Statistical delay computation considering spatial correlations

• Published in: Proceedings of the 2003 Asia and South Pacific Design Automation Conference pp. 271 - 276
• Main Authors: Agarwal, Aseem, Blaauw, David, Zolotov, Vladimir, Sundareswaran, Savithri, Zhao, Min, Gala, Kaushik, Panda, Rajendran
• Format: Conference Proceeding
• Language: English
• Published: New York, NY, USA ACM 21.01.2003
• Series: ACM Conferences
• Subjects: Mathematics of computing; Mathematics of computing > Probability and statistics; Mathematics of computing > Probability and statistics > Probabilistic reasoning algorithms; Mathematics of computing > Probability and statistics > Probabilistic reasoning algorithms > Markov-chain Monte Carlo methods
• ISBN: 0780376609; 9780780376601
• DOI: 10.1145/1119772.1119825

Process variation has become a significant concern for static timing analysis. In this paper, we present a new method for path-based statistical timing analysis. We first propose a method for modeling inter- and intra-die device length variations. Based on this model, we then present an efficient method for computing the total path delay probability distribution using a combination of device length enumeration for inter-die variation and an analytical approach for intra-die variation. We also propose a simple and effective model of spatial correlation of intra-die device length variation. The analysis is then extended to include spatial correlation. We test the proposed methods on paths from an industrial high-performance microprocessor and present comparisons with traditional path analysis which does not distinguish between inter- and intra-die variations. The characteristics of the device length distributions were obtained from measured data of 8 test chips with a total of 17688 device length measurements. Spatial correlation data was also obtained from these measurements. We demonstrate the accuracy of the proposed approach by comparing our results with Monte-Carlo simulation.