Abstract text (incl. figure legends and references)

Measurement of electric fields in scanning transmission electron microscopy is a field of research that has seen a lot of development during the last years. The basic idea of the method is that an electric field leads to a tilt of the focused probe that can be detected as a shift in the back focal plane. Although this principle seems rather simple, a quantitative field measurement is not always possible and sometimes only approximations can be obtained. Shifts of the beam in the back focal plane were first analysed in differential phase contrast scanning transmission electron microscopy (DPC-STEM) using segmented STEM detectors[1]. Many impressive results were obtained with this technique and huge improvement has also been achieved regarding the quantitative interpretability[2,3]. The development of new hardware[4] paved the way for the fast acquisition of the full diffraction pattern while the focussed electron beam is scanned across the sample. Using a probe with a high convergence angle, atomic electric fields can be measured evaluating the centre of mass of the diffraction pattern for samples with a thickness below 5nm[5]. Using a broader probe results in diffraction patterns with non-overlapping diffraction discs. Long-range electric fields can be measured from a shift of the central disc applying disc detection techniques[6,7].Whereas in some materials electric fields are expected at interfaces between two materials[7], in the present contribution[8] we show that a shift of the diffraction pattern occurs also at interfaces in a non-polar silicon germanium sample, where no electric fields are expected (see Fig. 1). We investigate by evaluation of simulations and experiment, whether this shift can be interpreted as originating from an electric field caused by differences in the mean inner potential between regions with different chemical composition.

Fig.1: A shift of the central disc is measured in nano-beam electron diffraction at interfaces between regions with different composition.

The mean inner potential has an influence on the measured shift indeed. On the other hand, the measured shift depends on several parameters such as specimen thickness and sample orientation with respect to the electron beam, all of them leading to changes in dynamic diffraction. Even the measured field direction changes with thickness (see Fig. 2). An improvement can be achieved if electron beam precession is used. This minimizes the effects of dynamic diffraction, still preserving information stemming from the change in mean inner potential. Fig. 2: Measured shift converted to electric field as a function of scan position and sample thickness. Direction and magnitude of the measured field strongly depend on the sample thickness. In conclusion, we show that the simple interpretation of the measured shift of the diffraction pattern as originating from an electric field only caused by differences in mean inner potential is not correct and will be misleading in the majority of cases.

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[2] J. Zweck et al., J. Magn. Magn. Mater. 104 (1992), p.315.

[3] N. Shibata et al., Nat. Physics 8 (2012), p.611.

[4] V. Özdol et al., Micros. Microanal. 20 (2014), p.1046.

[5] K. Müller et al., Nat. Commun. 5 (2014), p.5653.

[6] K. Müller et al., Micros. Microanal. 18 (2012), p. 995.

[7] T. Grieb et al., Ultramicroscopy 228 (2021) p.113321.

[8] C. Mahr et al., Ultramicroscopy 236 (2022), p.113503.