Curvature correction to the field emission current

Abstract

The curvature of field emitter tips leads to an altered tunneling potential that assumes significance when the radius of curvature is small. The authors provide here an analytical curvature corrected formula for the field emission current from axially symmetric emitters aligned in the direction of the asymptotic electric field. Its domain of applicability is tested across a range of apex radius, Ra, and local electric field, Ea. It is found to give excellent results for Ra>5nm and Ea>5V/nm with errors generally less than 10%. Surprisingly, for the uncorrected potential, the authors find the errors to be high even at Ra=100nm (>35% at Ea=3V/nm) and conclude that curvature correction is essential for apex radius less than a micron.