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

Alexandre Mayer, Marwan Mousa , Mark Hagmann, Richard Forbes

Résultats de recherche: Contribution à un journal/une revueArticle

Résumé

We test the consistency with which Simmons’ model can predict the local current density obtained for flatmetal-vacuum-metal junctions. The image potential energy used in Simmons’ original papers had a missingfactor of 1/2. Besides this technical issue, Simmons’ model relies on a mean-barrier approximation forelectron 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 comparethe results of this expression with those provided by a transfer-matrix technique. This technique is knownto provide numerically exact solutions of Schrodinger’s equation for this barrier model. We also considerthe current densities provided by a numerical integration of the transmission probability obtained with theWKB approximation and Simmons’ mean-barrier approximation. The comparison between these differentmodels shows that Simmons’ expression for the local current density actually provides results that are ingood agreement with those provided by the transfer-matrix technique, for a range of conditions of practicalinterest. We show that Simmons’ model provides good results in the linear and field-emission regimes ofcurrent density versus voltage plots. It loses its applicability when the top of the potential-energy barrierdrops below the Fermi level of the emitting metal.
langue originaleAnglais
Pages (de - à)63-77
Nombre de pages10
journalJordan Journal of Physics
Volume12
Numéro de publication1
étatPublié - 2019

Empreinte digitale

potential energy
current density
vacuum
metals
approximation
numerical integration
field emission
plots
electric potential

mots-clés

  • electronic field emission
  • transfer matrix
  • theory
  • junction
  • electronic transport

Citer ceci

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title = "Numerical testing by a transfer-matrix technique of Simmons' equation for the local current density in metal-vacuum-metal junctions",
abstract = "We test the consistency with which Simmons’ model can predict the local current density obtained for flatmetal-vacuum-metal junctions. The image potential energy used in Simmons’ original papers had a missingfactor of 1/2. Besides this technical issue, Simmons’ model relies on a mean-barrier approximation forelectron 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 comparethe results of this expression with those provided by a transfer-matrix technique. This technique is knownto provide numerically exact solutions of Schrodinger’s equation for this barrier model. We also considerthe current densities provided by a numerical integration of the transmission probability obtained with theWKB approximation and Simmons’ mean-barrier approximation. The comparison between these differentmodels shows that Simmons’ expression for the local current density actually provides results that are ingood agreement with those provided by the transfer-matrix technique, for a range of conditions of practicalinterest. We show that Simmons’ model provides good results in the linear and field-emission regimes ofcurrent density versus voltage plots. It loses its applicability when the top of the potential-energy barrierdrops below the Fermi level of the emitting metal.",
keywords = "electronic field emission, transfer matrix, theory, junction, electronic transport",
author = "Alexandre Mayer and Marwan Mousa and Mark Hagmann and Richard Forbes",
year = "2019",
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pages = "63--77",
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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; Hagmann, Mark; Forbes, Richard.

Dans: Jordan Journal of Physics, Vol 12, Numéro 1, 2019, p. 63-77.

Résultats de recherche: Contribution à un journal/une revueArticle

TY - JOUR

T1 - Numerical testing by a transfer-matrix technique of Simmons' equation for the local current density in metal-vacuum-metal junctions

AU - Mayer, Alexandre

AU - Mousa , Marwan

AU - Hagmann, Mark

AU - Forbes, Richard

PY - 2019

Y1 - 2019

N2 - We test the consistency with which Simmons’ model can predict the local current density obtained for flatmetal-vacuum-metal junctions. The image potential energy used in Simmons’ original papers had a missingfactor of 1/2. Besides this technical issue, Simmons’ model relies on a mean-barrier approximation forelectron 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 comparethe results of this expression with those provided by a transfer-matrix technique. This technique is knownto provide numerically exact solutions of Schrodinger’s equation for this barrier model. We also considerthe current densities provided by a numerical integration of the transmission probability obtained with theWKB approximation and Simmons’ mean-barrier approximation. The comparison between these differentmodels shows that Simmons’ expression for the local current density actually provides results that are ingood agreement with those provided by the transfer-matrix technique, for a range of conditions of practicalinterest. We show that Simmons’ model provides good results in the linear and field-emission regimes ofcurrent density versus voltage plots. It loses its applicability when the top of the potential-energy barrierdrops below the Fermi level of the emitting metal.

AB - We test the consistency with which Simmons’ model can predict the local current density obtained for flatmetal-vacuum-metal junctions. The image potential energy used in Simmons’ original papers had a missingfactor of 1/2. Besides this technical issue, Simmons’ model relies on a mean-barrier approximation forelectron 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 comparethe results of this expression with those provided by a transfer-matrix technique. This technique is knownto provide numerically exact solutions of Schrodinger’s equation for this barrier model. We also considerthe current densities provided by a numerical integration of the transmission probability obtained with theWKB approximation and Simmons’ mean-barrier approximation. The comparison between these differentmodels shows that Simmons’ expression for the local current density actually provides results that are ingood agreement with those provided by the transfer-matrix technique, for a range of conditions of practicalinterest. We show that Simmons’ model provides good results in the linear and field-emission regimes ofcurrent density versus voltage plots. It loses its applicability when the top of the potential-energy barrierdrops below the Fermi level of the emitting metal.

KW - electronic field emission

KW - transfer matrix

KW - theory

KW - junction

KW - electronic transport

UR - https://arxiv.org/abs/1812.07381

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SP - 63

EP - 77

JO - Jordan Journal of Physics

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SN - 1994-7607

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