Electrical characteristics of non-linear-barrier field emission: An attempt for a Fowler-Nordheim-like equation to be used with experimental data

It is well-known that for sharp emitters the traditional Fowler-Nordheim equation (FNE) is inadequate. In this paper we give a correction to the FNE. We include a second-order quadratic term to the potential and calculate numerically the Wentzel-Krammers-Brillouin (WKB) integral, thus obtaining the transmission coefficient and the corresponding current density. By fittings to the numerical results, we derive an expression giving the current density as a function of the electric field F, the work function W and the radius of curvature R. If this Fowler-Nordheim-like equation is used with experimental data from sharp field emitters to extract one of these parameters, it will give much more accurate results than the classical Fowler-Nordheim equation. We note that it may be used especially to extract the radius of curvature R of the emitter.