Accurate measurement of electron beam induced displacement cross sections for single-layer graphene

We present an accurate measurement and a quantitative analysis of electron-beam-induced displacements of carbon atoms in single-layer graphene. We directly measure the atomic displacement ("knock-on") cross section by counting the lost atoms as a function of the electron-beam energy and applied dose. Further, we separate knock-on damage (originating from the collision of the beam electrons with the nucleus of the target atom) from other radiation damage mechanisms (e.g., ionization damage or chemical etching) by the comparison of ordinary (12C) and heavy (13C) graphene. Our analysis shows that a static lattice approximation is not sufficient to describe knock-on damage in this material, while a very good agreement between calculated and experimental cross sections is obtained if lattice vibrations are taken into account.