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 \(\psi(x,0)\), representing a generalized eigenfunction when \(E=0\), we find \(\psi(x,t)\) and show that it approaches, as \(t\to\infty\), the Fowler-Nordheim tunneling wavefunction \(\psi_E\). The deviation of \(\psi\) from \(\psi_E\) 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. We plot the short-time evolution of the current and density.

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