Surface Reordering During Layer‐by‐Layer Growth on SrTiO₃

ABSTRACT

With the development of layer‐by‐layer growth techniques such as molecular beam epitaxy (MBE), it is now possible to construct materials with atomic‐level precision, with the layer sequence primarily determined by the growth recipe. However, materials can still restructure in the high‐temperature growth environment with surface thermodynamics strongly influencing growth behavior. Here, we demonstrate that growth on ${\mathrm{SrTiO}}_3$ (001), the principal platform for oxide electronics, does not occur in a layer‐by‐layer fashion but follows a more complex process in which a ${\mathrm{TiO}}_2$ plane continually diffuses toward the growth surface. Employing in situ synchrotron X‐ray scattering combined with ab initio thermodynamic calculations, we discover the existence of a stable ${\mathrm{TiO}}_2$ double‐layer structure on the pristine substrate and the occurrence of dynamic layer rearrangement during homoepitaxial growth by oxide MBE. Our findings suggest that the current methods used to precisely control ${\mathrm{SrTiO}}_3$ surfaces are limited, as well as our ability to dictate the composition of ultrathin films, resulting in important ramifications regarding the surface reactivity of perovskite materials grown on ${\mathrm{SrTiO}}_3$.

Surface structures (left) derived from DFT‐constrained fitting to crystal truncation rods measured by synchrotron X‐ray scattering (right) after each monolayer of deposition during the MBE growth of ${\mathrm{SrTiO}}_3$ (001). The bottom panel shows the bare substrate, the middle panel shows island formation upon deposition of a single layer of SrO, and the top panel shows island smoothing after the addition of a single layer of ${\mathrm{TiO}}_2$.

1. Introduction

Complex oxides in thin film form offer new and exciting strategies for meeting many technological challenges. Strongly correlated oxides, in particular, offer a myriad of ground states [1], and their interfacial properties suggest the potential development of novel devices in the field of oxide electronics [2, 3, 4]. The synthesis of the oxide must be controlled precisely, however, as the composition and stacking of each atomic plane can be critical to the resulting properties. In this regard, reactive molecular‐beam epitaxy (MBE) is the growth method of choice, as the sequential delivery of different cation fluxes to the surface permits the digital synthesis of different layered oxides [5, 6, 7, 8] and studies on the effects of cation order on ground‐state properties and phase transitions [9, 10, 11]. The usual in situ deposition monitor is reflection high‐energy electron diffraction (RHEED), which allows excellent thickness control and provides information on surface roughness evolution during growth. However, RHEED is only sensitive to the outermost layers, and due to multiple scattering, the atomic mechanisms that take place are difficult to probe in quantitative detail [12, 13]. On the other hand, X‐ray scattering is kinematic, and crystal truncation rods (CTRs) can be analyzed to extract the through‐thickness structure [14].

The (001) facet of ${\mathrm{SrTiO}}_3$ has long served as a universal substrate for the growth of complex oxides, including high $T_C$ superconducting thin films [15, 16, 17], multiferroics [18], and other correlated systems [19, 20, 21]. ${\mathrm{SrTiO}}_3$ is an archetype of the perovskite crystal structure and relatively unusual among these crystals in that it remains cubic over an extensive temperature range with a lattice parameter convenient for engineering specific strain‐dependent functionalities [22, 23]. For these reasons, considerable effort has been invested in ${\mathrm{SrTiO}}_3$ surface preparation, enabling the regular achievement of ${\mathrm{TiO}}_2$‐termination with step‐terrace morphology and unit‐cell step heights conducive to epitaxial growth [24, 25, 26, 27, 28].

Indeed, the chemical treatment of ${\mathrm{SrTiO}}_3$ first presented in Ref. [24] was critical to the development of oxide interface engineering [29, 30, 31]. For instance, in ${\mathrm{LaAlO}}_3$/${\mathrm{SrTiO}}_3$ heterostructures, 2D electron gas/superconducting behavior appears at the ${\mathrm{TiO}}_2$‐terminated ${\mathrm{SrTiO}}_3$ interface but not at the SrO‐terminated one [32, 33]. Furthermore, the bare ${\mathrm{TiO}}_2$‐terminated surface has been shown to exhibit a variety of interesting electronic phenomena [34, 35, 36, 37, 38]. Effective surface control enables the engineering of specific Schottky barriers [39] as well as other functionalities [40], and the ${\mathrm{TiO}}_2$ interface can alter the properties of adjacent superconducting FeSe films [41, 42, 43, 44]. In recent years, however, researchers have found that achieving the desired surface of ${\mathrm{SrTiO}}_3$ may be more challenging than previously believed, with reports suggesting that the surface is often ${\mathrm{TiO}}_2$‐rich [45, 46]. Interpretation of much of the recent thin film oxide literature should be reconsidered if the initial ${\mathrm{SrTiO}}_3$ surface is non‐stoichiometric.

Here, we present a detailed in situ synchrotron X‐ray study of the ${\mathrm{TiO}}_2$‐terminated ${\mathrm{SrTiO}}_3$ (001) surface and its behavior during homoepitaxial growth by reactive MBE, exploiting a unique MBE system at beamline 33‐ID‐E of the Advanced Photon Source (APS) [47, 48, 49, 50], density functional theory (DFT)‐constrained fitting [51], and the Coherent Bragg Rod Analysis (COBRA) phase retrieval technique [52, 53, 54]. We examine the appearance of diffuse scattering during growth, providing critical length scale information absent from the specular rod alone and at time scales appropriate for MBE. By comparing sequential deposition (alternating SrO and ${\mathrm{TiO}}_2$ monolayers) with that of co‐deposition [55], we find that while both techniques can be used to grow high‐quality films, unexpected behavior is observed during regular sequential deposition with SrO/${\mathrm{TiO}}_2$: a monolayer of SrO does not wet the ${\mathrm{TiO}}_2$‐terminated surface due to the presence of a ${\mathrm{TiO}}_2$ double layer, leading to a rough surface comprised of ${\mathrm{SrTiO}}_3$ islands. The surface re‐smooths only after the deposition of ${\mathrm{TiO}}_2$, reforming the ${\mathrm{TiO}}_2$ double layer. A similar phenomenon occurs for reverse sequential deposition with ${\mathrm{TiO}}_2$/SrO: islands form upon deposition of a monolayer of ${\mathrm{TiO}}_2$, and the surface smooths after the deposition of SrO. Our findings suggest that even for the simple case of homoepitaxy in the complex oxides, the processes at the surface can be highly dynamic due to the energetics of non‐stoichiometric interfaces. The surface structures derived from in situ X‐ray measurements at each growth step agree with ab initio thermodynamic calculations, clearly revealing a stable ${\mathrm{TiO}}_2$ double‐layer structure on the pristine substrate and the occurrence of dynamic layer rearrangement during homoepitaxial growth by oxide MBE.

2. In Situ Studies of Epitaxial Growth

The experimental setup and reciprocal space geometry for the X‐ray measurements are depicted in Figure 1. An area detector (PILATUS 100K) was used to record both the specular X‐ray scattering associated with the out‐of‐plane electron density profile and the diffuse X‐ray scattering associated with in‐plane correlations. As shown in the lower right of Figure 1, the atomic steps on the ${\mathrm{SrTiO}}_3$ (001) surface were aligned perpendicular to the incident beam such that X‐ray scattering along the in‐plane $Q_{\parallel }$ direction was sensitive to island correlations along the surface. Previous studies have used this technique to study the in‐ and out‐of‐plane processes that occur during homoepitaxial growth by pulsed laser deposition (PLD) [56, 57].

FIGURE 1.

Experimental geometry (left) and illustration of reciprocal space (right) for in situ, time‐resolved diffuse X‐ray scattering studies. Features in reciprocal space include Bragg peaks from the substrate (red), crystal truncation rods (green), and Henzler rings (light red) arising from 2D islands on the surface. The radius of the Henzler ring is correlated to the in‐plane island spacing, $d$. The tilt of the CTRs is due to the miscut of the crystal surface.

The shutter timing diagrams for co‐deposition, regular sequential deposition with SrO/${\mathrm{TiO}}_2$, and reverse sequential deposition with ${\mathrm{TiO}}_2$/SrO are shown in Figure 2a–c, respectively, for five unit cells of ${\mathrm{SrTiO}}_3$ growth. Shutter times were initially based on flux measurements made using a quartz crystal microbalance and then checked by optimizing Kiessig (thickness) fringes with a high‐resolution X‐ray reflection measurement on a calibration sample immediately prior to the growth of the experimental samples. Immediately following the deposition of five unit cells of ${\mathrm{SrTiO}}_3$, we measured the specular rod at the growth temperature to determine the stoichiometry and thickness of the films. Results from one‐dimensional COBRA (Figure S1, Supporting Information) indicate that all of the final samples have good stoichiometry with an out‐of‐plane lattice parameter consistent with bulk ${\mathrm{SrTiO}}_3$ at 700.

FIGURE 2.

Timing diagram of the strontium and titanium shutters during the (a) co‐deposition, (b) regular sequential deposition, and (c) reverse sequential deposition of five unit cells of ${\mathrm{SrTiO}}_3$. Oxygen is provided continuously during growth. The corresponding time‐resolved X‐ray scattering data along $Q_{\parallel }$ at $00\frac{1}{2}$ are shown in (d), (e), and (f), and the corresponding specular (red) and diffuse (green) integrated intensities during deposition are shown in (g), (h), and (i).

False color images of the specular intensity at the anti‐Bragg position, $00\frac{1}{2}$ (in reciprocal lattice units (r.l.u) of ${\mathrm{SrTiO}}_3$) and adjacent diffuse scatter during growth are shown in Figure 2d for co‐deposition, Figure 2e for regular sequential deposition, and Figure 2f for reverse sequential deposition. The diffuse scatter in Figure 2d–f are cuts through Henzler rings (Figure 1) arising from 2D islands on the perovskite surface [57, 58, 59]. While a distinct diffuse peak indicates a well‐defined in‐plane correlation length, the peak profile contains little information regarding feature shapes or size distributions [60]. The integrated specular and diffuse intensities for co‐deposition and regular sequential deposition are shown in Figure 2g,h, respectively, illustrating that the specular (red) and diffuse intensities (green) oscillate out of phase with each other. The specular oscillations indicate layer‐by‐layer growth of the ${\mathrm{SrTiO}}_3$ films [61], while the diffuse peak oscillations indicate the formation and evolution of in‐plane features during layer‐by‐layer growth [57, 62]. The oscillatory behavior of the specular intensity is in agreement with RHEED studies of the sequential deposition of ${\mathrm{SrTiO}}_3$ by MBE [12, 63] and a PLD study employing binary oxide targets [64]. We note an intriguing diffuse scatter behavior for reverse sequential deposition, as shown in Figure 2f,i, which is discussed in more detail below.

In the case of co‐deposition (Figure 2a,d,g), the specular intensity decreases to a minimum, and the diffuse intensity rises to a maximum at a time corresponding to 50% coverage of 1‐unit‐cell‐thick ${\mathrm{SrTiO}}_3$. With continued growth, the specular (diffuse) intensity rises (decays) to a maximum (minimum) at 100% unit‐cell coverage. The overall behavior is consistent with a 2D island growth mode, where unit‐cell‐high ${\mathrm{SrTiO}}_3$ islands are spaced approximately 40 nm apart, as determined from the diffuse scatter. These islands nucleate and grow on the terraces and then coalesce before the start of the next unit cell. This is similar to the growth behavior observed during PLD from a single ${\mathrm{SrTiO}}_3$ target [56, 57, 61]. During regular sequential deposition (Figure 2b,e,h), we also observe oscillatory behavior; however, the first minimum in specular intensity no longer corresponds to a half‐unit‐cell coverage of ${\mathrm{SrTiO}}_3$, but rather to a 1 monolayer (ML) coverage of SrO. The surface smooths again with ${\mathrm{TiO}}_2$ deposition, arriving at maximum in the specular rod intensity. If SrO had wet the ${\mathrm{TiO}}_2$‐terminated substrate, the intensity at $00\frac{1}{2}$ would first decrease when the Sr shutter is opened due to island formation (roughening) and then increase and return to a maximum as the SrO layer completes (smoothing), leaving a SrO‐terminated surface [65]. Here, however, the $00\frac{1}{2}$ intensity increases only during the deposition of ${\mathrm{TiO}}_2$ and reaches a maximum at the completion of one ${\mathrm{SrTiO}}_3$ unit cell, indicating SrO does not wet the ${\mathrm{TiO}}_2$‐terminated surface. In effect, the intensity versus time profile shown in Figure 2h has twice the expected period. This indicates that sequential deposition does not proceed by the nucleation and coalescence of single‐layer‐high SrO islands, followed by the same for ${\mathrm{TiO}}_2$. Instead, the scattering indicates that the SrO grows as islands and restructures into ${\mathrm{SrTiO}}_3$ unit cells only during the deposition of ${\mathrm{TiO}}_2$, leaving an atomically flat surface. The process repeats with every Sr and Ti growth cycle, the only difference being progressively narrower island size distributions and larger inter‐island spacings, from $\sim 10$ nm to 21 nm (Section S2 and Figure S2, Supporting Information), due to the nucleation of new islands prior to the completion of the previous layer [57].

On the other hand, for reverse sequential deposition (Figure 2c,f,i), the initial growth of ${\mathrm{TiO}}_2$ leads to a drop in the specular intensity; however, the diffuse intensity rises to a maximum near 1/2 ML coverage of ${\mathrm{TiO}}_2$, returning to a minimum before the Sr shutter is opened. This suggests 2D island growth of 1‐ML‐thick ${\mathrm{TiO}}_2$ islands — i.e., ${\mathrm{TiO}}_2$ appears to initially wet the ${\mathrm{TiO}}_2$‐terminated substrate. Interestingly, the same behavior occurs for the SrO deposition: the diffuse intensity peaks at roughly 1/2 ML coverage of SrO before the film restructures to form ${\mathrm{SrTiO}}_3$; the layer rearrangement mechanism may be similar to that observed earlier for the Ruddlesden‐Popper series [47]. The second through fifth ${\mathrm{TiO}}_2$/SrO cycles behave differently: the diffuse scatter continues to increase with ${\mathrm{TiO}}_2$ deposition and decreases substantially only after the Sr shutter is open, suggesting that ${\mathrm{TiO}}_2$ does not appear to wet the ${\mathrm{TiO}}_2$‐terminated film surface.

3. CTR Analysis

To investigate why SrO does not wet the ${\mathrm{TiO}}_2$‐terminated surface, we performed detailed, atomically‐resolved studies of the bare ${\mathrm{SrTiO}}_3$ (001) surface, the surface after 1 ML SrO deposition, and the surface after deposition of 1 ML SrO + 1 ML ${\mathrm{TiO}}_2$, all at the growth temperature and pressure. The X‐ray data was then inverted to determine surface structures using both density functional theory (DFT)‐constrained fitting (Figures 3 and 4) and COBRA (Figure S1, Supporting Information). We exploit two unique properties of synchrotron X‐ray scattering – the large coherence length (allowing phase retrieval) and tunability of the X‐ray energy (allowing elemental sensitivity), performing scattering near to and away from the Sr $K$‐edge (16.1 keV and 15.0 keV, respectively) [66]. The out‐of‐plane structure was determined by simultaneously fitting the non‐resonant and resonant specular CTRs. Here, we utilized the approach introduced in Plaza et al. [51] and extended in Cook et al. [50] to allow for simultaneous fits to multiple DFT structures. This method ensures the physicality of the fits by minimizing a residual that includes goodness‐of‐fit parameters for both non‐resonant and resonant scattering alongside a penalty function to prevent the fit positions from varying significantly from the DFT‐predicted positions. New software for DFT‐constrained fitting was utilized to initialize an ensemble of fits that more effectively explore parameter space. COBRA was performed only on the non‐resonant data, and the results were used to inform the starting structures optimized by the DFT‐constrained fitting procedure. All of the X‐ray scattering data and DFT‐constrained fits for the regular sequential deposition are shown on the right side of Figure 3 with results for the reverse sequential on the right side of Figure 4 as a function of $L$ in reciprocal lattice units (r.l.u.). Here $L=\left(Q_{z}a/2\pi \right)$, where $a$ is the lattice parameter of bulk ${\mathrm{SrTiO}}_3$ at 700 and $Q_z$ is the out‐of‐plane scattering vector. The notation describes an SrO layer using S and a ${\mathrm{TiO}}_2$ layer using T, with the layer closest to the substrate denoted by the first letter and the final surface layer denoted by the last letter. All DFT structural models utilized for fitting are shown in Figure S3 (Supporting Information).

FIGURE 3.

Atomic models (Sr = green, Ti = silver, O = red) of surface structures (left) derived from DFT‐constrained fitting to non‐resonant (15.0 keV) and resonant (16.1 keV) X‐ray scattering (right) at each growth step for the regular sequential deposition. The bottom panel shows the bare substrate (blue), the middle panel shows island formation upon deposition of a single layer of SrO (green), and the top panel shows island smoothing after a full ${\mathrm{SrTiO}}_3$ unit cell is deposited with the addition of a single layer of ${\mathrm{TiO}}_2$ (red). X‐ray scattering data (points), DFT‐constrained best fits (solid dark lines), and the ensemble of DFT‐constrained fits (solid pastel lines) are shown as a function of $L$.

FIGURE 4.

Atomic models (Sr = green, Ti = silver, O = red) of surface structures (left) derived from DFT‐constrained fitting to non‐resonant (15.0 keV) and resonant (16.1 keV) X‐ray scattering (right) at each growth step for the reverse sequential deposition. The bottom panel shows the bare substrate (blue), the middle panel shows island formation upon deposition of a single layer of ${\mathrm{TiO}}_2$ (red), and the top panel shows island smoothing after a full ${\mathrm{SrTiO}}_3$ unit cell is deposited with the addition of a single layer of SrO (green). X‐ray scattering data (points), DFT‐constrained best fits (solid dark lines), and the ensemble of DFT‐constrained fits (solid pastel lines) are shown as a function of $L$.

For the bare ${\mathrm{SrTiO}}_3$ surface, we find that it is terminated with a ${\mathrm{TiO}}_2$ double layer, i.e., a full ${\mathrm{TiO}}_2$ layer in the perovskite configuration, followed by an adlayer of ${\mathrm{TiO}}_2$ (bottom panel of Figure 3) [45, 46, 50, 67, 68, 69, 70]. This conclusion is very well supported by the chemically sensitive resonant scattering results. In the context of heteroepitaxial growth on ${\mathrm{SrTiO}}_3$ substrates, Cook et al. [50] found that structures with even a small deviation in the coverage of the excess ${\mathrm{TiO}}_2$ layer led to large changes in the resonant intensity at $L=0.97$ r.l.u., in sharp disagreement with the measured data. In the non‐resonant data, the minimum at $L=1.01$ r.l.u., as well as the shape of the resonant data between $L=0.5$ and $L=0.9$ r.l.u. are also highly impacted by the precise details of the surface termination. This sensitivity allows us to conclude that the coverage of the excess layer of ${\mathrm{TiO}}_2$ is approximately 90–100$\%$ for the bare substrate. While the exact nature of the ${\mathrm{TiO}}_2$ adlayer is challenging to ascertain conclusively due to the large number of potential surface reconstructions [38], the best quality of fit was obtained with a $\sqrt{2}\times \sqrt{2}$ reconstruction, which has the lowest surface energy of all predicted structures with 100% adlayer coverage.

Following the deposition of 1 ML SrO, the surface is observed to remain partly double ${\mathrm{TiO}}_2$‐terminated (middle panel of Figure 3). This surface structure derived from DFT‐constrained fitting implies that some of the deposited SrO must be inserted beneath the topmost ${\mathrm{TiO}}_2$ layer. The resulting islands of ${\mathrm{SrTiO}}_3$ have roughly 50% coverage, increasing the surface roughness and diffuse scattering, as observed in Figure 2e,h. The $Q_{\parallel }$ dependence shown in Figure 2e indicates that the deposition of first ML of SrO onto the ${\mathrm{TiO}}_2$ double layer results in an islanded surface with $\sim 10$ nm inter‐island spacing. Fits to the diffuse scattering show island heights of $\sim 0.4$ nm (Figure S2, Supporting Information), which is double the expected height for single‐layer SrO islands on an unreconstructed surface. This suggests that SrO interacts with the reconstructed ${\mathrm{SrTiO}}_3$ surface, forming islands with a height equivalent to one full ${\mathrm{SrTiO}}_3$ unit cell, in agreement with the DFT‐predicted surface structure. In other words, the deposition of 1 ML SrO leads to dynamic rearrangement of the surface, with approximately half of the incoming SrO layer exchanging places with the mostly occupied ${\mathrm{TiO}}_2$ surface plane and the remaining half of the SrO bonded to the resulting single‐layer ${\mathrm{TiO}}_2$ to form SrO‐terminated islands. This behavior is consistent with previous ex situ studies of homoepitaxial growth on ${\mathrm{SrTiO}}_3$ (001) substrates by PLD using scanning tunneling microscopy [71, 72].

As the structural changes occur on the same timescale as the deposition, the kinetic barriers to rearrangement appear to be low. To provide insight into the observed dynamic surface rearrangement, we have performed DFT calculations of the surface energy. According to DFT calculations of the surface energy in the SrO‐rich limit (Figure 5a), ${\mathrm{TiO}}_2$‐SrO‐${\mathrm{TiO}}_2$ (TST, red) is more stable than ${\mathrm{TiO}}_2$‐${\mathrm{TiO}}_2$‐SrO (TTS, magenta), providing a thermodynamic impetus for layer rearrangement. Furthermore, surface energy calculations indicate that the formation of ${\mathrm{TiO}}_2$‐SrO‐${\mathrm{TiO}}_2$‐SrO (TSTS, green) islands while leaving the ${\mathrm{TiO}}_2$ double layer (TT, blue) relatively undisturbed is also thermodynamically favored over other possible arrangements of the SrO layer in the region terminated by the ${\mathrm{TiO}}_2$ double layer (TTS or TST), leading to the growth mechanism proposed in Figure 5c. After SrO is deposited on double‐layer ${\mathrm{TiO}}_2$, dynamic layer swapping occurs, forming a single layer of ${\mathrm{TiO}}_2$, which is energetically unfavorable (TST, red). Additional SrO units are able to lower the surface energy by forming Sr‐terminated islands (TSTS, green) on the single‐layer ${\mathrm{TiO}}_2$ rather than depositing on the double‐layer ${\mathrm{TiO}}_2$ to form energetically unfavorable single (TTS, magenta) and double (TTSS, cyan) floating layers of SrO.

FIGURE 5.

Growth mechanisms derived from DFT‐determined surface energies. (a) DFT‐calculated surface energies for Sr‐rich surfaces are shown as a function of the chemical potential of Sr, with the dashed line at 0 eV representing the the chemical potential of Sr in bulk SrO. The low‐energy structures are double‐layer ${\mathrm{TiO}}_2$ (TT, blue), single‐layer SrO (TSTS, green), and double‐layer SrO (TSS, yellow), leading to (c) the hypothesized mechanism for the dynamic layer swap and the formation of islands after the deposition of a single layer of SrO during the regular deposition sequence. (b) DFT‐calculated surface energies for Ti‐rich surfaces are shown as a function of the chemical potential of Ti, with the dashed line at 0 eV representing the chemical potential of Ti in bulk ${\mathrm{TiO}}_2$. The low‐energy structures are double‐layer ${\mathrm{TiO}}_2$ (TT, blue), single‐layer SrO (S, green), and five layers of anatase ${\mathrm{TiO}}_2$ (TTTTT, magenta), leading to (d) the hypothesized mechanism for the formation of islands after the deposition of a single layer of ${\mathrm{TiO}}_2$ during the reverse deposition sequence.

After the deposition of ${\mathrm{TiO}}_2$ in the regular sequence, the ${\mathrm{SrTiO}}_3$ surface smooths, and the diffuse scatter disappears, as shown in Figure 2e. The results in the top panel of Figure 3 also show that the ${\mathrm{TiO}}_2$ double layer at the surface returns. In the ${\mathrm{TiO}}_2$‐rich limit (Figure 5b), the double layer of ${\mathrm{TiO}}_2$ (TT, blue) is favored over a wide range of Ti chemical potentials, leading to a smooth surface and lower total energy. Interestingly, with continued sequential deposition, the excess ${\mathrm{TiO}}_2$ layer is observed to “float” atop the growing surface such that it always remains primarily double ${\mathrm{TiO}}_2$ terminated after the deposition of each unit cell, as supported by the COBRA analysis after the deposition of five ${\mathrm{SrTiO}}_3$ unit cells (Figure S1, Supporting Information).

Finally, we note that similar structures can result even when the deposition sequence is reversed, i.e., when ${\mathrm{TiO}}_2$ is deposited onto the substrate first, followed by SrO. As indicated by the results above, both the bare substrate and the ${\mathrm{TiO}}_2$‐SrO deposition sequence result in a ${\mathrm{TiO}}_2$ double layer and a smooth surface: the corresponding atomic models and CTRs are shown in the bottom and top panels of Figure 4. When 1 ML of ${\mathrm{TiO}}_2$ is deposited onto double‐layer ${\mathrm{TiO}}_2$, the CTRs in the middle panel of Figure 4 and the diffuse scatter results in Figure 2f suggest that only part of ${\mathrm{TiO}}_2$ monolayer overlays the surface. This is especially evident in the growth of the third through fifth unit cells in Figure 2f,i, with islands forming upon deposition of ${\mathrm{TiO}}_2$ atop the double‐layer ${\mathrm{TiO}}_2$ and islands coalescing with the deposition of SrO. The less consistent island‐formation behavior in the first and second unit cells of growth in Figure 2f may be attributed to variations in the amount of the ${\mathrm{TiO}}_2$ adlayer on the bare substrate: DFT‐constrained fitting indicated a coverage of 70–100% (bottom panel of Figure 4). This uncertainty is primarily derived from the disagreement between the measured data and the DFT‐constrained fit observed below $L<0.9$ r.l.u. and just above $L>1.1$ r.l.u. in the non‐resonant (15 keV) data.

Just as for the regular deposition sequence, DFT surface energy calculations elucidate the thermodynamic impetus for island formation in the reverse deposition sequence. As shown in the middle panel of Figure 4, the DFT‐constrained fit to the CTR suggests 1 ML of ${\mathrm{TiO}}_2$ aggregates into islands of height 0.6–0.8 nm, which comprise a complete 5‐layer unit cell of anatase ${\mathrm{TiO}}_2$. Roughly one‐third of the surface is covered by these islands, while the other two‐thirds remains double‐layer ${\mathrm{TiO}}_2$. The ${\mathrm{TiO}}_2$‐rich surface energies in Figure 5b indicate that two layers of ${\mathrm{TiO}}_2$ (TT, blue) and five layers of anatase ${\mathrm{TiO}}_2$ (TTTTT, magenta) are the lowest surface energy terminations, while one (T, red), three (TTT, cyan), and four (TTTT, yellow) layers of ${\mathrm{TiO}}_2$ are less energetically favored. Therefore, a deposited ${\mathrm{TiO}}_2$ monolayer could minimize the surface energy by forming anatase islands rather than evenly distributing over the bare substrate to form an energetically less favorable triple‐layer ${\mathrm{TiO}}_2$ surface, leading to the growth mechanism proposed in Figure 5d. When ${\mathrm{TiO}}_2$ is deposited on double‐layer ${\mathrm{TiO}}_2$, formation of 3 (TTT, cyan) and 4 (TTTT, yellow) layers of ${\mathrm{TiO}}_2$ is not energetically favorable, leading to the formation of islands with a 5‐layer anatase structure (TTTTT, magenta) on approximately one‐third of the surface. Regardless of the exact nature of the islands formed during monolayer ${\mathrm{TiO}}_2$ deposition, a smooth double‐layer ${\mathrm{TiO}}_2$ surface is clearly recovered upon deposition of SrO, as shown in the top panel of Figure 4.

4. Conclusion

In summary, by combining results from in situ time‐resolved and resonant/non‐resonant X‐ray scattering with ab initio thermodynamic calculations, we find that although MBE allows for layer‐by‐layer control, ${\mathrm{TiO}}_2$ remains present at the film surface even after SrO deposition due to the presence of a ${\mathrm{TiO}}_2$ double layer on prepared ${\mathrm{SrTiO}}_3$ (001) substrates. This leads to dynamic layer rearrangement during epitaxial growth, with the ${\mathrm{TiO}}_2$ adlayer continually diffuses toward the surface. Our finding implies that the well‐known procedures used to precisely control ${\mathrm{SrTiO}}_3$ surface termination are likely to result in a non‐stoichiometric, ${\mathrm{TiO}}_2$‐rich surface, which significantly impacts our ability to control the electronic properties and surface reactivity of model oxide heterostructures. Interestingly, these results also suggest that the ideal, singly terminated ${\mathrm{TiO}}_2$ surface assumed in the field of complex oxides is unlikely to exist on ${\mathrm{SrTiO}}_3$. This highlights some of the challenges faced by thin film growth experts and emphasizes the importance of gaining detailed, quantitative insights into the atomic‐scale processes occurring during epitaxial growth. Furthermore, we find that the initial surface structure and composition, coupled with local thermodynamic factors, strongly influence our ability to atomically engineer new ultrathin oxides and their properties.

5. Methods

SrTiO₃ (001) Substrate Surface Preparation, Oxide MBE, In Situ SXRD Prior to growth, low‐miscut ($<0.1^{\circ }$) ${\mathrm{SrTiO}}_3$ (001) substrates from CrysTec were prepared using a termination recipe to achieve a ${\mathrm{TiO}}_2$‐terminated surface [24, 25]. The ${\mathrm{SrTiO}}_3$ films were grown using reactive molecular beam epitaxy at 700, in a background pressure of ${10}^{-6}$ Torr of molecular oxygen, using a Sr effusion cell and a Mini Ti‐Ball source. The thin‐film growth and in situ SXRD (surface X‐ray diffraction) measurements were performed using a unique MBE system at beamline 33‐ID‐E of the APS [48]. A Pilatus 100K area detector was used to measure the specular and diffuse intensities simultaneously. In performing the high‐resolution X‐ray specular CTR measurements, the atomic steps on the ${\mathrm{SrTiO}}_3$ (001) surface were aligned parallel to the plane of the incident and scattered X‐ray wave vectors, allowing for the projection of the sub‐rods emanating from each Bragg peak due to the surface miscut under a single combined rod. In performing the time‐resolved X‐ray scattering, the atomic steps on the ${\mathrm{SrTiO}}_3$ (001) surface were aligned perpendicular to the incident beam such that X‐ray scattering along the in‐plane $Q_{\parallel }$ direction was sensitive to island correlations along the surface [56, 57]. The time resolution of the time‐resolved X‐ray scattering measurements was set to 1s to have sufficient counting statistics.

Density Functional Calculations All first‐principles calculations were performed using the open‐source code JDFTx [73] with direct minimization via the conjugate gradients algorithm. We employed the PBE generalized‐gradient exchange‐correlation approximation [74] using a plane‐wave basis and a plane‐wave energy cutoff of 540 eV. We used fully periodic boundary conditions and a single unit cell of ${\mathrm{SrTiO}}_3$ for the bulk calculation with a 6$\times 6\times$6 k‐point mesh to sample the Brillouin zone. The DFT calculated lattice parameter of ${\mathrm{SrTiO}}_3$ was determined from the bulk calculation to be $a_0=3.942$ Å, less than 1% above the experimental lattice constant. All calculations presented employ GBRV ultrasoft pseudopotentials [75]. The supercells for the ${\mathrm{SrTiO}}_3$ surfaces were constructed using the minimal real‐space unit cell in the x,y directions (parallel to the surface) while maintaining k‐point sampling commensurate with the bulk calculation. All unit cells were constructed to be inversion symmetric about $z=0$ with a distance of approximately $20a_0$ between periodic images of the surface. In the z‐dimension, all slabs were at least 10 layers thick. We used the Coulomb truncation option within a slab geometry to prevent unphysical image interactions [76].

DFT‐Constrained Fitting of Specular CTR Curves The FoxPy Python software was utilized to perform DFT‐constrained fitting. Nonlinear least‐squares fitting allows the atoms to deviate from their DFT minimum energy positions, allowing for considering the effect of non‐equilibrium processes, and the resulting Debye–Waller factors account for defects and disorder [50, 51]. Simultaneous fits to multiple DFT calculations may be performed by coherently or incoherently averaging linear combinations of surface structures. We ensure the physicality of these fits by minimizing a residual $R^2$, which includes ${\chi }^2$ of both resonant (16.1 keV) and non‐resonant (15 keV) X‐ray signals and a penalty function (with weight $\kappa$) to prevent the fit positions $\{\eta \}$ from varying significantly from the DFT predicted positions $\{Z\}$ for the $N_I$ atoms included in the fit:

$$R^2=\frac{1}{2}{\chi }^2(\text{15 keV})+\frac{1}{2}{\chi }^2(\text{16.1 keV})+\frac{\kappa }{2N_I}\sum _I{({\eta }_I-Z_I)}^2$$

Further details regarding the fitting procedure are available in the Supporting Information. The FoxPy software, Python scripts used to perform fitting, and all relevant DFT calculations and experimental data are available in a GitHub repository.

Conflicts of Interest

The authors declare no conflict of interest.

Supporting information

Supporting File: adma72728‐sup‐0001‐SuppMat.pdf.

Data Availability Statement

The data that support the findings of this study are available in the supplementary material of this article.