We generate a series of amorphous carbon materials of densities varying between 2.0 and $3.5\mathrm{g}∕{\mathrm{cm}}^3$. Their dielectric functions are calculated within the density-functional theory approach, and the low-loss electron energy-loss spectra are evaluated. The dependence of the $\pi +\sigma$ plasmon energy $E_p$ on the valence electron density $\left(n_e\right)$ is determined. We find that the free-electron model in which $E_p\propto n_e^{0.5}$ is valid. The coefficient of proportionality leads to a ratio of the electron-effective band mass $m^{*}$ to the free-electron mass $m$ of $m^{*}∕m=0.87$, which is the value obtained using measurements based on the grazing-angle x-ray reflectivity and electron energy-loss spectroscopy [see A. C. Ferrari et al., Phys. Rev. B 62, 11089 (2000)]. This result supports the reliability of amorphous carbon mass densities obtained from EELS data when an electron-effective mass of $0.87m$ is used.

• Received 12 February 2004

DOI:https://doi.org/10.1103/PhysRevB.70.033101