Surface structure of $\mathrm{Sr}\mathrm{Ti}{\mathrm{O}}_3\left(001\right)$

We report on the structural determination of the surface of $\mathrm{Ti}{\mathrm{O}}_2$-terminated $\mathrm{Sr}\mathrm{Ti}{\mathrm{O}}_3\left(001\right)$ using surface x-ray diffraction. The detailed analysis of two surface diffraction data sets are presented, one (cold) taken at room temperature in vacuum, and the other (hot) under typical conditions used for thin film growth. 49 different combinations of possible surface terminations are described for the cold structure, from which the final structure was chosen, consisting of a weighted mixture of a $(1\times 1)$ relaxation and $(2\times 1)$ and $(2\times 2)$ reconstructions, simultaneously present at the surface. The structures are best modeled by a $\mathrm{Ti}{\mathrm{O}}_2$-rich surface similar to that proposed by Erdman et al. [Nature (London) 419, 55 (2002)]. The reconstructions are energetically favorable according to density functional theory. They disappear within several minutes upon heating to the hot conditions, forming a termination very similar to the cold $(1\times 1)$, but more puckered and higher in energy. Six additional models, suggested by direct methods and the literature, to describe the hot surface are also discussed. Direct methods confirm the $\mathrm{Ti}{\mathrm{O}}_2$-rich termination and the atomic positions of the hot surface. The atomic coordinates for the two $\mathrm{Ti}{\mathrm{O}}_2$-rich surfaces exhibit significant displacements down to three unit cells, which may have important implications on possible surface ferroelectric phenomena in $\mathrm{Sr}\mathrm{Ti}{\mathrm{O}}_3$. Surface energy considerations suggest a temperature-induced order-disorder transition, produced by a mixing of the $(2\times 1)$ and $(2\times 2)$ reconstructions, to form the hot pseudo $(1\times 1)$ structure. Electrostatic stability arguments provide circumstantial support for the experimentally determined $\mathrm{Ti}{\mathrm{O}}_2$-rich surfaces.

Figure 1

(Color online) AFM image of STO after chemical etching and thermal annealing. The step height of $4\mathrm{\AA }$ corresponds well to a unit cell step, while no $2\mathrm{\AA }$ steps, indicative of mixed $\mathrm{Sr}\mathrm{O}∕\mathrm{Ti}{\mathrm{O}}_2$ termination, were observed. The line profile (right) was generated by horizontal integration over the region marked by the white box.

Figure 2

(Color online) LEIS measurements of as-received (blue) and etched (red) (Refs. 23, 24) and re-etchted STO (green) (Ref. 27). In addition to Sr, Ti, and O, also $\mathrm{Ca}∕\mathrm{K}$, $\mathrm{P}∕\mathrm{S}$, $\mathrm{Na}∕\mathrm{Mg}$, and F are present in the outermost layer. The spectra show decreased intensities for the Sr and Ca species, but an enhanced Ti signal for prepared STO. The main contaminant Mg could be explained by adsorbates arising from the MgO crucible during the anneal process.

Figure 3

(Color) Cold $(1\times 1)$ terminations that are placed on STO bulk unit cells. The first two ALs of an ideal Ti-terminated bulk STO surface are shown in (a) and (b). All models are viewed from above onto the $ab$ plane and display the unit cell as a grey box, with the Sr bulk position at the cell corners. The number in the upper right corner indicates the AL of the opaque sites, labeling the surface layer of DL models as 1. The adopted surface symmetries are noted in black below the cells where they are unambiguous. Other considered symmetry elements and their descriptions are highlighted in brown and yellow. Atoms shown in lighter shades represent nominal positions that are one AL deeper down, but are required to unambiguously understand the termination. A detailed description of the structures is given in the text. Color code: Sr green, Ti red, and O blue.

Figure 4

(Color) The tested starting models for the cold $(2\times 1)$ structures, using the same representation as in Fig. 3.

Figure 5

(Color) Starting models for the cold $(2\times 2)$ structures. Notation is the same as for Fig. 3.

Figure 6

(Color online) Set of the SXRD data (black data points) and calculated intensities (gray solid line, red online) for the cold conditions. The top row contains the six SSRs that can be exclusively associated with the $(2\times 2)$ reconstruction. The central group of 12 SSRs can represent signal from both the $(2\times 2)$ and $(2\times 1)$ domains, and indeed we see that their intensities are about double those of the uppermost row, indicative that a $(2\times 1)$ does exist. The nine CTRs at integer positions in $k$ space are presented on a logarithmic scale in the lowest group.

Figure 7

(Color) The final models for the cold domains (a)–(c) and the hot structure (d), including their symmetries and percentage contributions. The $(1\times 1)$ structures [cold (a) and hot (d)] are viewed from the side, while the reconstructions are from above. Color code: Sr green, Ti red, and O blue.

Figure 8

(Color) Hot $(1\times 1)$ starting models using the same representation as in Fig. 3.

Figure 9

The evolution of ${\chi }_r^2$ (a) and $R$ factor (b) as a function of the fit ALs for hot STO under identical conditions and started from the same initial positions. The dotted lines are guides to the eyes.

Figure 10

(Color online) Cuts through the average electron density recovered by PARADIGM for coherently added domains at two different heights: O positions at $z∕a_0=2.97$ (a) and Ti positions at $z∕a_0=3.28$ (b). Representation is in bulk units of STO and analogously to Table , for direct comparison. The white line indicates the STO bulk unit cell.

Figure 11

(Color online) Set of the SXRD data (black data points) and calculated intensities using the $\mathrm{Ti}{\mathrm{O}}_2$-DL model (gray solid line, red online) for the hot structure.

Figure 12

(Color online) A schematic showing the similarity and simple transformation between the top layers of either the (ordered) $(1\times 1)$, $(2\times 1)$, and $(2\times 2)$ terminations. Transformation of the ordered $(1\times 1)$-DL structure and either reconstruction only requires a diagonal movement of every second Ti atom, with the possibility of forming a disordered $(1\times 1)$ relaxation (“grain boundaries”) in between the domains. The gray boxes indicate the surface unit cells of the terminations. Color code: Ti small red, O large blue circles.

Figure 13

(Color online) Displacements of Sr (green triangles), Ti (red circles), and O (blue crosses) in the $z$ direction from the high-symmetry positions in the starting models. The nominal surface is at $z=0$ and positive values of $\Delta z$ indicate displacements towards vacuum.