  We analyze transport in metallic single-wall carbon nanotubes (SWNTs) on
insulating substrates over the bias range up to electrical breakdown in air. To
account for Joule self-heating, a temperature-dependent Landauer model for
electrical transport is coupled with the heat conduction equation along the
nanotube. The electrical breakdown voltage of SWNTs in air is found to scale
linearly with their length, approximately as 5 V/um; we use this to deduce a
thermal conductance between SWNT and substrate g ~ 0.17 +/- 0.03 W/K/m per tube
length, which appears limited by the SWNT-substrate interface rather than the
thermal properties of the substrate itself. We examine the phonon scattering
mechanisms limiting electron transport, and find the strong temperature
dependence of the optical phonon absorption rate to have a remarkable influence
on the electrical resistance of micron-length nanotubes. Further analysis
reveals that unlike in typical metals, electrons are responsible for less than
15% of the total thermal conductivity of metallic nanotubes around room
temperature, and this contribution decreases at high bias or higher
temperatures. For interconnect applications of metallic SWNTs, significant
self-heating may be avoided if power densities are limited below 5 uW/um, or if
the SWNT-surrounding thermal interface is optimized.
