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 sp3 diamond grains and sp2-rich graphitic grain boundaries, current is carried by a high concentration of mobile electrons within large-volume grain-boundary networks. Fabricated in a simple thin-film 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 volts per micrometer, which makes it a promising material for designing electron sources. Despite 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 diodelike to a resistorlike behavior. Such a phenomenon resembles the current-density 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) 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 a high electric field. Theoretical calculations are consistent with the experiment.