EVALUATION OF THE [C(SP3)]/[C(SP2)] RATIO IN DIAMOND-LIKE 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 pi and pi* electronic densities of states in order to fit the contribution of pi-->pi* to the imaginary part, epsilon-2, of the dielectric constant in the low-energy region. Through the Kramers-Kronig relationships we deduce the corresponding values of the real part epsilon-1 of the dielectric constant for such transitions. By subtracting these values from the measured epsilon-1 we deduce the contribution of sigma-->sigma* to epsilon-1. 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.