Joule heating induced negative differential resistance in free standing metallic carbon nanotubes

The features of the $IV$ characteristics of metallic carbon nanotubes (m-NTs) in different experimental setups are studied using semi-classical Boltzmann transport equation together with the heat dissipation equation to account for significant thermal effects at high electric bias. Our model predicts that the shape of the m-NT characteristics is basically controlled by heat removal mechanisms. In particular we show that the onset of negative differential resistance in free standing nanotubes finds its origins in strong transport nonlinearities associated with poor heat removal unlike in substrate-supported nanotubes.