Field-emission from parabolic tips: current distributions, the net current and effective emission area

TL;DR

This paper derives analytical expressions for electron emission distributions, total current, and effective emission area from nano-structured tips, based on the variation of the enhancement factor near the apex.

Contribution

It introduces new analytical formulas linking emission characteristics to apex radius and local electric field, advancing understanding of field emission from nano-tips.

Findings

Derived surface distribution of emitted electrons

Formulated total and normal energy distributions

Expressed net current and emission area in terms of apex parameters

Abstract

Field emission from nano-structured emitters primarily takes place from the tips. Using recent results on the variation of enhancement factor around the apex (Biswas et al, Ultramicroscopy 185, 1-4 (2018)), analytical expressions for surface distribution of net emitted electrons as well as the total and normal energy distributions are derived in terms of the apex radius $R_a$ and the local electric field at the apex $E_a$. Formulae for the net emitted current and effective emission area in terms of these quantities are also obtained.