Analysis of nonuniform field emission from a sharp tip emitter of Lorentzian or hyperboloid shape
Ang, Ricky Lay Kee
Date of Issue2013
School of Electrical and Electronic Engineering
For a sharp tip emitter, due to the non-uniform emission feature and the electron beam expansion in the vacuum, it is difficult to precisely determine the average field enhancement factor β_c as well as the effective emission area S_eff for a single field emitter. In this paper, we conduct a numerical experiment to simulate the electron field emission from a sharp tip emitter (Lorentzian or hyperboloid shape). By collecting the emission current I_tot at the finite anode area S_tot, we establish the criteria in using Fowler-Nordheim plot to estimate both β_c and S_eff, which agree well with our initial emission condition. It is found that the values of β_c and S_eff depend on the emitter’s properties as well as the size of the anode area S_tot. In order to determine the precise value of β_c, S_tot must be large enough to collect all the emitted electrons from the sharp tip (e.g., I_tot reaches maximum). As an example, a Lorentzian type emitter with an aspect ratio of 10 (height over width), the effective enhancement factor is about β_c = 33 as compared to the maximal enhancement of 35 at the apex. At similar maximal enhancement factor at the apex (=360), both types of emitters will give different average field enhancement dependent on the collecting area. The extension of this simple model to a statistical more complicated model to simulate field emission from a cathode consisting of many field emitters is also briefly discussed. This paper should be useful to analyze and characterize field emission data together with experimental measurement.
Journal of applied physics
© 2013 American Institute of Physics. This paper was published in Journal of Applied Physics and is made available as an electronic reprint (preprint) with permission of American Institute of Physics. The paper can be found at the following official DOI: http://dx.doi.org/10.1063/1.4798926. One print or electronic copy may be made for personal use only. Systematic or multiple reproduction, distribution to multiple locations via electronic or other means, duplication of any material in this paper for a fee or for commercial purposes, or modification of the content of the paper is prohibited and is subject to penalties under law.