LVF2: A Statistical Timing Model based on Gaussian Mixture for Yield Estimation and Speed Binning

As transistor size continues to scale down, process variation has become an essential factor determining semiconductor yield and economic return. The Liberty Variation Format (LVF) is the current industrial standard that expresses statistical timing behaviors based on single Gaussian model. However, it loses accuracy when the timing distribution is non-Gaussian due to growing process variations. This paper proposes a novel LVF² distribution model that combines two weighted skewed-normal (SN) distributions, which better captures the multi-Gaussian timing distribution while maintaining backward compatibility with LVF. Experiments using TSMC 22nm standard cells show that, compared to LVF, LVF² reduces binning error by 7.74X in delay and 9.56X in transition time, and reduces 3σ-yield error by 4.79X and 7.18X in delay and transition time, respectively. The error reduction for path delay is diminished due to Central Limit Theorem (CLT). But it is still 2X for a typical circuit path with 8 Fanout-of-4 (FO4) inverter delays.