Simulation study on the influence of single and multiple atoms on quantitative STEM-DPC imaging of atomic charge distributions.

Differential phase contrast (DPC) imaging in scanning transmission electron microscopy (STEM) is an advanced technique to visualize and measure electric fields in a specimen. With state-of-the-art lens aberration correction, electric fields can be investigated with sub-atomic resolution, opening up the possibility to connect atomic fields to optoelectronic material properties. However, quantitative DPC imaging is only possible for sufficiently thin specimens for which the weak-phase object approximation (WPOA) is generally assumed to be valid. An unambiguous interpretation of DPC measurements remains challenging even for specimen thicknesses of only a few atoms as unexpected electric field and charge density distributions are observed. Here, we present multislice image simulations performed to study the influence of the number of atoms, their atomic number, and the interatomic spacing on quantitative DPC imaging. It is found that the central results of DPC imaging, such as beam deflection and charge density, do not increase linearly nor monotonically with increasing atomic number, making it difficult to quantitatively analyse materials with different atomic species. Furthermore, the presence of two atoms above each other leads to an unexpected increase in the derived maximum positive charge density, which increases for increasing atomic number and results in an overestimation of about 9%. We show that the interpretation of quantitative DPC images is challenging even in the case of only two atoms on top of each other.