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.
Highlights
Field electron emission (FE) is one of the paradigm examples of quantum-mechanical tunnelling, and has importance as such
(1) At this point in time, theory and simulations need to work with ideal FE devices/systems, so that the complications associated with non-ideality can be avoided
We need to establish how gn depends on emitter shape and on the assumptions made about the emission physics. (c) We need to investigate the behaviour of the shape contribution kA in the limit of large emitter apex radius
Summary
Field electron emission (FE) is one of the paradigm examples of quantum-mechanical tunnelling, and has importance as such. The finite-temperature core form of the MG FE equation gives the local emission current density (LECD) JLMGT in terms of the local work function φ, the emitter temperature T and the magnitude FL of the local surface electrostatic field (FL is called here the local barrier field). For an ideal FE device/system involving a point-form emitter, if some expression JL for LECD is available, and the local barrier field FL (and any other relevant parameters) are known at all relevant surface positions on the emitter, the total emission current. Because there is non-integral field dependence in the pre-exponential in equation (1.4), and partly because there is expected to be voltage dependence in An as well as in Ja (but mainstream FE theories usually take An as constant), the present work needs to employ a current–voltage FE equation different in form from those normally used. A preliminary account of this work was given as a conference poster in July 2019 [13]
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