Experimental determination of electron‐beam broadening in low‐energy STEM
Authors: Drees Holger , Müller Erich , Gerthsen Dagmar 
Published: December 2016

The interest in scanning transmission electron microscopy (STEM) at low primary electron energies
E
≤30keV has steadily grown in the past. The benefits of low‐keV STEM are high material contrast for low atomic number materials and prevention of knock‐on damage. Moreover, low‐keV STEM can be easily performed in a standard scanning electron microscope. However, the mean free path values decrease with lower
E
which substantially increases the number of scattering events and leads to plural and multiple scattering even at small specimen thicknesses. As a consequence, the beam is broadened within the sample which worsens the lateral resolution of the technique. Since single scattering events and the resulting beam broadening cannot be measured directly, we will present an approach to estimate beam broadening by using an amorphous carbon (aC) thin‐film.

The aC‐film was deposited by electron‐beam evaporation onto a cleaved mica substrate. The film thickness of 10nm was determined by TEM of a cross‐section TEM‐sample from a simultaneously coated Si‐substrate. The aC‐film is floated off the mica substrate on a distilled water surface and deposited on a copper grid. In this process, cracks are formed in the film which lead to multiple folding of the film at the crack edges. Such a crack edge is imaged with the bright‐field (BF) detector in Figure1. The film is folded in a way that regions are created where a discrete number of aC‐layers are stacked. Some of these regions are marked with the number of stacked layers. Averaging the 16‐bit gray‐scale values in these areas gives intensity values for several discrete film thicknesses. The red dots in Figure2 show the resulting intensities for the areas in Figure1 after subtracting the black value (intensity with blanked electron beam)

I
B

and normalization with the intensity of the incident electrons

I
0

.

The used STEM detector is a semiconductor detector which is composed of a circular BF segment, four separately controllable annular dark‐field (DF) segments and a large high‐angle annular dark‐field (HAADF) segment. Figure3b shows a scheme of the detector rings and the corresponding outer detection angles for the used working distance of 6.3mm. The region close to the crack edge (cf. Figure 1) was imaged with all detector segments. The accumulated normalized intensity values up to the indicated detector at
E
= 20 keV are plotted in Figure 2.

The radial intensity of an electron probe can be defined by the integration of a Gaussian intensity distribution [1]. We refer to the beam width
b
as the diameter of the circle that contains 68% (1σ of a Gaussian) of the total probe current which is marked by the dotted black line in Figure2. The crossings of the dashed vertical lines in Figure 2 with the dotted line indicate the film thicknesses at which the intensity falls below 68% for the different detector segments. At these thicknesses the beam is broadened to the outer detection angle of the indicated detector. Assuming the mean scattering position at half thickness of the film, the beam width at the bottom of the film can be calculated by
b
=
t
tan
φ
[2] (cf. Figure3a). The red curve in Figure4 shows the calculated beam widths as a function of the sample thickness for
E
= 20 keV derived from Figure2. The same procedure was repeated for various electron energies from 10 to 30keV and the resulting beam widths are plotted in Figure 4.

For all energies the beam width rises with increasing thickness. This behavior is expected due to the increasing scattering probability. Less pronounced broadening for higher E is expected for the same reason as well. The absolute values show that even for small thicknesses up to 90 nm, like in our experiment, and a low‐density material like amorphous carbon, the beam width increases to a multiple of the original beam diameter. This points out that thin samples for high‐resolution low‐keV STEM are required.