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Field emission from nano-structured emitters primarily takes place from thetips. Using recent results on the variation of enhancement factor around theapex (Biswas et al, Ultramicroscopy 185, 1-4 (2018)), analytical expressionsfor surface distribution of net emitted electrons as well as the total andnormal energy distributions are derived in terms of the apex radius $R_a$ andthe local electric field at the apex $E_a$. Formulae for the net emittedcurrent and effective emission area in terms of these quantities are alsoobtained.

Field-emission from parabolic tips: current distributions, the net current and effective emission area