Theoretical analysis of field electron emission must consider many parameters, one of the most critical being the field enhancement factor (FEF). In a single tip form, the FEF can vary several orders of magnitude and depends only on the system geometry, when the gap length between the emitter and counter-electrode is much greater than the height of the emitter. In this work, we determine very accurate analytical expressions for the FEF of five emitters with various shapes, which are often considered in the literature: Ellipsoidal, Hemisphere-on-Cylindrical post, Hemisphere-on-Orthogonal cone, Paraboloidal, and Hyperboloidal. We map the FEF as a function of the aspect ratio with an error smaller than 2% to serve as a quick reference database. Additionally, we calculate the electric field distribution over the emitters, which can give an insight into the effective notional emission area and the influence of the emitter’s base.

This article presents, for the first time, a comparative analysis of the emission characteristics of large-area field-effect cathodes (LAFE) based on carbon nanotubes (CNTs) of various morphologies according to key parameters using a unique computerized technique. The work presents a description of a technology for creating various CNT arrays and their comprehensive structure characterization. All CNT arrays synthesized by the catalytic PECVD method on a silicon substrate showed a high degree of chemical purity under the presented technological conditions. In some cases, nanoisland films of Fe were used as a catalyst; in others, thin films of NiO were used, which were deposited on a silicon wafer by chemical vapor deposition (CVD) and atomic layer deposition (ALD), respectively. As a result of these studies, it turned out that an array with a thick CNT coating has good resistance to the action of strong electric fields, fairly good uniformity of distribution of emission centers, a fairly high selection current (2.88 mA/cm² at 4.53 V/μm), and compliance with the normal current mode according to the “orthodox” test, which makes the morphology of such structures the most promising for further technological optimization of CNT-based cathodes for various practical applications.

A study of single-tip tungsten emitters with the construction of current–voltage dependences in quadratic Fowler–Nordheim coordinates and modified coordinates (Murphy–Good plot that depend on the value of the work function) in real-time has been carried out. The statistical data on the value of the emission area and the field enhancement factor were accumulated. The statistical data on the voltage power in the pre-exponential factor were obtained by plotting the dependence of the notional emission area on the dimensionless field at the tip apex in the coordinates ln(Im/Jk) versus ln(f). An empirical formula is proposed that uses a correction for the power of voltage, taking into account the shape of the tip.