Accurate setup/hold time characterization is crucial for modern chip timing closure, but its reliance on potentially millions of SPICE simulations across diverse process-voltage-temperature (PVT) corners creates a major bottleneck, often lasting weeks or months. Existing methods suffer from slow search convergence and inefficient exploration, especially in the multi-corner setting. We introduce SetupKit, a novel framework designed to break this bottleneck using statistical intelligence, circuit analysis and active learning (AL). SetupKit integrates three key innovations: BEIRA, a bias-enhanced interpolation search derived from statistical error modeling to accelerate convergence by overcoming stagnation issues, initial search interval estimation by circuit analysis and AL strategy using Gaussian Process. This AL component intelligently learns PVT-timing correlations, actively guiding the expensive simulations to the most informative corners, thus minimizing redundancy in multi-corner characterization. Evaluated on industrial 22nm standard cells across 16 PVT corners, SetupKit demonstrates a significant 2.4× overall CPU time reduction (from 720 to 290 days on a single core) compared to standard practices, drastically cutting characterization time. SetupKit offers a principled, learning-based approach to library characterization, addressing a critical EDA challenge and paving the way for more intelligent simulation management.

As transistor dimensions shrink, process variations significantly impact circuit performance, signifying the need for accurate statistical circuit analysis. In digital circuit timing analysis, the Liberty Variation Format (LVF) has emerged as an industrial leading representation of timing distributions in cell libraries at 22 nm and below. However, LVF characterization relies on the Monte Carlo (MC) method, which requires excessive SPICE simulations of cells with process variations. Similar challenges also exist for uncertainty propagation and quantification in chip manufacturing and the broader scientific communities. To resolve this foundational challenge, this paper presents LVFGen, a novel method that reduces the simulation costs of MC while generate high-accuracy LVF library. LVFGen utilizes an active learning strategy based on variational analysis to identify process variation samples that impact timing distributions more significantly. Compared to the state-of-the-art Quasi-MC method, LVFGen demonstrates an overall 2.27× speedup in LVF library generation within an accuracy level of 5k-sample MC and a 4.06× speedup within a 100k-sample MC accuracy.

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.