Curvature correction to the field emission current

TL;DR

This paper introduces an analytical curvature correction formula for field emission current that significantly improves accuracy for small emitter tip radii, especially below one micron, where uncorrected models fail.

Contribution

The authors develop and validate a curvature-corrected formula for field emission current, enhancing precision over existing models for small-radius emitter tips.

Findings

Curvature correction reduces errors to less than 10% for radii >10nm.

Uncorrected models have errors exceeding 35% at 100nm radius.

Correction is essential for accurate modeling below one micron radius.

Abstract

The curvature of field emitter tips leads to an altered tunneling potential that assumes significance when the radius of curvature is small. We provide here an analytical curvature-corrected formula for the field emission current from smooth vertically aligned emitter tips and test its applicability across a range of apex radius, $R_a$, and local electric field, $E_a$. It is found to give excellent results for $R_a > 10$nm with errors generally less than $10\%$. Surprisingly, for the uncorrected potential, we find the errors to be high even at $R_a = 100$nm ($ > 35\%$ at $E_a = 3$V/nm) and conclude that curvature correction is essential for apex radius less than a micron.