2, University of California, Irvine, Irvine, California, United States
Determination of the electric field at the atomic scale in materials is critical in understanding the mechanisms of functional materials such as ferroelectrics, light emitting diodes and heterogeneous catalyst. To map the electric field in such small scale, differential phase contrast imaging (DPC) in scanning transmission electron microscopy (STEM) has been developed by using segmented electron detectors to collect scattered electrons. The variation in electron count among the detectors is related to the shift of the electron beam by the local electro-magnetic field in materials; when coupled with the high spatial resolution in aberration corrected STEM, DPC can reveal the electric field at atomic resolution. Recently, the development of high speed direct electron detectors makes it possible to acquire the entire diffraction pattern during the scanning of the electron probe at the speed of ~1000 fps, which could improve the accuracy in the quantification of electron momentum transfer over regular DPC. However, from previous experiments and theoretical calculations, quantitative correlation between electron momentum transfer and the electric field remains a challenge.
We carried out a study on the calculation of electric field based on the measured average momentum transfer in both STEM experiment and simulations. SrTiO3 is employed as the model system. The momentum transfer map was calculated using the shift of center of weight (CoW) of each diffraction pattern. In the maps from simulation, the momentum transfer is not seen to increase uniformly around all atomic columns as the thickness of the modeled sample increases. For structures with one unit cell thickness, the momentum transfer map always points radially inwards from all atomic columns, as would be expected based on the projection of the coulomb potential surrounding each positive nucleus and the negative charge of the electrons in the beam. However, for larger structures, while the measured field near oxygen atoms only increased in magnitude, near Sr and Ti sites, the field also switches direction, pointing radially outwards in some regions.
To understand the behavior described above, we have examined the 3D trajectory of the electron probe in the model using a multislice simulation. From our preliminary results, we found that the electron probe does not propagate following a straight pathway and that the deviation depends on the atomic number of the closest atomic column. The electron momentum transfer measured using the diffraction pattern is therefore the average electric field along the path, not the localized average electric field where the electron probe enters the sample surface.