General form of the tunnelling barrier for nanometrically sharp electron emitters

TL;DR

This paper generalizes the tunneling barrier model for nanometric electron emitters, showing that the correction terms depend on the mean curvature of the emitter surface, improving the accuracy of emission predictions.

Contribution

It introduces a universal relation linking the correction terms in the tunneling potential to the mean curvature for any emitter geometry.

Findings

Correction terms are proportional to the mean curvature.

The model applies to arbitrary emitter shapes.

Improves understanding of field electron emission at the nanoscale.

Abstract

Field electron emission from nanometer-scale objects deviates from the predictions of the classical emission theory as both the electrostatic potential curves within the tunneling region and the image potential deviates from the planar one. This impels the inclusion of additional correction terms in the potential barrier. At the apex of a tip-like rotationally symmetric surface, these terms are proportional to the (single) local emitter curvature. The present paper generalizes this relation, showing that for any emitter geometry, the coefficient of the correction terms is given by the mean curvature, i.e. the average of the two principal curvatures.