Analysis of theπ*andσ*bands of the x-ray absorption spectrum of amorphous carbon

The same method used to determine ${\sigma }^{*}$ excitations in the x-ray-absorption spectra of organic molecules is applied to analyze the structure of the ${\sigma }^{*}$ band in the x-ray absorption spectra of amorphous carbon $(a-\mathrm{C})$ films. The analysis assumes that only a $\sigma$ bond interaction to first neighbors is relevant to explain the structure of the ${\sigma }^{*}$ band in a-C films. This is justified by the local character of the x-ray absorption probe and the short- range order existing in these films. The identification of the different ${\sigma }^{*}$ components is based on the dependence of the ${\sigma }^{*}$ binding energy with bond distance. The ${\sigma }^{*}$ band is built up by summing the components resulting from the possible different types of $\sigma$ bonds in a-C. This method serves to separate the ${\pi }^{*}$ states from the ${\sigma }^{*}$ states and to identify the kind of chemical bonds existing between carbon atoms. This analysis yields a proportion of ${\mathrm{sp}}^3$-bonded atoms of 60% in a film with a density of about 2.9 ${\mathrm{g}/\mathrm{c}\mathrm{m}}^3,$ which is a value closer to what is expected from theoretical calculations. The analysis identifies a component at about 288.5 eV which is associated to strained $\sigma$ bonds of the type of the existing in ${\mathrm{sp}}^3$ bonded rings like cyclopropene. Raman and photoemission spectroscopies help in the interpretation of the x-ray absorption spectra and the assignment of the ${\sigma }^{*}$ components.