Assessing the electric field sensitivity measured by pixelated differential phase contrast imaging in vacuum both in the absence of external fields and under field-bound conditions

Pixelated differential phase contrast (DPC) is a four-dimensional scanning transmission electron microscopy (4D-STEM) technique in which the position of the transmitted beam is tracked to reconstruct the electromagnetic fields of a sample. Although it can provide (semi-) quantitative information for a range of different applications, the measurements are greatly affected by the microscope's optical and acquisition settings in terms of sensitivity, accuracy, and spatial resolution, particularly when measuring weak electric fields. Herein, we focus on the nano-beam 4D-STEM configuration and systematically study the way in which all the parameters typically selected by users for pixelated-DPC experiments influence the lowest achievable electric field sensitivity. First, we define the metric by which the sensitivity is assessed, discussing the optimal ranges for parameters including convergence semi-angle, electron dose, and camera length in absence of external field, while also evaluating the effect of the scanning system. Next, the sensitivity and its error are assessed under field-bound conditions, realized by a coplanar capacitor that allows the position of the transmitted beam to be shifted controllably using an external bias. Comparison of the experimental results with finite element method calculations yields quantitative information about the accuracy that can be attained for these measurements, while the effects of microscope drift and sample charging are also discussed. Our findings provide a platform for the quantitative assessment of weak electric fields as calculated by pixelated-DPC experiments, while highlighting the challenges associated with these measurements.