Traceable size measurement of polysterene particles with sizes up to 500 nm using STEM-in-SEM together with simulation-based image analysis

Abstract text (incl. figure legends and references)

Nano and micro particles possess size-dependent, desirable properties, but also pose risks to health and the environment. For this reason, exhaust emission standards such as Euro6 stipulate limits for the number of emitted particles, which are checked in exhaust emission tests (AU). Such official measurements must be traceable to SI units. Hence, a traceable sizing method for polysterene particles with sizes between 200 nm and 500 nm has been developed. For this purpose, an already existing procedure for smaller particles [1] has been adapted to the new task.

The experimental procedure has already been described in Ref. [1]. In short, the polysterene particles are deposited on a TEM grid and imaged by STEM-in-SEM (or TSEM), using the bright field detector, see Fig. 1. The traceability to the SI unit meter is ensured by means of a two-dimensional grating standard.

For size determination, the image pixels belonging to the particle must be separated from the background pixels. To achieve highly accurate measurements, the signal profiles are linearly interpolated and an individual threshold dependent on the particle size is used [1]. For relatively large polysterene particles, the threshold is located in the outer, non-linear section of the signal profile. Thus, a two-step approach has been chosen as depicted in Fig. 2: First, a preliminary value for the size is determined at a fixed threshold of 60%, which lies in the linear region of the signal profile. To obtain the final size, a tabulated value is added that has been determined by Monte Carlo simulations in advance.

The simulation of the image formation process is performed using Geant4SEM. For this purpose, we have added our own physics classes [2] for single scattering processes of electrons to the powerful open source Monte Carlo framework Geant4 [3]. The elastic scattering cross sections have been calculated using ELSEPA [4] with muffin-tin radii. For the inelastic scattering cross sections, we have implemented a phenomenological model approximating the dielectric function.

We measured polysterene particles with three different nominal sizes: 200 nm (PSL200), 300 nm (PSL300), and 500 nm (PSL500). Table 1 lists our results in comparison to the reference values of two international intercomparisons [5, 6] and the manufacturer's data sheet for PSL500, respectively. In all three cases, a very good agreement is shown. In addition, preliminary studies reveal that the uncertainty of our measurements is generally smaller than the pixel size.

References
[1] T. Klein et al., Meas. Sci. Technol. 22, 094002 (2011)
[2] See also the MC2023 contribution of Martin Hermann et al.
[3] J. Allison et al., Nucl. Instrum. Methods Phys. Res. 835, 186 (2016)
[4] F. Salvat et al., Comput. Phys. Commun. 261, 107704 (2021)
[5] F. Meli et al., Meas. Sci. Technol. 23, 125005 (2012)
[6] H.-L. Lin et al., Metrologia 56, 04004 (2019)