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Numerical testing by a transfer-matrix technique of simmons’ equation for the local current density in metal-vacuum-metal junctions
Joint Authors
Forbes, Richard G.
Mayer, Alexandre
Hagmann, M. J.
Musa, Marwan S.
Source
Issue
Vol. 12, Issue 1 (30 Apr. 2019), pp.63-77, 15 p.
Publisher
Yarmouk University Deanship of Research and Graduate Studies
Publication Date
2019-04-30
Country of Publication
Jordan
No. of Pages
15
Main Subjects
Abstract EN
We test the consistency with which Simmons’ model can predict the local current density obtained for flat metal-vacuum-metal junctions.
The image potential energy used in Simmons’ original papers had a missing factor of 1/2.
Beside this technical issue, Simmons’ model relies on a mean-barrier approximation for electron transmission through the potential-energy barrier between the metals.
In order to test Simmons’ expression for the local current density when the correct image potential energy is included, we compare the results of this expression with those provided by a transfer-matrix technique.
We also consider the current densities provided by a numerical integration of the transmission probability obtained with the WKB approximation and Simmons’ mean-barrier approximation.
The comparison between these different models shows that Simmons’ expression for the local current density actually provides results that are in good agreement with those provided by the transfer-matrix technique, for a range of conditions of practical interest.
We show that Simmons’ model provides good results in the linear and field-emission regimes of current density versus voltage plots.
It loses its applicability when the top of the potential-energy barrier drops below the Fermi level of the emitting metal.
Keywords: Field Electron Emission, Theory, Metal-Vacuum-Metal Junction, Transmission Probability, Mean-Barrier Approximation, Transfer-Matrix Technique.
PACS: 85.30.Kk, 79.70.+q, 03.65.Nk.-
American Psychological Association (APA)
Hagmann, M. J.& Mayer, Alexandre& Musa, Marwan S.& Forbes, Richard G.. 2019. Numerical testing by a transfer-matrix technique of simmons’ equation for the local current density in metal-vacuum-metal junctions. Jordan Journal of Physics،Vol. 12, no. 1, pp.63-77.
https://search.emarefa.net/detail/BIM-1246445
Modern Language Association (MLA)
Mayer, Alexandre…[et al.]. Numerical testing by a transfer-matrix technique of simmons’ equation for the local current density in metal-vacuum-metal junctions. Jordan Journal of Physics Vol. 12, no. 1 (2019), pp.63-77.
https://search.emarefa.net/detail/BIM-1246445
American Medical Association (AMA)
Hagmann, M. J.& Mayer, Alexandre& Musa, Marwan S.& Forbes, Richard G.. Numerical testing by a transfer-matrix technique of simmons’ equation for the local current density in metal-vacuum-metal junctions. Jordan Journal of Physics. 2019. Vol. 12, no. 1, pp.63-77.
https://search.emarefa.net/detail/BIM-1246445
Data Type
Journal Articles
Language
English
Notes
Record ID
BIM-1246445