A new analytical expression for Fowler-Nordheim current density

Abstract

Field emission from metallic emitters is generally described by the Fowler-Nordheim equation. The standard Fowler-Nordheim formula is expressed in terms of elliptic integrals which are not easy to extract a physical interpretation. In this work a single analytical expression for the current density field emission is derived. We utilize one-dimensional model potential which is chosen to yield a reasonable physical representation of the real system. In order to calculate the electronic transmission through the surface barrier we have used the semi-classical (JWKB) approximation. The elliptic integral resulting is expanded in series which permits an analytical procedure that offers the advantage of simplicity and elegance of the final formula.