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W.S.M. Werner:
"Questioning a Universal Law for Electron Attenuation";
Physics, 12 (2019), 93; 1 - 3.

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
Figure 1: The thickness of a material can be measured with
nanometer precision by characterizing the transmission of an
electron beam. The beam attenuation is an exponential function of
the ratio between the material´s thickness (d) and the electron´s
inelastic mean-free path (IMFP). (APS/Alan Stonebraker)
⇤Institute of Applied Physics, Vienna University of Technology, Vienna,
Austria
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.

http://dx.doi.org/10.1103/Physics.12.93