Disorder and Urbach energy in hydrogenated amorphous carbon: a phenomenological model

We develop a phenomenological model describing the structural and topological effects of the disorder in hydrogenated amorphous carbons (a-C:H), through the analysis of the Raman G-peak width and the optical absorption spectra, providing information on the densities of electronic pi ad pi* states (pi-DOS). We show that the Urbach energy is not related to topological disorder but to the Gaussian width (s_pi) of the pi-DOS, peaked at ± E_pi energies above/below the Fermi level. s_pi, on its turn, is not related in a straightforward manner to the disorder. The disorder is better represented by the s_pi/E_pi ratio, expressing the disorder-induced narrowing of the Tauc optical gap.