Abstract
In this paper, we present a methodology to simulate heat transfer within an isolated carbon nanotube attached to an etched tungsten tip during field emission of an electron beam. The simulations predict the field enhancement, emission current, temperature of the carbon nanotube, and distribution of electrons arriving on a target surface. The method integrates electrostatic and transient thermal finite element analyses with algorithms for modeling the field emission (based on Fowler-Nordheim approximation), heating/cooling due to emitting energetic electrons (Nottingham effect), and computation of electron trajectories. Results are presented for the axisymmetric case of an open-ended carbon nanotube separated by a 13.43-μm-gap distance from a flat surface, with voltages ranging between 65 and 145 V. Results suggest that heating of the carbon nanotube is due to the combined Nottingham effect and Joule heating when the current is below about 0.1 pA and that it is solely due to Joule heating for higher currents. Comparisons with the experimental data show very good agreement for the case studied.
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