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Computational performance optimisation for statistical analysis of the effect of nano-CMOS variability on integrated circuits

Published: 01 January 2013 Publication History

Abstract

The intrinsic variability of nanoscale VLSI technology must be taken into account when analyzing circuit designs to predict likely yield. Monte-Carlo- (MC-) and quasi-MC- (QMC-) based statistical techniques do this by analysing many randomised or quasirandomised copies of circuits. The randomisation must model forms of variability that occur in nano-CMOS technology, including "atomistic" effects without intradie correlation and effects with intradie correlation between neighbouring devices. A major problem is the computational cost of carrying out sufficient analyses to produce statistically reliable results. The use of principal components analysis, behavioural modeling, and an implementation of "Statistical Blockade" (SB) is shown to be capable of achieving significant reduction in the computational costs. A computation time reduction of 98.7% was achieved for a commonly used asynchronous circuit element. Replacing MC by QMC analysis can achieve further computation reduction, and this is illustrated for more complex circuits, with the results being compared with those of transistor-level simulations. The "yield prediction" analysis of SRAM arrays is taken as a case study, where the arrays contain up to 1536 transistors modelled using parameters appropriate to 35 nm technology. It is reported that savings of up to 99.85% in computation time were obtained.

References

[1]
H. Onodera, "Variability: modeling and its impact on design," IEICE Transactions on Electronics, vol. E89-C, no. 3, pp. 342- 348, 2006.
[2]
A. Asenov, A. R. Brown, J. H. Davies, S. Kaya, and G. Slavcheva, "Simulation of intrinsic parameter fluctuations in decananometer and nanometer-scale MOSFETs," IEEE Transactions on Electron Devices, vol. 50, no. 9, pp. 1837-1852, 2003.
[3]
G. Roy, A. R. Brown, F. Adamu-Lema, S. Roy, and A. Asenov, "Simulation study of individual and combined sources of intrinsic parameter fluctuations in conventional nano-MOSFETs," IEEE Transactions on Electron Devices, vol. 53, no. 12, pp. 3063- 3069, 2006.
[4]
A. Srivastava, D. Sylvester, and D. Blaauw, Statistical Analysis and Optimization for VLSI: Timing and Power, Springer, Berlin, Germany, 2005.
[5]
B. Hargreaves, H. Hult, and S. Reda, "Within-die process variations: How accurately can they be statistically modeled?" in Proceedings of Asia and South Pacific Design Automation Conference (ASP-DAC '08), pp. 524-530, March 2008.
[6]
A. Singhee and R. A. Rutenbar, "Statistical blockade: a novel method for very fast Monte Carlo simulation of rare circuit events, and its application," in Proceedings of Design, Automation and Test in Europe Conference and Exhibition, pp. 1379- 1384, April 2007.
[7]
A. Singhee, J. Wang, B. H. Calhoun, and R. A. Rutenbar, "Recursive statistical blockade: an enhanced technique for rare event simulation with application to SRAM circuit design," in Proceedings of the 21st International Conference on VLSI Design, pp. 131-136, January 2008.
[8]
Z. Xie, Computation reduction for statistical analysis of the effect of nano-CMOS variability on integrated circuits [Ph. D. thesis], The University of Manchester, Manchester, UK, 2012.
[9]
Z. Xie and D. Edwards, "Computation reduction for statistical analysis of the effect of nano-CMOS variability on asynchronous circuits," in Proceedings of the 13th IEEE International Symposium on Design and Diagnostics of Electronic Circuits and Systems (DDECS '10), pp. 161-166, Vienna, Austria, April 2010.
[10]
E. J. Gumbel, Statistical Theory of Extreme Values and Some Practical Applications, vol. 33 of Applied Mathematical, US Department of Commerce, National Bureau of Standards, Washington, DC, USA, 1954.
[11]
D. Thain, T. Tannenbaun, and M. Livny, "Distributed computing in practice: the condor experience," Concurrency and Computation, vol. 17, no. 2-4, pp. 323-356, 2005.
[12]
"High Throughput Computing Using Condor at Manchester," October 2011, http://condor.eps.manchester.ac.uk/.
[13]
N. Metropolis and S. Ulam, "The Monte Carlo method," Journal of the American Statistical Association, vol. 44, no. 247, pp. 335- 341, 1949.
[14]
"NGSPICE release 23," June 2011, http://www.sourceforge.net,.
[15]
G. Peter Lepage, "A new algorithm for adaptive multidimensional integration," Journal of Computational Physics, vol. 27,no. 2, pp. 192-203, 1978.
[16]
H. Niederreiter, " Random Number Generation and Quasi-Monte Carlo Methods, vol. 63 of Regional Conference Series in Applied Mathematics, SIAM, Philadelphia, Pa, USA, 1992.
[17]
R. Bellman, Adaptive Control Processes: A Guided Tour, Princeton University Press, Princeton, NJ, USA, 1961.
[18]
C. Lemieux, Monte Carlo and Quasi-Monte Carlo Sampling, Springer Series in Statistics, Springer, New York, NY, USA, 2009.
[19]
H. Niederreiter, "Quasi-Monte Carlo methods and pseudorandom numbers," Bulletin of the American Mathematical Society, 1978.
[20]
S. K. Chaudhary, Acceleration of Monte Carlo methods using low discrepancy sequences [Ph. D. thesis], UCLA, Los Angeles, Calif, USA, 2004.
[21]
D. I. Asotsky, E. E. Myshetskaya, and I. M. Sobol', "The average dimension of a multidimensional function for quasi-Monte Carlo estimates of an integral," Computational Mathematics and Mathematical Physics, vol. 46, no. 12, pp. 2061-2067, 2006.
[22]
A. B. Owen, "Scrambled net variance for integrals of smooth functions," Annals of Statistics, vol. 25, no. 4, pp. 1541-1562, 1997.
[23]
W. H. Press and G. R. Farrar, "Recursive stratified sampling for multidimensional Monte Carlo integration," Computers in Physics, vol. 4, pp. 190-195, 1990.
[24]
R. Schürer, "Adaptive Quasi-Monte Carlo integration based on MISER and VEGAS," in Monte Carlo and Quasi-Monte Carlo Methods, pp. 393-406, Springer, Berlin, Germany, 2002.
[25]
G. P. Lepage, "A new algorithm for adaptive multidimensional integration," Journal of Computational Physics, vol. 27, pp. 192- 203, 1978.
[26]
G. P. Lepage, "VEGAS: an adaptive multi-dimensional integration program," Cornell preprint CLNS 80-447, March 1980.
[27]
J. Keiner and U. Waterhouse, "Fast principal components analysis method for finance problems with unequal time steps," in Monte Carlo and Quasi-Monte Carlo Methods 2008, P. L'Ecuyer and A. B. Owen, Eds., Springer, New York, NY, USA, 2010.
[28]
"RandomSPICE"[email protected] http://www.GoldStandardSimulations.com/services/circuitsimulation/random-spice/, 2013.
[29]
B. Bindu, B. Cheng, G. Roy, X. Wang, S. Roy, and A. Asenov, "Parameter set and data sampling strategy for accurate yet efficient statistical MOSFET compact model extraction," Solid-State Electronics, vol. 54, no. 3, pp. 307-315, 2010.
[30]
HSPICE User Guide: Simulation and Analysis, Version A-2007, Synopsys, Mountain View, Calif, USA, 2007.
[31]
J. P. Fishburn and A. E. Dunlop, "TILOS: a polynomial programming approach to transistor sizing," in Proceedings of IEEE International Conference on Computer-Aided Design (ICCAD '85), pp. 326-328, November 1985.
[32]
D. P. Marple and A. El Gamal, "Optimal selection of transistor sizes in digital VLSI," in Proceedings of the Stanford Conference on Advanced Research in VLSI, pp. 151-172, MIT Press, 1987.
[33]
W. Obermeier, An open architecture for improving VLSI circuit performance [Ph. D. thesis], University of California, Berkekey, Calif, USA, 1989.
[34]
S. M. Burns, Performance analysis and optimization of Asynchronous Circuits [Ph. D. thesis], California Institute of Technology, Pasadena, Calif, USA, 1990.
[35]
G. Mekhtarian, Composite Current Source (CCS) Modeling Technology Backgrounder, Synopsys, Mountain View, Calif, USA, 2005,. 11/05. KF. WO.05-13816.
[36]
R. Goyal and N. Kumar, Current Based Delay Models: A Must for Nanometer Timing, Cadence Design Systems, Noida, India, 2005.
[37]
Synopsys, "Liberty Library Modeling," July 2012, http://www.synopsys.com/community/interoperability/pages/libertylibmodel.aspx.
[38]
J. F. Croix and D. F. Wong, "Blade and Razor: cell and interconnect delay analysis using current-based models," in Proceedings of the 40th Design Automation Conference, pp. 386- 389, June 2003.
[39]
J. Li, H. Zhao, and H.-Y. Chiu, "Accuracy Timing Models for Integrated Circuit Verification," U. S. patent number 6721929, April 2004.
[40]
D. Dasx, W. Scotty, S. Nazariany, and H. Zhoux, "An efficient current-based logic cell model for crosstalk delay analysis," in Proceedings of the 10th International Symposium on Quality Electronic Design (ISQED '09), pp. 627-633, March 2009.
[41]
M. Rewieýski and J. White, "A trajectory piecewise-linear approach to model order reduction and fast simulation of nonlinear circuits and micromachined devices," IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems, vol. 22, no. 2, pp. 155-170, 2003.
[42]
P. Li, Z. Feng, and E. Acar, "Characterizing multistage nonlinear drivers and variability for accurate timing and noise analysis," IEEE Transactions on Very Large Scale Integration (VLSI) Systems, vol. 15, no. 11, pp. 1205-1214, 2007.
[43]
C. Visweswariah, K. Ravindran, K. Kalafala et al., "Firstorder incremental block-based statistical timing analysis," IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems, vol. 25, no. 10, pp. 2170-2179, 2006.
[44]
S. I. Resnick, Extreme Values, Regular Variation and Point Processes, Springer, New York, Ny, USA, 1987.
[45]
D. Edwards, A. Bardsley, L. Janin, and W. Toms, Balsa: A Tutorial Guide, School of Computer Science, University of Manchester, Manchester, UK, 2008, http://apt.cs.man.ac.uk/projects/tools/balsa/.
[46]
J. Sparsø and S. Furber, Principles of Asynchronous Circuit Design, Kluwer Academic Publishers, Norwell, Mass, USA, 2005.
[47]
A. Singhee, Novel Algorithms for Fast Statistical Analysis of Scaled Circuits [Ph. D. thesis], Carnegie Mellon University, Pittsburgh, Pa, USA, 2007.
[48]
R. E. Caflisch, "Monte Carlo and quasi-Monte Carlo methods," Acta Numerica, vol. 7, pp. 1-49, 1998.
[49]
L. Kuipers and H. Niederreiter, Uniform Distribution of Sequences, Dover Publications, Dover, UK, 2005.
[50]
J. Spanier, "Quasi-Monte Carlo methods for particle transport problems," in Monte Carlo and Quasi-Monte Carlo Methods in Scientific Computing, H. Niederreiter and P. J. -S. Shiue, Eds., pp. 121-148, Springer, New York, NY, USA, 1995.
[51]
E. J. Gumbel, "Statistical Theory of Extreme Values and Some Practical Applications", vol. 33 of Applied Mathematical, Series, US Department of Commerce, National Bureau of Standards, Washington, DC, USA, 1954.
  1. Computational performance optimisation for statistical analysis of the effect of nano-CMOS variability on integrated circuits

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      cover image VLSI Design
      VLSI Design  Volume 2013, Issue
      January 2013
      228 pages
      ISSN:1065-514X
      EISSN:1563-5171
      Issue’s Table of Contents

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      Hindawi Limited

      London, United Kingdom

      Publication History

      Accepted: 15 May 2013
      Revised: 15 May 2013
      Published: 01 January 2013
      Received: 16 November 2012

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