Statistical estimation of leakage-induced power grid voltage drop considering within-die process variations

Transistor threshold voltages (V_th) have been reduced as part of on-going technology scaling. The smaller V_th values feature increased fluctuations due to process variations, with a strong within-die component. Correspondingly, given the exponential dependence of leakage on V_th, circuit leakage currents are increasing significantly and have strong within-die statistical variations. With these currents loading the power grid, the grid develops large voltage drops, which is an unavoidable background level of noise on the grid. We develop techniques for estimation of the statistics of the leakage-induced power grid voltage drop based on given statistics of the circuit leakage currents.