Screened field enhancement factor for the floating sphere model of a carbon nanotube array

Abstract

The screened field enhancement factor for a carbon nanotube (CNT) placed in a CNT array (which is reduced due to the screening effect) is derived based on the "floating sphere" model. We obtain an expression for the field enhancement factor for a CNT in the array as gamma = 3 + 2 (1 + eta)/{(2 + eta)[2 pi alpha(2 + eta)delta(2) + eta] }, where rho is the radius of sphere, h is the distance from cathode to the center of sphere, and D is the distance between the nearest spheres, eta = rho/h, delta = rho/D, and a 1 for square or 2/root 3 p for hexagonal lattice made of CNTs. Explicit algebraic formulas for optimizing the distance between tubes, areal density of emitters, and the anode current are also obtained. (C) 2011 American Institute of Physics. [doi:10.1063/1.3665390]