Generalization of Fowler–Nordheim field emission theory for nonplanar metal emitters

Abstract

Field emitter tips can now be fabricated with radii of curvature of the order of nm or even the size of a single atom. To include these geometric effects, we have calculated the field emission tunneling currents for hyperboloidal and conical free-electron tip models using geometry-dependent image interactions and bias fields. The numerical results can be fitted by an equation of the form J=AV2 exp(−B/V−C/V2), where A, B, and C are constants depending on material and geometric parameters. The calculated results, plotted as log J/V2 vs 1/V, do not exhibit the straight line behavior predicted by the Fowler–Nordheim model for field emission from a planar surface. Furthermore, the calculated current densities are dramatically enhanced for both the hyperboloidal (rt=10 nm) and conical (cone half-angle=70°) emitter models. In addition, field emission energy distributions for both models are significantly different from that of the Fowler–Nordheim planar model.

An enhanced gas ionization sensor from Y-doped vertically aligned conductive ZnO nanorods

“…Theoretical analysis confirmed that for a metallic hyperbolical tip, the field emission current only increased sharply with the tip radius less than 25 nm [54]. However, our smallest NR diameter is about 86 nm, achieved with 0.17 at% of Y dopant concentration.…”

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

“…The inadequacy of the planar FN theory has been amply demonstrated since the 1990s [6][7][8][9]. In particular, Cutler et al [6][7][8] have shownusing the exact current integral WKB theory-that for sharp nanosized emitters the FN plot is not linear and the current may differ by orders of magnitude from the planar FN theory using in the theory the local field at the apex. Furthermore, extracted values for the local electric field at the emitting surface or the emission area itself may be quite wrong.…”

Field Emission from Graphene Nanosheets

“…Much sophisticated emission theory is developed by several authors (He et al, 1991;Liang & Chen, 2008;Forbes, 2001), and these theories will explain the difference between the straight line obtained by the simple FN plot and the experimentally obtained slightly curved feature (dotted line) in the inset of Fig. 3.…”