A Probabilistic Collocation Method Based Statistical Gate Delay Model Considering Process Variations and Multiple Input Switching

Kumar, Y. Satish; Li, Jun; Talarico, Claudio; Wang, Janet

doi:10.1109/date.2005.31

Cited by 28 publications

(8 citation statements)

References 10 publications

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“…The term "Homogeneous Chaos" was first defined by Wiener [5] as the span of Hermite polynomials of a Gaussian process, and then extended to a more general concept as polynomial chaos, which has been introduced to the circuit analysis first by J. Wang for solving a stochastic ODE problem in interconnect analysis [6] and a stochastic function approximation problem in delay modeling [7]. In this paper, we propose a more efficient Spectral Stochastic Collocation method based on Homogeneous Chaos to solve the stochastic PDE problem in the variation-aware parasitic extraction of on-chip interconnects.…”

Section: Introductionmentioning

confidence: 99%

A Sparse Grid based Spectral Stochastic Collocation Method for Variations-Aware Capacitance Extraction of Interconnects under Nanometer Process Technology

Zhu

Zeng

Cai

et al. 2007

2007 Design, Automation &Amp; Test in Europe Conference &Amp; Exhibition

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In this paper, a Spectral Stochastic Collocation Method(SSCM) is proposed for the capacitance extraction of interconnects with stochastic geometric variations for nanometer process technology. The proposed SSCM has several advantages over the existing methods. Firstly, compared with the PFA (Principal Factor Analysis) modeling of geometric variations, the K-L (Karhunen-Loeve) expansion involved in SSCM can be independent of the discretization of conductors, thus significantly reduces the computation cost. Secondly, compared with the perturbation method, the stochastic spectral method based on Homogeneous Chaos expansion has optimal (exponential) convergence rate, which makes SSCM applicable to most geometric variation cases. Furthermore, Sparse Grid combined with a MST (Minimum Spanning Tree) representation is proposed to reduce the number of sampling points and the computation time for capacitance extraction at each sampling point. Numerical experiments have demonstrated that SSCM can achieve higher accuracy and faster convergence rate compared with the perturbation method.

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Section: Introductionmentioning

confidence: 99%

A Sparse Grid based Spectral Stochastic Collocation Method for Variations-Aware Capacitance Extraction of Interconnects under Nanometer Process Technology

Zhu

Zeng

Cai

et al. 2007

2007 Design, Automation &Amp; Test in Europe Conference &Amp; Exhibition

View full text Add to dashboard Cite

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“…Second order Hermite polynomials are sufficient in practice. The coefficients cj can be determined using the stochastic collocation method [5], [15]. Using Equation (8), the delay of a logic gate at time t can then be expressed as follows.…”

Section: B Considering Process Variations In Nbti Aging Modelingmentioning

confidence: 99%

“…Due to fabrication-induced process variations, the NBTI aging process and its impact on circuit timing become a random process. To model NBTI-induced aging under process variation, we apply the stochastic collocation method, which was originally proposed to model the gate delay under uncertainty [15]. Considering a set of process parameters as a random variable vector with normal distribution…”

Section: B Considering Process Variations In Nbti Aging Modelingmentioning

confidence: 99%

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Statistical reliability analysis under process variation and aging effects

Shang

Zhou

et al. 2009

Proceedings of the 46th Annual Design Automation Conference

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Abstract-Circuit reliability is affected by various fabrication-time and run-time effects. Fabrication-induced process variation has significant impact on circuit performance and reliability. Various aging effects, such as negative bias temperature instability, cause continuous performance and reliability degradation during circuit run-time usage. In this work, we present a statistical analysis framework that characterizes the lifetime reliability of nanometer-scale integrated circuits by jointly considering the impact of fabrication-induced process variation and run-time aging effects. More specifically, our work focuses on characterizing circuit threshold voltage lifetime variation and its impact on circuit timing due to process variation and the negative bias temperature instability effect, a primary aging effect in nanometer-scale integrated circuits. The proposed work is capable of characterizing the overall circuit lifetime reliability, as well as efficiently quantifying the vulnerabilities of individual circuit elements. This analysis framework has been carefully validated and integrated into an iterative design flow for circuit lifetime reliability analysis and optimization.

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“…PCE [9,10], probabilistic collocation method [11,12], and KLE [9,13,14] have been utilized to illustrate random processes in porous media. This method is applied to decompose the solution to Boussinesq equations for the velocity, density, and pressure elds [15].…”

Section: Introductionmentioning

confidence: 99%

Uncertainty analysis of open channel flow: stochastic approach to Advection–Diffusion equation

2017

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Abstract. In uid mechanics applications, transport occurs through the combination of advection and di usion. This paper presents a stochastic approach to describe uncertainty and its propagation based on Advection-Di usion Equation. To assess the uncertainty in initial water depth, random initial condition is imposed on the framework of 1D open cannel ow. Karhunen-Loeve Expansion is adopted to decompose the uncertain parameter in terms of in nite series containing a set of orthogonal Gaussian random variables. Eigenstructures of covariance function associated with the random parameter, which play a key role in computing coe cients of the series, are extracted from Fredhulm's equation. The ow depth is also represented as an in nite series of its moments, obtained via polynomial expansion decomposition in terms of the products of random variables. Coe cients of these series are obtained by a set of recursive equations derived from the ADE. Results highlight the e ect of various statistical properties of initial water depth. The mean value and variance for the ow depth are compared with Monte Carlo Simulation as a reliable stochastic approach. It is found that when higher-order approximations are used, KLE results would be as accurate as the results of MCS, however, with much less computational time and e ort.

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A Probabilistic Collocation Method Based Statistical Gate Delay Model Considering Process Variations and Multiple Input Switching

Cited by 28 publications

References 10 publications

A Sparse Grid based Spectral Stochastic Collocation Method for Variations-Aware Capacitance Extraction of Interconnects under Nanometer Process Technology

A Sparse Grid based Spectral Stochastic Collocation Method for Variations-Aware Capacitance Extraction of Interconnects under Nanometer Process Technology

Statistical reliability analysis under process variation and aging effects

Uncertainty analysis of open channel flow: stochastic approach to Advection–Diffusion equation

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