Corrected field enhancement factor for the floating sphere model of carbon nanotube emitter

Abstract

We have corrected the field enhancement factor for the "floating sphere at emitter-plane potential" model with the finite anode-cathode distance. If rho is the radius of sphere, h is the distance from cathode to the center of sphere, and l is the distance from the center to the anode, then the field enhancement factor is given as the following expression beta(sph) = (2 + 7 eta-eta(2))(lambda(2)-2 lambda + 2)/[2 eta(1 - lambda) X (2 - lambda)], where eta=rho/h, lambda=rho/l. This expression demonstrates reasonable behavior for three limiting cases: if h -> rho, if l -> infinity, and if l -> rho. We have compared our factor beta(sph) with the field enhancement factor beta(tube) for the "hemisphere on a post" model and the factor beta(ell) for the "hemiellipsoid on plane" model. We have shown realization of the approximate evaluation beta(tube) approximate to (beta(sph) + beta(ell))/2. (C) 2010 American Institute of Physics. [doi:10.1063/1.3466992]