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

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

Research output: Contribution to journalArticlepeer-review

4 Scopus citations

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→∞, the Fowler-Nordheim tunneling wavefunction ψE. The deviation of ψ from ψE decays asymptotically as a power law t-32. 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.

Original languageEnglish (US)
Article number213104
JournalJournal of Applied Physics
Volume124
Issue number21
DOIs
StatePublished - Dec 7 2018

All Science Journal Classification (ASJC) codes

  • Physics and Astronomy(all)

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