The origin of the work function

TL;DR

This paper investigates the mechanisms behind electron bonding and emission at metal surfaces, proposing that the work function reflects Hartree-Fock exchange energy and that photoelectric emission involves a phase transition in the electron gas.

Contribution

It introduces a method to measure electron energy distributions at ambient conditions and links the work function to exchange energy, offering a new perspective on photoelectric emission.

Findings

Sharp energy structures at metal surfaces correspond to electron emission thresholds.

The work function is directly related to Hartree-Fock exchange energy.

Photoelectric emission involves a phase transition in the electron gas.

Abstract

In this paper we analyse the mechanisms responsible for the bonding of electrons to metal surfaces. We present and validate a method to measure the energy distribution of dense electron ensembles at ambient conditions. We have found sharp structures in the energy distribution of charge confined at metal surfaces. These structures correspond to the onset of space charge i.e. electron emission. The threshold energy for emission increases linear with the free electron density. We conclude that the work function is a direct measure of the Hartree-Fock exchange energy. Remarkably, the emissions that have been observed do not obey the Einstein-Millikan threshold relation for the photo electric effect. By discrimination between requirements for energy and momentum we deduce that electron emissions are trigged by photon momentum. We claim that the photo electric effect is the result of a phase transition in an electron gas that connects a surface bound, condensed state to a free continuum state. The assignment of a phase transition to the effect under consideration is justified by analyzing the behaviour of the Fermi-Dirac energy distribution upon raising the Fermi level. We predict an abrupt increment in the number of electrons in the continuum that exceeds 70 orders of magnitude. Both the observed threshold energy and the line shape of the transition are in good agreement with theoretical predictions.