Local electric field and enhancement factor around nanographitic structures embedded in amorphous carbon

Abstract Amorphous pure sp 2 bonding carbon films are believed to contain elongated or columnar regions of graphitic character. Although these regions must be very rare, as all molecular dynamics simulations show, they have a profound effect on the field emission capability of this flat material because they provide an internal field‐enhancement mechanism. In this paper, we calculate the internal local field around such columnar regions, with the additional restriction that they do not make contact with the cathode; otherwise the problem has a well‐known solution. Our problem is physically and mathematically more complicated, as now the ‘metallic region’ surface is not equipotential with the cathode. We have managed to solve it by requiring that the total charge on the columnar metallic structure is zero. Our findings show that such regions produce an enhancement factor that is a fraction (typically 0.5) of the known ratio h / r ( h = height and r = radius). As these structures become longer and approach the cathode, this fraction increases towards unity, but not linearly. A sudden jump occurs when contact with the cathode is established. The most interesting result is the following: Just before contact with the cathode, the local field at the cathode‐facing end of such a structure increases considerably above the value h / r . The physical ramifications of these results are discussed, especially in relation to emission onset. Copyright © 2007 John Wiley & Sons, Ltd.