Low-field semiclassical carrier transport in semiconducting carbon nanotubes

The theory of semiclassical carrier transport in semiconducting single-walled carbon nanotubes is presented. The focus is on transport in response to a small, axially applied field. Carriers are considered to scatter with longitudinal, torsional, and radial breathing acoustic phonons. Theory predicts large mobilities and large mean free paths, each increasing with increasing tube diameter. This results from a small effective mass, which varies inversely with the nanotube diameter. In large diameter tubes, the carrier mobility at $300\mathrm{K}$ is approximately ${10}^5{\mathrm{cm}}^2\mathrm{V}\mathrm{s}$, while the mean free path approaches $0.5-0.8\mu \mathrm{m}$. Results depend on the lattice temperature, Poisson’s ratio, and the chirality angle of the nanotube. Theoretical results compare very well with experiments on long semiconducting carbon nanotubes. This indicates that transport in long single-walled carbon nanotubes is likely limited by phonon scattering at temperatures above $\approx 200\mathrm{K}$.

Figure 1

(Color online) Single-walled carbon nanotube unit cell (Ref. 21). The length and diameter of the unit cell are given in terms of the fundamental tube indices $(n,m)$ and the lattice constant of graphene $(a=2.45\mathrm{\AA })$.

Figure 2

(Color online) Wave vector space for an $(n,m)=(4,2)$ semiconducting single-walled carbon nanotube (solid line segments), superimposed onto the hexagonal Brillouin zone of graphene.

Figure 3

Wave vector space for a semiconducting single-walled carbon nanotube near the Fermi point of graphene $\left(K\right)$ (Ref. 33).

Figure 4

Band energy for the first and second subbands of a semiconducting single- walled carbon nanotube. Here, $\Delta k_{\theta }$ is the displacement of $k_{\theta }$ from the $K$ point of graphene, while $\beta$ is the slope of the low-energy graphene band structure cone.

Figure 5

(Color online) Comparison between the tight-binding effective mass $\left(m_{\mathit{TB}}^{*}\right)$ and the model mass of Eq. (11) $\left(m^{*}\right)$. Semiconducting single-walled carbon nanotubes of all chiralities up to $d=8\mathrm{nm}$ are represented.

Figure 6

(Color online) Orientations of long-wavelength acoustic phonon vibrations in a single-walled carbon nanotube.

Figure 7

(Color online) Effects of subband nonparabolicity on the model low- field mobility in Eq. (40). Nonparabolic effects decrease the mobility more significantly as the tube diameter increases. Results are shown at room temperature for a chiral angle and Poisson’s ratio of 0° and 0.2, respectively.

Figure 8

(Color online) Effects of subband nonparabolicity on the model low- field mobility in Eq. (40). Nonparabolic effects decrease the mobility more significantly as the temperature increases. Results are shown at room temperature for a chiral angle and Poisson’s ratio of 0° and 0.2, respectively.

Figure 9

(Color online) SWCNT-FET of Ref. 14.

Figure 10

(Color online) Comparison of the model low-field mobility in Eq. (40) with the experimental results of Ref. 14. Results using maximum and minimum values for the chiral angle ${\varphi }_c$ and Poisson’s ratio $\nu$ are given. The theoretical results use a value of $2.7\mathrm{eV}$ for the hopping integral $\gamma$.

Figure 11

(Color online) Effects of subband nonparabolicity on the model low-field momentum relaxation length $\left(L_m\right)$ in Eq. (44). Nonparabolic effects decrease $L_m$ more significantly as the tube diameter increases. Results are shown for a range of values for Poisson’s ration $\nu$. The lattice temperature and chiral angle are fixed at $300\mathrm{K}$ and 0°, respectively.

Figure 12

(Color online) Effects of subband nonparabolicity on the model low- field momentum relaxation length $\left(L_m\right)$ in Eq. (44). Nonparabolic effects decrease $L_m$ more significantly as the temperature increases. Results are shown at room temperature for a chiral angle and Poisson’s ratio of 0° and 0.2, respectively.