Sensitivity computation of interconnect capacitances with respect to geometric parameters

Bi, Yu; Kolk, Kees-Jan van der; Dumitrache, Ioan; Meijs, N.P. van der

doi:10.1109/epep.2008.4675916

Cited by 17 publications

(9 citation statements)

References 6 publications

(11 reference statements)

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“…Novel extraction methodologies can efficiently generate such sensitivity information [5,26]. A nice feature of this representation is that this explicit parameter dependence allows to obtain a reduced, yet similar representation when a projection scheme is applied Some questions may be raised about the order neccessary for an accurate representation of the parametric model.…”

Section: Representation Of Parametric Systemsmentioning

confidence: 99%

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Parameterized Model Order Reduction

Ciuprina

Villena

Dumitrache

et al. 2015

Mathematics in Industry

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Document VersionPublisher's PDF, also known as Version of Record (includes final page, issue and volume numbers) Please check the document version of this publication:• A submitted manuscript is the author's version of the article upon submission and before peer-review. There can be important differences between the submitted version and the official published version of record. People interested in the research are advised to contact the author for the final version of the publication, or visit the DOI to the publisher's website.• The final author version and the galley proof are versions of the publication after peer review.• The final published version features the final layout of the paper including the volume, issue and page numbers. Link to publication Citation for published version (APA):Ciuprina, G., Fernández Villena, J., Ioan, D., Ilievski, Z., Kula, S., Maten, ter, E. J. W., ... Striebel, M. (2015). Parameterized model order reduction. (CASA-report; Vol. 1508). Eindhoven: Technische Universiteit Eindhoven. General rightsCopyright and moral rights for the publications made accessible in the public portal are retained by the authors and/or other copyright owners and it is a condition of accessing publications that users recognise and abide by the legal requirements associated with these rights.• Users may download and print one copy of any publication from the public portal for the purpose of private study or research.• You may not further distribute the material or use it for any profit-making activity or commercial gain • You may freely distribute the URL identifying the publication in the public portal ? Take down policyIf you believe that this document breaches copyright please contact us providing details, and we will remove access to the work immediately and investigate your claim. Abstract This Chapter introduces parameterized, or parametric, Model Order Reduction (pMOR). The Sections are offered in a prefered order for reading, but can be read independently. Section 4.1, written by Jorge Fernández Villena, L. Miguel Silveira, Wil H.A. Schilders, Gabriela Ciuprina, Daniel Ioan and Sebastian Kula, overviews the basic principles for pMOR. Due to higher integration and increasing frequency-based effects, large, full Electromagnetic Models (EM) are needed for accurate prediction of the real behavior of integrated passives and interconnects. Furthermore, these structures are subject to parametric effects due to small variations of the geometric and physical properties of the inherent materials and manufacturing process. Accuracy requirements lead to huge models, which are expensive to simulate and this cost is increased when parameters and their effects are taken into account. This Section introduces the framework of pMOR, which aims at generating reduced models for systems depending on a set of parameters. Section 4.2, written by Gabriela Ciuprina, Alexandra Ş tefȃnescu, Sebastian Kula and Daniel Ioan, provides robust procedures for pMOR. This Section proposes a robust specialized technique to extrac...

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Section: Representation Of Parametric Systemsmentioning

confidence: 99%

“…The nominal value chosen was p 3 = 3µm and samples in the interval [1,5]µm were considered. The reference result was obtained by simulated the samples separately (each sample was discretized and solved).…”

Section: Parametric Modelsmentioning

confidence: 99%

Parameterized Model Order Reduction

Ciuprina

Villena

Dumitrache

et al. 2015

Mathematics in Industry

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“…The width and thickness of interconnect wire are often set to be random variables. This model was employed for sensitivity calculation [7,8], and for statistical extraction of 2-D cross-section structure in [9]. Among the three models, the VAW model is the simplest one, which does not consider the detailed fluctuation of surface panels.…”

Section: A Existing Geometric Variation Modelsmentioning

confidence: 99%

“…Step 4, the values of derived variables are calculated with interpolation as that in (8). In Step 6, the statistical expression of capacitance is firstly calculated [6], and then the values of mean and Std, or the PDF can be obtained.…”

Section: A Implementation Detailsmentioning

confidence: 99%

“…As a result, the error of the DSV model shown in experiments was not larger than 7%, and the Std was as small as 1% of the capacitance mean value in [6]. Besides, another geometric model, where each nominal conductor surface is assumed to vary as a whole, was used in [7,8] for calculation of sensitivity, or in [9] for 2-D structures. We refer to this model as variation as a whole (VAW) model in this paper.…”

Section: Introductionmentioning

confidence: 99%

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Parallel statistical capacitance extraction of on-chip interconnects with an improved geometric variation model

Yu¹,

Hu$^{²,

Zhang³

2011

16th Asia and South Pacific Design Automation Conference (ASP-DAC 2011)

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-In this paper, a new geometric variation model, referred to as the improved continuous surface variation (ICSV) model, is proposed to accurately imitate the random variation of on-chip interconnects. In addition, a new statistical capacitance solver is implemented to incorporate the ICSV model, the HPC [5] and weighted PFA [6] techniques. The solver also employs a parallel computing technique to greatly improve its efficiency. Experiments show that on a typical 65nm-technology structure, ICSV model has significant advantage over other existing models, and the new solver is at least 10X faster than the MC simulation with 10000 samples. The parallel solver achieves 7X further speedup on an 8-core machine. We conclude this paper with several criteria to discuss the trade-off between different geometric models and statistical methods for different scenarios.1

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Introduction

Yu¹,

Wang²

2014

Advanced Field-Solver Techniques for RC Extraction of Integrated Circuits

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Sensitivity computation of interconnect capacitances with respect to geometric parameters

Cited by 17 publications

References 6 publications

Parameterized Model Order Reduction

Parameterized Model Order Reduction

Parallel statistical capacitance extraction of on-chip interconnects with an improved geometric variation model

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