Abstract
A Point Charge Model of conical field emitters, in which the emitter is defined by an equipotential surface of judiciously placed charges over a planar conductor, is used to confirm Schottky’s conjecture that field enhancement factors are multiplicative for a small protrusion placed on top of a larger base structure. Importantly, it is shown that Schottky’s conjecture for conical / ellipsoidal field emitters remains unexpectedly valid even when the dimensions of the protrusion begin to approach the dimensions of the base structure. The model is analytic and therefore the methodology is extensible to other configurations.
Highlights
(Received March 2016; accepted May 2016; published online 7 June 2016)
A Point Charge Model of conical field emitters, in which the emitter is defined by an equipotential surface of judiciously placed charges over a planar conductor, is used to confirm Schottky’s conjecture that field enhancement factors are multiplicative for a small protrusion placed on top of a larger base structure
Schottky speculated that field enhancement factors for hemispherical-like bumps were multiplicative;[7] Stern, et al.,[8] quantified the relation by observing that a hemisphere on top of another hemisphere would experience an enhancement of β = 32 = 9, and suggested that the process was iterative to more than two bumps
Summary
(Received March 2016; accepted May 2016; published online 7 June 2016) A Point Charge Model of conical field emitters, in which the emitter is defined by an equipotential surface of judiciously placed charges over a planar conductor, is used to confirm Schottky’s conjecture that field enhancement factors are multiplicative for a small protrusion placed on top of a larger base structure.
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