Questioning a Universal Law for Electron Attenuation

In nanoscale science and technology, the ability to measure an object’s dimensions with nanometer accuracy is of paramount importance. The most precise tool for determining the lateral dimensions of patterns on a surface is scanning probe microscopy. Along the vertical coordinate, dimensions can be inferred using the fact that an incoming electron beam is attenuated depending on a material’s thickness (Fig. 1). For the past 50 years, researchers have thought that a universal law could be used to convert electron-attenuation factors into thicknesses for a broad range of electron energies (see note in Ref. [1]). The law, however, has barely been tested for low energies (1–50 eV)—a range of increasing scientific and technological importance. Now Daniël Geelen at Leiden University in the Netherlands and co-workers have characterized the propagation of electrons through multilayer graphene at these energies, showing clear deviations from the expected universal behavior [2]. Their analysis indicates that electron-beam attenuation is significantly affected by the band structure of the solid and is thus material dependent. The result will benefit the quantitative understanding of many techniques employing low-energy electron beams, including photoemission, microscopy, diffraction, and electron-beam lithography.