Derivation of a generalized Fowler–Nordheim equation for nanoscopic field-emitters

Abstract

In this paper, we derive analytically from first principles a generalized Fowler-Nordheim (FN) type equation that takes into account the curvature of a nanoscopic emitter and is generally applicable to any emitter shape provided that the emitter is a good conductor and no field-dependent changes in emitter geometry occur. The traditional FN equation is shown to be a limiting case of our equation in the limit of emitters of large radii of curvature R. Experimental confirmation of the validity of our equation is given by the data of three different groups. Upon applying our equation to experimental FN plots complying with the above limitations, one may deduce (i) R and (ii) standard field emission parameters-e.g. enhancement factor-with better accuracy than by using the FN equation.

Ab initio calculation of field emission from metal surfaces with atomic-scale defects

“…It has already been shown that the FN equation is valid only for surfaces with radii of curvature larger than ≈ 20 nm 31,32 . Although the behaviour of non-planar emitters has been studied extensively [33][34][35][36][37][38] , these works relied on analytical approximations for the surface potential barrier, the assumption of a smooth, well defined surface for the emitter and a semi-classical approach for the transmission probability.…”

The tunneling potential for field emission from nanotips

“…For axially symmetric emitters, the form of the nonlinear external potential has recently been studied using a different approach 22 . It has been shown that along the symmetry axis of the emitter, for ∆s < R a , the external potential energy V ext takes the form…”

Switch-on Phenomena and Field Emission from Multi-Walled Carbon Nanotubes Embedded in Glass

“…As for the current steps, they most likely reflect changes in the surface structure (Swanson & Bell, 1973) and/or in the adsorbate coverage (adsorption, desorption or diffusion) ( Lee et al, 1995). The former possibility is unlikely because of the structure of the cap, whereas it is well known that small changes in adsorbate coverage result in large variations of the work function (Kyritsakis & Xanthakis, 2015;Lee et al, 1995). This effect is probably enhanced by the non-metallic character of the tip.…”