The anode proximity effect for generic smooth field emitters

Abstract

The proximity of the anode to a curved field electron emitter alters the electric field at the apex and its neighbourhood. A formula for the apex field enhancement factor, ${\gamma }_a(D)$, for generic smooth emitters is derived using the line charge model when the anode is at a distance $D$ from the cathode plane. The resulting approximately modular form is such that the anode proximity contribution can be calculated separately (using geometric quantities such as the anode-cathode distance $D$, the emitter height $h$ and the emitter apex radius of curvature $R_a$) and plugged into the expression for ${\gamma }_a(\infty )$. It is also shown that the variation of the enhancement factor on the surface of the emitter close to the apex is unaffected by the presence of the anode and continues to obey the generalized cosine law. These results are verified numerically for various generic emitter shapes using COMSOL Multiphysics. Finally, the theory is applied to explain experimental observations on the scaling behavior of the $I-V$ field emission curve.

10 pages, numerical verification added, references updated

References in corpus (6)

• A universal formula for the field enhancement factor
• Shielding effects in random large area field emitters, the field enhancement factor distribution and current calculation
• Scale invariance of a diodelike tunnel junction
• Field-emission from parabolic tips: current distributions, the net current and effective emission area
• Variation of field enhancement factor near the emitter tip
• The cosine law of field enhancement factor variation: generic emitter shapes

Cited by in corpus (12)

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• Enhanced space charge limited current for curved electron emitters
• 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
• 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