A sparse grid based spectral stochastic collocation method for variations-aware capacitance extraction of interconnects under nanometer process technology

Authors:
Hengliang Zhu;Xuan Zeng;Wei Cai;Jintao Xue;Dian Zhou
Affiliations:
Fudan University, Shanghai, P.R. China;Fudan University, Shanghai, P.R. China;University of North Carolina at Charlotte;Fudan University, Shanghai, P.R. China;Fudan University, Shanghai, P.R. China and The University of Texas at Dallas
Venue:
Proceedings of the conference on Design, automation and test in Europe
Year:
2007

Citing 12
Cited 17

Stochastic finite elements: a spectral approach

Stochastic finite elements: a spectral approach
Numerical recipes in C (2nd ed.): the art of scientific computing

Numerical recipes in C (2nd ed.): the art of scientific computing
Introduction to Algorithms

Introduction to Algorithms
The Wiener--Askey Polynomial Chaos for Stochastic Differential Equations

SIAM Journal on Scientific Computing
A Probabilistic Collocation Method Based Statistical Gate Delay Model Considering Process Variations and Multiple Input Switching

Proceedings of the conference on Design, Automation and Test in Europe - Volume 2
Stochastic Power Grid Analysis Considering Process Variations

Proceedings of the conference on Design, Automation and Test in Europe - Volume 2
Asymptotic probability extraction for non-normal distributions of circuit performance

Proceedings of the 2004 IEEE/ACM International conference on Computer-aided design
FastSies: a fast stochastic integral equation solver for modeling the rough surface effect

ICCAD '05 Proceedings of the 2005 IEEE/ACM International conference on Computer-aided design
Efficient statistical capacitance variability modeling with orthogonal principle factor analysis

ICCAD '05 Proceedings of the 2005 IEEE/ACM International conference on Computer-aided design
A fast hierarchical algorithm for three-dimensional capacitance extraction

IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems
Sparse transformations and preconditioners for 3-D capacitance extraction

IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems
Robust Extraction of Spatial Correlation

IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems

Variational capacitance modeling using orthogonal polynomial method

Proceedings of the 18th ACM Great Lakes symposium on VLSI
Stochastic integral equation solver for efficient variation-aware interconnect extraction

Proceedings of the 45th annual Design Automation Conference
An efficient method for chip-level statistical capacitance extraction considering process variations with spatial correlation

Proceedings of the conference on Design, automation and test in Europe
Variational capacitance extraction of on-chip interconnects based on continuous surface model

Proceedings of the 46th Annual Design Automation Conference
PiCAP: a parallel and incremental capacitance extraction considering stochastic process variation

Proceedings of the 46th Annual Design Automation Conference
Robust simulation methodology for surface-roughness loss in interconnect and package modelings

IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems
Stochastic dominant singular vectors method for variation-aware extraction

Proceedings of the 47th Design Automation Conference
Variation-aware interconnect extraction using statistical moment preserving model order reduction

Proceedings of the Conference on Design, Automation and Test in Europe
New simulation methodology of 3D surface roughness loss for interconnects modeling

Proceedings of the Conference on Design, Automation and Test in Europe
Variational capacitance extraction and modeling based on orthogonal polynomial method

IEEE Transactions on Very Large Scale Integration (VLSI) Systems
Efficient sensitivity-based capacitance modeling for systematic and random geometric variations

Proceedings of the 16th Asia and South Pacific Design Automation Conference
Parallel statistical capacitance extraction of on-chip interconnects with an improved geometric variation model

Proceedings of the 16th Asia and South Pacific Design Automation Conference
Statistical extraction and modeling of inductance considering spatial correlation

Analog Integrated Circuits and Signal Processing
A dynamic method for efficient random mismatch characterization of standard cells

Proceedings of the International Conference on Computer-Aided Design
A parallel and incremental extraction of variational capacitance with stochastic geometric moments

IEEE Transactions on Very Large Scale Integration (VLSI) Systems
Efficient variation-aware EM-semiconductor coupled solver for the TSV structures in 3D IC

DATE '12 Proceedings of the Conference on Design, Automation and Test in Europe
Uncertainty quantification for integrated circuits: stochastic spectral methods

Proceedings of the International Conference on Computer-Aided Design

Quantified Score

Hi-index	0.00

Visualization

Abstract

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.