Statistical timing analysis using Kernel smoothing

Abstract

We have developed a new statistical timing analysis approach that does not impose any assumptions on the nature of manufacturing variability and takes into account an arbitrary model of spatial correlation as well as all types of functional correlations (e.g. reconvergence-based correlations). The starting point for statistical timing analysis is small scale Monte Carlo (MC) simulation. In order to speed-up the MC simulation process we use stratified balanced sampling and postprocessing of the simulation data using non-parametric kernel estimation. The MC simulation and the statistical analysis procedure are interleaved with the calculation of the critical paths. In order to speed up simulation, we identify and simulate only gates relevant for calculation of the clock cycle time. The application of statistical techniques enable not only accurate statistical timing analysis, but also stability and scalability analysis. The approach is evaluated using MCNC benchmarks and yields more than six orders of magnitude speed improvement compared with the standard MC simulation.