Physical basis for applying the Fowler–Nordheim <i>J</i>–<i>E</i> relationship to experimental <i>I</i>–<i>V</i> data

Abstract

The purpose of this work is to show that the Fowler–Nordheim (FN) current–voltage (I–V) plot [log(I/V2) as a function of 1/V] must be treated, on principle, as nonlinear. The cause of this behavior is outlined to be the fact that the electric field and current density are not constant over the emitter’s surface. Traditional approach of the FN I–V plot as being linear may lead to physical contradictions. These contradictions are brought into light. A field emitter model is then developed, which allows to express in closed analytical equations the above statements. Expressions for field enhancement factor, area factor and also for the I–V relationship are obtained. The FN I–V plot nonlinearities are shown to be greater for smaller voltages. Within this model, the FN I–V plot can be taken as quasilinear, under some assumptions. Suggestions for technological parameter extraction from I–V data through nonlinear or linear least-squares optimization techniques are done.