Semianalytical model of electron source potential barriers

Abstract

Potential barrier profiles are developed for the study of field and thermionic emission electron sources. The model consists of the exchange and correlation potential, an ionic core potential to correct the “jellium” model, a triangular representation of the barrier, and a numerical integration of Poisson’s equation to evaluate the dipole potential. As a test, evaluations of the work function of various metals are made which rely on “effective” ionic radii which are often close to the actual ionic radii, and a good correspondence is found between the potential profiles and an “analytic” image charge potential. Modifications to the parameters inherent in the Richardson–Laue–Dushman and Fowler–Nordheim equations, so as to obtain current density estimates, are described. The method is suggested to be suitable for the analysis of more complex potential barrier profiles which are encountered in actual (realistic) thermionic and field emission electron sources, in that it captures the behavior of the exchange–correlation potential near the surface and includes those effects in the image charge potential.