Further comments on interpreting nearly linear Fowler-Nordheim plots taken from large area field electron emitters

This paper discusses issues relating to the current-voltage characteristics of large-area field electron emitters (LAFEs). It forms part of a continuing project to investigate how the statistical distribution of individual-emitter characteristics affects the interpretation of Fowler-Nordheim plots taken from the LAFE as a whole. It is assumed that tunneling takes place through a Schottky-Nordheim barrier, and that the height and radius of the emitters are Gaussian and uniformly-distributed, respectively. The macroscopic current density, J_M is found to relate to the LAFE kernel current density J_kC as ln{J_M}~ω₀ln{J_kC}. This finding extends previous results that considered site-FEF distributions where the site efficiency σf was not dependent on the site FEF. We conclude that if ω₀ is not considered when extracting values from FN plots, the relative discrepancy between the extracted FEF and the true LAFE characteristic FEF could reach as much as 60%, even in cases where the FN plot passes an orthodoxy test.