Scaling the Dynamic Electron Scattering in Imaging the Graphene Sheets by the High-Angle Annular Dark-Field Microscopy

Abstract

Employing the graphene sheets (GSs), the electron scattering constants are measured in the high-angle annular dark-field (HAADF) imaging by the scanning transmission electron microscopy. Single scattering is found to be dominant until the layer number of 200, complying with a simple relation of I = Io(1 - e(-tau/lambda)). The discrete layer counting of the GSs enables precise determination of incident depths. This work results values of lambda = 48.2, 61.4, 97.9 and 115.6 nm for 80, 120, 160 and 200 keV electrons, respectively. The uncertainties with the mean free paths and the cross sections are confined to 10 percent. The dependences on the electron beam energy and the collection angle are discussed based on a multislice simulation.