Fowler-Nordheim theory for a spherical emitting surface

摘要

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 of 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 of 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)~(0.73).