Electromigration induced stress evolution under alternate current and pulse current loads

Abstract

Stress evolution in a metal line embedded in a rigid confinement caused by the arbitrary wave-form time-dependent current loads is resolved by a direct analytic solution of the one-dimensional (1-D) Korhonen's equation. Electromigration induced stress buildup and relaxation kinetics resulted by time-dependent current density are obtained as functions of the relevant physical parameters. A novel methodology for physics based conversion between the time-dependent and effective DC current densities is developed based on a condition of equal void nucleation times resulted by these currents. It is shown that in the case of high frequency currents, with periods much smaller than the characteristic time of stress evolution, the stress buildup is proportional to the pulse duty factor. It is demonstrated that very short metal lines with preexisted thermal voids loaded with symmetrical bi-directional currents can demonstrate a notable resistance increase when a specific temperature oscillation is generated in the line by active devices of the integrated circuit.