Calculation of the field-emission current from a surface using the Bardeen transfer Hamiltonian method

Abstract

We have developed a method for calculating the field-emission current from a clean or adsorbate-covered metal surface using the transfer Hamiltonian method of Bardeen. The present formalism can be incorporated in accurate atomistic electronic structure methods, and so is capable of addressing system specific band structure effects, adsorbate-induced resonances, and is amenable to accurate treatments of the exchange-correlation potential close to as well as far from the metal surface. It therefore goes beyond the conventional Fowler-Nordheim treatment of field emission from a metal surface. We illustrate the utility of our method by calculating the field-emission current from a model jellium surface, using a local-density approximation exchange-correlation potential, modified to include the correct $\ensuremath{\sim}1/4x$ asymptotic behavior in the vacuum region. We find that the Fowler-Nordheim behavior can be recovered in the limit of low fields; in the limit of high fields, where the details of the self-consistent effective potential in the neighborhood of the surface become important, meaningful deviations from the Fowler-Nordheim current result.