LVFGen: Efficient Liberty Variation Format (LVF) generation using variational analysis and active learning

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.