Emergence of a non-Fowler-Nordheim-type behavior for a general planar tunneling barrier

TL;DR

This paper explores a generalized tunneling barrier in planar emitters, revealing a non-Fowler-Nordheim behavior for field emission when the Fermi energy is comparable to or smaller than the decay width, suggesting corrections for certain materials.

Contribution

It introduces a generalized tunneling barrier model and demonstrates the emergence of non-Fowler-Nordheim behavior in specific regimes, extending the understanding of field emission beyond traditional theories.

Findings

Non-Fowler-Nordheim behavior appears when Fermi energy is small.

Standard Fowler-Nordheim theory applies for large Fermi energy.

Corrections are needed for non-metals with small Fermi energy.

Abstract

In this work we investigate a generalized tunneling barrier for planar emitters at zero-temperature. We present the evidence of the emergence of a non-Fowler-Nordheim-type general behavior for the field emission current density in the case that the Fermi energy ($\mu$) is comparable with or smaller that the decay width ($d_F$). Therefore, for some non-metals or materials that have very small Fermi energy the standard Fowler-Nordheim-type theory may require a correction. In the opposite regime, i.e., for $\mu$ much larger that $d_F$, we confirm that the conventional theory is suitable for metals.