Curvature correction to the field emission current

Abstract

The curvature of field emitter tips leads to an altered tunneling potential that assumes significance when the radius of curvature is small. We provide here an analytical curvature-corrected formula for the field emission current from smooth vertically aligned emitter tips and test its applicability across a range of apex radius, $R_a$, and local electric field, $E_a$. It is found to give excellent results for $R_a>10$nm with errors generally less than $10\%$. Surprisingly, for the uncorrected potential, we find the errors to be high even at $R_a=100$nm ($>35\%$ at $E_a=3$V/nm) and conclude that curvature correction is essential for apex radius less than a micron.

arXiv comment7 pages

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Cited by in corpus (15)

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• 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
• Fast and accurate determination of the curvature-corrected field emission current
• Scaling in large area field emitters and the emission dimension
• Gamow factors and current densities in cold field emission theory: a comparative study
• The pre-exponential voltage-exponent as a sensitive test parameter for field emission theories
• 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