Theoretical comparison between field-emission properties of carbon protrusions ranging from an isolated atom to multi-wall nanotubes

We present a review of field-emission properties of carbon protrusions standing on a metallic substrate. The transfer-matrix technique used for the scattering calculations takes account of three-dimensional aspects of the potential energy. The structures considered consist of a single carbon atom, half of a C60 molecule on a flat metallic substrate or on top of a metallic cylinder, open and closed (5, 5) nanotubes and the (5, 5) at (10, 10) at (15, 15) multi-wall structure. The results indicate that enhanced emission is obtained from the protrusions having the largest aspect ratio, (quasi-)localized states or allowing for the highest field penetration (due to an open rather than closed configuration, a reduced polarizability or because of adsorbed/bonded species). From the comparison between the total-energy distributions, it is found that the half C60 molecule has a (quasi-)localized state, which gives rise to a resonance in the emission (also when present at the apex of the closed (5, 5) nanotube). The results show that the field enhancement factor, as derived from a Fowler-Nordheim analysis of our data, is only an indicator for the quality of the emitter and does not justify all differences in the rates of emission. (topical review)