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

Abstract

Abstract-It is well known that graphene demonstrates spatial dispersion properties, i.e., its conductivity is nonlocal and a function of spectral wave number (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 timedomain (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 (ADE) method 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, are presented.

Numerical Methods for Electromagnetic Modeling of Graphene: A Review

“…This facilitates the formulation of a secondorder PDE in electric field and current density that is solved together with Maxwell equations using the DGTD method. The nonlocal properties of GNRs have been simulated by this DGTD framework [22]. In addition to RBC and SIBC, in [93], the impedance transmission boundary condition (ITBC) has been used within a wave-equation based DGTD with the same purpose of avoiding a very fine mesh around and inside the graphene layer.…”

“…On the other hand, the channel of the logical devices making use of graphene cannot be switched off since graphene has no band gap. To overcome this problem by opening up the band gap, graphene nanoribbon (GNR) [22] and biased bilayer graphene [23] have been proposed and implemented. Furthermore, the possibility of molecular-scale electronics has been certified by the invention of graphene-based quantum dot devices developed to achieve electron transport [24].…”

A Locally-Implicit Discontinuous Galerkin Time-Domain Method to Simulate Metasurfaces Using Generalized Sheet Transition Conditions

“…It is assumed here that χ ab are time-varying but not dispersive [25]- [27], [44], [45]. The proposed method can easily be extended to simulate dispersive metasurfaces using the well-known auxiliary differential equation method that accounts for susceptibility dispersion models in the time domain [39], [42], [46]- [48].…”

An Elliptically Polarized Wave Injection Technique via Tf/Sf Boundary in Subdomain Level DGTD Method

“…On the other hand, the Discontinuous-Galerkin Time-Domain (DGTD) method [10][11][12][13][14][15][16][17][18][19][20][21][22][23][24][25] to estimate the mutual characteristics of the finite volume time domain (FVTD) method [26] and the FETD method [27,28] have many advantages in dealing with complex and fine structure with high accuracy. As an extension of the isotropic DGTD methods [29,30], the recently emerging anisotropic subdomain level DGTD method exhibits more advantages [31,32] including non-conformal mesh that can alleviate meshing difficulties for large scale problems, and EB-scheme that is more efficient than the EH-scheme.…”