TY - GEN
T1 - Numerical Modeling of Graphene Nano-Ribbon by DGTD Taking into Account the Spatial Dispersion Effects
AU - Li, Ping
AU - Jiang, L. J.
AU - Bagci, Hakan
N1 - KAUST Repository Item: Exported on 2020-10-01
Acknowledgements: This work is supported by the National Natural Science Foundation of China (NSFC) under Grant 61701423, and in part by NSFC 61674105, NSFC 61622106, NSFC 61701424, and in part by UGC of Hong Kong (AoE/P-04/08).
PY - 2019/2/28
Y1 - 2019/2/28
N2 - 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 nano-ribbon (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.
AB - 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 nano-ribbon (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.
UR - http://hdl.handle.net/10754/631670
UR - https://ieeexplore.ieee.org/document/8597805
UR - http://www.scopus.com/inward/record.url?scp=85060914115&partnerID=8YFLogxK
U2 - 10.23919/PIERS.2018.8597805
DO - 10.23919/PIERS.2018.8597805
M3 - Conference contribution
SN - 9784885523168
SP - 2269
EP - 2272
BT - 2018 Progress in Electromagnetics Research Symposium (PIERS-Toyama)
PB - Institute of Electrical and Electronics Engineers (IEEE)
ER -