Generalization of FowlerNordheim 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 freeelectron tip models using geometrydependent image interactions and bias fields. The numerical results can be fitted by an equation of the form J=AV^{2} exp(B/VC/V^{2}), where A, B, and C are constants depending on material and geometric parameters. The calculated results, plotted as log J/V^{2} vs 1/V, do not exhibit the straight line behavior predicted by the FowlerNordheim model for field emission from a planar surface. Furthermore, the calculated current densities are dramatically enhanced for both the hyperboloidal (r_{t}=10 nm) and conical (cone halfangle=70°) emitter models. In addition, field emission energy distributions for both models are significantly different from that of the FowlerNordheim planar model.
 Publication:

Applied Physics Letters
 Pub Date:
 September 1991
 DOI:
 10.1063/1.106257
 Bibcode:
 1991ApPhL..59.1644H