Analytical treatment of cold field electron emission from a nanowall emitter

TL;DR

This paper develops an analytical model for cold field electron emission from nanowalls, highlighting quantum confinement effects and deriving generalized equations beyond Fowler-Nordheim theory using conformal transformations.

Contribution

It introduces a simple analytical approach to model CFE from nanowalls, incorporating quantum effects and providing a more general framework than traditional FN-type equations.

Findings

Quantum confinement significantly affects emission characteristics.

Derived analytical expression for tunnelling probability.

Identified shape 'fall-off' in local field with distance.

Abstract

This paper presents an elementary, approximate analytical treatment of cold field electron emission (CFE) from a classical nanowall. A simple model is used to bring out some of the basic physics of a class of field emitter where quantum confinement effects exist transverse to the emitting direction. A high-level methodology is presented for developing CFE equations more general than the usual Fowler-Nordheim-type (FN-type) equations, and is applied to the classical nanowall. If the nanowall is sufficiently thin, then significant transverse-energy quantization effects occur, and affect the overall form of theoretical CFE equations; also, the tunnelling barrier shape exhibits "fall-off" in the local field value with distance from the surface. A conformal transformation technique is used to derive an analytical expression for the on-axis tunnelling probability.