Scaling the dynamic electron scattering in HAADF-imaging the graphene sheets

High-angle annular dark field (HAADF) imaging proves an atomic-level probe in weighing the three-dimensional nanostructures [1]. Atom-counting will become routine if an accurate knowledge of the scattering cross-section (Ω) of the realistic electrons, or the mean free path (L), is provided. However, the scattering is a dynamic process involving complex issues such as the experimental configurations, multiple electron scattering, thermal diffuse scattering and partial coherence of the electron probe [1, 2]. Ab initio prediction of the scattering constants (Ω and L) is still of much theoretical debates [3], hence their experimental determination remains an interesting topic. Within the depth of L, single scattering plays a dominant role. The collected electrons in a solid angle is given by the formula I=I ₀(1-e^t/L), where L is the mean free path of the scattering and t is the thickness of sample films [2]. The accurate measurement of L expects a substrate with a good set of precise thicknesses. Graphene sheets (GSs), with a large L and exactly-determined layer numbers, present an ideal candidate for determining L as shown here.