Breakdown of plane-wave-based theories of field emission from a subnanometer-radius tip

Abstract

We present a combined experimental and theoretical study of field electron emission from an ultrasharp carbon tip with a subnanometer radius formed by a field-emission-induced structural modification of a diamond needle-like microcrystallite. The tip dimensions were measured by high-resolution transmission electron microscopy and used to calculate the potential distribution outside the emitter. Substitution of the calculated field into the Fowler-Nordheim (FN) theory and the more refined theory based on the Simmons equation overestimate the field emission current by six and five orders, respectively. We show that such a strong discrepancy is due to the incorrect use of plane wavefunctions to describe electrons inside a subnanometer emitter. We present a theory based on more realistic non-planar wavefunctions, which takes into account the effect of localization and one-dimensional density of states inside the emitter. These modifications of the FN theory allowed us to obtain a good order-of-magnitude agreement with the experimental values of the field emission current. The presented results are of great practical importance, since field emitters with nanometer radius are intensively studied experimentally and are the basis of state-of-the-art vacuum nanoelectronic devices.