Uncertainty quantification of electronic and photonic ICs with non-Gaussian correlated process variations

Cui, Chunfeng; Zhang, Zheng

doi:10.1145/3240765.3240860

Cited by 19 publications

(10 citation statements)

References 47 publications

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“…In this paper, we use Gaussian mixture models to describe non-Gaussian correlated uncertainties, and we employ the functional tensor-train method [57] for moment computation.…”

Section: B Numerical Implementation Issuesmentioning

confidence: 99%

Stochastic Collocation With Non-Gaussian Correlated Process Variations: Theory, Algorithms, and Applications

Cui

Zhang

2019

IEEE Trans. Compon., Packag. Manufact. Technol.

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Stochastic spectral methods have achieved great success in the uncertainty quantification of many engineering problems, including electronic and photonic integrated circuits influenced by fabrication process variations. Existing techniques employ a generalized polynomial-chaos expansion, and they almost always assume that all random parameters are mutually independent or Gaussian correlated. However, this assumption is rarely true in real applications. How to handle non-Gaussian correlated random parameters is a long-standing and fundamental challenge. A main bottleneck is the lack of theory and computational methods to perform a projection step in a correlated uncertain parameter space. This paper presents an optimization-based approach to automatically determinate the quadrature nodes and weights required in a projection step, and develops an efficient stochastic collocation algorithm for systems with non-Gaussian correlated parameters. We also provide some theoretical proofs for the complexity and error bound of our proposed method. Numerical experiments on synthetic, electronic and photonic integrated circuit examples show the nearly exponential convergence rate and excellent efficiency of our proposed approach. Many other challenging uncertainty-related problems can be further solved based on this work.

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“…In this paper, we use Gaussian mixture models to describe non-Gaussian correlated uncertainties, and we employ the functional tensor-train method [57] for moment computation.…”

Section: B Numerical Implementation Issuesmentioning

confidence: 99%

Stochastic Collocation With Non-Gaussian Correlated Process Variations: Theory, Algorithms, and Applications

Cui

Zhang

2019

IEEE Trans. Compon., Packag. Manufact. Technol.

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“…Using correlated samples for the linear regression would instead imply the calculation of a suitable set of new orthogonal polynomial basis functions [10,11]. It should be noted that more general and viable approaches were recently proposed to handle non-Gaussian correlated uncertain parameters [12,20]. Nevertheless, using the described procedure to build the PCE approximation works well for correlated Gaussian parameters.…”

Section: Analysis Of Photonic Circuits With Correlated Variablesmentioning

confidence: 99%

Performance robustness analysis in machine-assisted design of photonic devices

Melati

Grinberg

Waqas

et al. 2019

Smart Photonic and Optoelectronic Integrated Circuits XXI

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Machine-assisted design of integrated photonic devices (e.g. through optimization and inverse design methods) is opening the possibility of exploring very large design spaces, novel functionalities and non-intuitive geometries. These methods are generally used to optimize performance figures-of-merit. On the other hand, the effect of manufacturing variability remains a fundamental challenge since small fabrication errors can have a significant impact on light propagation, especially in high-index-contrast platforms. Brute-force analysis of these variabilities during the main optimization process can become prohibitive, since a large number of simulations would be required. To this purpose, efficient stochastic techniques integrated in the design cycle allow to quickly assess the performance robustness and the expected fabrication yield of each tentative device generated by the optimization. In this invited talk we present an overview of the recent advances in the implementation of stochastic techniques in photonics, focusing in particular on stochastic spectral methods that have been regarded as a promising alternative to the classical Monte Carlo method. Polynomial chaos expansion techniques generate so called surrogate models by means of an orthogonal set of polynomials to efficiently represent the dependence of a function to statistical variabilities. They achieve a considerable reduction of the simulation time compared to Monte Carlo, at least for mid-scale problems, making feasible the incorporation of tolerance analysis and yield optimization within the photonic design flow.

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“…The key idea of stochastic spectral method is to represent the stochastic solution as the linear combination of basis Some preliminary results of this work have been published in ICCAD 2018 [1]. This work was supported by NSF CAREER Award CCF 1846476, NSF CCF 1763699 and the UCSB start-up grant.…”

Section: Introductionmentioning

confidence: 99%

High-Dimensional Uncertainty Quantification of Electronic and Photonic IC With Non-Gaussian Correlated Process Variations

Cui

Zhang

2020

IEEE Trans. Comput.-Aided Des. Integr. Circuits Syst.

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Uncertainty quantification based on generalized polynomial chaos has been used in many applications. It has also achieved great success in variation-aware design automation. However, almost all existing techniques assume that the parameters are mutually independent or Gaussian correlated, which is rarely true in real applications. For instance, in chip manufacturing, many process variations are actually correlated. Recently, some techniques have been developed to handle non-Gaussian correlated random parameters, but they are timeconsuming for high-dimensional problems. We present a new framework to solve uncertainty quantification problems with many non-Gaussian correlated uncertainties. Firstly, we propose a set of smooth basis functions to well capture the impact of non-Gaussian correlated process variations. We develop a tensor approach to compute these basis functions in a highdimension setting. Secondly, we investigate the theoretical aspect and practical implementation of a sparse solver to compute the coefficients of all basis functions. We provide some theoretical analysis for the exact recovery condition and error bound of this sparse solver in the context of uncertainty quantification. We present three adaptive sampling approaches to improve the performance of the sparse solver. Finally, we validate our methods by synthetic and practical electronic/photonic ICs with 19 to 57 non-Gaussian correlated variation parameters. Our approach outperforms Monte Carlo by thousands of times in terms of efficiency. It can also accurately predict the output density functions with multiple peaks caused by non-Gaussian correlations, which are hard to capture by existing methods.Index Terms-High dimensionality, uncertainty quantification, electronic and photonic IC, non-Gaussian correlation, process variations, tensor, sparse solver, adaptive sampling.

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Uncertainty quantification of electronic and photonic ICs with non-Gaussian correlated process variations

Cited by 19 publications

References 47 publications

Stochastic Collocation With Non-Gaussian Correlated Process Variations: Theory, Algorithms, and Applications

Stochastic Collocation With Non-Gaussian Correlated Process Variations: Theory, Algorithms, and Applications

Performance robustness analysis in machine-assisted design of photonic devices

High-Dimensional Uncertainty Quantification of Electronic and Photonic IC With Non-Gaussian Correlated Process Variations

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