Exact analysis of surface field reduction due to fieldemitted vacuum space charge, in parallelplane geometry, using simple dimensionless equations
Forbes, RG (2008) Exact analysis of surface field reduction due to fieldemitted vacuum space charge, in parallelplane geometry, using simple dimensionless equations JOURNAL OF APPLIED PHYSICS, 104 (8). ?  ?. ISSN 00218979

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Abstract
This paper reports (a) a simple dimensionless equation relating to fieldemitted vacuum space charge (FEVSC) in parallelplane geometry, namely 9 zeta(2)theta(2)3 theta4 zeta+3=0, where zeta is the FEVSC "strength" and theta is the reduction in emitter surface field (theta=fieldwith/fieldwithout 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 nearzero kinetic energy. They yield existing and additional basic formulas in planar FEVSC theory. The first equation also yields the wellknown 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 FowlerNordheim plots, a "turnover" effect is predicted in the high FEVSC limit. The higher the voltagetolocalfield 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 worstcase 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, CHILDLANGMUIR LAW, ELECTRONEMISSION, MICROELECTRONIC DEVICES, DISCHARGE, BREAKDOWN, CATHODES, CURRENTS, BARRIER, METALS, DIODES 
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Divisions:  Faculty of Engineering and Physical Sciences > Electronic Engineering > Advanced Technology Institute > NanoElectronics 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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