Probabilistic analysis of interconnect coupling noise

Noise simulators and noise avoidance tools are playing an increasingly critical role in the design of deep submicron circuits. However, noise estimates produced by these simulators are often very pessimistic. For large, high-performance industrial ICs, which can contain hundreds of thousands of nets, the worst case estimates of the noise results in thousands of reported violations, without any information about the likelihood of the possible noise violation. In this paper, we present a probabilistic approach to prioritize the violating nets based on the likelihood of occurrence of the reported noise. We derive an upper bound on the probability that the total noise injected on a given victim net by a specific set of aggressors exceeds a threshold. This is equivalent to a lower bound on the expected number of clock cycles required to realize the noise violation for the first time, i.e., mean time-to-failure. If the probability of a failure in a victim is sufficiently small, it is possible that even during the operation of the part for a number of years, the probability of failure on the net is negligible and the net can be assigned a lower priority for the application of noise avoidance strategies. We demonstrate the utility of this approach through experiments carried out on an large industrial processor design using a state-of-the-art industrial noise analysis tool.