A three dimensional numerical quantum mechanical model of electronic field emission from metallic surfaces with nanoscale corrugation

Abstract

The effects on the electronic emission of the presence of nanoscale steps on a tungsten surface are investigated for the first time using three dimensional quantum mechanical models. The plane wave periodic version of the density functional theory is used to obtain the electronic wavefunctions and potentials for flat and corrugated structures. Local and averaged emitted current densities are obtained from them using time dependent perturbation theory. The orders of magnitude of the averaged current densities resulting from these calculations are similar for both flat and corrugated cases; however, strong enhancements are observed on the local current densities near the edges of the steps. These numerical results are compared with those of the analytical Fowler-Nordheim type models. The slopes of the Fowler-Nordheim plots are in good agreement for both numerical and analytical models, but the magnitudes of the emitted currents are significantly different. This is related to weaknesses in the description of the electronic structure of the metal in the analytical models.