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Broadband electromagnetic modeling of on-chip passives using a differential surface admittance operator for 3-D piecewise homogeneous structures

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Abstract
Accurate modeling of on-chip passive components is vital for reliable integrated circuit (IC) design. However, this is non-trivial due to the inherent heterogeneity of the structures and the wide range of material parameters involved. In this work, we present a single-source boundary integral equation (BIE) for modeling on-chip interconnects and passive elements. To reduce the number of discretization elements-and thus the number of unknowns-we construct a 3-D differential surface admittance (DSA) operator for piecewise homogeneous cuboidal and rectilinear polyhedral objects. Specifically, a novel method is proposed to handle material interfaces efficiently. By combining this new formulation of the DSA operator with the augmented electric field integral equation (EFIE), we obtain a framework that enables accurate modeling and fast broadband impedance extraction of on-chip structures. The proposed approach is validated through several numerical experiments, including important applications such as metal-insulator-metal (MIM) capacitors, and demonstrates excellent agreement with reference solutions while significantly reducing computational cost compared to state-of-the-art solvers.
Keywords
Surface impedance, Electric fields, System-on-chip, Integral equations, Vectors, Three-dimensional printing, Faces, Magnetic fields, Surface waves, Mathematical models, 3-D differential surface admittance (DSA) operator, material interfaces, on-chip passives, piecewise homogeneous media, single-source boundary integral equation (BIE), IMPEDANCE BOUNDARY-CONDITION, INTEGRAL-EQUATION, FORMULATION

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Citation

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MLA
Pattyn, Tim, et al. “Broadband Electromagnetic Modeling of On-Chip Passives Using a Differential Surface Admittance Operator for 3-D Piecewise Homogeneous Structures.” IEEE TRANSACTIONS ON MICROWAVE THEORY AND TECHNIQUES, vol. 73, no. 12, 2025, pp. 10199–212, doi:10.1109/TMTT.2025.3600958.
APA
Pattyn, T., Sun, X., Beyne, E., De Zutter, D., Huynen, M., & Vande Ginste, D. (2025). Broadband electromagnetic modeling of on-chip passives using a differential surface admittance operator for 3-D piecewise homogeneous structures. IEEE TRANSACTIONS ON MICROWAVE THEORY AND TECHNIQUES, 73(12), 10199–10212. https://doi.org/10.1109/TMTT.2025.3600958
Chicago author-date
Pattyn, Tim, Xiao Sun, Eric Beyne, Daniël De Zutter, Martijn Huynen, and Dries Vande Ginste. 2025. “Broadband Electromagnetic Modeling of On-Chip Passives Using a Differential Surface Admittance Operator for 3-D Piecewise Homogeneous Structures.” IEEE TRANSACTIONS ON MICROWAVE THEORY AND TECHNIQUES 73 (12): 10199–212. https://doi.org/10.1109/TMTT.2025.3600958.
Chicago author-date (all authors)
Pattyn, Tim, Xiao Sun, Eric Beyne, Daniël De Zutter, Martijn Huynen, and Dries Vande Ginste. 2025. “Broadband Electromagnetic Modeling of On-Chip Passives Using a Differential Surface Admittance Operator for 3-D Piecewise Homogeneous Structures.” IEEE TRANSACTIONS ON MICROWAVE THEORY AND TECHNIQUES 73 (12): 10199–10212. doi:10.1109/TMTT.2025.3600958.
Vancouver
1.
Pattyn T, Sun X, Beyne E, De Zutter D, Huynen M, Vande Ginste D. Broadband electromagnetic modeling of on-chip passives using a differential surface admittance operator for 3-D piecewise homogeneous structures. IEEE TRANSACTIONS ON MICROWAVE THEORY AND TECHNIQUES. 2025;73(12):10199–212.
IEEE
[1]
T. Pattyn, X. Sun, E. Beyne, D. De Zutter, M. Huynen, and D. Vande Ginste, “Broadband electromagnetic modeling of on-chip passives using a differential surface admittance operator for 3-D piecewise homogeneous structures,” IEEE TRANSACTIONS ON MICROWAVE THEORY AND TECHNIQUES, vol. 73, no. 12, pp. 10199–10212, 2025.
@article{01KE6VZ4TG83HABQTMK6K015FC,
  abstract     = {{Accurate modeling of on-chip passive components is vital for reliable integrated circuit (IC) design. However, this is non-trivial due to the inherent heterogeneity of the structures and the wide range of material parameters involved. In this work, we present a single-source boundary integral equation (BIE) for modeling on-chip interconnects and passive elements. To reduce the number of discretization elements-and thus the number of unknowns-we construct a 3-D differential surface admittance (DSA) operator for piecewise homogeneous cuboidal and rectilinear polyhedral objects. Specifically, a novel method is proposed to handle material interfaces efficiently. By combining this new formulation of the DSA operator with the augmented electric field integral equation (EFIE), we obtain a framework that enables accurate modeling and fast broadband impedance extraction of on-chip structures. The proposed approach is validated through several numerical experiments, including important applications such as metal-insulator-metal (MIM) capacitors, and demonstrates excellent agreement with reference solutions while significantly reducing computational cost compared to state-of-the-art solvers.}},
  author       = {{Pattyn, Tim and Sun, Xiao and Beyne, Eric and De Zutter, Daniël and Huynen, Martijn and Vande Ginste, Dries}},
  issn         = {{0018-9480}},
  journal      = {{IEEE TRANSACTIONS ON MICROWAVE THEORY AND TECHNIQUES}},
  keywords     = {{Surface impedance,Electric fields,System-on-chip,Integral equations,Vectors,Three-dimensional printing,Faces,Magnetic fields,Surface waves,Mathematical models,3-D differential surface admittance (DSA) operator,material interfaces,on-chip passives,piecewise homogeneous media,single-source boundary integral equation (BIE),IMPEDANCE BOUNDARY-CONDITION,INTEGRAL-EQUATION,FORMULATION}},
  language     = {{eng}},
  number       = {{12}},
  pages        = {{10199--10212}},
  title        = {{Broadband electromagnetic modeling of on-chip passives using a differential surface admittance operator for 3-D piecewise homogeneous structures}},
  url          = {{http://doi.org/10.1109/TMTT.2025.3600958}},
  volume       = {{73}},
  year         = {{2025}},
}

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