# Electron Emission Area Depends on Electric Field and Unveils Field Emission Properties in Nanodiamond Films

## TL;DR

This study investigates how the actual electron emission area in (N)UNCD films varies with electric field, revealing non-uniform emission sites, a novel image processing method, and deviations from classical Fowler-Nordheim behavior.

## Contribution

It introduces an automated image analysis algorithm to quantify field emission area dependence on electric field in (N)UNCD films, uncovering non-uniform emission and deviations from FN law.

## Key findings

- Actual FE area is much smaller than the total cathode surface.
- FE area increases with electric field, from 0.005% to 1.5%.
- Normalized current density saturates at ~100 mA/cm², deviating from FN law.

## Abstract

In this paper we study the effect of actual, locally resolved, field emission (FE) area on electron emission characteristics of uniform semimetallic nitrogen-incorporated ultrananocrystalline diamond ((N)UNCD) field emitters. To obtain the actual FE area, imaging experiments were carried out in a vacuum system in a parallel-plate configuration with a specialty anode phosphor screen. Electron emission micrographs were taken concurrently with $I$-$V$ characteristics measurements. It was found that in uniform (N)UNCD films the field emitting site distribution is not uniform across the surface, and that the actual FE area depends on the applied electric field. To quantify the actual FE area dependence on the applied electric field, a novel automated image processing algorithm was developed. The algorithm processes extensive imaging datasets and calculates emission area per image. By doing so, it was determined that the emitting area was always significantly smaller than the FE cathode surface area of 0.152 cm$^2$ available. Namely, the actual FE area would change from $5\times10^{-3}$ \% to 1.5 \% of the total cathode area with the applied electric field increased. Finally and most importantly, it was shown that when $I$-$E$ curves as measured in the experiment were normalized by the field-dependent emission area, the resulting $j$-$E$ curves demonstrated a strong kink and significant deviation from Fowler-Nordheim (FN) law, and eventually saturated at a current density of $\sim$100 mA/cm$^2$. This value was nearly identical for all studied (N)UNCD films, regardless of the substrate.