Atomic-resolution DPC STEM of a SrTiO 3 single crystal

Figure 2 shows simultaneously acquired atomic-resolution ADF and DPC STEM images of a SrTiO 3 single crystal observed from the [001] direction. These images are obtained with an aberration-corrected STEM (JEOL ARM-300CF, 300 kV) equipped with a newly developed, high-speed, segmented detector. The optical conditions and detector settings are described in the Methods section and Supplementary Fig. 1. These images constitute the average, after alignment, over very fast scan STEM images acquired in 10 sequential frames, each containing 1,024 × 1,024 pixels at a dwell time of 4 μs per pixel. This process significantly reduces image drift while improving signal-to-noise ratio29. Figure 2a shows the ADF STEM image. The strong and weak-intensity peaks correspond to the Sr and Ti–O atomic columns, respectively. Oxygen atomic columns are only faintly visible in the ADF image because of their weak scattering power at higher angles. Using eight detector segment images as shown in Supplementary Fig. 2, the CoM of the diffraction pattern on the detector is estimated for each raster position24 (the detailed processing is described in the Methods). The left hand side of Fig. 2b shows the constructed projected electric field vector map, or, more precisely, the local electric field map blurred by the intensity distribution of the sub-Å electron probe used in the experiment. The colour contrast corresponds to the relative direction and strength of the electric field at each raster position in the image. Comparing with the simultaneous ADF image, disks of rotating colour contrast are seen at each atomic column position, including the oxygen columns, in the electric field vector map. This reinforces the fact that the electric field vector map is sensitive to both heavy and light element atomic columns23,24. The direction of rotating colour contrast is the same in all the atomic columns irrespective of the atomic species, indicating that the (projected) atomic electric field points outwards from the centre of the atomic columns. The right hand side of Fig. 2b shows the electric field strength map constructed from the segmented-detector STEM images, the image contrast indicating the strength of the (projected) in-plane electric field at each raster position, that is, the modulus of the vector field shown on the left in that figure. The electric field strength map of each atomic column has a local intensity minimum at its centre because the projected in-plane component of the atomic electric field should be zero at the centre of the atomic columns, where the field is parallel to the incident electron beam direction. It should be noted that these electric field vector and strength maps can be constructed in real-time, simultaneously with the recording of the atomic-resolution segmented detector and ADF STEM images, as shown in the Supplementary Movie 1 (explained in Supplementary Fig. 3). The 512 × 512 scanning pixel movie was recorded with a dwell time of 3 μs per pixel, or less than 2 s per frame (including fly back time), and shows electric field vector maps of Sr, Ti–O and O columns clearly. Using a charge-coupled device detector would give much finer detail in the scattering distribution, but at the expense of significantly greater recording time: a recent report on electric field mapping in SrTiO 3 (ref. 23) showed a 20 × 20 scanning pixel image with a dwell time of 50 ms per pixel, or 4 min for the single electric field vector map (including drift compensation, but excluding the data post-processing). Since STEM imaging is always susceptible to electronic noise, sample drift, damage and contamination during scanning, the ability to construct atomic-scale electric field maps during a rapid scan should be essential for characterizing local structures such as single atoms, clusters and interfaces and opens the door to real-time visualization of electromagnetic fields in in situ experiments. However, in both segmented detector and pixelated detector cases, dynamical electron scattering hampers a simple connection between CoM, and projected electric field such that detailed comparison with image simulations is necessary for full quantitative analysis in crystalline materials22,23,24.

Figure 2: Simultaneous atomic-resolution STEM images of SrTiO 3 [001]. (a) ADF STEM image. (b) Projected electric field vector colour map (left side) and electric field strength map (right side) constructed from the segmented-detector STEM images. The inset colour wheel indicates how colour and shade denote the electric field orientation and strength in the vector colour map. It is seen that both heavy and light element columns are sensitively imaged. Intensity dips are clearly visible at the centre of each atomic column position. Full size image

To determine whether the observed atomic electric field contains information on the outer valence electron distribution, we performed dynamical image simulations based on the frozen phonon model30 to explore the sensitivity of atomic-resolution DPC STEM to charge redistribution and bonding. Figure 3a shows magnified, unit-cell-averaged ADF, electric field vector and electric field strength maps. Figure 3b,c shows the simulated images using ionic and neutral atom potentials, respectively. These theoretical simulations follow exactly the procedures used in the experiments (that is, the segmented-detector CoM approximation) to construct the electric field vector and strength maps. Thus, quantitative comparison between the experimental and simulated images is valid. In the simulation using ionic potentials, we assume that the structure consists of Sr2+, Ti4+ and O2− ions, thereby including charge redistribution. By contrast, the simulations using neutral atom potentials assume that all the constituent atoms are neutral, meaning that there are no chemical bonds between them. Comparing Fig. 3a–c, there are almost no visible differences. In the experimental electric field strength map in Fig. 3a, faint diagonal line contrast crosses the centre of the atomic column positions. These are artefacts of our segmented-detector edges, the contrast transfer in these directions being weak because of the presence of detector edges along these directions. That even such faint contrast artefacts are reproduced in simulations reinforces the good contrast agreement between experiment and theory.

Figure 3: Quantitative comparison between experimental and simulated images. (a) Experimental repeat-unit averaged ADF (left), electric field vector (centre) and electric field strength (right) images. (b,c) Simulations for these same imaging modes based on ionic and neutral atom potentials, respectively. These simulations assume identical imaging conditions to the experiment, with a sample thickness of 8 nm and a defocus value of −5.1 nm (underfocus). (d) The normalized intensity profiles across the same Sr and Ti–O atomic columns in the averaged images from the ADF and electric field strength maps. While the ADF profile (grey) has been normalized for convenience, the experimental electric field strength (blue) and simulated electric field strength profiles, labelled Sim(ionic) and Sim(neutral) (red and green, respectively), are shown on the same absolute scale, that is, CoM angle units. It is seen that the Sim(ionic) profile shows better quantitative agreement with the experimental electric field strength profile than the Sim(neutral) profile. Note, too, that the intensity dips in the electric field strength are in identical positions to the ADF intensity peaks. Moreover, the full width half maxima of the intensity dips of the electric field strength are much narrower than those of the ADF intensity peaks. Full size image

Further quantitative comparison between the experimental and simulated electric field strength is shown in the line profiles in Fig. 3d. The simulated profiles across the Sr and Ti–O columns based on both the ionic and neutral atom potentials are shown. It is apparent that, even using exactly the same optical conditions and sample thickness, the electric field strength profiles based on the ionic and neutral atom potentials differ slightly. In the present case, differences of almost 0.4 mrad in CoM angle are found at the peaks of electric field strength about the Ti–O columns. This suggests that charge redistribution can be detected experimentally, provided we use detectors sensitive enough to detect 0.4 mrad CoM differences. In Supplementary Note 1, we experimentally measured the relationship between the total electron-dose and the statistical errors in CoM angle detection for the segmented detector used in this study. From this relationship, the present electron-dose condition is estimated to be capable of detecting much finer CoM differences of 0.032 mrad. Our detector is thus more than sensitive enough to detect 0.4 mrad CoM differences. The experimental profile shows better agreement with simulations based on ionic potentials than those based on neutral potentials, consistent with the established nature of bonding in SrTiO 3 . More detailed comparisons with varying sample thickness are shown in Supplementary Note 2, but the general tendency is the same. Thus, we conclude that the atomic-resolution DPC STEM images are sensitive to charge redistribution.

Figure 3d also compares intensity profiles across the same Sr and Ti–O atomic columns in the electric field strength map and the ADF image. The intensity dips in the electric field strength map are in identical positions to the intensity peaks in the ADF image, indicating that the electric field strength map can equally be used to determine atomic column positions. Intriguingly, the full width half maxima of the intensity dips in the electric field strength map are much narrower than those of the intensity peaks in the ADF image, meaning that electric field strength maps should enable the determination of atomic column positions with very high precision. Although picometre column position determination has been achieved previously by fitting Gaussian functions to the broader ADF atomic columns, for example, by Yankovich et al.31, the sharper contrast profiles of the electric field strength map should facilitate such analysis.

Atomic-resolution DPC STEM of isolated Au single atoms

The projected electric field strength is enhanced in crystalline materials viewed on axis because the atoms line up in columns. To demonstrate the ultimate sensitivity of quantitative DPC STEM electric field mapping down to the single-atom level, we use a model sample consisting of single atoms of Au dispersed on an amorphous carbon support film via a vacuum evaporation technique. The sample preparation is described in detail in the Methods section. The same method has been applied successfully to disperse noble metal single atoms on crystalline and amorphous substrates32,33,34. Figure 4a–c shows simultaneously imaged ADF, electric field vector and strength maps of Au single atoms, respectively. As detailed in the Methods section, a much lower electron-dose condition (∼3 pA) than that for the SrTiO 3 case (∼27 pA) was used to minimize Au atom motion during the beam scan. Since Au atoms (Z=79) are much heavier than carbon atoms (Z=6), the ADF intensity of Au atoms stands out clearly as intensity peaks above the background contribution of carbon atoms in the supporting film. Indeed, many bright contrast peaks that correspond to Au single atoms and small clusters can be clearly seen in the ADF image. The distinction is less clear in the electric field vector map in Fig. 4b, since the range of colours complicates visual interpretation, and in the electric field strength map in Fig. 4c, since the electric field strength scales approximately as the atomic number, whereas the ADF image scales more strongly as the atomic number squared. However, using the ADF image as a reference for finding Au single-atom positions in the corresponding electric field vector and strength maps, we focus on three well-separated, isolated Au single atoms in the field of view. Numbered from 1 to 3, magnified ADF, electric field vector and strength maps of each atom are shown to the right of the full images. The electric field vector and strength maps at these atom positions show the distinctive contrast features identified in the SrTiO 3 crystalline case. In particular, radially outward electric field contrast is again found in the electric field vector maps about the Au atom positions. However, there are many positions in Fig. 4b,c where the electric field vector and electric field strength maps show appreciable image contrast, but the ADF image does not. This contrast is considered to come from the amorphous carbon support. Since atomic-resolution DPC sensitively images the local electric fields, DPC variations arise not only because of the Au atoms, but also because of local sample thickness changes, surface steps and density variation of the amorphous carbon support. Therefore, single-atom imaging by DPC will be more susceptible to background contributions compared with ADF imaging. To consider the amorphous carbon support effect, we simulated electric field vector and strength maps of an Au single atom on a 10 nm-thick amorphous carbon substrate. The simulated images are shown below the magnified Au single-atom images. It is seen that, because of the supporting film’s amorphous structure and the weak scattering power of its constituent carbon atoms, the Au single-atom contrast stands out from the background contrast. However, if single atoms were located in more strongly diffracting environments such as on crystalline substrates or within crystalline interfaces, diffraction effects would likely confound determination of the true electric field contributions. That diffraction can cause additional and misleading contributions to DPC image contrast at crystalline interface regions has been shown in the literature35. Nevertheless, in regions with minimal background contribution, such as on top of non-diffracting amorphous structures, this study shows that DPC imaging of single atoms is indeed possible.

Figure 4: Simultaneous atomic-resolution ADF STEM image and electric field vector map and electric field strength map of Au single atoms. (a) ADF STEM image. (b,c) Electric field vector and electric field strength maps constructed from the segmented-detector STEM images. The dwell time is 300 μs per pixel. The inset colour wheel indicates how colour and shade denote the electric field orientation and strength. Magnified images from three isolated Au atom positions (3), identified from the ADF image but extractable from all the simultaneously acquired images, are shown to the right of the full images. The enlarged sections of the electric field vector and electric field strength maps show the distinctive contrast features seen at the column locations in Fig. 2. Simulated single Au atom images are also shown, which include a 10 nm-thick amorphous carbon substrate beneath the single Au atom. Because of the random structure of amorphous carbon, the diffraction effect is weak and thus the single Au atom contrast stands out from the background amorphous carbon contrast. (d) Comparison between the projected electric field strength line profile of Au atom number 2 and the simulated projected electric field strength line profiles of a single Au atom. For the experimental electric field strength line profile, the zero CoM angle is set to the average intensity of the nearby amorphous carbon region, and thus the comparison simulations do not include an amorphous carbon substrate. The experimental electric field strength using the eCoM approximation (blue line) and the simulated electric field profile assuming the same eCoM approximation (light green) are in good quantitative agreement. For comparison, the ideal atomic electric profile (including finite temperature effect) blurred by the diffraction-limited probe intensity profile and incoherent source size (red dashed line) is also shown. It is seen that the eCoM is a quantitatively good approximation to the (probe-blurred) atomic electric field. Full size image

Figure 4d compares the line profiles of the experimental (projected) electric field strength map for Au atom number 2 (blue line) and two theoretical electric field strength maps, one from effective segmented-detector CoM approximation simulations described below (light green line, labelled eCoM) and the other from direct calculation of the projected electric field of a neutral Au single atom (including finite temperature effect) convolved with the intensity distribution of the electron probe (red dashed line). Vertical axes are given in units of both CoM angle and projected electric field strength. For simplicity, these simulations ignore the effect of the amorphous carbon support. The effective segmented-detector CoM analysis is the modified version of the segmented-detector CoM approximation that involves fitting its phase-contrast transfer function to that of the pixelated detector CoM, thereby improving the accuracy of the CoM determination. A detailed derivation and discussion of the eCoM approximation is given in the Supplementary Note 3. It is seen that the experimental and theoretical electric field strength line profiles show quantitative agreement in both CoM angles and the estimated projected electric field strength. Going out from the atom centre, the theoretical electric field strength profile increases, turns around and decreases again, in a shape that relates to the spatial variation of total charge density within the Au single atom blurred by the sub-Å electron probe. Our experimental electric field strength exhibits a quantitatively similar profile, albeit perturbed by scan noise, indicating that the electric field vector and strength maps are indeed visualizing the atomic electric field of a single Au atom in real-space. To increase the accuracy of the electric field profile quantification beyond simple analysis using the present segmented detector, a pixelated detector23,36,37,38 could be used. However, pixelated detectors do not yet favour fast real-time imaging, and the difference between the simulated effective segmented-detector CoM approximation electric field profile and the ideal result, that is, the input-projected electric field blurred by the sub-Å electron probe, appears to be minimal in the case of single atoms as shown in Fig. 4d and Supplementary Fig. 10.