Material normal energy distribution for field emission analyses from monocrystalline surfaces

Abstract

Electron field emission is a complicated phenomenon which is sensitive not only to the particular material under illumination but also to the specific crystalline orientation of the surface. Summarizing the ability for a crystal to emit in a particular direction would be of great use when searching for good field emitters. In this paper we propose a material normal energy distribution which describes the ability of the bound electrons to tunnel under an intense electric field. This framework breaks a computationally expensive 3-D system down to a source distribution representation applicable for more efficient 1-D models. We use the Fowler-Nordheim framework to study the yield and MTE (mean transverse energy) from sources including gold, copper, and tungsten in both monocrystalline and polycrystalline forms. We find an increase in effective work function for field emission in the (111) direction for gold and copper associated with the Bragg plane intersections of the Fermi surface.