Electronic and atomic structure of amorphous carbon

The electronic structure of amorphous carbon and hydrogenated amorphous carbon (a-C:H) has been investigated through calculations on a number of model structures containing different configurations of ${\mathrm{sp}}^2$ and ${\mathrm{sp}}^3$ sites. We find that the most stable arrangement of ${\mathrm{sp}}^2$ sites is in compact clusters of fused sixfold rings, i.e., graphitic layers. The width of the optical gap is found to vary inversely with the ${\mathrm{sp}}^2$ cluster size, and the ∼0.5-eV optical gap of evaporated amorphous carbon is found to be consistent with a model of disordered graphitic layers of about 15 Å in diameter, bounded by ${\mathrm{sp}}^3$ sites. It is argued that a-C forms such finite clusters in order to relieve strain. It is then shown that the 1.5–2.5-eV optical gap of a-C:H is unusually small and requires that both its valence and conduction band consist of π states on ${\mathrm{sp}}^2$ sites and that these sites must also be significantly clustered, such as in graphitic clusters containing four or more rings. In other words, the optical gap of both a-C and a-C:H depends on their degree of medium-range order, rather than just on their short-range order as is the case in most amorphous semiconductors. We have also studied the nature of states away from the gap in order to interpret the photoemission data and the carbon 1s core-level absorption spectra. The nature of defects and midgap states is discussed, and it is predicted that the defect density decreases with increasing band gap. Finally it is argued that the doping of a-C:H by group-III and -V elements proceeds via a substitution mechanism, as in a-Si:H, in spite of the coordination disorder present in a-C:H. Doping is also expected to be accompanied by an increase in gap states, as in a-Si:H.