Cohesive band structure of carbon nanotubes for applications in quantum transport

Abstract

An integrated cohesive band structure of carbon nanotubes (CNTs) applicable to all chirality directions (n, m), starting from the Dirac cone of a graphene nanolayer in k-space, is demarcated, in direct contrast to dissimilar chiral and achiral versions in the published literature. The electron wave state of a CNT is quantized into one-dimensional (1-D) nanostructure with a wrapping mode, satisfying the boundary conditions from one Dirac K-point to an equivalent neighboring one with an identical phase and returning to the same K point. The repetitive rotation for an identical configuration with added band index (n-m)mod3, yields one metallic (M) with zero bandgap corresponding to (n-m)mod3 = 0, semiconducting state SC1 with (n-m)mod3 = 1 and SC2 with (n-m)mod3 = 2. The band gap and effective mass of SC2 state are twice as large as those of SC1 state. A broad-spectrum expression signifying the linear dependence of the effective mass on the bandgap is obtained. Both the Fermi energy and the intrinsic velocity limiting the current to the saturation level is calculated as a function of the carrier concentration. Limitations of the parabolic approximation are pointed out. Several new features of the band structure are acquired in a seamlessly unified mode for all CNTs, making it suitable for all-encompassing applications. Applications of the theory to high-field transport are advocated with an example of a metallic CNT, in agreement with experimental observations. The mechanism behind the breakdown of the linear current-voltage relation of Ohm's law and the associated surge in resistance are explained on the basis of the nonequilibrium Arora's distribution function (NEADF). These results are important for the performance evaluation and characterization of a variety of applications on CNT in modern nanoscale circuits and devices.

Comment on “Theoretical analysis of high-field transport in graphene on a substrate” [J. Appl. Phys. 116, 034507 (2014)]

“…In a recent paper, 8 NEADF is extended to metallic and semiconducting carbon nanotube (CNT) in agreement with the experimental data on metallic CNT. 9 Yes, if the electric field is not high enough to reach saturation, the velocity will appear to saturate to a much lower value; however, march towards ultimate saturation is on in a finite electric field below the threshold of breakdown, consistent with what Ref.…”

Unified bandgap engineering of graphene nanoribbons

“…The central to all reviewed theories is the band gap and associated effective mass in a semiconducting mode. A cohesive bandgap engineering, similar to what has been reported for a CNT will encourage exploration of ways to enhance its response to external perturbations, doping, and chemical modifications, as well as developing sensors and actuators. Both theory and experiments differ in their outcomes giving metallic or semiconducting GNR depending on the band index similar to what was used for a CNT .…”

“…A cohesive bandgap engineering, similar to what has been reported for a CNT will encourage exploration of ways to enhance its response to external perturbations, doping, and chemical modifications, as well as developing sensors and actuators. Both theory and experiments differ in their outcomes giving metallic or semiconducting GNR depending on the band index similar to what was used for a CNT . The underlying intent of this work is to close that gap in unifying theories that exist in the published literature.…”

“…Dutta and Pati review the importance of two different edge geometries, namely zigzag and armchair, arising from the finite termination of graphene, resulting in vast variety of electronic properties of GNR. A number of theories are at odds in predicting the metallic or semiconducting states of a GNR, necessitating transformation of the mindset similar to what has been reported for carbon nanotube (CNT) . The GNR edges are open without any insulator and hence boundary conditions demand antinodes on the edges.…”

An analytical approach to evaluate the performance of graphene and carbon nanotubes for NH3 gas sensor applications

“…Arora, Tan, and Gupta [12] have studied the carrier statistics of graphene and response of carriers to high electric fields. Arora and Bhattacharyya [13] have combined the carrier statistics of CNTs and discussed the band structure and its applications to quantum transport. In a recent paper [14], Chin et.…”