2011
DOI: 10.1098/rspa.2011.0025
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Transmission coefficients for the exact triangular barrier: an exact general analytical theory that can replace Fowler & Nordheim's 1928 theory

Abstract: In field electron emission theory, evaluating the transmission coefficient D ET for an exact triangular (ET) potential energy barrier is a paradigm problem. This paper derives a compact, exact, general analytical expression for D ET , by means of an Airy function approach that uses a reflected barrier and puts the origin of coordinates at the electron's outer classical turning point. This approach has simpler mathematics than previous treatments. The expression derived applies to both tunnelling and 'flyover' … Show more

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Cited by 88 publications
(56 citation statements)
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“…k M is the macroscopic pre-exponential correction factor. m F is correction factor having value of principal Schottky-Nordheim barrier function m. The constants a = 1.54 9 10 -6 AeV/V 2 and b = 6.83 9 10 7 eV 3/2 V/cm are known as first and second FN constants [33]. The enhancement factor b is calculated from the FN plots of the form ln {J/E 2 }versus 1/E, where E is the applied macroscopic field and J M is the emitter-average current density.…”
Section: Field Emission Studies Of Hybrid Structurementioning
confidence: 99%
“…k M is the macroscopic pre-exponential correction factor. m F is correction factor having value of principal Schottky-Nordheim barrier function m. The constants a = 1.54 9 10 -6 AeV/V 2 and b = 6.83 9 10 7 eV 3/2 V/cm are known as first and second FN constants [33]. The enhancement factor b is calculated from the FN plots of the form ln {J/E 2 }versus 1/E, where E is the applied macroscopic field and J M is the emitter-average current density.…”
Section: Field Emission Studies Of Hybrid Structurementioning
confidence: 99%
“…These excited states, if occupied in the bulk, may emit electrons into the vacuum under the necessary energy-momentum conservation by either above barrier photoemission or photo-assisted tunneling; respectively, paths A and B in figure 1. The transmission through or over the triangular barrier generated by an applied surface acceleration field E acc of the electron gun is described by Forbes and Deane's recent exact analytical one-dimensional quantum solution [30]. In our extension of this formalism into the transverse dimension parallel to the planar photocathode surface, we invoke transverse momentum conservation in the electron emission [22], employ the energy-momentum relationships of both the bulk and vacuum states, and include their local density of states (LDS).…”
Section: Photoemission Formalismmentioning
confidence: 99%
“…which then allows the bulk band dispersion to be included in the transmission coefficient of the triangular barrier for emitted electrons [30];ˊṕ…”
Section: Photoemission Formalismmentioning
confidence: 99%
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