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

Abstract

For field electron emission (FE), an empirical equation for measured current Im as a function of measured voltage Vm has the form Im = CVmk exp[–B/Vm], where B is a constant and C and k are constants or vary weakly with Vm. Values for k can be extracted (i) from simulations based on some specific FE theory, and in principle (ii) from current–voltage measurements of sufficiently high quality. This paper shows that a 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 modernized ‘least residual’ method, and existing knowledge concerning k-values is summarized. 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 eventually be able to help investigate are indicated.

Keywords

• field electron emission
• empirical field emission equation
• pre-exponential voltage exponent
• field electron emission theory–experiment comparisons
• least-residual method
• local-gradient method