The band gap

In the process of the calculations many samples of amorphous carbon with different structures were generated. For most of these, the width of the band gap was measured. The width of the band gap depends not only on the fraction of the differently coordinated atoms, but also on their individual configuration, i.e clustering of the $sp^2$ bonded atoms, etc. We plotted the graph of the width of the bandgap as a function of the fraction of $sp^2$ coordinated atoms (see Fig. 8.19). There are some discrepancies with experimental works in these dependences, for example, McCulloch et al [54] found band gap of 2.5 eV at 85 % of $sp^3$ bonded atoms, in our graph the value of 3.3 eV corresponds the fraction of 84 % of the $sp^3$ atoms. There is a noticable scattering of the points between 60 and 70 % of $sp^3$ bonded atoms. We presume that in this interval the fraction of $sp^2$ bonded atoms increases enough to begin create clusters. If the fraction of the $sp^2$ atoms is smaller than 30 %, then only separated $sp^2$ atoms are embedded in the $sp^3$ amorphous network. If the fraction of the $sp^2$ atoms is larger than 40 %, the $sp^2$ clusters begin to connect with one another. The band gap disappears when the fraction of the $sp^2$ bonded atoms reaches 55 %.

Figure 8.19: The width of the band gap as a function of the percentage of $sp^3$ bonded atoms.