An SIE Formulation With Triangular Discretization and Loop Analysis for Parameter Extraction of Arbitrarily Shaped Interconnects

A surface integral equation (SIE) formulation under the magneto-quasi-static assumption is proposed to efficiently and accurately model arbitrarily shaped interconnects in packages. Through decently transferring all electromagnetic quantities into circuit elements, the loop analysis is used to caref...

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Bibliographic Details
Published in:IEEE transactions on microwave theory and techniques 2023-10, Vol.71 (10), p.1-13
Main Authors: Zhu, Zekun, Chen, Zhizhang, Yang, Shunchuan
Format: Article
Language:English
Subjects:
Circuits
Current
Electromagnetics
Fast Fourier transformations
Graph theory
Impedance
Integral equations
Integrated circuit interconnections
Integrated circuit modeling
Interconnections
Interconnects
loop analysis
Mathematical models
Packages
parameter extraction
pre-corrected fast Fourier transform (pFFT)
Surface impedance
surface integral equation (SIE)
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Summary:A surface integral equation (SIE) formulation under the magneto-quasi-static assumption is proposed to efficiently and accurately model arbitrarily shaped interconnects in packages. Through decently transferring all electromagnetic quantities into circuit elements, the loop analysis is used to carefully construct matrix equations with an independent and complete set of unknowns based on graph theory. In addition, an efficient preconditioner is developed, and the proposed formulation is accelerated by the pre-corrected fast Fourier transform (pFFT). Four practical examples, including a rectangular metallic interconnect, bonding wire arrays, interconnects in a real-life circuit, and the power distribution network (PDN) used in packages, are carried out to validate its accuracy, efficiency, and scalability. Results show that the proposed formulation is accurate, efficient, and flexible to model complex interconnects in packages.
ISSN:0018-9480
1557-9670
DOI:10.1109/TMTT.2023.3259520