Phonon populations and electrical power dissipation in carbon nanotube transistors

Carbon nanotubes and graphene are candidate materials for nanoscale electronic devices(1,2). Both materials show weak acoustic phonon scattering and long mean free paths for low-energy charge carriers. However, high-energy carriers couple strongly to optical phonons(1,3), which leads to current saturation(4-6) and the generation of hot phonons(7). A non-equilibrium phonon distribution has been invoked to explain the negative differential conductance observed in suspended metallic nanotubes(8), while Raman studies have shown the electrical generation of hot G-phonons in metallic nanotubes(9,10). Here, we present a complete picture of the phonon distribution in a functioning nanotube transistor including the G and the radial breathing modes, the Raman-inactive zone boundary K mode and the intermediate-frequency mode populated by anharmonic decay. The effective temperatures of the high- and intermediate-frequency phonons are considerably higher than those of acoustic phonons, indicating a phonon-decay bottleneck. Most importantly, inclusion of scattering by substrate polar phonons is needed to fully account for the observed electronic transport behaviour.