Experimental and computational study of field emission characteristics from amorphous carbon single nanotips grown by carbon contamination - II. Theory

The theory for field emission from a smooth cold metallic surface has been developed to describe emission from a spherical cap. The potential distribution in the barrier region, image potential and transmission function are modified from their planar equivalents. The change in transmission modifies the pre-exponential term in the current density. An effective solid angle is defined so that the variation in emission over the surface is taken into account without requiring knowledge of the apex radius. These modifications have been used in comparing the current-voltage characteristics measured on a single carbon tip made as described in part I with values calculated using the known dimensions of the tip. The field at the surface, required for consistency with the known work function, is found to exceed the calculated field by a factor of about 2.6. This could be caused by roughness of deposition on the atomic scale. An estimate of the radius of the emitting surface can be obtained by using both the slope and the intercept of a plot of 1n(I) against (anode voltage)(-1).