Influence of thermal contact resistance on the field emission characteristics of a carbon nanotube

Abstract

A recent algorithm developed by Tripathi et al. [J. Appl. Phys. 128, 025017 (2020); Erratum, J. Appl. Phys. 131, 169901 (2022)] is modified to study the effects of thermal contact resistance on the field emission (FE) properties of a carbon nanotube (CNT). The model takes into account the temperature dependence of the CNT electrical and thermal conductivities. The boundary condition proposed by Huang et al. [Phys. Rev. Lett. 93, 7 (2004)] is used to include the effects of thermal contact resistance at a CNT/chuck interface located at x=0, i.e., Tc=T(x=0)=λπr2κ(Tc)(∂T/∂x)x=0+T0, where r is the CNT radius, κ(Tc) is the heat conduction coefficient at x=0, and λ is the thermal resistivity of the CNT/chuck interface. The chuck is assumed to be a perfect heat sink at temperature T0. For a given set of CNT parameters and values of the applied external electric field, it is shown that current constriction at the CNT/chuck contact point leads to self-heating effects which increase with the value of the thermal contact resistance, leading to an increase in the temperature profile along the CNT (including the temperature at its tip) and the FE current above their values obtained assuming the CNT/chuck interface is at the heat sink temperature T0. The fractional change of the emission current versus applied external electric field is calculated for increasing values of the parameter λ.