For STEM imaging, the pattern on the detector is a result of interference between elastically scattered wave and the incident wave. By recording the constructive interference and destructive interference with separate detectors, as well as by subtracting the two parts of intensity from each other, one can remove the background intensity as well as nonlinear information. As result, the remaining signal is enhanced phase contrast . A recent experimental demonstration of differential contrast in STEM achieved by matching the detector geometry and the physical phase plates in STEM mode has been reported in .
On an aberration-corrected STEM, an optimized differential phase contrast can be obtained by well designing the PCTF of the objective lens, and detector geometry accordant with the designed phase plate. The integrated spatial frequencies corresponding to positive contrast transfer is equal to those corresponding to negative contrast transfer. This ensures that nonlinear information cancels when the two parts of detector signals subtract each other.
Our calculation in Fig. 1 for Cc/Cs-corrected STEM without damping factors illustrates the advantage of differential contrast compared with the conventional bright-field imaging in STEM. The differential contrasts of single-layer graphene are dominantly stronger than the contrasts achieved in STEM-BF mode equipped with the same corrector. The differential contrast can reach 12, 18 and 26 times of the bright-field contrast at 20kV, 50kV and 80kV, respectively! This demonstrates that in STEM mode equipped with an aberration corrector and a detector, matching the geometry of the phase plate, phase objects can be imaged with descent contrast.
With further improvement of the corrected state of the microscope, our calculation show that phase contrast imaging in STEM offers even more exciting possibilities. When the 5th-order spherical aberration is corrected, the illumination angle dependent on the largest usable aperture, also increases, resulting in a shallow depth of field. This allows accurate focus at certain thickness of the sample, as shown in Fig. 2. At the 8th layer of a total 16-layer (28nm) thick sample of Si, one silicon atom is replaced by a Germanium atom. A focal series through the sample shows that the layer marked by a substituted Ge atom is in focus at ∆f=-12Å.
As a summary, the method of obtaining differential contrast in an aberration-corrected STEM can be powerful for investigating weak scattering objects. Under a further improved corrected state of the Cc/Cs corrector, the differential contrast realized with this technique is extremely thickness-sensitive, and focussing through atomic planes may come into reach.
 H. Rose. Ultramicroscopy 2(1977), p. 251-267.
 C. Ophus, J. Ciston, J. Pierce et al. Nature Communications 7(2016), p. 10719.
 The authors greatly acknowledge funding from the German Research Foundation (DFG) and the Ministry of Science, Research and the Arts (MWK) of the federal state Baden-Württemberg, Germany in the frame of the SALVE project.
To cite this abstract:Zhongbo Lee, Ute Kaiser, Harald Rose; Calculation of phase contrast in Cc/Cs-corrected STEM. The 16th European Microscopy Congress, Lyon, France. https://emc-proceedings.com/abstract/calculation-of-phase-contrast-in-cccs-corrected-stem/. Accessed: December 1, 2022
EMC Abstracts - https://emc-proceedings.com/abstract/calculation-of-phase-contrast-in-cccs-corrected-stem/