SELF-CONSISTENT SOLUTIONS FOR ALLOWED INTERCONNECT CURRENT-DENSITY .2. APPLICATION TO DESIGN GUIDELINES

We apply the newly developed approach for obtaining self-consistent so lutions of the maximum allowed interconnect peak current density as a function of duty cycle, which simultaneously comprehend both electromi gration and Joule heating. We demonstrate how to generalize this appro ach for arbitrary time-varying current density waveforms by introducin g an effective duty cycle. We find that bipolar stressing is not alway s 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 t o determine these worst-case solutions, We also study interlevel inter actions in a multilevel metal system. Intralevel and interlevel intera ctions can cause marked reduction in the maximum allowed peak current density in a lead compared to an equivalent isolated lead, most strong ly when its duty cycle is large and the duty cycles of the other inter acting leads are small. Complexities due to waveshapes and interaction s as described here, coupled with the complexities of real circuit lay out and operation, motivate the need for sophisticated circuit simulat ors which can accurately determine electromigration reliability while self-consistently comprehending JouIe heating.