Phonon-Limited Mobility in H/F-functionalized Nanotubes with 1D $π$-chains

TL;DR

This work addresses phonon-limited carrier mobility in zig-zag carbon nanotubes functionalized with hydrogen or fluorine in a chain configuration, focusing on 1D π-channels. Mobility is computed via the Boltzmann transport equation in the self-energy relaxation-time approximation, with τ(ε) derived from electron–phonon coupling using DFTB+ SCC, Phonopy, and DFTBephy, and σ expressed as $σ = \frac{4 e^2}{h L} \sum_n \int_{E_C^n}^{\infty} d\varepsilon \left[-\frac{\partial f(\varepsilon)}{\partial \varepsilon}\right] v_n(\varepsilon) \tau_n(\varepsilon)$, while μ = σ/(e n). The study reveals very small mobility due to the strictly one-dimensional conducting channels, with mean free paths around $λ(ε)=v(ε)τ(ε)$ of order 10 Å at room temperature, making ballistic transport unobservable at 300 K. A central result is a periodic mobility pattern with diameter (chirality index $N$): even $N$ tubes suppress transverse acoustic (TA) phonon scattering due to mirror symmetry, whereas odd $N$ tubes have a doubly degenerate lower π-channel that enhances scattering, yielding distinct temperature dependencies and a decreasing group velocity with diameter. Hydrogenated and fluorinated tubes show similar trends, and the group velocity decreases with diameter, contrary to pure CNTs. These findings imply limited electronic-device utility but potential for gas-sensing applications, particularly for odd-$N$ tubes with more temperature-stable mobility. The study demonstrates that a tight-binding/SERTA framework based on DFTB+ and related tools can efficiently capture phonon-limited transport in large, functionalized CNTs.

Abstract

Electron mobility due to electron-phonon interaction is investigated for fully fluorinated/hydrogenated zig-zag carbon nanotubes containing one-dimensional alternating chains of carbon atoms with $π$-bonds. The behavior of mobility associated with changes in the tube diameter, coating type (F/H) and temperature is revealed. In particular, it is shown that the dependence of mobility on the diameter in such tubes is periodic with the chirality index, which is associated with the absence of scattering on TA phonons in the tubes with an even number of conducting chains due to mirror symmetry. The obtained small values of phonon-limited mobility indicate that tubes with one-dimensional conducting chains are more promising for use as gas sensors than as elements of electronic devices. Calculations are performed within the self-energy relaxation time approximation (SERTA) using the non-orthogonal tight-binding approach.

Figures (8)

• Figure 1: Functionalized by F/H carbon nanotubes in a “chain” configuration. It is evident that with an increase in the chirality indices, the number of one-dimensional $\pi$-chains increases by one from 5 for (10, 0) to 8 for (16,0) tube.
• Figure 2: Band structure near the Fermi level for H-functionalized “chain” carbon nanotubes of different diameters. All branches of $\pi$-chains in both the conduction and valence bands are shown. Values of n are indicated along the $x$ axis. For tubes with n=10 and 14, the lower level is doubly degenerate. F-functionalized CNTs have a similar band structure (not shown). $\Delta E$ is given by Eq. (\ref{['eq.4']}).
• Figure 3: Group velocity for the first branch of hydrogenated CNTs as a function of energy measured from the bottom of the conduction band. The curves run sequentially from top to bottom from the tube with the smallest diameter (10, 0) to the tube with the largest diameter (16, 0). The inset shows the ratio $v_{1,F}(\varepsilon)/v_{1,H}(\varepsilon)$.
• Figure 4: Spectrum of acoustic phonons near the $\Gamma$ point for hydrogenated (10, 0) CNT. From zero there emerge a doubly degenerate quadratic branch TA, as well as linear branches LA and TW.
• Figure 5: (a) Mobility as a function of concentration for all tubes considered. (b) Mobility as a function of diameter: solid lines correspond to a fixed concentration $n = 2\times 10^{12}$ cm$^{-2}$ (intersection points with the vertical curve in the upper plot), dashed lines correspond to the peak (maximum) mobility; $T = 300$ K.