Stress That Counteracts Electromigration: Threshold Versus Kinetic Approach

Abstract

AbstractThe paper analyzes electromigration (EM) conditions and material properties that determine the maximum EM induced stress, σa, and stress gradient, ∇σ, which counteract EM flow in interconnects.The first systematic data on the drift velocity vs. stripe length, L, current density, j, and temperature are presented for Al lines. In contrast to the conventional approach to the Blech problem with σa taken to be a material constant (“yield strength”), the observations suggest that σa increases with j. The stress adjustment is shown to result from the imperative coupling of the net flux of material directed to the downwind end of the stripe with the flux of plastic flow (creep) responsible for stress relaxation. The effect of parameters of the constitutive equation assumed to describe the plastic flow kinetics, namely that of strain rate exponent, threshold stress, and creep, effective viscosity, on the stress cya is considered. To account for the creep viscosity, η, obtained unpassivated aluminum stripes from EM experiments, a model for the attachment-controlled Coble creep is suggested.