  We describe the electro-thermal transport in metallic carbon nanotubes
(m-CNTs) by a semi-classical approach that takes into account the high-field
dynamical interdependence between charge carrier and phonon populations. Our
model is based on the self-consistent solution of the Boltzmann transport
equation and the heat equation mediated by a phonon rate equation that accounts
for the onset of non-equilibrium (optical) phonons in the high-field regime.
Given the metallic nature of the nanostructures, a key ingredient of the model
is the assumption of local thermalization of charge carriers. Our theory
remarkably reproduces the room temperature electrical characteristics of m-CNTs
on substrate and free standing (suspended), shedding light on charge-heat
transport in these one dimensional nanostructures. In particular, the negative
differential resistance observed in suspended m-CNTs under electric stress is
attributed to inhomogeneous field profile induced by self-heating rather than
the presence of hot phonons.
