Three-Dimensional Imaging of Individual Dopant Atoms in ${\mathrm{SrTiO}}_3$

We report on three-dimensional (3D) imaging of individual Gd dopant atoms in a thin ($\sim 2.3\mathrm{nm}$) foil of ${\mathrm{SrTiO}}_3$, using quantitative scanning transmission electron microscopy. Uncertainties in the depth positions of individual dopants are less than 1 unit cell. The overall dopant concentration measured from atom column intensities agrees quantitatively with electrical measurements. The method is applied to analyze the 3D arrangement of dopants within small clusters containing 4–5 Gd atoms.

Figure 1

(a) Probe channeling characteristics for $C_s$-corrected and noncorrected probes, respectively. The probe is positioned above a Sr column in ${\mathrm{SrTiO}}_3$, along 100. Weak, superimposed oscillations are due to the dechanneling and rechanneling of the probe as it passes through the individual planes of ${\mathrm{SrTiO}}_3$ (SrO and ${\mathrm{TiO}}_2$, respectively). (b) HAADF image of 3.4%-Gd-doped ${\mathrm{SrTiO}}_3$. (c) Experimental (left) PACBED pattern from the area shown in (b) and (right) simulated pattern for a 2.3 nm thick sample. (d) Magnified image of the region indicated by the square in (b). The circles indicate the areas over which $I_{\mathrm{Sr}}$ and $I_{\mathrm{Ti}\mathrm{\text{−}}\mathrm{O}}$ were averaged. (e) $I_{\mathrm{Sr}}$ and (f) $I_{\mathrm{Ti}\mathrm{\text{−}}\mathrm{O}}$ map from the image shown in (b). Scale bars indicate the intensity value normalized to the incident beam intensity.

Figure 2

(a) Experimental $I_{\mathrm{Sr}}$ vs $I_{\overline{\mathrm{Ti}\mathrm{\text{−}}\mathrm{O}}}$ plot for undoped ${\mathrm{SrTiO}}_3$, before (green open circles) and after (black triangles) subtraction of $I_B$. Multislice simulations are shown as blue filled circles. The inset shows the 2D error function calculated from the experimental data. (b) Experimental $I_{\mathrm{Sr}}$ vs $I_{\overline{\mathrm{Ti}\mathrm{\text{−}}\mathrm{O}}}$ plot for Gd-doped ${\mathrm{SrTiO}}_3$ after the background subtraction, and fit for undoped ${\mathrm{SrTiO}}_3$ (solid line). The experimental error as defined by the inset in (a) is also shown (dashed lines). (c) Multislice simulations (blue circles) of column intensities for all possible dopant locations in a 5 unit cell thick region of Gd-doped ${\mathrm{SrTiO}}_3$. The labels (numbers) indicate the dopant position in the column as defined in (d). The filled darker blue circle is the simulation for a 5 unit cell thick undoped ${\mathrm{SrTiO}}_3$. Experimental points, labeled $A\mathrm{\text{−}}G$, the undoped ${\mathrm{SrTiO}}_3$ fit from (a) (solid line), and error cutoff (dashed line) are also shown. The large, shaded triangle and the ellipsoid indicate the dopant clusters shown in Figs. 3a, 3b. (e) Histograms of the relative difference between $I_{\mathrm{Sr}}$ in Gd-doped and undoped ${\mathrm{SrTiO}}_3$.

Figure 3

(a),(b) $I_{\mathrm{Sr}}$ maps (left) and HAADF images (right) of the areas containing $A–B$ columns (a) and $C–F$ columns (b), for which the intensity data were shown in Fig. 2c. Yellow circles in the images indicate the areas over which the $I_{\mathrm{Sr}}$ were averaged. (c),(d) Schematics showing the configurations of dopant atoms in $A–B$ (c) and $C–E$ (d) columns. The most probable dopant position is shown in red and the expectation values and uncertainties are labeled (yellow numbers). (e) 3D illustration of the area in (b) with the most probable Gd dopant configuration in columns $C–F$. For clarity, Sr atoms are not shown and some Ti and O atoms were also removed.