Modified Forouhi and Bloomer dispersion model for the optical constants of amorphous hydrogenated carbon thin films

The model of Forouhi and Bloomer (F-B) for the optical properties of amorphous semiconductors is modified in order to more accurately describe the dispersion of the optical constants observed for amorphous carbon (a-C) and amorphous hydrogenated carbon (a-C:H) thin films. The F-B model represents the optical absorption as the product of a lineshape function and a joint density of states function, which is derived by assuming the conduction and valence bands to be parabolic and separated by an energy gap with in which no allowed electronic states lie. Two modifications to this model are discussed to address the cases of non-parabolic bands and/or electron energy levels in the energy gap. These parametric models are then fit to a large number of experimentally determined optical constant spectra, and results are presented which indicate that non-parabolicity of the conduction and valence bands is the most important correction to the standard F-B model required to describe a-C:H thin films. The modified model incorporating non-parabolic bands is shown to fit a broad range of both a-C and a-C:H spectra very well, and provides useful information about the optical absorption process and physical properties of the films.