Theory of electron emission from atomically sharp metallic emitters in high electric fields

A systematic theoretical investigation of the effect of tip geometry on the field emission current voltage characteristics from atomically sharp metallic field emitters is presented. A free electron model is used for the metal emitters with non-planar geometries in studying the dependence of the current density on tip geometry, local field, and temperature. To construct the surface potential barriers, the classical image interaction is derived exactly for the metal emitters modeled as cones, paraboloids, hyperboloids and sphere on cones. Numerical results show that the classical image interaction for these non-planar emitter geometries is diminished in magnitude relative to the planar image interaction. It is found that the bias potential for the model emitter significantly modifies the shape of the tunneling barriers, and the resulting form predicts a dramatically enhanced current relative to the classical Fowler-Nordheim result.;The transmission coefficients for the surface potential barriers are evaluated within the WKB approximation. The current-voltage characteristics are then calculated for these models using the kinetic formulation of the current density integral. The calculated results, plotted as log J/V;An approximate analytic expression for the J(V) characteristics of a prototype sharp emitter is derived which exhibits explicitly the dependence of the current density on geometric and material parameters.;The adequacy of a ;Lastly, the effect of tip geometry on the Nottingham energy exchange and temperature stability is studied. The calculated results show that the lower replacement energy yields significant lowering of the inversion temperature. The calculation of current density versus inversion temperature suggests that the non-planar hyperboloidal emitter can be operated at a higher current density.