Signal Propagation in Carbon Nanotubes of Arbitrary Chirality

Abstract

In carbon nanotubes (CNTs) with large radii, either metallic or semiconducting, several subbands contribute to the electrical conduction, while in metallic nonarmchair nanotubes with small radii the wall curvature induces a large energy gap. In this paper, we propose a model for the signal propagation along single wall CNTs (SWCNTs) of arbitrary chirality, at microwave through terahertz frequencies, which takes into account both these characteristics in a self-consistent way. We first study an SWCNT, disregarding the wall curvature, in the frame of a semiclassical treatment based on the Boltzmann equation in the momentum-independent relaxation time approximation. It allows expressing the longitudinal dynamic conductivity in terms of the number of effective conducting channels. Next, we study the behavior of this number as the nanotube radius varies and its relation with the kinetic inductance and quantum capacitance. Furthermore, we show that the effects of the spatial dispersion are negligible in the collision dominated regimes, whereas they may be important in the collisionless regimes, giving rise to sound waves propagating with the Fermi velocity. Then, we study the effects on the electron transport of the terahertz quantum transition induced by the wall curvature by using a quantum kinetic approach. The nanotube curvature modifies the kinetic inductance and gives arise to an additional RLC branch in the equivalent circuit, related to the terahertz quantum transition. The proposed model can be used effectively for analyzing the signal propagation in complex structures composed of SWCNTs with different chirality, such as bundles of SWCNTs and multiwall CNTs, providing that the tunneling between adjacent shells may be disregarded

Electrical Properties of Graphene for Interconnect Applications

“…By coupling such a relation to Maxwell equations, it is possible to derive a generalized transmission line model for such nano-interconnects. This approach has been followed by the authors to model isolated metallic CNTs in [16], CNTs with arbitrary radius and chirality in [17,18], multi-walled CNTs [19] and GNRs [20]. The semi-classical model gives results consistent with those provided by an alternative hydrodynamic model [21].…”

“…For typical dimensions of the nano-interconnects for the 14 nm technology node and below, this assumption limits the model to a frequency up to some THz. Following the stream of what is done in [18,19,24], in such a condition, the electrodynamics of the π-electrons may be described by the quasi-classical Boltzmann equation. In the following, we start from the 2D case (graphene infinite layer) and then particularize the results to the 1D case (GNRs).…”

“…A detailed discussion on the behavior of such a number M for CNTs and GNRs may be found in [18][19][20], where it is clearly shown how such a quantity strongly depends on the chirality, size and temperature of such carbon nanostructures.…”

A New Mechanism for THz Detection Based on the Tunneling Effect in Bi-Layer Graphene Nanoribbons

“…If the tunneling effect is neglected, the current density along the n-th signal line (n = 1,2) only depends on the electric field on the same line, and the following generalized Ohm's law may be written in the wavenumber domain [32,33]:…”

“…Following the stream of [32,33], by coupling generalized Ohm's law (8) to Maxwell's equations it is possible to model the interconnects in Figure 2 as a lossy multiconductor transmission line (MTL), and, thus, the vectors of the spatial distributions of voltages, ), (z V and currents, I(z), are solutions of the telegraphers' equations, which read in the frequency domain:…”