Compact modeling of variational waveforms

In ultra-deep sub-micron technologies, modeling waveform shapes correctly is essential for accurate timing and noise analysis. Due to process and environmental variations, there is a need for a variational waveform model that is compact, efficient and accurate. The model should capture correlations due to common dependence on process parameters. This paper proposes a waveform model derived from basic transformations of a nominal waveform in the absence of variations. The transformations are parameterized by variational quantities that capture the sensitivity of the waveform to process parameters. The resulting waveform model works well with current-source models for static timing analysis. Numerical results are presented to demonstrate the accuracy of the model both in capturing variational waveforms and in propagating waveforms through logic gates.