Empirical expression for the emission site density of nanotube film emitters

The influence of surface roughness on emission site density (ESD) is investigated for nanotube film emitters. An empirical expression for film emitters, [Formula: see text], where B is the intercept in the modified Fowler-Nordheim (FN) plots, A(CNT) the emission area of one site, and C related to the work function, is derived from the FN theory and experimentally proved. This expression effectively excludes the influence of electric field strength, being different from the conventional method of counting site numbers from emission patterns. By using this equation and emission patterns, variation in ESD, induced by the change in cathode-anode distance, is confirmed for film emitters with rough surfaces. This variation is ascribed to the change in screen-effect strength among emission sites. It is also found that the smaller gaps produce the higher emission uniformity and site densities for rough-surface film emitters.