Density, sp(3) fraction, and cross-sectional structure of amorphous carbonfilms determined by x-ray reflectivity and electron energy-loss spectroscopy

Grazing-angle x-ray reflectivity (XRR) is described as an efficient, nondes tructive, parameter-free means to measure the mass density of various types of amorphous carbon films down to the nanometer thickness range. It is sho wn how XRR can also detect layering if it is present-in the films, in which case the reflectivity profile must be modeled to derive the density. The m ass density can also be derived from the valence electron density via the p lasmon energy, which is measured by electron energy-loss spectroscopy (EELS ). We formally define an interband effective electron mass m*, which accoun ts for the finite band gap. Comparison of XRR and EELS densities allows us to fit an average m* = 0.87m for carbon systems, m being the free-electron mass. We show that, within the Drude-Lorentz model of the optical spectrum, m* = [1-n(0)(-2)]m, where n(0) is the refractive index at zero optical fre quency. The fraction of sp(2) bonding is derived from the carbon K-edge EEL S spectrum, and it is shown how a choice of "magic" incidence and collectio n angles in the scanning transmission electron microscope can give sp(2) fr action values that are independent of sample orientation or anisotropy. We thus give a general relationship between mass density and sp(3) content for carbon films.