Exact analysis of surface field reduction due to fieldemitted vacuum space charge, in parallelplane geometry, using simple dimensionless equations
Abstract
This paper reports (a) a simple dimensionless equation relating to fieldemitted vacuum space charge (FEVSC) in parallelplane geometry, namely 9ζ^{2}θ^{2}3θ4ζ+3=0, where ζ is the FEVSC "strength" and θ is the reduction in emitter surface field (θ =fieldwith/fieldwithout FEVSC), and (b) the formula j =9θ^{2}ζ/4, where j is the ratio of emitted current density J_{P} 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 J_{P} 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 ζ on the basis of Monte Carlo calculations might yield formulae adequate for real situations.
 Publication:

Journal of Applied Physics
 Pub Date:
 October 2008
 DOI:
 10.1063/1.2996005
 Bibcode:
 2008JAP...104h4303F
 Keywords:

 79.70.+q;
 77.22.Jp;
 52.80.s;
 Field emission ionization evaporation and desorption;
 Dielectric breakdown and spacecharge effects;
 Electric discharges