Evaluation of [C(sp3)/[C(sp2)] ratio in diamondlike films through the use of a complex dielectric constant

The evaluation of the amount of tetrahedral and trigonal cross-linking, that is, the sp3- and sp2-hybridized carbon, is of great importance in understanding the properties of amorphous carbon films. In this paper we report a method for deducing the [sp3]/[sp2] ratio from the experimental values of the complex dielectric constant as obtained by optical transmittance and reflectance measurements. We assume a Gaussian-like distribution of π and π* electronic densities of states in order to fit the contribution of π→π* to the imaginary part, ε2, of the dielectric constant in the low-energy region. Through the Kramers-Kronig relationships we deduce the corresponding values of the real part ε1 of the dielectric constant for such transitions. By subtracting these values from the measured ε1 we deduce the contribution of σ→σ* to ε1. The Wemple-Didomenico model has been used to obtain the dispersion energy and the average excitation energy. Knowing the plasmon energies, we apply the ‘‘f-sum rule’’ to deduce the [sp3]/[sp2] ratio. The method applied to a-C:H films deposited by rf diode sputtering provides results in agreement with those obtained by other techniques.