Generalized analytical solution and study of conductive ellipsoidal field emitters

This thesis presents new analytical solutions to a core set of field emission parameters for two field emitter geometries---the ellipsoid and the spheroid, a special case of the ellipsoid. Expressions are found for the potential, electric field, field enhancement, current density, and total current. As anticipated, the localized field and current density at the emitter surface are strong functions of the surface location and the emitter shape. Unlike other work where the field enhancement factor is treated as constant, it is shown that the field enhancement at the surface of both emitter geometries is dependent, and only dependent, upon the surface location and the emitter's geometric dimensions.;An analytic solution is presented for the averaged, integrated field enhancement factor, betaI, for spheroidal emitters, where betaI is the enhancement factor found when curve fitting field emission data with the Fowler-Nordheim equation. Unlike the local field enhancement factor, beta(theta,gamma), which is a function of location on the emitter and independent of the applied field intensity, betaI is shown to be dependent on the applied field in the common experimental range. betaI's saturation value at very high applied fields is evaluated and suggested as an alternative non-field dependent integrated field enhancement factor. This thesis examines the common method for obtaining betaI from the slope of the Fowler-Nordheim plot of field emission data, where the slope is assumed to be inversely proportional to betaI. An expression is given for betaI, obtained via the slope method, which is shown to differ from the betaI obtained by solving the full version of the modified Fowler-Nordheim equation.;For both emitter geometries, equations are developed to determine the field emitter surface area that significantly contributes to overall field emitter performance. Two methods are used to determine the significant emission area. In the first method, the significant area is defined as the area that provides a significant amount of current density, as compared to the maximum current density. The second method involves determining the emitter area that contributes a significant portion of the overall field emission current. It is found that in both cases, the significant emission area is highly dependent on the applied field.