Electrostatic shielding versus anode-proximity effect in large area field emitters

Abstract

Field emisison of electrons crucially depends on the enhancement of the local electric field around nanotips. The enhancement is maximum when individual emitter-tips are well separated. As the distance between two or more nanotips decreases, the field enhancement at individual tips reduces due to the shielding effect. The anode-proximity effect acts in quite the opposite way, increasing the local field as the anode is brought closer to the emitter. For isolated emitters, this effect is pronounced when the anode is at a distance less than three times the height of the emitter. It is shown here that for a large area field emitter (LAFE), the anode proximity effect increases dramatically and can counterbalance shielding effects to a large extent. Also, it is significant even when the anode is far away. The apex field enhancement factor for a LAFE in the presence of an anode is derived using the line charge model. It is found to explain the observations well and can accurately predict the apex enhancement factors. The results are supported by numerical studies using COMSOL Multiphysics.

arXiv comment6 pages

References in corpus (10)

• A universal formula for the field enhancement factor
• Physical electrostatics of small field emitter arrays/clusters
• Shielding effects in random large area field emitters, the field enhancement factor distribution and current calculation
• Minimal domain size necessary to simulate the field enhancement factor numerically with specified precision
• Field-emission from parabolic tips: current distributions, the net current and effective emission area
• Curvature correction to the field emission current
• Variation of field enhancement factor near the emitter tip
• The cosine law of field enhancement factor variation: generic emitter shapes
• Verification of shielding effect predictions for large area field emitters
• The anode proximity effect for generic smooth field emitters

Cited by in corpus (10)

• Field emitter electrostatics: a review with special emphasis on modern high-precision finite-element modelling
• Enhanced space charge limited current for curved electron emitters
• Predicting space-charge affected field emission current from curved tips
• A hybrid approach to modelling large area field emitters
• 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
• 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