Abstract
This paper presents an exact analytical theory for field emission from dielectric coated cathode surfaces, by solving the one-dimensional (1D) Schrödinger equation with a double-triangular potential barrier introduced by the coating. The effects of the cathode material (work function and Fermi energy), dielectric properties (dielectric constant, electron affinity, and thickness), applied dc field strength, and cathode temperature are analyzed in detail. For 1D flat cathode surfaces with coating, it is found that the emission current density can be larger than the uncoated case when the dielectric constant is smaller than a certain value ɛdielth and the dielectric thickness is larger than the threshold value dth[nm]≈ɛdielW/eF with the dielectric constant ɛdiel<ɛdielth, where W is the work function of the cathode material, F the applied dc field, and e the elementary charge. Our quantum model is also compared with a modified Fowler-Nordheim equation for a double barrier, showing qualitatively good agreement. Our study provides insights for designing field emitters with higher efficiency and better stability.1 MoreReceived 19 October 2020Accepted 14 December 2020DOI:https://doi.org/10.1103/PhysRevResearch.2.043439Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.Published by the American Physical SocietyPhysics Subject Headings (PhySH)Research AreasField emissionStrong electromagnetic field effectsThermionic emissionPhysical SystemsElectron sourcesTechniquesField emission & field-ion microscopySchroedinger equationAccelerators & BeamsGeneral PhysicsCondensed Matter, Materials & Applied PhysicsInterdisciplinary Physics
Highlights
We develop a quantum analytical solution for field emission from the dielectric coated cathode surface, by solving the one-dimensional (1D) Schrödinger equation subject to the double barrier introduced by the coating layer
In summary, we have developed an exact theory for field emission from dielectric coated cathode surfaces, by solving the one-dimensional time-independent Schrödinger equation with a double-triangular barrier, which is formed by applying dc electric field to the dielectric coated cathode surface
It is found that the combination of a small dielectric constant and a large dielectric electron affinity tends to induce a larger emission current density than bare metal for 1D flat cathode surfaces, under a given dc electric field
Summary
Electron field emission [1,2] attracts intensive attention in many applications, such as flat panel display [3,4,5], electron microscopes [6,7,8], vacuum microelectronics [9,10], x-ray sources [11], high power microwave sources and amplifiers, and high current cathodes [12,13,14,15,16,17,18,19], for its high efficiency, high brightness, low emittance, and miniaturized device size [20,21]. Common challenges of field emission include the operation requirement of high vacuum condition and current instabilities [27,28] To overcome these problems, ultrathin coatings, such as graphene, graphene oxide, and zinc oxide [29,30,31,32], are fabricated onto the emitter to provide chemical and mechanical protection. The solution is applicable for arbitrary electric dc field, cathode properties (i.e., work function and Fermi level), and dielectric coating properties (i.e., dielectric constant, electron affinity, and thickness). It includes field emission and thermionic emission, and can be further extended to include photoemission. The model predicts that for 1D flat surfaces, coatings of small dielectric constant and large electron affinity tend to enhance the field emission current, which provides insights for the design of a stable and efficient field emitter
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