Electrical and thermal transport in metallic single-wall carbon nanotubes on insulating substrates

We analyze transport in metallic single-wall carbon nanotubes (SWCNTs) 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 SWCNTs in air is found to scale linearly with their length, approximately as $5V∕μm$⁠; we use this to deduce a thermal conductance between SWCNT and substrate $g≈0.17±0.03WK−1m−1$ per tube length, which appears limited by the SWCNT-substrate interface rather than the thermal properties of the substrate itself. We examine the phonon scattering mechanisms that limit 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 SWCNTs, significant self-heating may be avoided if power densities are limited below $5μW∕μm$⁠, or if the SWCNT-surrounding thermal interface is optimized.