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

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.