Computationally efficient yield estimation procedures based on simplicial approximation

Director, Stephen W.; Hachtel, Gary D.; Vidigal, L.M.

doi:10.1109/tcs.1978.1084450

Cited by 42 publications

(21 citation statements)

References 4 publications

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“…hypersphere or hyperellipsoid (Director et al 1978, Abdel-Malek and Hassan 1991, Hassan 2003, Wojciechowski et al 2004). This approach is in practice more efficient than statistical methods, but its complexity grows proportionally to the number of parameters (Graeb 2007).…”

Section: Introductionmentioning

confidence: 99%

A new hybrid method for optimal circuit design using semi-definite programming

Hassan

Abdel-Naby

2012

Engineering Optimization

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In this article a new method for yield optimization (design centring) is introduced. The method has a statistical-geometrical nature, hence it is called hybrid. The method exploits the semi-definite programming applications in approximating the feasible region with two bounding ellipsoids. These ellipsoids are obtained using a two phase algorithm. In the first phase, the minimum volume ellipsoid enclosing the feasible region is obtained. The largest ellipsoid that can be inscribed inside the feasible region is obtained in the second phase. The centres of these bounding ellipsoids are used as design centres. In the second phase, an additional polytopic region approximation is constructed. A comparison between the obtained region approximations is given. Saving in the number of circuit simulations needed for yield optimization is also considered. Practical examples are given to show the effectiveness of the new method.

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Section: Introductionmentioning

confidence: 99%

A new hybrid method for optimal circuit design using semi-definite programming

Hassan

Abdel-Naby

2012

Engineering Optimization

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“…In [11], [12], the boundary surface in parameter space separating success/failure performance regions is approximated by a series of linear constraints. The utility of the approximate linear constraints is that testing whether a point is in the success region is sped up significantly for most (but not all) Monte-Carlo samples.…”

Section: Introductionmentioning

confidence: 99%

“…The method in [11], [12], like the present work, is concerned with boundaries in the parameter space. Given a region of desired (e.g., worst-case) performances of the circuit, the corresponding boundary in the parameter space is determined, as depicted by the blue (lower) arrow in Fig.…”

Section: Introductionmentioning

confidence: 99%

An efficient, fully nonlinear, variability-aware non-monte-carlo yield estimation procedure with applications to SRAM cells and ring oscillators

Gu¹,

Roychowdhury²

2008

2008 Asia and South Pacific Design Automation Conference

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Abstract-Failures and yield problems due to parameter variations have become a significant issue for sub-90-nm technologies. As a result, CAD algorithms and tools that provide designers the ability to estimate the effects of variability quickly and accurately are being urgently sought. The need for such tools is particularly acute for static RAM (SRAM) cells and integrated oscillators, for such circuits require expensive and high-accuracy simulation during design. We present a novel technique for fast computation of parametric yield. The technique is based on efficient, adaptive geometric calculation of probabilistic hypervolumes subtended by the boundary separating pass/fail regions in parameter space. A key feature of the method is that it is far more efficient than Monte-Carlo, while at the same time achieving better accuracy in typical applications. The method works equally well with parameters specified as corners, or with full statistical distributions; importantly, it scales well when many parameters are varied. We apply the method to an SRAM cell and a ring oscillator and provide extensive comparisons against full MonteCarlo, demonstrating speedups of 100-1000×.

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“…These methods are computationally expensive. Another group of methods treats the problem geometrically [7][8][9][10][11][12][13][14][15][16]. In this approach, the feasible region in the parameter space where the design specifications are satisfied is approximated assuming it to be convex and bounded.…”

Section: Introductionmentioning

confidence: 99%

Design centering and polyhedral region approximation via parallel-cuts ellipsoidal technique

Hassan¹,

Abdel-Malek²,

Rabie³

2004

Engineering Optimization

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A new technique for constructing a polyhedral approximation of the feasible region and finding the associated design center through a parallel-cuts ellipsoidal technique is presented. The linearizations of the feasible region boundary required to implement the parallel-cuts ellipsoidal technique are saved from one iteration to another in a non-redundant form. These linearizations are used in the construction of the parallel cuts as well as in the generation of an exterior polyhedral approximation of the feasible region at no additional cost. Numerical and practical examples are given to demonstrate the effectiveness of the new technique.

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Computationally efficient yield estimation procedures based on simplicial approximation

Cited by 42 publications

References 4 publications

A new hybrid method for optimal circuit design using semi-definite programming

A new hybrid method for optimal circuit design using semi-definite programming

An efficient, fully nonlinear, variability-aware non-monte-carlo yield estimation procedure with applications to SRAM cells and ring oscillators

Design centering and polyhedral region approximation via parallel-cuts ellipsoidal technique

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