### Abstract

Original language | English |
---|---|

Pages (from-to) | 63-77 |

Number of pages | 10 |

Journal | Jordan Journal of Physics |

Volume | 12 |

Issue number | 1 |

Publication status | Published - 2019 |

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*Jordan Journal of Physics*,

*12*(1), 63-77.

}

*Jordan Journal of Physics*, vol. 12, no. 1, pp. 63-77.

**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.

Research output: Contribution to journal › Article

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

M3 - Article

VL - 12

SP - 63

EP - 77

JO - Jordan Journal of Physics

JF - Jordan Journal of Physics

SN - 1994-7607

IS - 1

ER -