A novel technique for full-wave modeling of large-scale three-dimensional high-speed on/off-chip interconnect structures

Jiao, Dan; Mazumder, Md. Mohiuddin; Chakravarty, S.; Dai, Changhong; Kobrinsky, Mauro J.; Harmes, M.; List, S.

doi:10.1109/sispad.2003.1233632

Cited by 33 publications

(10 citation statements)

References 9 publications

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“…By imposing the orthogonality condition (26) we obtain the following recursive formulation for and , shown in (27) at the bottom of the page, where and denote the th derivative of and at the expansion point . Since the bandwidth of Taylor expansion is limited, we convert Taylor series into a Padé rational function, which has a larger radius of convergence.…”

Section: E Fast Frequency Sweep Techniquementioning

confidence: 99%

“…In this paper, we propose a fast frequency-domain eigenvalue-based method for fullwave modeling of large-scale 3-D on-chip interconnect structures. Initial study of this method has been briefed in [27]. In this method, the complexity of 3-D interconnects is overcome by seeking the full-wave solution of a few 2-D problems, which are then postprocessed to obtain the solution of the original 3-D problem.…”

mentioning

confidence: 99%

“…In this method, the complexity of 3-D interconnects is overcome by seeking the full-wave solution of a few 2-D problems, which are then postprocessed to obtain the solution of the original 3-D problem. In this paper, we will introduce segmentation of the interconnect structure and identification of the structure seeds, detail the eigenvalue-based formulation, present a new on-chip mode-matching technique that was not described in [27], introduce a junction matrix acceleration technique, present a fast frequency sweep analysis, and demonstrate the accuracy and high capacity of the proposed method by a number of numerical and experimental results.…”

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confidence: 99%

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A Fast Frequency-Domain Eigenvalue-Based Approach to Full-Wave Modeling of Large-Scale Three-Dimensional On-Chip Interconnect Structures

Jiao

Zhu

Chakravarty

2008

IEEE Trans. Adv. Packag.

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S., "A fast frequency-domain eigenvalue-based approach to full-wave modeling of large-scale three-dimensional on-chip interconnect structures" (2008) Abstract-As on-chip circuits have scaled into the deep submicron regime, electromagnetics-based analysis has increasingly become essential for high-performance integrated circuit (IC) design. Not only fast, but also high-capacity electromagnetic solutions are demanded to overcome the large problem size facing on-chip design community. In this paper, we present a novel, high-capacity, and fast approach to the full-wave modeling of 3-D on-chip interconnect structures. In this approach, the interconnect structure is decomposed into a number of seeds. In each seed, the original wave propagation problem is represented as a generalized eigenvalue problem. The resulting eigenvalue representation can comprehend both conductor and dielectric losses, arbitrary dielectric and conductor configuration in the transverse cross section, and arbitrary material. A new mode-matching technique applicable to on-chip interconnects is developed to solve large-scale 3-D problems by using 2-D-like CPU time and memory. A junction matrix acceleration technique is proposed to speed up the mode matching process. A fast frequency sweep technique is employed to obtain the response over the entire frequency band by solving at one or a few frequency points only. An extraction technique is developed to obtain S-parameters from the solution of the eigenvalue system. The entire procedure is numerically rigorous without making any theoretical approximation. Experimental and numerical results demonstrate its accuracy and efficiency.

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Section: E Fast Frequency Sweep Techniquementioning

confidence: 99%

mentioning

confidence: 99%

mentioning

confidence: 99%

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A Fast Frequency-Domain Eigenvalue-Based Approach to Full-Wave Modeling of Large-Scale Three-Dimensional On-Chip Interconnect Structures

Jiao

Zhu

Chakravarty

2008

IEEE Trans. Adv. Packag.

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“…Significant mismatch between measurements and RLC models was observed at multigigahertz frequencies on 3-D interconnect bus structures [1]. In contrast, full-wave electromagnetic-based modeling accurately captured the measured behavior over the entire frequency band [1], [2]. The mismatch between RLC models and measurements was attributed to the decoupled E and H model employed in static modeling by extracting the capacitance and inductance independent of each other [1].…”

Section: Introductionmentioning

confidence: 99%

“…Having realized the importance of full-wave electromagnetic analysis in high frequency chip design, and the unique modeling challenges of IC problems, researchers in both circuit and fields have been working on developing innovative electromagnetic solutions [2]- [13]. However, most of the research efforts have been placed on enriching existing electromagnetic modeling techniques with new capabilities to address on-chip intricacy.…”

Section: Introductionmentioning

confidence: 99%

A Layered Finite Element Method for Electromagnetic Analysis of Large-Scale High-Frequency Integrated Circuits

Jiao

Chakravarty

Dai

2007

IEEE Trans. Antennas Propagat.

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A high-capacity electromagnetic solution, layered finite element method, is proposed for high-frequency modeling of large-scale three-dimensional on-chip circuits. In this method, first, the matrix system of the original 3-D problem is reduced to that of 2-D layers. Second, the matrix system of 2-D layers is further reduced to that of a single layer. Third, an algorithm of logarithmic complexity is proposed to further speed up the analysis. In addition, an excitation and extraction technique is developed to limit the field unknowns needed for the final circuit extraction to a single layer only, as well as keep the right-hand side intact during the matrix reduction process. The entire procedure is numerically rigorous without making any theoretical approximation. The computational complexity only involves solving a single layer irrespective of the original problem size. Hence, the proposed method is equipped with a high capacity to solve large-scale IC problems. The proposed method was used to simulate a set of large-scale interconnect structures that were fabricated on a test chip using conventional Si processing techniques. Excellent agreement with the measured data has been observed from dc to 50 GHz.Index Terms-Electromagnetics, finite element method, high capacity, high frequency, on-chip circuits, three dimension.

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A Multistep Extrapolated S-Parameter Model for Arbitrary On-Chip Interconnect Structures

Bacinschi¹,

Glesner²

2011

VLSI-SoC: Technologies for Systems Integration

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Accurate high-frequency interconnect models are needed for the precise estimation of signal delays, crosstalk, and energy losses in complex on-chip communication structures, such as hierarchical bus architectures and networks-on-chip. In this chapter we introduce a computationally-efficient wide-bandwidth characterization method based on an incremental extrapolation of S-parameters for arbitrary interconnect structures. Our method defines a systematic set of a priori parameter extractions and performs on-demand multistep extrapolations for interconnect segments with specified wire length, widths, spacings, metal layer, and neighboring routing information. Experimental evaluations show a maximum absolute error of less than 2·10 −2 (magnitude) and 7 degrees (angle) between our model and an industry-standard full-wave field simulator for a 90-nm CMOS process. We consistently enforce the passivity of the admittance matrices for each set of measured or generated parameters to eliminate the possible errors introduced during parameter measurements and extrapolation. Circuit-level simulations with the extrapolated model show a maximum signal delay error of less than 12.5% across multiple metal layers and wire configurations.

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A novel technique for full-wave modeling of large-scale three-dimensional high-speed on/off-chip interconnect structures

Cited by 33 publications

References 9 publications

A Fast Frequency-Domain Eigenvalue-Based Approach to Full-Wave Modeling of Large-Scale Three-Dimensional On-Chip Interconnect Structures

A Fast Frequency-Domain Eigenvalue-Based Approach to Full-Wave Modeling of Large-Scale Three-Dimensional On-Chip Interconnect Structures

A Layered Finite Element Method for Electromagnetic Analysis of Large-Scale High-Frequency Integrated Circuits

A Multistep Extrapolated S-Parameter Model for Arbitrary On-Chip Interconnect Structures

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