FIELD-EMISSION FROM AN ELLIPTIC BOSS - EXACT AND APPROXIMATE FORMS FOR AREA FACTORS AND CURRENTS

Field emission from metallic or semiconductor tips, in comparison to planar surfaces, is complicated by current enhancement effects and changes in the image charge. It is shown that the approximations typically used for the calculation of the transmission coefficient, namely, a ''linearized'' Wentzel-Kramers-Brillouin approach and methods based upon the Fowler-Nordheim approach, are inappropriate for small spherical surfaces but adequate for elliptical surfaces. The derivation of the approximate approaches is given, as well as a simple analytical formula for the average emitting area, which may be derived based on the Fowler-Nordheim equation. By use of the elliptical approximation for the tip geometry, a simple scale factor is sufficient to deal with spherical and pointed tips.