Simulation of electromigration failure by variable resistance model

Abstract

The electromigration failure in a thin metallic conductor has been simulated by the temporal resistance change. This change is related to the crack propagation on both sides of the conductor. The geometrical change affects the two-dimensional electric field distribution, which in turn influences the two-dimensional current density distribution in the conductor. The two-dimensional electric field and current density maps can be realized by solving the Laplace equation. By integrating the power density over the entire conductor, the resistance change due to the crack development can be obtained. On the other hand, the development of the crack is attributed to the accumulation of vacancies over the cross section of the conductor. We assume that the crack length is proportional to the excess vacancies over the cross section. From the one-dimensional diffusion-drift equation, we obtained the temporal growth of crack length. The temporal resistance change can thus be simulated. The effects of vacancy diffusion, and field-induced drift on the crack-growth kinetics have been demonstrated.