A Variable Current Exponent Model for Electromigration Lifetime Relaxation in Short Cu Interconnects

The short length effect on the electromigration (EM) lifetime is a valuable resource to increase current limits in advanced circuits. We model the effect with variable (current density j sensitive) current exponent n for short leads and calculate how much lifetime margin should be observed for a certain EM rule relaxation. The shorter leads have larger (variable) n so that the EM lifetime decreases faster as the current density increases. We utilize an empirical relationship for the dependence of n on j, which includes a parameter n_BS for short leads. We find that to achieve a 2times EM rule relaxation, we must confirm > 25times EM lifetime for n_BS = 3 and > 125times for n_BS = 5. We illustrate an empirical approach for determining n_BS