skip to main content
OSTI.GOV title logo U.S. Department of Energy
Office of Scientific and Technical Information

Title: Extension of the general thermal field equation for nanosized emitters

Abstract

During the previous decade, Jensen et al. developed a general analytical model that successfully describes electron emission from metals both in the field and thermionic regimes, as well as in the transition region. In that development, the standard image corrected triangular potential barrier was used. This barrier model is valid only for planar surfaces and therefore cannot be used in general for modern nanometric emitters. In a recent publication, the authors showed that the standard Fowler-Nordheim theory can be generalized for highly curved emitters if a quadratic term is included to the potential model. In this paper, we extend this generalization for high temperatures and include both the thermal and intermediate regimes. This is achieved by applying the general method developed by Jensen to the quadratic barrier model of our previous publication. We obtain results that are in good agreement with fully numerical calculations for radii R > 4 nm, while our calculated current density differs by a factor up to 27 from the one predicted by the Jensen's standard General-Thermal-Field (GTF) equation. Our extended GTF equation has application to modern sharp electron sources, beam simulation models, and vacuum breakdown theory.

Authors:
;  [1]
  1. Department of Electrical and Computer Engineering, National Technical University of Athens, Zografou Campus, Athens 15700 (Greece)
Publication Date:
OSTI Identifier:
22494957
Resource Type:
Journal Article
Resource Relation:
Journal Name: Journal of Applied Physics; Journal Volume: 119; Journal Issue: 4; Other Information: (c) 2016 AIP Publishing LLC; Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND SUPERFLUIDITY; 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; CURRENT DENSITY; ELECTRON EMISSION; ELECTRON SOURCES; FIELD EQUATIONS; FOWLER-NORDHEIM THEORY; METALS; NANOSTRUCTURES

Citation Formats

Kyritsakis, A., E-mail: akyritsos1@gmail.com, and Xanthakis, J. P. Extension of the general thermal field equation for nanosized emitters. United States: N. p., 2016. Web. doi:10.1063/1.4940721.
Kyritsakis, A., E-mail: akyritsos1@gmail.com, & Xanthakis, J. P. Extension of the general thermal field equation for nanosized emitters. United States. doi:10.1063/1.4940721.
Kyritsakis, A., E-mail: akyritsos1@gmail.com, and Xanthakis, J. P. Thu . "Extension of the general thermal field equation for nanosized emitters". United States. doi:10.1063/1.4940721.
@article{osti_22494957,
title = {Extension of the general thermal field equation for nanosized emitters},
author = {Kyritsakis, A., E-mail: akyritsos1@gmail.com and Xanthakis, J. P.},
abstractNote = {During the previous decade, Jensen et al. developed a general analytical model that successfully describes electron emission from metals both in the field and thermionic regimes, as well as in the transition region. In that development, the standard image corrected triangular potential barrier was used. This barrier model is valid only for planar surfaces and therefore cannot be used in general for modern nanometric emitters. In a recent publication, the authors showed that the standard Fowler-Nordheim theory can be generalized for highly curved emitters if a quadratic term is included to the potential model. In this paper, we extend this generalization for high temperatures and include both the thermal and intermediate regimes. This is achieved by applying the general method developed by Jensen to the quadratic barrier model of our previous publication. We obtain results that are in good agreement with fully numerical calculations for radii R > 4 nm, while our calculated current density differs by a factor up to 27 from the one predicted by the Jensen's standard General-Thermal-Field (GTF) equation. Our extended GTF equation has application to modern sharp electron sources, beam simulation models, and vacuum breakdown theory.},
doi = {10.1063/1.4940721},
journal = {Journal of Applied Physics},
number = 4,
volume = 119,
place = {United States},
year = {Thu Jan 28 00:00:00 EST 2016},
month = {Thu Jan 28 00:00:00 EST 2016}
}
  • Strong field electron emission from a nanoscale tip can cause a temperature rise at the tip apex due to Joule heating. This becomes particularly important when the current value grows rapidly, as in the pre-breakdown (the electrostatic discharge) condition, which may occur near metal surfaces operating under high electric fields. The high temperatures introduce uncertainties in calculations of the current values when using the Fowler–Nordheim equation, since the thermionic component in such conditions cannot be neglected. In this paper, we analyze the field electron emission currents as the function of the applied electric field, given by both the conventional Fowler–Nordheimmore » field emission and the recently developed generalized thermal field emission formalisms. We also compare the results in two limits: discrete (atomistic simulations) and continuum (finite element calculations). The discrepancies of both implementations and their effect on final results are discussed. In both approaches, the electric field, electron emission currents, and Joule heating processes are simulated concurrently and self-consistently. We show that the conventional Fowler–Nordheim equation results in significant underestimation of electron emission currents. We also show that Fowler–Nordheim plots used to estimate the field enhancement factor may lead to significant overestimation of this parameter especially in the range of relatively low electric fields.« less
  • The carbon nanotube (CNT) field emitters have been fabricated by attaching a CNT film on a graphite rod using graphite adhesive material. The CNT field emitters showed much improved field emission properties due to increasing crystallinity and decreasing defects in CNTs after the high temperature thermal annealing at 900 °C in vacuum ambient. The CNT field emitters showed the low turn-on electric field of 1.15 V/μm, the low threshold electric field of 1.62 V/μm, and the high emission current of 5.9 mA which corresponds to a current density of 8.5 A/cm{sup 2}. In addition, the CNT field emitters indicated themore » enhanced field emission properties due to the multi-stage effect when the length of the graphite rod increases. The CNT field emitter showed good field emission stability after the high temperature thermal annealing. The CNT field emitter revealed a focused electron beam spot without any focusing electrodes and also showed good field emission repeatability.« less
  • The flow of an inviscid incompressible stratified dielectric fluid in gravitational and electric fields is considered. The problem is reduced to a linear equation analogous to the Schrodinger one. The existence of eddies caused by the electric field is shown. A model based on the operator extension theory for the description of stratified flows near a small obstacle and an obstacle with small aperture is constructed.