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

Published: 07 November 2024 Publication History

Abstract

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.

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            cover image ACM Conferences
            DAC '24: Proceedings of the 61st ACM/IEEE Design Automation Conference
            June 2024
            2159 pages
            ISBN:9798400706011
            DOI:10.1145/3649329
            This work is licensed under a Creative Commons Attribution International 4.0 License.

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            Published: 07 November 2024

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            Author Tags

            1. speed binning
            2. yield estimation
            3. statistical timing modeling
            4. process variation
            5. LVF

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            June 23 - 27, 2024
            CA, San Francisco, USA

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