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Field emission tips with apex radius of curvature below 100nm are notadequately described by the standard theoretical models based on theFowler-Nordheim and Murphy-Good formalisms. This is due to the breakdown of the`constant electric field' assumption within the tunneling region leading tosubstantial errors in current predictions. A uniformly applicablecurvature-corrected field emission theory requires that the tunneling potentialbe approximately universal irrespective of the emitter shape. Using the linecharge model, it is established analytically that smooth generic emitter tipsapproximately follow this universal trend when the anode is far away. This isverified using COMSOL for various emitter shapes including the locallynon-parabolic `hemisphere on a cylindrical post'. It is also found numericallythat the curvature-corrected tunneling potential provides an adequateapproximation when the anode is in close proximity as well as in the presenceof other emitters.

Approximate universality in the tunneling potential for curved field emitters -- a line charge model approach