Arc-evaporated carbon films: Optical properties and electron mean free paths

The real and imaginary parts of the complex refractive index, ñ(ω)=n(ω)+ik(ω), of arc-evaporated carbon films have been obtained over the range of photon energies ħω from 0.5 to 62.0 eV. Values of k(ω) obtained from transmission measurements in this energy range were combined with values of k(ω) from the literature in the infrared and soft-x-ray regions. A Kramers-Kronig analysis then yielded the values of n(ω). The density of the arc-evaporated carbon films was found to be 1.90±0.05 g ${\mathrm{cm}}^{\mathrm{-}3}$ by the ‘‘sink-float’’ method, and their thicknesses were determined optically. A sum-rule calculation yielded the effective numbers of valence and core electrons to be 4.2 and 1.8, respectively. The experimental values determined for ñ(ω) have been used to estimate values of the inelastic mean free path Λ(E) for electrons of energy E from 200 to 3000 eV in amorphous carbon. Good agreement is found between Λ(E) and experimentally determined values of electron attenuation length L(E) from the literature.