Acoustic Phonons and Phonon Bottleneck in Single Wall Nanotubes

Abstract

Acoustic phonons are modeled by applying the elastic continuum model to single wall nanotubes (SWNTs) with the nanotube approximated as an elastic membrane with cylindrical symmetry. Donnell’s equations of motion for a cylindrical membrane are solved using the Rayleigh-Ritz method to give the acoustic vibrational modes of SWNTs. The dispersion relations are compared for various diameter nanotubes. These calculations provide the full set of phonon modes for the SWNTs; this is in contrast to most calculations that consider a subset of these modes. The allowed phonon assisted electronic transitions are considered for intravalley-intrasubband and intravalley-intersubband transitions. Finally, these results indicate that phonon-bottleneck effects should be important for the short nanotubes being considered for nanotube-based devices exhibiting quasi-ballistic transport.