Abstract
It is well known that graphene demonstrates spatial dispersion properties [1]-[3], i.e., its conductivity is nonlocal and a function of spectral wave number (momentum operator) q. In this work, to fully account for effects of spatial dispersion on transmission of high-speed signals along graphene nanoribbon (GNR) interconnects, a discontinuous Galerkin time-domain (DGTD) algorithm is proposed. The atomically thick GNR is modeled using a nonlocal transparent surface impedance boundary condition (SIBC) [4] incorporated into the DGTD scheme. Since the conductivity is a complicated function of q (and one cannot find an analytical Fourier transform pair between q and spatial differential operators), an exact time domain SIBC model cannot be derived. To overcome this problem, the conductivity is approximated by its Taylor series in spectral domain under low-q assumption. This approach permits expressing the time domain SIBC in the form of a second-order partial differential equation (PDE) in current density and electric field intensity. To permit easy incorporation of this PDE with the DGTD algorithm, three auxiliary variables, which degenerate the second order (temporal and spatial) differential operators to first-order ones, are introduced. Regarding to the temporal dispersion effects, the auxiliary differential equation (ADE) method [4] is utilized to eliminates the expensive temporal convolutions. To demonstrate the applicability of the proposed scheme, numerical results, which involve characterization of spatial dispersion effects on the transfer impedance matrix of GNR interconnects, will be presented.
Recommended Citation
P. Li et al., "Numerical Modeling Of Graphene Nano-Ribbon By DGTD Taking Into Account The Spatial Dispersion Effects," Progress in Electromagnetics Research Symposium, pp. 2269 - 2272, article no. 8597805, Institute of Electrical and Electronics Engineers, Dec 2018.
The definitive version is available at https://doi.org/10.23919/PIERS.2018.8597805
Department(s)
Electrical and Computer Engineering
International Standard Book Number (ISBN)
978-488552315-1
International Standard Serial Number (ISSN)
1931-7360; 1559-9450
Document Type
Article - Conference proceedings
Document Version
Citation
File Type
text
Language(s)
English
Rights
© 2024 Institute of Electrical and Electronics Engineers, All rights reserved.
Publication Date
31 Dec 2018
Comments
National Natural Science Foundation of China, Grant AoE/P-04/08