Estimation of signal arrival times in the presence of delay noise

Delay due to capacitive coupling of interconnects has become an important reliability issue in the design of nanometer circuits. In this paper we present a probabilistic approach towards analyzing the impact of capacitive coupling noise on signal delay. The variation in the delay is due to the variation in the relative arrival times of the aggressors and the victim. We derive expressions for the moments of the victim voltage in the presence of noise. From these we compute estimates of the earliest and latest possible arrival times of the victim. We compare the analytical results with Monte Carlo simulations using SPICE. Even though the analytical calculations are 200 times faster than the Monte Carlo simulations, the differences in the estimates of the mean and standard deviation of the arrival time is no more than 2.8%. In addition, the width of the timing intervals using the proposed approach is reduced by as much as 48% with a confidence level of 0.984. That is 98.4% of the Monte Carlo simulations result in an arrival time that falls within the derived interval which is 48% shorter.