Gamow factors and current densities in cold field emission theory: a comparative study

TL;DR

This study compares methods for calculating cold field emission current, highlighting the importance of linearization energy choice and Kemble correction to minimize errors.

Contribution

It demonstrates that selecting an appropriate linearization energy and applying Kemble correction significantly improves the accuracy of current density calculations.

Findings

Errors can be kept below 3% with proper linearization and correction.

Choice of linearization energy impacts accuracy more than the method for Gamow factor approximation.

Kemble correction enhances the precision of current density estimates.

Abstract

The factors that contribute to the accuracy of the cold field emission current within the contemporary frameworks are investigated. It is found that so long as the net current is evaluated using an expression for the local current density obtained by linearizing the Gamow factor, the primary source of error is the choice of the energy at which the Taylor expansion is done, but not as much on the choice of the method used to arrive at the approximate Gamow factor. A suitable choice of linearization energy and the implementation of the Kemble correction, allows the restriction of errors to below 3\% across a wide range of local fields.