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arXiv · 1808.00936

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

Ovidiu Costin·Rodica D. Costin·Ian Jauslin·Joel L. Lebowitz
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Abstract

We solve the time-dependent Schrödinger 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 $t^{-\frac32}$. The time scales involved for typical metals and fields of several V/nm are of the order of femtoseconds.

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Ovidiu Costin, Rodica D. Costin, Ian Jauslin, Joel L. Lebowitz. 2019-01-22. Solution of the time dependent Schrödinger equation leading to Fowler-Nordheim field emission. https://doi.org/10.1063/1.5066240

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