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Fowler-Nordheim theory for a spherical emitting surface

ABSTRACT: The standard theory of cold field emission from a plane surface was found to over-estimate the apex radius of a well-characterised tip by a factor o f 2.6 . This theory has been modified to use the potential distribution near an apex whose surface forms a spherical cap. The modified theory predicts a range o f values for the apex radius, in which the best estimate is within 20 % of the measured value. The effective solid angle is found to vary approximately as (applied field)°'73.