Electromigration median time-to-failure based on a stochastic current waveform

The estimation of the median time-to-failure (MTF) due to electromigration in the power and ground buses of VLSI circuits is addressed. In their previous work (Proc. 25th ACM/IEEE Design Autom. Conf., p.294-9, 1988), the authors presented a novel technique for MTF estimation based on a stochastic current waveform model. They derived the mean (or expected) waveform (not a time average) of such a current model and conjectured that it is the appropriate current waveform to be used for MTF estimation. The authors prove that conjecture and present new theoretical results which show the exact relationship between the MTF and the statistics of the stochastic current. This leads to a more accurate technique for deriving the MTF which requires the variance waveform of the current, in addition to its mean waveform. The authors then show how the variances of the bus branch currents can be derived from those of the gate currents, and describe several simplifying approximations that can be used to maintain efficiency and, therefore, make possible the analysis of VLSI circuits