Static electric field enhancement in nanoscale structures

Abstract

We study the effect of local atomic- and nano-scale protrusions on field emission and, in particular, on the local field enhancement which plays a key role as known from the Fowler-Nordheim model of electronic emission. We study atomic size defects which consist of right angle steps forming an infinite length staircase on a tungsten surface. This structure is embedded in a 1 GV/m ambient electrostatic field. We perform calculations based upon density functional theory in order to characterize the total and induced electronic densities as well as the local electrostatic fields taking into account the detailed atomic structure of the metal. We show how the results must be processed to become comparable with those of a simple homogeneous tungsten sheet electrostatic model. We also describe an innovative procedure to extrapolate our results to nanoscale defects of larger sizes, which relies on the microscopic findings to guide, tune, and improve the homogeneous metal model, thus gaining predictive power. Furthermore, we evidence analytical power laws for the field enhancement characterization. The main physics-wise outcome of this analysis is that limited field enhancement is to be expected from atomic- and nano-scale defects.