Physically based models of electromigration

Interconnect lifetimes due to electromigration (EM) failures are traditionally described by a modified Black equation [1] equation (1) where t_f is the time to failure (TTF), A is a constant, j is the electrical current density, n is a fitting parameter which describes the impact of the current density, E_a is the fitted activation energy representing the failure mechanism, k is Boltzmann´s constant, and T is the temperature. Originally, Black´s derivation resulted in n = 2 [1]. However, this was the source of an extensive debate [2], until more physically sound models showed that n = 2 is associated with a failure dominated by the void nucleation time [3], while n = 1 implies a failure dominated by the void growth time [4].