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, the Fowler-Nordheim tunneling wavefunction ψE. The deviation of ψ from ψE decays asymptotically as a power law t32. 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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