Article

A framework for statistical timing analysis using non-linear delay and slew models

Authors:

Sarvesh Bhardwaj,

Praveen Ghanta,

Sarma VrudhulaAuthors Info & Claims

ICCAD '06: Proceedings of the 2006 IEEE/ACM international conference on Computer-aided design

Pages 225 - 230

https://doi.org/10.1145/1233501.1233546

Published: 05 November 2006 Publication History

Abstract

In this paper we propose a framework for Statistical Static Timing Analysis (SSTA) considering intra-die process variations. Given a cell library, we propose an accurate method to characterize the gate and interconnect delay as well as slew as a function of underlying parameter variations. Using these accurate delay models, we propose a method to perform SSTA based on a quadratic delay and slew model. The method is based on efficient dimensionality reduction technique used for accurate computation of the max of two delay expansions. Our results indicate less than 4% error in the variance of the delay models compared to SPICE Monte Carlo and less than 1% error in the variance of the circuit delay compared to Monte Carlo simulations.

References

[1]

http://vlsicad.eecs.umich.edu/bk/pdtools/.

[2]

A. Agarwal, D. Blaauw, and V. Zolotov. Statistical timing analysis for intra-die process variations with spatial correlations. In Proc. of ICCAD, 2003.

Digital Library

[3]

V. Barthelmann, E. Novak, and K. Ritter. High dimensional polynomial interpolation on sparse grids. Advances in Comp. Math., pages 273--288, 2000.

[4]

S. Bhardwaj, S. Vrudhula, P. Ghanta, and Y. Cao. Modeling of intra-die process variations for accurate analysis and optimization of nano-scale circuits. In Proc. of IEEE/ACM Design Automation Conference, 2006.

Digital Library

[5]

H. Chang and S. Sapatnekar. Statistical timing analysis considering spatial correlations using a single pert-like traversal. In Proc. of ICCAD, 2003.

Digital Library

[6]

R. G. Ghanem and P. Spanos. Stochastic Finite Elements: A Spectral Approach. Springer-Verlag, 1991.

Digital Library

[7]

A. Keese and H. G. Matthies. Numerical methods and smolyak quadrature for nonlinear stochastic partial differential equations. Technical report, Institute of Scientific Computing, Brunswick, 2003.

[8]

M. Orshansky and K. Kuetzer. A General Probabilistic Framework for Worst Case Timing Analysis. In Proc. of DAC, 2002.

Digital Library

[9]

A. Papoulis. Probability, Random Variables and Stochastic Processes. McGraw-Hill, 3rd edition, 1991.

[10]

R. Rao, A. Devgan, D. Blaauw, and D. Sylvester. Parametric yield estimation considering leakage variability. In Proc. of DAC, 2004.

Digital Library

[11]

J. Singh and S. Sapatnekar. Statistical Timing Analysis with Correlated Non-Gaussian Parameters using Independent Component Analysis. In IEEE TAU Workshop, February 2006.

Digital Library

[12]

C. Visweswariah et al. First-order incremental Block-Based Statistical Timing Analysis. In IEEE/ACM Design Automation Conference, pages 331--336, 2004.

Digital Library

[13]

J. Wang, P. Ghanta, and S. Vrudhula. Stochastic Analysis of Interconnect Performance in the Presence of Process Variations. In Proc. of ICCAD, 2004.

Digital Library

[14]

Y. Zhan et al. Correlation-aware statistical timing analysis with non-gaussian delay distributions. In Proc. of ICCAD, Nov 2005.

Digital Library

[15]

L. Zhang, J. Shao, and C. C.-P. Chen. Non-Gaussian Statistical Parameter Modeling for SSTA with Confidence Interval Analysis. In International Symposium on Physical Design, 2006.

Digital Library

[16]

L. Zhang et al. Correlation-Preserved Non-Gaussian Statistical Timing Analysis with Quadratic Timing Model. In Proc. of DAC, 2005.

Digital Library

Cited By

Rao VSinha DSrimal NMaurya P(2016)Statistical path tracing in timing graphsProceedings of the 53rd Annual Design Automation Conference10.1145/2897937.2898096(1-6)Online publication date: 5-Jun-2016
https://dl.acm.org/doi/10.1145/2897937.2898096
Sinha DVisweswariah CVenkateswaran NXiong JZolotov VGroeneveld PSciuto DHassoun S(2012)Reversible statistical max/min operationProceedings of the 49th Annual Design Automation Conference10.1145/2228360.2228554(1067-1073)Online publication date: 3-Jun-2012
https://dl.acm.org/doi/10.1145/2228360.2228554
Zolotov VSinha DHemmett JForeman EVisweswariah CXiong JLeitzen JVenkateswaran NGroeneveld PSciuto DHassoun S(2012)Timing analysis with nonseparable statistical and deterministic variationsProceedings of the 49th Annual Design Automation Conference10.1145/2228360.2228553(1061-1066)Online publication date: 3-Jun-2012
https://dl.acm.org/doi/10.1145/2228360.2228553
Show More Cited By

Index Terms

A framework for statistical timing analysis using non-linear delay and slew models
1. Hardware
  1. Hardware validation
    1. Functional verification
      1. Simulation and emulation
  2. Integrated circuits
    1. Digital switches
      1. Logic families
    2. Interconnect

Recommendations

Practical variation-aware interconnect delay and slew analysis for statistical timing verification
ICCAD '06: Proceedings of the 2006 IEEE/ACM international conference on Computer-aided design

Interconnects constitute a dominant source of circuit delay for modern chip designs. The variations of critical dimensions in modern VLSI technologies lead to variability in interconnect performance that must be fully accounted for in timing ...
Fast variational interconnect delay and slew computation using quadratic models

Interconnects constitute a dominant source of circuit delay for modern chip designs. The variations of critical dimensions in modern VLSI technologies lead to variability in interconnect performance that must be fully accounted for in timing ...
Statistical timing analysis of coupled interconnects using quadratic delay-change characteristics

With continuing scaling of CMOS process, process variations in the form of die-to-die and within-die variations become significant which cause timing uncertainty. Statistical design methods have been proposed in the past to model the impact of process ...

Comments

Information & Contributors

Information

Published In

cover image ACM Conferences

ICCAD '06: Proceedings of the 2006 IEEE/ACM international conference on Computer-aided design

November 2006

147 pages

ISBN:1595933891

DOI:10.1145/1233501

General Chair:
Soha Hassoun
Tufts Univ., Medford, MA

Copyright © 2006 ACM.

Permission to make digital or hard copies of all or part of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. Copyrights for components of this work owned by others than ACM must be honored. Abstracting with credit is permitted. To copy otherwise, or republish, to post on servers or to redistribute to lists, requires prior specific permission and/or a fee. Request permissions from [email protected]

Sponsors

SIGDA: ACM Special Interest Group on Design Automation
IEEE-CAS: Circuits & Systems
IEEE-CS: Computer Society

Publisher

Association for Computing Machinery

New York, NY, United States

Publication History

Published: 05 November 2006

Permissions

Request permissions for this article.

Request Permissions

Check for updates

Qualifiers

Article

Conference

ICCAD06

Sponsor:

SIGDA
IEEE-CAS
IEEE-CS

ICCAD06: The International Conference on Computer-Aided Design 2006

November 5 - 9, 2006

California, San Jose

Acceptance Rates

Overall Acceptance Rate 457 of 1,762 submissions, 26%

Contributors

Other Metrics

View Article Metrics

Bibliometrics & Citations

Bibliometrics

Article Metrics

30
Total Citations
View Citations
256
Total Downloads

Downloads (Last 12 months)7
Downloads (Last 6 weeks)0

Reflects downloads up to 07 Mar 2025

Other Metrics

View Author Metrics

Citations

Cited By

Rao VSinha DSrimal NMaurya P(2016)Statistical path tracing in timing graphsProceedings of the 53rd Annual Design Automation Conference10.1145/2897937.2898096(1-6)Online publication date: 5-Jun-2016
https://dl.acm.org/doi/10.1145/2897937.2898096
Sinha DVisweswariah CVenkateswaran NXiong JZolotov VGroeneveld PSciuto DHassoun S(2012)Reversible statistical max/min operationProceedings of the 49th Annual Design Automation Conference10.1145/2228360.2228554(1067-1073)Online publication date: 3-Jun-2012
https://dl.acm.org/doi/10.1145/2228360.2228554
Zolotov VSinha DHemmett JForeman EVisweswariah CXiong JLeitzen JVenkateswaran NGroeneveld PSciuto DHassoun S(2012)Timing analysis with nonseparable statistical and deterministic variationsProceedings of the 49th Annual Design Automation Conference10.1145/2228360.2228553(1061-1066)Online publication date: 3-Jun-2012
https://dl.acm.org/doi/10.1145/2228360.2228553
Cheng LGong FXu WXiong JHe LSarrafzadeh M(2012)Fourier series approximation for max operation in non-Gaussian and quadratic statistical static timing analysisIEEE Transactions on Very Large Scale Integration (VLSI) Systems10.1109/TVLSI.2011.215784320:8(1383-1391)Online publication date: 1-Aug-2012
https://dl.acm.org/doi/10.1109/TVLSI.2011.2157843
Ni CRussell GBystrov A(2012)Statistical delay modelling of manufacturing process variations at system level10th IEEE International NEWCAS Conference10.1109/NEWCAS.2012.6328974(133-136)Online publication date: Jun-2012
https://doi.org/10.1109/NEWCAS.2012.6328974
Veetil VChopra KBlaauw DSylvester D(2011)Fast Statistical Static Timing Analysis Using Smart Monte Carlo TechniquesIEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems10.1109/TCAD.2011.210803030:6(852-865)Online publication date: 1-Jun-2011
https://dl.acm.org/doi/10.1109/TCAD.2011.2108030
Lotze NGöppert JManoli YDe Micheli GAl-Hashimi BMueller WMacii E(2010)Timing modeling for digital sub-threshold circuitsProceedings of the Conference on Design, Automation and Test in Europe10.5555/1870926.1870999(299-302)Online publication date: 8-Mar-2010
https://dl.acm.org/doi/10.5555/1870926.1870999
Lotze NGoppert JManoli Y(2010)Timing modeling for digital sub-threshold circuits2010 Design, Automation & Test in Europe Conference & Exhibition (DATE 2010)10.1109/DATE.2010.5457192(299-302)Online publication date: Mar-2010
https://doi.org/10.1109/DATE.2010.5457192
Cheng LGupta PHe LWakabayashi K(2009)Accounting for non-linear dependence using function driven component analysisProceedings of the 2009 Asia and South Pacific Design Automation Conference10.5555/1509633.1509747(474-479)Online publication date: 19-Jan-2009
https://dl.acm.org/doi/10.5555/1509633.1509747
Gong MZhou HTao JZeng XRoychowdhury J(2009)Binning optimization based on SSTA for transparently-latched circuitsProceedings of the 2009 International Conference on Computer-Aided Design10.1145/1687399.1687462(328-335)Online publication date: 2-Nov-2009
https://dl.acm.org/doi/10.1145/1687399.1687462
Show More Cited By

View Options

Login options

Check if you have access through your login credentials or your institution to get full access on this article.

Full Access

Get this Publication

View options

PDF

View or Download as a PDF file.

eReader

View online with eReader.

Figures

Tables

Media

View Table of Conten