Thermal instability of field emission from carbon nanotubes

Abstract

The mechanism that limits the emission current of a carbon-nanotube-based cathode due to the temperature dependence of the emissivity of the nanotube is studied. This limitation has the character of thermal instability that shows up as an infinite increase in the emitter temperature after a certain emission current is exceeded. The heat conduction equation is solved for a nanotube at various model temperature dependences of the thermal and electrical conductivities of the nanotube in order to derive the limiting emission current as a function of the electrical conductivity of the nanotube.