A universal formula for the field enhancement factor

Abstract

The field enhancement factor (FEF) is an important quantity in field emission calculations since the tunneling electron current depends very sensitively on its magnitude. The exact dependence of FEF on the emitter height $h$, the radius of curvature at the apex $R_a$, as well as the shape of the emitter base is still largely unknown. In this work, a universal formula for the field enhancement factor is derived. It depends on the ratio $h/R_a$ and has the form ${\gamma }_a=(2h/R_a)/[{\alpha }_1\log (4h/R_a)-{\alpha }_2]$ where ${\alpha }_1$, ${\alpha }_2$ depend on the charge distribution on the emitter. Numerical results show that a simpler form ${\gamma }_a=(2h/R_a)/[\log (4h/R_a)-\alpha ]$ is equally valid with $\alpha$ depending on the class of emitter and indicative of the shielding by the emitter-base. For the hyperboloid, conical and ellipsoid emitters, the value of $\alpha$ is $0,0.88$ and $2$ while for the cylindrical base where shielding is minimum, $\alpha \simeq 2.6$.

References in corpus (3)

• 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

Cited by in corpus (22)

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• Field emitter electrostatics: a review with special emphasis on modern high-precision finite-element modelling
• 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
• Simulating multiscale gated field emitters -- a hybrid approach
• Approximate universality in the tunneling potential for curved field emitters -- a line charge model approach
• Scaling in large area field emitters and the emission dimension
• Fast and accurate determination of the curvature-corrected field emission current
• Interpreting the empirical field emission equation for large area field emitters
• Gamow factors and current densities in cold field emission theory: a comparative study
• Semi-analytical theory of emission and transport in a LAFE-based diode
• Approximate universality in the electric field variation on a field-emitter tip in the presence of space charge
• Analytical Advances about the apex Field Enhancement Factor of a Hemisphere on a Post Model