Model-Based Design Analysis and Yield Optimization

Pfingsten, Tobias; Herrmann, Daniel; Rasmussen, Carl Edward

doi:10.1109/tsm.2006.883589

Cited by 11 publications

(9 citation statements)

References 28 publications

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“…Rasmussen and Ghahramani [3] have shown that GP-based BMC can significantly outperform Monte Carlo importance sampling (MCIS). Several applications of the Bayes-Hermite quadrature have then been proposed in the literature and among them, the work of Pfingsten et al [4] is particularly interesting in the way they derive a closed-form solution. However, it is not suited to the particularities of spherical functions we are faced with in global illumination problems.…”

Section: Related Workmentioning

confidence: 99%

A Spherical Gaussian Framework for Bayesian Monte Carlo Rendering of Glossy Surfaces

Marques¹,

Bouville

Ribardière

et al. 2013

IEEE Trans. Visual. Comput. Graphics

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Abstract-The Monte Carlo method has proved to be very powerful to cope with global illumination problems but it remains costly in terms of sampling operations. In various applications, previous work has shown that Bayesian Monte Carlo can significantly outperform importance sampling Monte Carlo thanks to a more effective use of the prior knowledge and of the information brought by the samples set. These good results have been confirmed in the context of global illumination but strictly limited to the perfect diffuse case. Our main goal in this paper is to propose a more general Bayesian Monte Carlo solution that allows dealing with non-diffuse BRDFs thanks to a spherical Gaussian-based framework. We also propose a fast hyperparameters determination method which avoids learning the hyperparameters for each BRDF. These contributions represent two major steps towards generalizing Bayesian Monte Carlo for global illumination rendering. We show that we achieve substantial quality improvements over importance sampling at comparable computational cost.

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Section: Related Workmentioning

confidence: 99%

A Spherical Gaussian Framework for Bayesian Monte Carlo Rendering of Glossy Surfaces

Marques¹,

Bouville

Ribardière

et al. 2013

IEEE Trans. Visual. Comput. Graphics

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“…Although the theory of Bayesian Quadrature has been known since 1991 [O'H91], it is only recently that it has been put into practice (e.g. [PHR06, KNKS08]) and to the authors' knowledge, no research in this direction has yet been reported in the computer graphics literature. In the field of global illumination, most research works are based on importance sampling and although this variance reduction technique can be applied to many cases (e.g.…”

Section: Related Workmentioning

confidence: 99%

A Bayesian Monte Carlo Approach to Global Illumination

Brouillat

Bouville

Loos

et al. 2009

Computer Graphics Forum

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International audienceMost Monte Carlo rendering algorithms rely on importance sampling to reduce the variance of estimates. Importance sampling is efficient when the proposal sample distribution is well-suited to the form of the integrand but fails otherwise. The main reason is that the sample location information is not exploited. All sample values are given the same importance regardless of their proximity to one another. Two samples falling in a similar location will have equal importance whereas they are likely to contain redundant information. The Bayesian approach we propose in this paper uses both the location and value of the data to infer an integral value based on a prior probabilistic model of the integrand. The Bayesian estimate depends only on the sample values and locations, and not how these samples have been chosen. We show how this theory can be applied to the final gathering problem and present results that clearly demonstrate the benefits of Bayesian Monte Carlo

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“…In addition, magnetometers adopted multiphysics-based optimization and nonlinear situations [ 14 ], and gyroscopes focused on the packaging with double yield [ 15 ]. Except for unique device analysis, methods that are generally applicable have advanced the processing improvement further [ 3 , 16 , 17 , 18 , 19 , 20 , 21 , 22 , 23 , 24 , 25 , 26 ]. Mirzazaden et al [ 16 , 17 , 18 ] investigated morphology uncertainties with reduced-order models through on-chip tests.…”

Section: Introductionmentioning

confidence: 99%

“…For those non-linear actuated MEMS devices, high fidelity optimization schemes have also been realized. To avoid the brute-force Monte Carlo (MC) scheme, Pfingsten et al [ 21 ] considered a Bayesian Monte Carlo approach for yield estimation, with 90.0% computational savings but the same accuracy, compared with MC schemes. Vudathu et al [ 22 , 26 ] applied a sensitivity analyzer for MEMS (SAM) by worst-case analysis, revealing the effects of parametric variations on performance and yield.…”

Section: Introductionmentioning

confidence: 99%

Modeling of the Effect of Process Variations on a Micromachined Doubly-Clamped Beam

Gao¹,

Zhou²,

Huang³

2017

Micromachines

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In the fabrication of micro-electro-mechanical systems (MEMS) devices, manufacturing process variations are usually involved. For these devices sensitive to process variations such as doubly-clamped beams, mismatches between designs and final products will exist. As a result, it underlies yield problems and will be determined by design parameter ranges and distribution functions. Topographical changes constitute process variations, such as inclination, over-etching, and undulating sidewalls in the Bosch process. In this paper, analytical models are first developed for MEMS doubly-clamped beams, concerning the mentioned geometrical variations. Then, finite-element (FE) analysis is performed to provide a guidance for model verifications. It is found that results predicted by the models agree with those of FE analysis. Assigning process variations, predictions for performance as well as yield can be made directly from the analytical models, by means of probabilistic analysis. In this paper, the footing effect is found to have a more profound effect on the resonant frequency of doubly-clamped beams during the Bosch process. As the confining process has a variation of 10.0%, the yield will have a reduction of 77.3% consequently. Under these circumstances, the prediction approaches can be utilized to guide the further MEMS device designs.

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Model-Based Design Analysis and Yield Optimization

Cited by 11 publications

References 28 publications

A Spherical Gaussian Framework for Bayesian Monte Carlo Rendering of Glossy Surfaces

A Spherical Gaussian Framework for Bayesian Monte Carlo Rendering of Glossy Surfaces

A Bayesian Monte Carlo Approach to Global Illumination

Modeling of the Effect of Process Variations on a Micromachined Doubly-Clamped Beam

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