Numerical analysis of the notional area in cold field electron emission from arrays

The notional area of field emission is an important parameter to correlate characteristic current density to the emission current, linking field emission theories to experimental observations. Recently, it has been reported that the notional area of emission contributes to the high brightness of large diameter emitters. Thus, it is necessary to understand how the notional area of emission depends on physical and geometrical parameters. In this work, we carried out numerical simulations to evaluate the notional area, A _n, considering cold field electron emission from a hemisphere on a cylindrical post (HCP) emitter in an array. An HCP is suitable to model classically carbon nanotubes or carbon nanofibres-like emitters. We provide the dependence of A _n on a wide range of physical and geometrical parameters, namely: the separation between the HCP emitters, the aspect ratio, radius, local work function and the macroscopic emission current. We explain the behavior of A _n as a function of these parameters and show in which cases A _n can be considered nearly constant. Our numerical results are within the framework of the standard Fowler-Nordheim (FN) theory and can simplify the modeling of the field emission phenomenon, because it directly relates simulation predictions to the currents observable experimentally. Also, this work provides information for experimentalists that can be useful to check the validity of the Schottky-Nordheim (SN) barrier upon the elementary FN theory.