Thickness and defocus dependence of inter-atomic electric fields measured by scanning diffraction

Scanning diffraction uses the diffraction pattern from the sub-angstrom electron probe in scanning transmission electron microscopy (STEM) to record the probe's interaction with the sample structure. The diffraction intensity distribution carries information about the Coulomb interaction between the probe and the sample, from which the local electric field can be calculated. Although measurement of the electric field from scanning diffraction data is relatively simple under ideal conditions, theoretical and simulation studies indicate that interpretation of momentum transfer measurements is still complicated by the effects of sample thickness, dynamic scattering, and the depth of focus from the electron probe. Especially for thick samples of more than a few nanometers, simulations predicted that the measured momentum transfer in scanning diffraction is not directly correlated with the electric field. However, in our experiments, we have found that the technique is more robust than previously predicted when using specific imaging conditions. Here we systematically studied the effect of sample thickness and probe defocus on the momentum transfer of the electron probe in STEM, showing that the strong electric field close to atoms can be measured quantitatively for samples up to 5 nm and that the weak electric field in inter-atomic regions can be measured for samples up to 15 nm while maintaining qualitative accuracy in the full electric field image.