact and via regimes where the thermal stresses are highest. Via and contact structures with the attached refractory layers usually block entirely the electromigration flux; hence, EM voids are likely to form here. In this paper we first model the migration of atoms due to gradients in composition, stress, and electric potential. We seek a formulation in the spirit of irreversible thermodynamics, i.e. without reference to any specific micromechanisms of diffusion. We then apply the general developments to predict the stress evolution and void growth in Al based interconnect lines confined between entirely blocking Wstuds. We also analyze the effects of Cu depletion at vias, either by interfacial or grain boundary diffusion, on the stress evolution and void growth. Finally we demonstrate that the change in the line resistance due to void growth will display apparent incubation times even if the void grows linearly with time.