Field emission from a nanometric paraboloidal emitter

Highlights: • The field emitted current from a paraboloid of radius of curnature R• The incident current density used was calculated from the exact wavefunctions of the paraboloid. • A 3-dimensional WKB method was used for the transmission coefficient. • The Fowler-Nordheim plots obtained exhibit strong non-linearities. • The importance of the non-linearities is discussed. - Abstract: When the radius of curvature R of an electron emitter is below 5 nm existing theories of field emission from curved surfaces fail because they assume a constant supply of electrons which is a characteristic only of planar surface emitters. In a previous work of ours we proved that the eigenfuctions of a rotationally symmetric parabolic emitter-the common shape of present nanoscopic emitters- are Whittaker functions and exhibit strong localization. In this paper we calculate the transmitted current density of such an emitter as a function of angle of emission θ and R. The angular dependence of the emitted current density is not very different from that of the classical model of a hemisphere on a post. However, when use is made of the parabolic image potential it is observed that the emission falls significantly. Finally, strongly non-linear Fowler-Nordheim plots are obtained. The significance of this is discussed.