Displacement cross sections of electron irradiated graphene and carbon nanotubes

We calculate the displacement cross-sections (DCS) of low dimensional carbon systems under electron irradiation and present an analytical formula being able to evaluate displacement creations under various conditions. The calculations consider Mott scattering, charge screening effects and thermal vibrations of target atoms. DCS values of graphene and single-walled carbon nanotubes (SWNTs) as a function of electron beam energies, substrate temperatures, and tube diameters are calculated through combination with carbon threshold displacement energies obtained from molecular dynamics simulations. For SWNTs, the smaller the tube diameters the higher the DCS values. Such diameter dependence is the most pronounced for low energy electron beams. Furthermore, DCS values are most sensitive to temperatures when electron beam energy is low. However, the temperature sensitivity disappears at higher electron energy, specifically at 200 keV and beyond.