Field enhancement factor and optimal emitter density in a nanowall array

The field emission from carbon nanowalls has excited the interest of researchers as a potential electron source for a variety of device applications. We derive an explicit analytical expression for the field enhancement factor of a nanowall placed in a nanowall array using the “floating cylinder” model. We show that if the thickness of the walls and the distance between them remain invariable while the height of walls becomes taller, the field enhancement factor increases monotonically but never exceeds a certain constant value. We propose an explicit algebraic formula for finding the optimal distance between the nanowalls at which the anode current reaches a maximum. The optimal emitter density depends only on the applied electric field and the work function of the material; it does not depend on the height of nanowalls. We analyze published experimental data and specify the resource to increase the total current.