Electrostatic field enhancement on end-caps of cylindrical field-emitters

The apex field enhancement factor (AFEF) ya of a cylindrical emitter depends sensitively on its end-cap geometry. The hemispherical end -cap is well studied due to its simplicity, but, in general, a cylindrical emitter may terminate in a variety of end-cap shapes. It is well known that the AFEF depends on the ratio h IRa, where h is the total height of the emitter and Ra is the apex radius of curvature. The authors show here that there can be a large variation in ya as the end -cap geometry is altered while keeping h IRa fixed. They carry out a systematic numerical study and determine an approximate formula for ya in terms of measurable end -cap geometry parameters such as its height 7-1, the radius of the cylinder R, and the apex radius of curvature Ra. They show that the formula is robust and can predict the net field emission current with errors generally less than 40%. Published by the AVS.