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Numerical testing by a transfer-matrix technique of Simmons' equation for the local current density in metal-vacuum-metal junctions

Mayer, Alexandre, Mousa, Marwan S., Hagmann, Mark J. and Forbes, Richard (2018) Numerical testing by a transfer-matrix technique of Simmons' equation for the local current density in metal-vacuum-metal junctions Jordan Journal of Physics.

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Abstract

We test the consistency with which Simmons' model can predict the local current density obtained for at metal-vacuum-metal junctions. The image potential energy used in Simmons' original papers had a missing factor of 1=2. Besides 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. This technique is known to provide numerically exact solutions of Schrodinger's equation for this barrier model. 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 weld-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.

Item Type: Article
Divisions : Faculty of Engineering and Physical Sciences
Authors :
NameEmailORCID
Mayer, Alexandre
Mousa, Marwan S.
Hagmann, Mark J.
Forbes, RichardR.Forbes@surrey.ac.uk
Date : 8 October 2018
Uncontrolled Keywords : Field electron emission, theory, metal-vacuum-metal junction, transmission probability, mean-barrier approximation, transfer-matrix technique
Depositing User : Rebecca Cooper
Date Deposited : 11 Jan 2019 14:13
Last Modified : 11 Jan 2019 15:13
URI: http://epubs.surrey.ac.uk/id/eprint/850125

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