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The curvature of field emitter tips leads to an altered tunneling potentialthat assumes significance when the radius of curvature is small. We providehere an analytical curvature-corrected formula for the field emission currentfrom smooth vertically aligned emitter tips and test its applicability across arange of apex radius, $R_a$, and local electric field, $E_a$. It is found togive 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 evenat $R_a = 100$nm ($ > 35\%$ at $E_a = 3$V/nm) and conclude that curvaturecorrection is essential for apex radius less than a micron.

Curvature correction to the field emission current