The image-charge correction for curved field emitters

Abstract

The image-charge potential plays a key role in field emission by lowering the potential barrier, thereby leading to an increase in current density by orders of magnitude. The classical image-charge potential is however strictly applicable to planar emitters rather than the curved protrusions characteristic of field emission sites. Using recent results [Jensen et al., J. Vac. Sci. Technol. B 35, 02C101 (2017)] for a hyperboloid emitting surface, we show that for a charge close to the emitter surface, the image charge magnitude and location are well approximated by replacing the surface locally by a sphere having the same radius of curvature. Corrections to the image-charge potential under this approximation are calculated and found to be significant for field emission when the radius of curvature is in the nanometer regime. In such cases, there is reduced electron emission and the effect is more pronounced at lower external field strengths.