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 π ad π* states (πDOS). We show that the Urbach energy is not related to topological disorder but to the Gaussian width (σπ) of the πDOS, peaked at ±Eπ energies above∕below the Fermi level. σπ, on its turn, is not related in a straightforward manner to the disorder. The disorder is better represented by the σπ∕Eπ ratio, expressing the disorder-induced narrowing of the Tauc optical gap.