Statistical Timing Analysis using Weibull Waveform Modeling

Timing analysis is crucial for the design of integrated circuits. Downscaling to sub-micron regions results in higher influence of process variations which leads to overly pessimistic timing when using worst-case analysis. Therefore the process parameters need to be considered as random variables. This allows to perform statistical timing analysis. Existing approaches propagate arrival times through the circuit to obtain a distribution of the arrival time at the output. Experiments on industrial circuits showed insufficient accuracy when confining the analysis to the arrival time only. Thus a more sophisticated method is proposed, which uses a waveform model based on the Weibull function and analog simulations on transistor level to propagate the waveform parameters through the circuit. This enables the consideration of slope and load variations. The aim of this approach is a reference tool, similar in accuracy to Monte Carlo simulation on transistor level to evaluate simpler approaches when Monte Carlo simulation of the entire circuit is infeasible. Thus it can be accepted that the computational effort.