Variation of field enhancement factor near the emitter tip

Abstract

The field enhancement factor at the emitter tip and its variation in a close neighbourhood determines the emitter current in a Fowler-Nordheim like formulation. For an axially symmetric emitter with a smooth tip, it is shown that the variation can be accounted by a $\cos \tilde{\theta }$ factor in appropriately defined normalized co-ordinates. This is shown analytically for a hemi-ellipsoidal emitter and confirmed numerically for other emitter shapes with locally quadratic tips.

arXiv comment5 pages, 6 figures

References in corpus (2)

• Physical electrostatics of small field emitter arrays/clusters
• Calculating field emission currents in nanodiodes - a multi-group formalism with space charge and exchange-correlation effects

Cited by in corpus (22)

• 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
• Curvature correction to the field emission current
• The cosine law of field enhancement factor variation: generic emitter shapes
• 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
• The tunneling potential for field emission from nanotips
• 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
• Gamow factors and current densities in cold field emission theory: a comparative study
• Interpreting the empirical field emission equation for large area field emitters
• 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