Equipotential shells for efficient inductance extraction

To make three-dimensional (3-D) on-chip interconnect inductance extraction tractable, it is necessary to ignore parasitic couplings without compromising critical properties of the interconnect system. It is demonstrated that simply discarding faraway mutual inductance couplings can lead to an unstab...

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Bibliographic Details
Published in:IEEE transactions on computer-aided design of integrated circuits and systems 2001-01, Vol.20 (1), p.70-79
Main Authors: Beattie, M., Krauter, B., Alatan, L., Pileggi, L.
Format: Article
Language:English
Subjects:
Approximation
Capacitance
Coupling circuits
Couplings
Effectiveness
Eigenvalues and eigenfunctions
Ellipsoids
Equipotentials
Extraction
Inductance
Integrated circuit interconnections
Integrated circuit modeling
Mutual coupling
Shells
Sparse matrices
Symmetric matrices
System-on-a-chip
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Summary:To make three-dimensional (3-D) on-chip interconnect inductance extraction tractable, it is necessary to ignore parasitic couplings without compromising critical properties of the interconnect system. It is demonstrated that simply discarding faraway mutual inductance couplings can lead to an unstable approximate inductance matrix. In this paper, we describe an equipotential shell methodology, which generates a partial inductance matrix that is sparse yet stable and symmetric. We prove the positive definiteness of the resulting approximate inductance matrix when the equipotential shells are properly defined. Importantly, the equipotential shell approach also provably preserves the inductance of loops if they are enclosed entirely within the shells of their segments. Methods for sizing the shells to control the accuracy are presented. To demonstrate the overall efficacy for on-chip extraction, ellipsoid shells, which are a special case of the general equipotential shell approach, are presented and demonstrated for both on-chip and system-level extraction examples.
ISSN:0278-0070
1937-4151
DOI:10.1109/43.905676