The pre-exponential voltage-exponent as a sensitive test parameter for field emission theories

TL;DR

This paper proposes using the voltage-exponent k as a sensitive parameter to compare and evaluate different field emission theories against experimental data, aiding in theory validation and selection.

Contribution

It introduces a method to extract and compare the k-value from experiments and simulations, providing a new tool for testing and differentiating field emission theories.

Findings

k-values are reliably extracted when analytical solutions are known.

Extracted k-values are sensitive to emission theory details and emitter shape.

The method can help discriminate between competing FE theories.

Abstract

For field electron emission (FE), an empirical equation for measured current I_m as a function of measured voltage V_m has the form I_m = C*(V_m)^k*exp[-B/(V_m)], where B is a constant and C and k are constants or vary weakly with V_m. Values for k can be extracted (a) from simulations based on some specific FE theory, and in principle (b) from current-voltage measurements of sufficiently high quality. This paper shows that comparison of theoretically derived and experimentally derived k-values could provide a sensitive and useful tool for comparing FE theory and experiment, and for choosing between alternative theories. Existing methods of extracting k-values from experimental or simulated current-voltage data are discussed, including a modernised "least residual" method, and existing knowledge concerning k-values is summarised. Exploratory simulations are reported. Where an analytical result for k is independently known, this value is reliably extracted. More generally, extracted k-values are sensitive to details of the emission theory used, but also depend on assumed emitter shape; these two influences will need to be disentangled by future research, and a range of emitter shapes will need examination. Other procedural conclusions are reported. Some scientific issues that this new tool may be able to help investigate are indicated.