Self-consistent solutions for allowed interconnect current density. I. Implications for technology evolution

We comprehend both interconnect electromigration and Joule heating to study for the first time the self-consistent solutions for the maximum allowed interconnect peak current density j_peak as a function of wave shape. The maximum allowed temperature and j_peak solutions monotonically increase as the duty cycle r decreases. Self-consistent solutions indicate that there are diminishing returns in the usefulness of increasing the electromigration capability of the interconnect system. While the greatest increase in allowed j_peak occurs at de stress (r=1), the increases becomes less as r is reduced below 1, and becomes negligible for r<0.01. Further increases in j_peak will have to come at some future time from technology options which lower the temperatures at which the interconnects operates