Effect of the space charge of emitted electrons on field electron emission

Abstract

It is shown that the conventional technique of substituting the field strength at the space charge-emitter interface that is calculated with the Poisson equation into the Fowler-Nordheim formula considerably overestimates the effect of space charge on field electron emission. In this work, the space-charge-induced field attenuation as a function of the emission current density and radius of curvature of the emitter surface is derived using the model of a planar space-charge layer. It is argued that field electron emission cannot be studied in terms of the spherical diode model, since it assumes the presence of a space charge on the back (nonemitting) emitter surface, which is in fact absent. It is stated that one should consider the discrete character of the charges when investigating the space charge in field electron emission, because the mean spacing between the electrons emitted far exceeds the emission barrier width.