  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.

Mesoscale and Nanoscale Physics