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Exact analysis of surface field reduction due to field-emitted vacuum space charge, in parallel-plane geometry, using simple dimensionless equations

Forbes, RG (2008) Exact analysis of surface field reduction due to field-emitted vacuum space charge, in parallel-plane geometry, using simple dimensionless equations JOURNAL OF APPLIED PHYSICS, 104 (8). ? - ?. ISSN 0021-8979

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Abstract

This paper reports (a) a simple dimensionless equation relating to field-emitted vacuum space charge (FEVSC) in parallel-plane geometry, namely 9 zeta(2)theta(2)-3 theta-4 zeta+3=0, where zeta is the FEVSC "strength" and theta is the reduction in emitter surface field (theta=field-with/field-without FEVSC ), and (b) the formula j=9 theta(2)zeta/4, where j is the ratio of emitted current density JP to that predicted by Child's law. These equations apply to any charged particle, positive or negative, emitted with near-zero kinetic energy. They yield existing and additional basic formulas in planar FEVSC theory. The first equation also yields the well-known cubic equation describing the relationship between JP and applied voltage; a method of analytical solution is described. Illustrative FEVSC effects in a liquid metal ion source and in field electron emission are discussed. For Fowler-Nordheim plots, a "turn-over" effect is predicted in the high FEVSC limit. The higher the voltage-to-local-field conversion factor for the emitter concerned, then the higher is the field at which turn over occurs. Past experiments have not found complete turn over; possible reasons are noted. For real field emitters, planar theory is a worst-case limit; however, adjusting zeta on the basis of Monte Carlo calculations might yield formulae adequate for real situations.

Item Type: Article
Uncontrolled Keywords: Science & Technology, Physical Sciences, Physics, Applied, Physics, CHILD-LANGMUIR LAW, ELECTRON-EMISSION, MICROELECTRONIC DEVICES, DISCHARGE, BREAKDOWN, CATHODES, CURRENTS, BARRIER, METALS, DIODES
Related URLs:
Divisions: Faculty of Engineering and Physical Sciences > Electronic Engineering > Advanced Technology Institute > Nano-Electronics Centre
Depositing User: Mr Adam Field
Date Deposited: 27 May 2010 14:08
Last Modified: 23 Sep 2013 18:27
URI: http://epubs.surrey.ac.uk/id/eprint/307

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