Analysis of nonuniform field emission from a sharp tip emitter of Lorentzian or hyperboloid shape

• Main Authors: Sun, Sheng, Ang, Ricky Lay Kee
• Other Authors: School of Electrical and Electronic Engineering
• Format: Article
• Language: English
• Published: 2013
• Subjects: DRNTU::Science::Physics
• Online Access: https://hdl.handle.net/10356/96424; http://hdl.handle.net/10220/9929
• Institution: Nanyang Technological University

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.