Universal expansion of the tunnelling electrostatic potential for field electron emission from sharp surfaces

Andreas Kyritsakis

Published 2022-07-13Version 1

Field electron emitters with radii of curvature less than about 20 nm exhibit a significant deviation from the predictions of the classical field emission theory, because the electrostatic potential becomes significantly curved within the tunnelling distance. This issue has been tackled by introducing a second-order correction to the classical field emission equations, based on expanding the electrostatic potential near the emitting surface and keeping up to the quadratic term. Furthermore, it has been shown that at the apex of a tip-like rotationally symmetric emitting surface, where the two principal curvatures of the surface coincide, the coefficient of the quadratic term is proportional to the single local emitter curvature. In this work, we generalize this, showing rigorously that at any point of an arbitrary emitting equipotential surface, the coefficient of the quadratic term in the expansion of the electrostatic potential is given by the mean curvature of the surface, i.e. the average of the two principal curvatures.