Systematic Errors of Electric Field Measurements in Ferroelectrics by Unit Cell Averaged Momentum Transfers in STEM

When using the unit cell average of first moment data from four-dimensional scanning transmission electron microscopy (4D-STEM) to characterize ferroelectric materials, a variety of sources of systematic errors needs to be taken into account. In particular, these are the magnitude of the acceleration voltage, STEM probe semi-convergence angle, sample thickness, and sample tilt out of zone axis. Simulations show that a systematic error of calculated electric fields using the unit cell averaged momentum transfer originates from violation of point symmetry within the unit cells. Thus, values can easily exceed those of potential polarization-induced electric fields in ferroelectrics. Importantly, this systematic error produces deflection gradients between different domains seemingly representing measured fields. However, it could be shown that for PbZr0.2Ti0.8O3, many adjacent domains exhibit a relative crystallographic mistilt and in-plane rotation. The experimental results show that the method gives qualitative domain contrast. Comparison of the calculated electric field with the systematic error showed that the domain contrast of the unit cell averaged electric fields is mainly caused by dynamical scattering effects and the electric field plays only a minor role, if present at all.