Extraction of emission parameters for large-area field emitters, using a technically complete Fowler–Nordheim-type equation

Abstract

In papers on cold field electron emission from large area field emitters (LAFEs), it has become widespread practice to publish a misleading Fowler-Nordheim-type (FN-type) equation. This equation over-predicts the LAFE-average current density by a large highly-variable factor thought to usually lie between 10 3 and 10 9 . This equation, although often referenced to FN's 1928 paper, is a simplified equation used in undergraduate teaching, does not apply unmodified to LAFEs, and does not appear in the 1928 paper. Technological LAFE papers often do not cite any theoretical work more recent than 1928, and often do not comment on the discrepancy between theory and experiment. This usage has occurred widely, in several high-profile American and UK applied-science journals (including Nanotechnology), and in various other places. It does not inhibit practical LAFE development, but can give a misleading impression of potential LAFE performance to non-experts. This paper shows how the misleading equation can be replaced by a conceptually complete FN-type equation that uses three high-level correction factors. One of these, or a combination of two of them, may be useful as an additional measure of LAFE quality; this paper describes a method for estimating factor values using experimental data, and discusses when it can be used. Suggestions are made for improved engineering practice in reporting LAFE results. Some of these should help to prevent situations arising whereby an equation appearing in high-profile applied-science journals is used to support statements that an engineering regulatory body might deem to involve professional negligence.2

Height distribution of equipotential lines in a region confined by a rough conducting boundary

“…Technological applications such as conducting-field emitter devices that operate in Ultra High Vacuum (UHV) conditions, require the control of several properties such as the surface morphology. It is well known that large values of the current intensity on field emitter devices are connected to extremely small values of the effective emitting area [3]. One method to increase the effective area of emission is to use surfaces with an ending fractal boundary with self-affine scale invariance instead of considering structurally regular tips.…”

Epoxylite Influece on Field Electron Emission Properties of Tungsten and Carbon Fiber Tips

“…The first clear review of experimental FE phenomena (then called "autoelectronic emission") was given by Lilienfeld (1922). Many modern emitters operate in the so-called "cold field electron emission (CFE)" regime, which is a regime where (i) the electrons in the emitting region are effectively in local thermodynamic equilibrium and (ii) most electrons escape by deep tunneling from states close to the emitter's Fermi level (Forbes, 2012;Forbes et al, 2015). The first scientist to attempt a presumptive theory for the CFE regime was Schottky (in 1923).…”

“…This theory was later improved by Murphy and Good (1956) and many others. CFE from a bulk emitter is described by approximate equations known as Fowler-Nordheim-type (FN-type) equations (Forbes, 2012;Forbes et al, 2015). The technically complete (generalized) FN-type equation for the local emission current density J L can be written in the form (Forbes, 2012;Lilienfeld, 1922).…”

“…Of course, these two correction factors also depend on the applied field F, as well as material parameters. This equation has been called the "technically complete FN-type equation for J L in terms of ϕ and F" (Forbes, 2012). For the Schottky-Nordheim (SN) barrier (Forbes, 2012), the barrier form correction factor is given by a welldefined special mathematical function v F , sometimes called the "principal SN-barrier function".…”

“…This equation has been called the "technically complete FN-type equation for J L in terms of ϕ and F" (Forbes, 2012). For the Schottky-Nordheim (SN) barrier (Forbes, 2012), the barrier form correction factor is given by a welldefined special mathematical function v F , sometimes called the "principal SN-barrier function". General aims when manufacturing composite micropoint cathodes have been to avoid degradation of the electron emitter tip due to ion sputtering processes during emission, to obtain an electron emitter with long lifetime, and improve the emission characteristics (Mousa, 1990;Mousa & Al Share, 1999;Mousa et al, 2001).…”