Theoretical evaluation of electronic density-of-states and transport effects on field emission from n-type ultrananocrystalline diamond films

Abstract

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.

High power conditioning and benchmarking of planar nitrogen-incorporated ultrananocrystalline diamond field emission electron source

“…It should be noted that in the context of the obtained results and the proposed emission mechanism, the near surface region always has a certain amount of accumulated charge that makes the charge-field relation Fowler-Nordheim-like, with no observable saturation effects [26] due to low duty cycle of the ACT beamline. Therefore, the application of the classical Fowler-Nordheim law is plausible: it simplifies analysis and makes comparison between different geometries and material modifications reasonably good.…”

“…Given the strong overlap (enhanced charge exchange) between π − π * bands, a large number of electrons is expected to collect near the surface (metalizing it), and to tunnel through the surface barrier with a larger probability as they have higher energy positions inside the material as compared to the states normally occupied without external field perturbation. It results in high charge carrier concentration and metallic-like behavior which further leads to a high field enhancement factor and low turn-on field [26]. In sp 2 -poor (N)UNCD, on the other hand, electrons could only come from the π (or Σ) band with lower probability of tunneling through the thicker surface barrier, resulting in a low field enhancement factor and high turn-on field [26].…”

“…It results in high charge carrier concentration and metallic-like behavior which further leads to a high field enhancement factor and low turn-on field [26]. In sp 2 -poor (N)UNCD, on the other hand, electrons could only come from the π (or Σ) band with lower probability of tunneling through the thicker surface barrier, resulting in a low field enhancement factor and high turn-on field [26]. Under the same macroscopic field, the current density of sp 2 -rich (N)UNCD should be higher than that of sp 2 -poor (N)UNCD.…”

“…Detailed emission properties were recorded as the macroscopic E-field was conditioned from ∼8 MV/m to ∼42 MV/m; these included current and current density, effective emission area, field enhancement factor and microscopic electric field, turn-on field, and temporal emission stability. The metrics evolution of the emission parameters was analyzed and interpreted in the framework of a unique density-of-states structure of (N)UNCD [26]. In addition, the (N)UNCD emitting surface was visualized in the rf gun environment with high resolution which showed a large number of localized emitters (density over 100/cm 2 ) distributed across the surface.…”

“…Surface barrier under the same external macroscopic electric field for sp 2 -rich sites (b) and sp 2 -poor sites (c). The complete selfconsistently solved theory based on Stratton-Baskin-Lvov-Fursey formalism can be found in Ref [26]…”