In this paper, we study the effect of the actual, locally resolved, field emission area on electron emission characteristics of uniform planar conductive nitrogen-incorporated ultrananocrystalline diamond ((N)UNCD) field emitters. High resolution imaging experiments were carried out in a field emission microscope with a specialty imaging anode screen such that electron emission micrographs were taken concurrently with measurements of I-V characteristics. An automated image processing algorithm was applied to process the extensive imaging data sets and calculate the emission area per image. It was routinely found that field emission from as-grown planar (N)UNCD films was always confined to a counted number of discrete emitting centers across the surface, which varied in size and electron emissivity. It was established that the actual field emission area critically depends on the applied electric field and that the field emission area and overall electron emissivity improve with the sp-fraction present in the film, irrespective of the original substrate roughness or morphology. Most importantly, when as-measured I-E characteristics were normalized by the electric field-dependent emission area, the resulting j-E curves demonstrated a strong kink and departed from the Fowler-Nordheim law, finally saturating at a value on the order of 100 mA/cm. This value was nearly identical for all studied films regardless of substrate. It was concluded that the saturation value is specific to the intrinsic fundamental properties of (N)UNCD.

In the nitrogen-incorporated ultrananocrystalline diamond ((N)UNCD) films, representing an n-type highly conductive two-phase material comprised of sp 3 diamond grains and sp 2rich graphitic grain boundaries, the current is carried by a high concentration of mobile electrons within the large-volume grain boundary networks. Fabricated in a simple thinfilm planar form, (N)UNCD was found to be an efficient field emitter capable of emitting a significant amount of charge starting at the applied electric field as low as a few V/µm which makes it a promising material for designing electron sources. Despite the semimetallic conduction, field emission (FE) characteristics of this material demonstrate a strong deviation from the Fowler-Nordheim law in a high-current-density regime when (N)UNCD field emitters switch from a diode-like to resistor-like behavior. Such phenomenon resembles the currentdensity saturation effect in conventional semiconductors. In the present paper, we adapt the formalism developed for conventional semiconductors to study current-density saturation in (N)UNCD field emitters. We provide a comprehensive theoretical investigation of (i) the influence of partial penetration of the electric field into the material, (ii) transport effects (such as electric-field-dependent mobility), and (iii) features of a complex density-of-states structure (position and shape of π−π * bands, controlling the concentration of charge carriers) on the FE characteristics of (N)UNCD. We show that the formation of the current-density saturation plateau can be explained by the limited supply of electrons within the impurity π − π * bands and decreasing electron mobility in high electric field. Theoretical calculations are consistent with experiment.

A methodology of modeling nonplanar surfaces, in which the microscale features of the emission sites can be orders of magnitude smaller than the mesoscale features defining the active emission area, has been developed and applied to both ordered arrays of identical emitters and random variations characteristic of a roughened surface. The methodology combines a general thermal-field-photoemission model for electron emission, a point charge model for the evaluation of field enhancement factors and surface geometry, and a Ballistic-Impulse model to account for the trajectories of electrons close to the cathode surface. How microscale and mesoscale features can both undermine the estimation of thermal-field emission parameters, such as characteristic field enhancement and total current predictions, as well as give rise to changes in the distribution of transverse velocity components used to estimate beam quality features such as emittance that are important to photocathodes, is quantified. The methodology is designed to enable both the proper characterization of emitters based on experimental current-voltage data and the development of a unit cell model of emission regions that will ease the emission model demands in beam optics codes.