Shielding effects in random large area field emitters, the field enhancement factor distribution and current calculation

Abstract

A finite-size uniform random distribution of vertically aligned field emitters on a planar surface is studied under the assumption that the asymptotic field is uniform and parallel to the emitter axis. A formula for field enhancement factor is first derived for a 2-emitter system and this is then generalized for $N$-emitters placed arbitrarily (line, array or random). It is found that geometric effects dominate the shielding of field lines. The distribution of field enhancement factor for a uniform random distribution of emitter locations is found to be closely approximated by an extreme value (Gumbel-minimum) distribution when the mean separation is greater than the emitter height but is better approximated by a Gaussian for mean separations close to the emitter height. It is shown that these distributions can be used to accurately predict the current emitted from a large area field emitter.

arXiv comment10 pages

References in corpus (7)

• Extraction of emission parameters for large-area field emitters, using a technically complete Fowler-Nordheim-type equation
• A universal formula for the field enhancement factor
• Physical electrostatics of small field emitter arrays/clusters
• Field-emission from parabolic tips: current distributions, the net current and effective emission area
• Variation of field enhancement factor near the emitter tip
• Origin of the literature discrepancies in the fractional reduction of the apex-field enhancement factor considering small clusters of field emitters
• The tunneling potential for field emission from nanotips

Cited by in corpus (18)

• Minimal domain size necessary to simulate the field enhancement factor numerically with specified precision
• Curvature correction to the field emission current
• Field emitter electrostatics: a review with special emphasis on modern high-precision finite-element modelling
• The cosine law of field enhancement factor variation: generic emitter shapes
• Verification of shielding effect predictions for large area field emitters
• Electrostatic shielding versus anode-proximity effect in large area field emitters
• The anode proximity effect for generic smooth field emitters
• Enhanced space charge limited current for curved electron emitters
• Higher order curvature corrections to the field emission current density
• Predicting space-charge affected field emission current from curved tips
• A hybrid approach to modelling large area field emitters
• The Schottky Conjecture and beyond
• Approximate universality in the tunneling potential for curved field emitters -- a line charge model approach
• Fast and accurate determination of the curvature-corrected field emission current
• Scaling in large area field emitters and the emission dimension
• Interpreting the empirical field emission equation for large area field emitters
• Semi-analytical theory of emission and transport in a LAFE-based diode
• Near-field thermal emission from metasurfaces constructed of SiC ellipsoidal particles