Interpretation of field emission current–voltage data: Background theory and detailed simulation testing of a user-friendly webtool

Abstract

In field electron emission (FE) studies, interpretation of measured current–voltage characteristics and extraction of emitter characterization parameters are usually carried out within the framework of “smooth planar metal-like emitter (SPME) methodology”, using a data-analysis plot. This methodology was originally introduced in the 1920s. Three main data-plot types now exist: Millikan–Lauritsen (ML) plots, Fowler–Nordheim (FN) plots, and Murphy–Good (MG) plots. ML plots were commonly used in early FE studies, but most modern analysis uses FN plots. MG plots are a recent introduction. Theoretically, it is now known that ML and FN plots are predicted to be slightly curved in SPME methodology, but a Murphy–Good plot will be very nearly straight. Hence (because 1956 Murphy–Good emission theory is “better physics” than 1928 Fowler–Nordheim emission theory as corrected in 1929), expectation is that parameter extraction using a MG plot will be more precise than extraction using either ML plots or FN plots. In technological FE studies, current–voltage characteristics are often converted into other forms. Thus, measured voltage may be converted to (apparent) macroscopic field, and/or current values may be converted to macroscopic current densities. Thus, four data-input forms can be found in the context of analysing FE current–voltage results. It is also the case that over-simplified models of measurement-system behaviour are very widely assumed, and the question of whether simple use of a data-analysis plot is a valid data-interpretation procedure for the particular system under investigation has often been neglected. Past published studies on field emitter materials development appear to contain a high incidence of spurious values for the emitter characterization parameter “characteristic field enhancement factor”. A procedure (the so-called “Orthodoxy Test”) was described in 2013 that allows a validity check on measurement-system behaviour, and found that around 40% of a small sample of results tested were spuriously high, but has had limited uptake so far. To assist with FE current–voltage data interpretation and validity checks, a simple user-friendly webtool has been under design by the lead author. The webtool needs as user input some system specification data and some “range-limits” data from any of the three forms of data-analysis plot, using any of the four data-input variations. The webtool then applies the Orthodoxy Test, and—if the Test is passed—calculates values of relevant emitter characterization parameters. The present study reports the following: (1) systematic tests of the webtool functionality, using simulated input data prepared using Extended Murphy–Good field electron emission theory; and (2) systematic comparisons of the three different data-plot types, again using simulated input data, in respect of the accuracy with which extracted characterization parameter values match the simulation input values. The paper is introduced by a thorough summary review of the theory on which modern SPME-based current–voltage data-analysis procedures are based. The need in principle to move on (in due course) to data-analysis procedures based on curved-emitter emission theory is noted. An important result is to confirm (by simulations) that, particularly in respect of the extraction of formal emission areas, the performance of the Murphy–Good plot is noticeably better than the performances of Fowler–Nordheim and Millikan–Lauritsen plots. This result is important for field electron emission science because it is now known that differences as between different theories of field electron emission often affect the formal emission area.