Influence of barrier form on Fowler-Nordheim plot analysis

Recent research has described an improved method of Fowler-Nordheim plot analysis, based on the definition and evaluation of a slope correction factor and a new form of intercept correction factor. In this improved approach there exists a basic approximation that neglects certain terms in the general theory, and focuses on the influence of the form of the tunneling barrier on the values of basic slope ({\sigma}B) and intercept ({\rho}B) correction factors. Simple formulae exist that allow these to be evaluated numerically for a barrier of arbitrary well-behaved form. This paper makes an initial exploration of the effects of barrier form on FN plot analysis. For a planar emitter, two models for the correlation-and-exchange (C and E) potential energy (PE) are used. For the Schottky-Nordheim barrier, it is shown that numerical and analytical approaches generate equivalent results. This agreement supports the validity of the numerical methods used. Comparisons with results for the Cutler-Gibbons barrier show that small differences in the assumed C and E PE make little difference to values of {\sigma}B and {\rho}B. Schottky's planar image PE has then been used, in conjunction with the electrostatic PE variation associated with a spherical emitter model, to explore the influence of apex radius r_a on correction-factor values, for values of r_a greater than 20 nm. Both {\sigma}B and {\rho}B increase significantly as r_a decreases, especially {\rho}B. At low values of barrier field F, {\sigma}B depends approximately linearly on 1/F, with a slope that depends on r_a. Suggestions are made for how the exploratory work described in this paper might be extended.