Corrected field enhancement factor and emission current of carbon nanotube array

Excellent electron-field emission properties of carbon nanotubes (CNTs) attract essential scientific and practical interests. The small gap between top of the emitter and the anode essentially increases the field enhancement facto. The screening effect reduces the field emission current of a CNT placed in an array of CNTs. This paper presents an analytical expression of the field enhancement factor for the "floating sphere at emitter-plane potential" and the "hemi-ellipsoid on plane" model of CNT array. The field enhancement factor for the "floating sphere at emitter-plane potential" model of CNT array in diode configuration is shown. The explicit formulas for optimum distance between tubes, the areal density of emitters, and the maximum of anode are suggested.