Abstract
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 beta(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 beta(c) and S-eff, which agree well with our initial emission condition. It is found that the values of beta(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 beta(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 beta(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. (C) 2013 American Institute of Physics. [http://dx.doi.org/10.1063/1.4798926]