Auger-electron cascades in diamond and amorphous carbon

We have analyzed cascades of secondary electrons in diamond and amorphous carbon generated by the thermalization of a single Auger electron. The elastic electron mean free path was calculated as a function of impact energy in the muffin-tin potential approximation. The inelastic scattering cross section and the energy loss of electrons (expressed in terms of the differential inverse mean free path) were estimated from two ``optical'' models that utilize the measured dielectric constants of the materials. Using these data, a Monte Carlo model describing the time evolution of the cascade was constructed. The results show that at most around 20--40 secondary cascade electrons are released by a single Auger electron in a macroscopic sample of diamond or amorphous carbon. Consideration of the real band structure of diamond reduces this number further. The release of the cascade electrons happens within the first $100$ fs after the emission of the primary Auger electron. The results have implications to planned experiments with femtosecond x-ray sources.