Abstract text (incl. figure legends and references)

Mapping the local electric field of ferroelectric materials under biasing conditions can enlighten the mechanisms of switching domain evolution phenomena [1], with consequences in energy harvesting and computing applications. Quantification of the electric field in ferroelectric perovskite oxides, inside a transmission electron microscope (TEM), has been demonstrated using off-axis electron holography [2]. However, this technique is limited by the need for a vacuum region close to the area of interest which make these measurements under applied bias challenging. On the other hand, differential phase contrast (DPC) technique performed in 4D scanning TEM (STEM) configuration can provide an evaluation of the electric field without these restrictions [3].

Pixelated-DPC can provide an evaluation of electric fields but quantitative measurements are prone to artifacts. The result of the measurement is also influenced by the material characteristics since from these depends the mean inner potential. Our objective is to evaluate the accuracy of the technique in vacuum for the mapping of electrostatic fields in a model system. For this purpose, we used a coplanar micrometric capacitor fabricated on a MEMS chip for in-situ biasing.

A DensSolutions Lightning holder was used to apply a potential to the plates of the capacitor and 4D-STEM acquisition was performed in a Thermo Fisher Scientific Titan Themis microscope operated at 300 kV equipped with a MerlinEM detector. The electric field generated by the micro-device was simulated with finite element modeling (FEM) using COMSOL 5.5 software. This allows for a direct comparison of the electric field of the model system with the pixelated-DPC experiment.

The electron beam deflection induced by the capacitor is mapped and then quantitatively converted into electric field using the center of mass (COM) method that allows to quantify the shift of the transmitted beam [4]. The difference of COM maps (object and reference) is used to measure the beam deflection free from descan artifacts. This results in a measure of the integral of the in-plane component of the electric field over the electron path. This quantitative measurement is directly compared to the FEM model by computing the projection (or integral) of the field along the z direction, assumed as the direction of electron propagation. Overall, the pixelated-DPC measurement shows a quantitative agreement with the model. Although the sensitivity of the measurement is very good, the accuracy of the measurement suffers from artifacts.

In conclusion, we developed a workflow for quantitative evaluation of electric fields in vacuum using a model capacitor system, which results in reasonable agreement with the simulated projected field.

References:

[1] R. Ignatans et al., Physical Review Letters 127.16 (2021)
[2] T. Matsumoto et al., Applied Physics Letters 92 (2008)
[3] K. Moore et al., APL Materials 9.2 (2021)
[4] V. Boureau et al., Journal of Physics D: Applied Physics, 54 (8) (2021)