Modified Fowler-Nordheim Field-Emission Formulae from a Nonplanar-Emitter Model

TL;DR

This paper derives modified Fowler-Nordheim formulas for nonplanar hyperboloidal emitters, revealing how emitter geometry influences field emission and analyzing experimental data with the new model.

Contribution

It introduces analytical modifications to Fowler-Nordheim formulas accounting for nonplanar emitter geometry, specifically hyperboloidal shapes.

Findings

Modified formulas include a sharpness parameter for hyperboloidal emitters.

Analysis of experimental data supports the new model's relevance.

Reconsideration of planar assumptions in traditional F-N models.

Abstract

Field emission formulae, current-voltage characteristics and energy distribution of emitted electrons, are derived analytically for a nonplanar (hyperboloidal) metallic emitter model. The traditional Fowler-Nordheim formulae, which are derived from a planar emitter model, are modified, and the assumption of the planar emitter in the F-N model is reconsidered. Our analytical calculation also reveals the backgrounds of the previous numerical discussion by He et al. on the effect of the geometry of emitter on field emission. The new formulae contain a parameter which characterizes the sharpness of the hyperboloidal emitter, and experimental data of field emissions from clean tungsten emitters and nanotip emitters are analyzed by making use of this feature.