Interdependency of optical constants in a-C and a-C:H thin films interpreted in light of the density of electronic states

The real and imaginary parts of the dielectric constants for several a-C(:H) thin films were measured in the energy range 1.5-4.5 eV. The data were analyzed assuming Gaussian shapes for the "valence" and "conduction" π bands and scaling the energy by means of the Gaussian width parameter σ. At any given scaled energy Y an approximately linear relationship was obtained between the real and the imaginary part of dielectric constant. The energy dependence of the slope and intercept of such lines are analytically determined on the basis of the quoted Gaussian-shaped density of states. The existence of a Cauchy behavior for the contribution to the real part of the dielectric constant due to the transitions other than π-π* is shown. The role of disorder in determining the necessity for a scaled energy based analysis was addressed.