Statistical Verification of Power Grids Considering Process-Induced Leakage Current Variations

Transistor threshold voltages (V{th}) have been reduced as partof on-going technology scaling. The smaller V{th} values featureincreased variations due to underlying process variations, witha strong within-die component. Correspondingly, given the exponential dependence of leakage on V{th}, circuit leakage currentsare increasing significantly and have strong within-die statistical variations.With these leakage currents loading the powergrid, the grid develops correspondingly large statistical voltagedrops. This leakage-induced voltage drop is an unavoidable background level of noise on the grid. Any additional non-leakagecurrents due to circuit activity will lead to voltage drop which isto be added to this background noise. We propose a techniquefor checking whether the statistical voltage drop on every node iswithin user-specified bounds, given user-specified statistics of theleakage currents.