Computation of bus current variance for reliability estimation of VLSI circuits

Abstract
This paper deals with the estimation of the median time-to-failure (MTF) due to elec-tromigration in the power and ground busses of CMOS VLSI circuits. In our previous work [3, 4], we presented a novel technique for MTF estimation based on a stochastic cur-rent waveform model. In [6], we argued that including the variance waveform of the current, in addition to its expected waveform derived in [3, 4], would further improve the accuracy of the MTF estimate. In this paper, we present a novel technique for deriving the variance waveform for CMOS circuits. Using this technique, we establish the importance of the vari-ance waveform by showing that its contribution to the MTF estimate can be in the range of 100% to 200% relative to that of the expected waveform. The technique has been built into the probabilistic simulator CREST [3, 4], and has shown good agreement with SPICE, as well as excellent speedup.

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