Hypersphere Sampling for Accelerating High-Dimension and Low-Failure Probability Circuit-Yield Analysis

Shiho HAGIWARA; Takanori DATE; Kazuya MASU; Takashi SATO

doi:10.1587/transele.E97.C.280

Hypersphere Sampling for Accelerating High-Dimension and Low-Failure Probability Circuit-Yield Analysis

Shiho HAGIWARA, Takanori DATE, Kazuya MASU, Takashi SATO

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This paper proposes a novel and an efficient method termed hypersphere sampling to estimate the circuit yield of low-failure probability with a large number of variable sources. Importance sampling using a mean-shift Gaussian mixture distribution as an alternative distribution is used for yield estimation. Further, the proposed method is used to determine the shift locations of the Gaussian distributions. This method involves the bisection of cones whose bases are part of the hyperspheres, in order to locate probabilistically important regions of failure; the determination of these regions accelerates the convergence speed of importance sampling. Clustering of the failure samples determines the required number of Gaussian distributions. Successful static random access memory (SRAM) yield estimations of 6- to 24-dimensional problems are presented. The number of Monte Carlo trials has been reduced by 2-5 orders of magnitude as compared to conventional Monte Carlo simulation methods.

Publication: IEICE TRANSACTIONS on Electronics Vol.E97-C No.4 pp.280-288

Publication Date: 2014/04/01

Publicized

Online ISSN: 1745-1353

DOI: 10.1587/transele.E97.C.280

Type of Manuscript: Special Section PAPER (Special Section on Solid-State Circuit Design,---,Architecture, Circuit, Device and Design Methodology)

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Authors

Shiho HAGIWARA
  Tokyo Institute of Technology
Takanori DATE
  Tokyo Institute of Technology
Kazuya MASU
  Tokyo Institute of Technology
Takashi SATO
  Kyoto University

Keyword

design for manufacturing, Monte Carlo method, importance sampling, SRAM, process variation, yield, norm minimization, Gaussian mixture models, clustering, hypersphere sampling

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Shiho HAGIWARA, Takanori DATE, Kazuya MASU, Takashi SATO, "Hypersphere Sampling for Accelerating High-Dimension and Low-Failure Probability Circuit-Yield Analysis" in IEICE TRANSACTIONS on Electronics, vol. E97-C, no. 4, pp. 280-288, April 2014, doi: 10.1587/transele.E97.C.280.
Abstract: This paper proposes a novel and an efficient method termed hypersphere sampling to estimate the circuit yield of low-failure probability with a large number of variable sources. Importance sampling using a mean-shift Gaussian mixture distribution as an alternative distribution is used for yield estimation. Further, the proposed method is used to determine the shift locations of the Gaussian distributions. This method involves the bisection of cones whose bases are part of the hyperspheres, in order to locate probabilistically important regions of failure; the determination of these regions accelerates the convergence speed of importance sampling. Clustering of the failure samples determines the required number of Gaussian distributions. Successful static random access memory (SRAM) yield estimations of 6- to 24-dimensional problems are presented. The number of Monte Carlo trials has been reduced by 2-5 orders of magnitude as compared to conventional Monte Carlo simulation methods.
URL: https://globals.ieice.org/en_transactions/electronics/10.1587/transele.E97.C.280/_p

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@ARTICLE{e97-c_4_280,
author={Shiho HAGIWARA, Takanori DATE, Kazuya MASU, Takashi SATO, },
journal={IEICE TRANSACTIONS on Electronics},
title={Hypersphere Sampling for Accelerating High-Dimension and Low-Failure Probability Circuit-Yield Analysis},
year={2014},
volume={E97-C},
number={4},
pages={280-288},
abstract={This paper proposes a novel and an efficient method termed hypersphere sampling to estimate the circuit yield of low-failure probability with a large number of variable sources. Importance sampling using a mean-shift Gaussian mixture distribution as an alternative distribution is used for yield estimation. Further, the proposed method is used to determine the shift locations of the Gaussian distributions. This method involves the bisection of cones whose bases are part of the hyperspheres, in order to locate probabilistically important regions of failure; the determination of these regions accelerates the convergence speed of importance sampling. Clustering of the failure samples determines the required number of Gaussian distributions. Successful static random access memory (SRAM) yield estimations of 6- to 24-dimensional problems are presented. The number of Monte Carlo trials has been reduced by 2-5 orders of magnitude as compared to conventional Monte Carlo simulation methods.},
keywords={},
doi={10.1587/transele.E97.C.280},
ISSN={1745-1353},
month={April},}

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TY - JOUR
TI - Hypersphere Sampling for Accelerating High-Dimension and Low-Failure Probability Circuit-Yield Analysis
T2 - IEICE TRANSACTIONS on Electronics
SP - 280
EP - 288
AU - Shiho HAGIWARA
AU - Takanori DATE
AU - Kazuya MASU
AU - Takashi SATO
PY - 2014
DO - 10.1587/transele.E97.C.280
JO - IEICE TRANSACTIONS on Electronics
SN - 1745-1353
VL - E97-C
IS - 4
JA - IEICE TRANSACTIONS on Electronics
Y1 - April 2014
AB - This paper proposes a novel and an efficient method termed hypersphere sampling to estimate the circuit yield of low-failure probability with a large number of variable sources. Importance sampling using a mean-shift Gaussian mixture distribution as an alternative distribution is used for yield estimation. Further, the proposed method is used to determine the shift locations of the Gaussian distributions. This method involves the bisection of cones whose bases are part of the hyperspheres, in order to locate probabilistically important regions of failure; the determination of these regions accelerates the convergence speed of importance sampling. Clustering of the failure samples determines the required number of Gaussian distributions. Successful static random access memory (SRAM) yield estimations of 6- to 24-dimensional problems are presented. The number of Monte Carlo trials has been reduced by 2-5 orders of magnitude as compared to conventional Monte Carlo simulation methods.
ER -