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

We have corrected the field enhancement factor for the “floating sphere at emitter-plane potential” model with the finite anode-cathode distance. If ρ 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 βsph=(2+7η-η2)(λ2-2λ+2)/[2η(1-λ)(2-λ)], where η=ρ/h, λ=ρ/l. This expression demonstrates reasonable behavior for three limiting cases: if h→ρ, if l→∞, and if l→ρ. We have compared our factor βsph with the field enhancement factor βtube for the “hemisphere on a post” model and the factor βell for the “hemiellipsoid on plane” model. We have shown realization of the approximate evaluation βtube≈(βsph+βell)/2. [ABSTRACT FROM AUTHOR]