Ian Jauslin

Solution of the time dependent Schrodinger equation leading to Fowler-Nordheim field emission

Ovidiu Costin, Rodica Costin, Ian Jauslin, Joel L. Lebowitz

2018

Abstract

We solve the time-dependent Schrodinger equation describing the emission of electrons from a metal surface by an external electric field $E$ , turned on at $t = 0$ . Starting with a wave function $ψ (x, 0)$ , representing a generalized eigenfunction when $E = 0$ , we find $ψ (x, t)$ and show that it approaches, as $t \to \infty$ , the Fowler-Nordheim tunneling wavefunction $ψ_{E}$ . The deviation of $ψ$ from $ψ_{E}$ decays asymptotically as a power law $t^{- \frac{3}{2}}$ . The time scales involved for typical metals and fields of several V/nm are of the order of femtoseconds. We plot the short-time evolution of the current and density.

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Costin_Costin_Jauslin_Lebowitz_2018.pdf

LaTeX source:

tarball: 18ccjl-1.1.tar.gz
git repository: 18ccjl-git (the git repository contains detailed information about the changes in the paper as well as the source code for all previous versions).

Other releases

arXiv preprint: arXiv:1808.00936.
peer reviewed version, published in Journal of Applied Physics, volume 124, number 213104.

[CCJL19]: Exact solution of the 1D time-dependent Schrodinger equation for the emission of quasi-free electrons from a flat metal surface by a laser
Ovidiu Costin, Rodica Costin, Ian Jauslin, Joel L. Lebowitz, 2019
(published in Journal of Physics A: Mathematical and Theoretical, volume 53, issue 36, number 365201, 2020)
pdf, source

Talks

This work has been presented at the following conferences:

[HF19]: Time-evolution of electron emission from a metal surface
Mathematical Physics at the Crossings, VirginiaTech, Blacksburg, Virginia, USA, May 24 2019
pdf

[MSU19]: Time-evolution of electron emission from a metal surface
Michigan State University, East Lansing, Michigan, USA, May 02 2019
pdf

[GT19]: Field electron emission and the Fowler-Nordheim equation
GeorgiaTech, Atlanta, Georgia, USA, Feb 22 2019
pdf

[Pr18b]: Field electron emission and the Fowler-Nordheim equation
Princeton University, New Jersey, USA, Nov 13 2018
pdf

[Rut18]: Solution of time-dependent Schrodinger equation for field emission
Rutgers University, New Brunswick, New Jersey, USA, Sep 27 2018
pdf