Black’s Law in Light of Low Frequency Pulsed Power Electromigration

The microelectronics industry continues to be plagued by pervasive electromigration (EM) failures at advanced node conductors. The continuous scaling coupled with higher operating current densities further accentuate the problem. EM testing with Pulsed Direct Current (PDC) show interesting results with how the current induced stress gradient evolves in absence of the electromigration driving force. It is well known that the current induced stress acts opposite to electromigration driving force, but that is not always the case. During the nucleation phase of the EM failure, the current induced stress gradient does act opposite to EM force but once the void is nucleated, stress gradient switches direction and acts in the direction of EM force causing damage even when the current is turned off.In such a scenario, Black’s law with a constant value of current density exponent can show errors while calculating the lifetime of devices under test. What can be of great interest is to see if this variation in the value of n is observed at different duty cycles of a pulsed current. And if yes, how disparate are the results from a conventional power law that is used for lifetime extrapolations for EM failure. A study of the current density exponent is therefore conducted as a function of duty cycle at accelerated test conditions. It was observed that in addition to the extended lifetime at lower duty cycles there was a gradual change in the value of the current density exponent as we went from lower duty cycles to direct current stress.