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Statistical timing analysis using levelized covariance propagation considering systematic and random variations of process parameters

Published: 01 October 2006 Publication History

Abstract

Variability in process parameters is making accurate timing analysis of nano-scale integrated circuits an extremely challenging task. In this article, we propose a new algorithm for statistical static timing analysis (SSTA) using levelized covariance propagation (LCP). The algorithm simultaneously considers the effect of die-to-die variations in process parameters as well as within-die variation, including systematic and random variations. In order to efficiently handle complicated process variation models while contending with the arbitrary correlation among timing signals, we employ a compact form of the levelized statistical data structure. Furthermore, we propose two enhancements to the LCP algorithms to the make it practical for the analysis of large sized circuits. Results on several ISCAS'85 benchmark circuits in predictive 70nm technology show an average of 0.19% and 0.57% errors in the mean and standard deviation, respectively, of timing analysis using the proposed technique, as compared to the Monte Carlo-based approach.

References

[1]
Agarwal, A., Blaauw, D., Zolotov, V., Sundareswaran, S., Zhao, M., Gala, K., and Panda, R. 2002. Path-Based statistical timing analysis considering inter- and intra-die correlations. In Proceedings of the TAU Conference.
[2]
Agarwal, A., Zolotov, V., and Blaauw, D. 2003. Statistical timing analysis using bounds and selective enumeration. IEEE Trans. Comput. Aided Des. Integrated Circ. Syst. 22, 1243--1260.
[3]
Berkelaar, M. 1997. Statistical delay calculation, a linear time method. In Proceedings of the TAU Conference.
[4]
Berkeley. 1996. Predictive Technology Model. http://www-device.eecs.berkeley.edu/~ptm.
[5]
Borkar, S., Karnik, T., Narendra, S., Tschanz, J., Keshavarzi, A., and De, V. 2003. Parameter variations and impact on circuits and microarchitecture. In Proceedings of the Design Automation Conference. 338--342.
[6]
Bowman, K. A., Duvall, S. G., and Meindl, J. D. 2002. Impact of die-to-die and within-die parameter fluctuations on the maximum clock frequency distribution for gigascale integration. IEEE J. Solid-State Circ. 37, 2, 183--190.
[7]
Chang, E., Stine, B., Maung, T., Divecha, R., Boning, D., Chung, J., Chang, K., Ray, G., Bradbury, D., Nakagawa, O. S., Oh, S., and Bartelink, D. 1995. Using a statistical metrology framework to identify systematic and random sources of die- and wafer-level ILD thickness variation in CMP processes. In Proceedings of the International Electron Devices Meeting. 499--502.
[8]
Chang, H. and Sapatnekar, S. S. 2003. Statistical timing analysis considering spatial correlations using a single PERT-like traversal. In Proceedings of the International Conference on Computer-Aided Design (ICCAD). 621--625.
[9]
Clark, C. E. 1961. The Greatest of a Finite Set of Random Variable, vol. 9. Operations Research, 85--91.
[10]
Devgan, A. and Kashyap, C. 2003. Block-Based static timing analysis with uncertainty. In Proceedings of the International Conference on Computer-Aided Design (ICCAD). 607--614.
[11]
Gupta, P. and Heng, F. 2004. Toward a systematic-variation aware timing methodology. In Proceedings of the Design Automation Conference. 321--326.
[12]
Hitchcock, R. B. 1982. Timing verification and the timing analysis problem. In Proceedings of the ACM Design Automation Conference. 594--604.
[13]
Jess, J. A. G., Kalafala, K., Naidu, S. R., Otten, R. H. J. M., and Visweswariah, C. 2003. Statistical timing for parametric yield prediction of digital integrated circuits. In Proceedings of the Design Automation Conference. 932--937.
[14]
Jouppi, N. P. 1987. Timing analysis and performance improvement of MOS VLSI design. IEEE Trans. Comput. Aided Des. Integrated Circ. Syst. 6, 650--665.
[15]
Jyu, H. F., Malik, S., Devadas, S., and Keutzer, K. W. 1993. Statistical timing analysis of combinational logic circuits. IEEE Trans. VLSI Syst. 1, 126--137.
[16]
Le, J., Li, X., and Pileggi, L. T. 2004. STAC: Statistical timing analysis with correlation. In Proceedings of the Design Automation Conference. 343--348.
[17]
McWilliams, T. M. 1980. Verification of timing constraints on large digital systems. In Proceedings of the 17th Design Automation Conference. 139--147.
[18]
Nassif, S. R. 2001. Modeling and analysis of manufacturing variations. In Proceedings of the Custom Integrated Circuits Conference. 223--228.
[19]
Orshansky, M., Milor, L., Chen, P., Keutzer, K., and Hu, C. 1997. Intrinsic MOSFET parameter fluctuations due to random dopant placement. IEEE Trans. Comput. Aided Des. Integrated Circ. Syst. 5, 369--376.
[20]
Papoulis, A. 1991. Probability, Random Variables, and Stochastic Processes, 3rd Ed. McGraw-Hill, New York.
[21]
Rubinstein, R. Y. 1981. Simulation and the Monte Carlo Method. John Wiley and Sons, New York.
[22]
Sakurai, T. and Newton, R. 1991. Delay analysis of series-connected MOSFET circuits. IEEE J. Solid-State Circ., 122--131.
[23]
Tang, X., De, V., and Meindl, J. D. 1997. Intrinsic MOSFET parameter fluctuations due to random dopant placement. IEEE Trans. VLSI Syst. 5, 369--376.
[24]
Taur, Y. and Ning, T. H. 1998. Fundamentals of Modern VLSI Devices. Cambridge University Press, New York.
[25]
Visweswariah, C. 2003. Death, taxes and failing chips. In Proceedings of the Design Automation Conference. 343--347.
[26]
Visweswariah, C., Ravindran, K., Kalafala, K., Walker, S. G., and Narayan, S. 2004. First-Order incremental block-based statistical timing analysis. In Proceedings of the Design Automation Conference. 331--336.

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Published In

cover image ACM Transactions on Design Automation of Electronic Systems
ACM Transactions on Design Automation of Electronic Systems  Volume 11, Issue 4
October 2006
177 pages
ISSN:1084-4309
EISSN:1557-7309
DOI:10.1145/1179461
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Association for Computing Machinery

New York, NY, United States

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Publication History

Published: 01 October 2006
Published in TODAES Volume 11, Issue 4

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Author Tags

  1. Process variation
  2. spatial correlation
  3. statistical timing analysis

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  • (2016)Gate-level modelling of NBTI-induced delays under process variations2016 17th Latin-American Test Symposium (LATS)10.1109/LATW.2016.7483343(75-80)Online publication date: Apr-2016
  • (2015)Runtime Optimization of System Utility with Variable HardwareACM Transactions on Embedded Computing Systems10.1145/265633814:2(1-25)Online publication date: 17-Feb-2015
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