Direct Observation of Sr Vacancies in ${\mathrm{SrTiO}}_3$ by Quantitative Scanning Transmission Electron Microscopy

Unveiling the identity, spatial configuration, and microscopic structure of point defects is one of the key challenges in materials science. Here, we demonstrate that quantitative scanning transmission electron microscopy (STEM) can be used to directly observe Sr vacancies in ${\mathrm{SrTiO}}_3$ and to determine the atom column relaxations around them. By combining recent advances in quantitative STEM, including variable-angle, high-angle annular dark-field imaging and rigid registration methods, with frozen phonon multislice image simulations, we identify which Sr columns contain vacancies and quantify the number of vacancies in them. Picometer precision measurements of the surrounding atom column positions show that the nearest-neighbor Ti atoms are displaced away from the Sr vacancies. The results open up a new methodology for studying the microscopic mechanisms by which point defects control materials properties.

Popular Summary

Revealing the identity, spatial configuration, and microscopic structure of point defects is a key challenge in materials science and condensed-matter physics—even small concentrations of point defects can fundamentally alter the behavior of a material. Methods to quantify the global concentration of point defects exist, but determining the spatial arrangement of these defects and the atomic structure around them is challenging. Here, we apply recent advances in quantitative scanning transmission electron microscopy (STEM) to study intentionally nonstoichiometric ${\mathrm{SrTiO}}_3$ films in which strontium vacancies are a likely defect.

Imaging a 3- to 4-nanometer-thick crystal of ${\mathrm{SrTiO}}_3$, we show that atom columns that contain strontium vacancies can be identified in STEM. We quantify the number of vacancies in the columns by comparing column intensities calculated in image simulations of a total of 512 potential vacancy configurations with the experimental column intensities. We verify that the electron beam does not damage the ${\mathrm{SrTiO}}_3$ sample. Picometer-precision measurements of the atom columns’ positions reveal that the surrounding titanium columns are displaced away from the strontium vacancies. The experimental results differ from the outcomes predicted by density-functional theory, a finding that highlights that density-functional theory alone may be inadequate at revealing the atomic-level structure of real-world materials.

Our results provide new research directions for further advances in quantitative STEM. We also expect that our findings will motivate new methods to study the microscopic mechanisms by which point defects control material properties.

Figure 1

Quantitative, rigidly registered, variable-angle HAADF-STEM images of Sr vacancies in a ${\mathrm{SrTiO}}_3$ film grown by MBE. (a,d) HAADF STEM images of the ${\mathrm{SrTiO}}_3$ film recorded with detectors 1 and 2, respectively. Image intensities are normalized to the incident beam intensity (see scale bars). $I_{\mathrm{Sr}}$ and $I_{\mathrm{Ti}\text{−}\mathrm{O}}$ maps are displayed in (b,e) and (c,f), respectively. The Sr columns containing Sr vacancies are labeled A and B and indicated by white arrows in (b) and (e). The four nearest-neighboring Ti-O columns for columns A and B are marked by white boxes in (c) and (f), showing relatively uniform image contrast.

Figure 2

Determination of vacancy configurations. (a,b) Simulated $I_{\mathrm{Sr}}$ vs $I_{\mathrm{Ti}\text{−}\mathrm{O}}$ plots using detector angular ranges corresponding to detectors 1 and 2. Red and green squares represent the intensities from columns A and B, respectively, while orange circles are the simulated data points for all possible vacancy configurations.

Figure 3

Local structure relaxation around Sr vacancies. (a,c) Magnified HAADF STEM images near column-A recorded with detectors 1 and 2, respectively. (b,d) Atomic distance maps, where each pixel value indicates the average distance from one cation to its four nearest-neighbor unlike cations, showing Ti-O columns being displaced away from Sr vacancies. The overlay in (a) shows an example of a distance measurement from a Sr column (orange circle) to the Ti-O columns (blue circle).