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

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.