Self-consistent solutions for allowed interconnect current density. II. Application to design guidelines

We apply the newly developed approach for obtaining self-consistent solutions of the maximum allowed interconnect peak current density as a function of duty cycle, which simultaneously comprehends both electromigration and Joule heating. We demonstrate how to generalize this approach for arbitrary time-varying current density waveforms by introducing an effective duty cycle. We find that bipolar stressing is not always more optimistic than unipolar stressing, depending on the duty cycle. We illustrate worst-case intralevel interactions for multiple leads in a single-level metal system, and show that an effective duty cycle which depends on individual width ratios and duty cycles can be used to determine these worst-case solutions. We also study interlevel interactions in a multilevel metal system. Intralevel and interlevel interactions can cause marked reduction in the maximum allowed peak current density in a lead compared to an equivalent isolated lead, most strongly when its duty cycle is large and the duty cycles of the other interacting leads are small. Complexities due to waveshapes and interactions as described here, coupled with the complexities of real circuit layout and operation, motivate the need for sophisticated circuit simulators which can accurately determine electromigration reliability while self-consistently comprehending Joule heating.