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Journal of Computational Physics
Iterative Methods for Sparse Linear Systems
Iterative Methods for Sparse Linear Systems
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ISQED '00 Proceedings of the 1st International Symposium on Quality of Electronic Design
Proceedings of the 2004 IEEE/ACM International conference on Computer-aided design
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ACM Transactions on Mathematical Software (TOMS)
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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
Statistical model order reduction for interconnect circuits considering spatial correlations
Proceedings of the conference on Design, automation and test in Europe
Proceedings of the conference on Design, automation and test in Europe
A New Methodology for Interconnect Parasitics Extraction Considering Photo-Lithography Effects
ASP-DAC '07 Proceedings of the 2007 Asia and South Pacific Design Automation Conference
Stochastic extended Krylov subspace method for variational analysis of on-chip power grid networks
Proceedings of the 2007 IEEE/ACM international conference on Computer-aided design
Variational capacitance modeling using orthogonal polynomial method
Proceedings of the 18th ACM Great Lakes symposium on VLSI
Proceedings of the conference on Design, automation and test in Europe
A fast hierarchical algorithm for three-dimensional capacitance extraction
IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems
Rapid method to account for process variation in full-chip 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
Hermite Polynomial Based Interconnect Analysis in the Presence of Process Variations
IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems
Fast Variational Analysis of On-Chip Power Grids by Stochastic Extended Krylov Subspace Method
IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems
Uncertainty quantification for integrated circuits: stochastic spectral methods
Proceedings of the International Conference on Computer-Aided Design
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In this paper, we propose a novel statistical capacitance extraction method for interconnect conductors considering process variations. The new method is called statCap, where orthogonal polynomials are used to represent the statistical processes in a deterministic way. We first show how the variational potential coefficient matrix is represented in a first-order form using Taylor expansion and orthogonal decomposition. Then, an augmented potential coefficient matrix, which consists of the coefficients of the polynomials, is derived. After this, corresponding augmented system is solved to obtain the variational capacitance values in the orthogonal polynomial form. Finally, we present a method to extend statCap to the second-order form to give more accurate results without loss of efficiency compared to the linear models. We show the derivation of the analytic second-order orthogonal polynomials for the variational capacitance integral equations. Experimental results show that statCap is two orders of magnitude faster than the recently proposed statistical capacitance extraction method based on the spectral stochastic collocation approach and many orders of magnitude faster than the Monte Carlo method for several practical conductor structures.