  We show that the local temperature dependence of thermalized electron and phonon populations along metallic carbon nanotubes is the main reason behind this non-linear transport characteristics in the high bias regime. Our model that considers optical and zone boundary phonon emission as well as absorption by charge carriers is based on the solution of the Boltzmann transport equation that assumes a local temperature along the nanotube, determined self-consistently with the heat transport equation. By using realistic transport parameters, our results not only reproduce experimental data for electronic transport, but also provide a coherent interpretation of thermal breakdown under electric stress. In particular, electron and phonon thermalization prohibits ballistic transport in short nanotubes. 
Non-linear transport and heat dissipation in metallic carbon nanotubes