Modelization of resistive heating of carbon nanotubes during field emission

In this paper we simulate the resistive heating of carbon nanotubes (CNT's) during field emission (FE) using the one-dimensional heat equation including radiation and conductive losses. The simulations are in relatively good agreement with our recent experiments in which we measured the heating of individual CNT's to as high as 2000 K during FE for currents ${I}_{\mathrm{FE}}$ of $\ensuremath{\approx}2 \ensuremath{\mu}\mathrm{A}.$ For low temperatures where radiation is negligible the simulations reduce to an analytic solution that provides a universal guide to estimating current-induced heating in CNT's. The effects of this heating are included in the calculations of ${I}_{\mathrm{FE}}$ as a function of voltage.