Postvoiding Stress Evolution in Confined Metal Lines

Electromigration (EM)-induced voiding is an important reliability concern in modern integrated circuits. Resistance degradation in interconnect metal lines caused by voiding was studied in this paper theoretically by solving the continuity equation describing the stress evolution caused by growing void. A rigid confinement surrounding a metal line makes inapplicable an approximation of the line edge drift for modeling the void volume evolution unless a line is in a stress-free equilibrium state caused by the presence of a saturated void. Derived analytical solution to the continuity equation with a voidless initial condition provides drastically different stress evolution kinetics in comparison with the case of the line edge drift model. It demonstrates that a large stress gradient, which was developed between the surface of a void precursor (flaw) and a metal, becomes a major driving force for the atom migration from the void surface to the metal. In this case, the initial evolution of the void volume does not depend on the electric current density contrary to the case of the line edge drift approximation characterized by the linear dependence of the void growth rate on the current density. At long time limit, the derived solution provides the same kinetics and the steady state with the stress linearly distributed along the line as in the case of preexisted void. The proposed model results much faster kinetics of the void growth and the line resistance degradation than the line edge drift approximation. Void nucleation time can be employed as a reasonable approximation of the EM-induced time to failure in the confined metal line.