Imaging the Electric Field with X-Ray Diffraction Microscopy

The properties of semiconductors and functional dielectrics are defined by their response in electric fields, which may be perturbed by defects and the strain they generate. In this work, we demonstrate how diffraction-based X-ray microscopy techniques may be utilized to image the electric field in insulating crystalline materials. By analysing a prototypical ferro- and piezoelectric material, BaTiO$_{3}$, we identify trends that can guide experimental design towards imaging the electric field using any diffraction-based X-ray microscopy technique. We explain these trends in the context of dark-field X-ray microscopy, but the framework is also valid for Bragg scanning probe X-ray microscopy, Bragg coherent diffraction imaging and Bragg X-ray ptychography. The ability to quantify electric field distributions alongside the defects and strain already accessible via these techniques offers a more comprehensive picture of the often complex structure-property relationships that exist in many insulating and semiconducting materials.