Semiclassical transport and phonon scattering of electrons in semiconducting carbon nanotubes

Abstract

Current flow, considering a semiclassical electron--electric-field interaction and electron scattering by acoustic phonons, is studied in semiconducting zig-zag carbon nanotubes. The $\ensuremath{\pi}$-electronic band structure and the phonon spectrum of the nanotube are both calculated from graphene by the zone-folding method. Scattering rates are calculated using first-order perturbation theory and the deformation-potential approximation, while the selection rules for the electron-phonon interaction are developed based on the conservation of crystal momentum. The steady-state transport properties of electrons in small-diameter nanotubes are simulated using the Monte Carlo method. Results show negative differential mobility occurring at smaller threshold fields as the tube diameter increases. The peak drift velocity is also found to depend on the tube diameter, and reaches values as high as $5\ifmmode\times\else\texttimes\fi{}{10}^{7}\mathrm{c}\mathrm{m}/\mathrm{s}$ in the largest tube considered with a diameter of $\ensuremath{\cong}4.6\mathrm{nm}.$ The simulated low-field mobility is as large as in graphite, $\ensuremath{\cong}2\ifmmode\times\else\texttimes\fi{}{10}^{4}{\mathrm{cm}}^{2}/\mathrm{V}/\mathrm{s},$ for the larger tubes, but decreases as the tube diameter decreases.