The cosine law of field enhancement factor variation: generic emitter shapes
arXiv:1810.11830 · doi:10.1016/j.physe.2019.01.005
Abstract
The cosine law of field enhancement factor variation was recently derived for a hemi-ellipsoidal emitter and numerically established for other smooth emitter shapes (Biswas et al, Ultramicroscopy, 185, 1 (2018)). An analytical derivation is provided here for general smooth vertical emitter shapes aligned in the direction of the asymptotic electrostatic field. The law is found to hold in the neighbourhood of the emitter apex from where field emisson pre-dominantly occurs.
5 pages
References in corpus (4)
- A universal formula for the field enhancement factor
- Shielding effects in random large area field emitters, the field enhancement factor distribution and current calculation
- 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 (17)
- Curvature correction to the field emission current
- 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
- Higher order curvature corrections to the field emission current density
- Predicting space-charge affected field emission current from curved tips
- The Schottky Conjecture and beyond
- A hybrid approach to modelling large area field emitters
- 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