Refining the application of Fowler–Nordheim theory

This paper contributes to Fowler–Nordheim (FN) theory, i.e. the theory of cold field emission of electrons from metals, by summarising recent developments in standard FN theory and its application to FN plots. The paper is part of a theoretical `tidy up’ and consolidation at the level of the Murphy and Good 1956 treatment, and is a step towards further developments. It re-states the FN equation, in elementary and generalised forms, using modern conventions and the 1986 values of the fundamental physical constants. It presents a formal theory for interpreting FN plots, using a slope correction factor and an intercept correction factor, and relates these to parameters in the generalised FN equation. It explains the concept of an exact emission-area extraction function, and shows how values of this parameter may be used to extract emission-area estimates from FN plots, in the presence of uncertainty about values of field, work-function and current density. It compares the new procedures with existing procedures based on numerical approximations. It briefly explores possible effects of the recently reported field dependence in local work-function. It presents formulae defining the onset of field-induced ballistic emission, and discusses implications. The standard physical assumptions behind the theory are stated, and some ways in which they can break down are noted.