Discontinuous Galerkin Time-Domain Modeling of Graphene Nanoribbon Incorporating the Spatial Dispersion Effects

Ping Li*, Li Jun Jiang, Hakan Bagci

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

20 Scopus citations


It is well known that graphene demonstrates spatial dispersion properties, i.e., its conductivity is nonlocal and a function of spectral wavenumber (momentum operator) q. In this paper, to 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) 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 method is utilized to eliminate 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, are presented.

Original languageEnglish (US)
Pages (from-to)3590-3598
Number of pages9
JournalIEEE Transactions on Antennas and Propagation
Issue number7
StatePublished - Jul 2018


  • Auxiliary differential equation (ADE) method
  • discontinuous Galerkin time-domain (DGTD) method
  • graphene nanoribbon (GNR)
  • nonlocal conductivity
  • spatial dispersion
  • surface impedance boundary condition (SIBC)

ASJC Scopus subject areas

  • Electrical and Electronic Engineering


Dive into the research topics of 'Discontinuous Galerkin Time-Domain Modeling of Graphene Nanoribbon Incorporating the Spatial Dispersion Effects'. Together they form a unique fingerprint.

Cite this