Engineering ordered arrangements of oxygen vacancies at the surface of superconducting La₂CuO₄ thin films

Crystal surfaces tend to form energetically favored atomic arrangements. In the layer-by-layer synthesis of charged surfaces, electrostatic terms are major contributors to the energetics governing surface formation. In metal oxide systems, surface reconstructions, which are distinct from the bulk of the film in their composition and structure, directly affect chemical¹ and physical² properties. Reflection high-energy electron diffraction (RHEED) using a collimated electron beam irradiating the sample surface [Fig. 1(a)] provides real-time information about the surface crystallinity^3–5 during the epitaxial growth of thin films. It allows for real-time growth monitoring, the study of surface reconstructions, and can be complemented by low-energy electron diffraction (LEED)⁶ for more detailed analyses. Although RHEED has been successfully utilized in the growth of semiconductor systems by molecular-beam epitaxy (MBE),^7,8 the interpretation of characteristic RHEED patterns in complex oxide systems presents multifaceted challenges^9–11 due to the presence of mobile oxygen atoms/ions on the surface.

The discovery of high-temperature superconductivity (HTS) in the hole-doped La₂CuO₄ (LCO) system¹² has given rise to considerable interest by the scientific community¹³ and triggered the high-quality synthesis of superconducting cuprate thin films.^14,15 In bulk form, the HTS cuprates exhibit intrinsic inhomogeneity on the scale of the superconducting coherence length as has been realized through not only the experimental observations of incommensurate charge density waves,^16–19 stripes,¹⁷ nanoscale “puddles,”^20,21 and chessboardlike surfaces,^22,23 but also through alternative theories such as (percolative) “plaquettes”^24,25 and pair density waves.²⁶ In addition to being able to tap the bulk properties, oxide heterostructure engineering^27–30 paves the way to exploit high-temperature interface superconductivity at the interface of nonsuperconducting copper oxides,^31,32 where superconductivity is confined within a single CuO₂ plane.³³ Unfortunately, independent of interface functionalities, cationic intermixing is usually present at LCO-based heterointerfaces. This intermixing is affected by growth kinetics,³⁴ the individual layer thicknesses,³⁵ and the sizes of the cations involved.³⁶ A key factor in tuning the properties of oxide interfaces³⁷ is the real-time control of the surface termination and stoichiometry during film growth.

In this work, we in situ engineer the surface structure and comprehensively examine the surface reconstruction mechanisms utilizing the flexibility of ozone-assisted atomic layer-by-layer MBE. We focus on qualitative RHEED investigations conducted during the growth of LSCO thin films using (1) different substrates [(100) SrTiO₃ (STO), (001) LaSrAlO₄ (LSAO), (001) LaSrGaO₄ (LSGO) (001)], (2) different dopant atoms (Sr, Ca), (3) different oxidation conditions (vacuum versus ozone atmosphere), and (4) different doping concentrations. The surface reconstructions caused by the coherent ordering of the surface atoms emerges due to the interrelation of dopant atoms and oxygen vacancies, which results in orthogonal “stripes.”

The LCO epitaxial films were grown in the layer-by-layer regime using an ozone-assisted MBE system (DCA Instruments Oy). Monolayer-by-monolayer doses from molecular beams of the constituents were supplied in the same order that the corresponding layers occur along the c-axis of the LCO crystal structure, i.e., LaO-LaO-CuO₂-…. In a nominal Sr-doped LCO [La_2−xSr_xCuO₄, (LSCO)] growth, the deposition of two (La,Sr)O atomic layers is followed by the deposition of one CuO₂ atomic layer. To replace some of the La atoms by Sr atoms, the La, Sr, and O₃ molecular beams are codeposited (in proportion to the doping level) to form the (La,Sr)O-(La,Sr)O double layer. The typical time for forming one molecular layer of L(S)CO was ∼3 min. The substrate temperature was measured by an infrared pyrometer and kept at 650 °C. The total background pressure—ozone (O₃), molecular oxygen (O₂), and atomic oxygen (O)—was ∼1.5 × 10⁻⁵  Torr provided by continuous evaporation of the distilled ozone. The “vacuum” experiments were conducted via the interruption of the ozone delivery. To control the epitaxial strain, we have used three different substrates manufactured by Crystec GmbH that impart biaxial strain on sufficiently thin, commensurately strained doped or undoped LCO films. For optimally doped LSCO, the strained imposed are (001) LSAO (0.6% compressive strain), (100) SrTiO₃ (STO, 3.4% tensile strain), and (001) LSGO (1.7% tensile strain). To examine the chemical pressure effect, we used two dopants (i.e., Ca and Sr) with different ionic radii.

The real-time monitoring of the growth is conducted using an electron beam emanated from the RHEED gun—operated at 25 kV—that irradiates the substrate surface at an incident angle of 1°–2°. The time dependence of the RHEED patterns and the intensities of the diffraction streaks were monitored with a CCD camera and analyzed using k-Space 400 software. Video recordings of the RHEED were analyzed using the machine learning techniques principal component analysis (PCA) and K-means clustering as described previously.³⁸ The PCA calculates a new basis of six vectors for each data point. This transformation allows for compression of each frame while retaining 95+% of the variance. Using PCA to compress the frames of the RHEED recording greatly decreases the computation time required to perform the K-means clustering without significant loss of data or precision. Once compressed, K-means clustering then separates the frames into k clusters such that each frame is in the cluster with the closest mean value. This clustering quantitatively relates each frame of the growth to a set of k clusters and constructs mean RHEED images of each cluster that clearly show the different surface reconstructions present during each section of growth.

The LEED pattern is acquired with a reverse-view ErLEED optics (SPECS GmbH) at an energy range of 50–500 eV. Electrical measurements were conducted in a Van der Pauw (four-point-probe) configuration with alternate DC currents of ±20 μA. Simultaneous measurements of the imaginary and real parts of the mutual inductance M(T) were carried out by magnetic susceptibility measurements in a two-coil configuration (parallel geometry) with an AC current of 50 μA at a frequency of 1 kHz. The temperature was varied from room temperature to 4.2 K (liquid helium) using a motorized custom-designed dipstick (T change rate <0.1 K/s). The crystal structure and surface morphology were characterized by high-resolution x-ray diffraction (Bruker D8 Cu-Kα1 = 1.5406 Å) and atomic force microscopy (Nanoscope III), respectively. The microstructure of the films was characterized by scanning transmission electron microscopy (STEM). For the STEM investigations of the La₂CuO₄-based system,³⁹ a probe-aberration-corrected JEOL JEM-ARM200F STEM equipped with a cold field-emission electron source and a probe C_s-corrector (DCOR, CEOS GmbH) was used. STEM imaging was performed at probe semiconvergence angles of 20 mrad resulting in a probe size of 0.8 Å. The collection angle range for high-angle annular dark-field (HAADF) images was 75–310 mrad.

The formation of the tetragonal A₂BO₄ crystal structure of LCO requires A-site (A = La, Sr), B-site (Cu), and oxygen (O) atoms. Depending on the sequence and the period of the controlled shutter openings in the layer-by-layer regime, we believe that first, neutral nanometer-sized La₂O₃ and SrO clusters of adatoms complete a layer, and after the deposition of Cu atoms, one molecular layer of the LSCO is formed via the following chemical reaction on the surface:

where x is the Sr doping level and δ is oxygen nonstoichiometry (or the concentration of oxygen vacancies). Surface kinetics controlled by the substrate temperature and surface stoichiometry and the difference in the electronegativity of the constituent metals⁴⁰ govern this iterative process. In the case of Sr doping, the local charge difference as a consequence of Sr²⁺–La³⁺ substitution is compensated by generating carriers (i.e., holes) and/or oxygen vacancies.⁴¹ 

Although some extent of stoichiometric uncertainty is inherent in oxide-MBE synthesis, e.g., due to the precision limit in the initial calibration of the element fluxes, monitoring the in situ RHEED patterns (and the intensity evolution of the specular spot) permits a precise control of growth and allows the operator to avoid any undesired precipitation of secondary phases. Characteristic RHEED patterns of nonstoichiometric phases are easily detected by the superposition of additional diffraction spots due to the formation of three-dimensional islands with a different crystal structure. Related examples of the RHEED intensity evolution during the LCO growth are presented in Figs. S1 and S2.⁵⁴ A representative, 10 unit cell (20 molecular layer) thick, optimally doped (x = 0.16) LSCO film was grown on a (001) LSAO substrate. Figures 1(b) and 1(c) display the characteristic 5a RHEED patterns, where a corresponds to the in-plane Cu–O–Cu distance, and the specular spot intensity oscillations, respectively. The sample exhibits a high superconducting transition temperature, T_c, of around ∼44 K [Fig. 1(d)] with a sharp superconducting transition (less than 1 K width), as evidenced by the mutual inductance setup [Fig. 1(e)]. The structural quality and atomically smooth surfaces are confirmed by x-ray diffraction and atomic force microscopy, respectively (Fig. S3).⁵⁴ The excellent epitaxy of the sample is evident from atomic-resolution HAADF imaging in STEM [Fig. 1(f)].

In order to tune the surface structure by tailoring the epitaxial strain, we grow optimally doped (x = 0.16) LSCO films on two additional substrates: (100) STO and (001) LSGO [Figs. 2(a) and 2(b)]. In the case of STO (a_STO = 3.905 Å) and LSGO (a_LSGO = 3.840 Å) substrates, the substrate lattice constants are larger than of the LSCO film (a_LSCO = 3.777 Å) and impart biaxial tensile strains of 3.4% and 1.7%, respectively, on commensurate films. Oppositely, a LSCO film strained commensurately to an LSAO substrate (a_LSAO = 3.755 Å) is under 0.6% compressive strain. In contrast to the 5a surface reconstruction observed for growth on a (001) LSAO substrate [Fig. 1(c)], the films under tensile strain exhibit 4a surface reconstructions for the growths on (100) STO and (001) LSGO substrates [Figs. 2(a) and 2(b)], respectively. These results indicate that the lattice mismatch between the LSCO film and the substrate (in the high-quality growth regime) influences the atoms arrangement at the surface: the larger the in-plane lattice constant of the substrate, the smaller the size of the coherent atomic arrangement.

Another way to control the surface motif is adjusting the chemical pressure by using dopants of different ionic radii. We next focus on the Ca- and Sr-doped LCO samples grown on LSAO (001) substrates. When a smaller Ca²⁺ dopant is used, with a Shannon ionic radius of 118 pm,⁴² a 4a surface reconstruction is obtained [Fig. 2(c)] for growth on LSAO (001) rather than the 5a surface reconstruction observed in the case of Sr²⁺ [cf. Fig. 1(a)]. Therefore, it is evident that the dopant ions play a role in the “coherent atomic surface arrangement.” In principle, one could use Ba atoms with larger ionic radii as well; however, the growth of Ba-doped LCO on (001) LSAO substrates always results in the segregation of Ba atoms (due to higher chemical pressure) to the surface. The result is a 5a surface reconstruction (similar to optimal Sr doping) as reported in our previous study.³⁶ 

Considering the role of oxygen and oxygen vacancies on the surface reconstruction, we next modulate the oxygen pressure during growth of doped LCO on LSAO (001) substrates and monitor the surface reconstruction (Fig. 3). As a first experiment, after depositing A-site atoms (e.g., La and Sr) under our standard oxidation conditions (∼1.5 × 10⁻⁵  Torr of distilled ozone), we deposit B-site (Cu) atoms in “vacuum” (i.e., no ozone delivery). In this case, one can still expect the reaction according to Eq. (1). Nevertheless, due to the reduced oxygen concentration more oxygen vacancies form, resulting in a 4a surface reconstruction.

In a second experiment, we attempt to compensate for the lack of oxygen in the 214 structure by adding oxygen. Optimally doped LSCO films on LSAO (001) substrates show a 4a reconstruction in vacuum [Fig. 3(a)], similar to LSCO films under tensile strain [cf. Fig. 2(a)]. This is consistent with the expected increase in the oxygen vacancy concentration. Remarkably, postannealing in ozone provides a fast, i.e., in a few seconds, and straightforward recovery to the nominal 5a surface reconstruction [Figs. 1(a) and 3(b)]. Thus, we observe that Cu deposition in vacuum (ozone) always results in a 4a (5a) surface reconstruction. We infer that the high oxygen activity provided by the ozone functions to remove imperfections such as oxygen vacancies. These observations demonstrate not only the vital contribution of surface oxygen atoms on the structure but also how the oxide surfaces can be engineered during the layer-by-layer MBE growth of LCO-based systems.

To probe the time evolution of the surface reconstructions, K-means clustering was performed on the RHEED images acquired by video. K-means clustering does a quantitative comparison of each frame of the growth and groups them into k clusters, where each frame in the cluster is more similar to the mean image of that cluster than the mean image of any other cluster. The mean images of the clusters are able to show clear distinctions in the surface reconstruction between the different stages of the growth, allowing for a greater understanding of the growth process. As shown in Fig. 4(a), it is observed that the clusters form clear boundaries that closely correspond to the shuttering times of the growth. Although a slight delay occurs between the shutter actuation and the beginning of the next clustering, this is attributable to the time it takes for the physical shuttering to take place in the system in addition to the time needed for enough adatoms to deposit or oxygen vacancies to significantly change the surface reconstruction. In Figs. 4(b) and 4(e), the mean RHEED image for cluster 1 shows a 5a surface reconstruction while cluster 4 shows a 4a surface reconstruction. Since cluster 1 is deposited in the presence of ozone while cluster 4 is in vacuum, these data suggest that the oxygen saturation can cause a change in surface reconstruction. Clusters 2 and 3 show surface reconstructions (weaker for cluster 2) during the deposition of La and Sr cations on the A site of LSCO. The brief transition to cluster 1 at ∼110 s is likely attributable to the presence of a weak surface reconstruction in cluster 3 that resembles the reconstruction in cluster 1 momentarily. Such transients during transitions between clusters for K-means clustering of RHEED have been observed elsewhere⁴³ and are likely an artifact of the decomposition process that has little physical significance. Collectively, these results show that the surface reconstruction for Cu-terminated layers track closely with the oxygen environment during growth.

After revealing the direct control on the surface decoration by different parameters to understand the shape of the atomic-scale clusters, we combined 90° rotated RHEED patterns (corresponding to [010] reflections) with LEED patterns acquired at room temperature after the growth. Figure 5(a) exhibits the [010] azimuthal RHEED pattern of the optimally doped LSCO surface showing a 5a surface reconstruction suggesting either square-shaped atomic ordering or orthogonal domains contributing to the surface diffraction patterns. An LEED image acquired at an energy of 115 eV [Fig. 5(b)] and LEED simulations [Fig. 5(c)] elucidates the shape of the surface atomic arrangements: orthogonal {5 × 1} and {1 × 5} domains. Note that the surface reconstructions observed by RHEED do not change while cooling from the growth temperature down to room temperature; therefore, the surface reconstruction maintains as 5a.

Our in situ experiments demonstrate that surfaces of high-T_c L(S)CO films can be engineered by tuning the local strain and the oxygen vacancy concentration as qualitatively monitored by RHEED during a layer-by-layer ozone-assisted MBE synthesis. The optimal RHEED intensity evolution and related surface reconstructions indicate high-quality synthesis of epitaxial LSCO films with homogeneous superconducting properties and sharpest transition.⁴⁴ Any deviation from the optimal picture due to critical nonstoichiometry or structural defects degrades the superconductivity and suppresses T_c. Considering our experimental findings, we propose that in the layer-by-layer growth regime, the dopants do not randomly distribute on the topmost molecular layer; instead, they form characteristic chessboardlike structures that we describe below. Furthermore, this ordering of dopants is associated with the oxygen vacancy positions and results in characteristic surface reconstructions, as we describe in more detail shortly. Considering the characteristic ionic bonding in LCO, which is composed of charged (LaO)⁺ and (CuO₂)²⁻ layers, the equilibrium bond distance is determined by the (cooperative) competition between the attractive electrostatic interaction and the repulsive closed-shell interaction. In the layer-by-layer deposition of L(S)CO, the topmost layer is CuO_2−δ with a certain amount of oxygen vacancies to compensate the intrinsic polar discontinuity,⁴⁵ and the surface reconstructions observed after Cu deposition are a result of a distinct coherent arrangement of surface atoms. The CuO_2−δ terminated plaquettes forming the periodic commensurate structures can be initially ascribed with a perfect “checkerboard” model with a 5a-sized atomic arrangement (Fig. 6) similar to the previously proposed “two-component” model⁴⁶ and a “distorted” chessboard approach.⁴⁷ 

Our interpretation based on in situ evidence does not directly support the report claiming LaO-terminated surfaces due to the rigidity of the CuO₆ octahedron,⁴⁸ where the final surface terminations are discussed rather than layer-by-layer growth. Nevertheless, other ex situ scanning tunneling microscopy investigations and our findings are in agreement concerning the 4a-characteristic length in the case of LSCO films grown on Nb:STO substrates by MBE.⁴⁹ We conclude that the terminating layer of our LSCO films is the CuO_2−δ layer during the growth, similar to what was observed in the case of the BaBiO₃ films, where BiO₂ is the terminating layer.⁵⁰ 

Concerning the atomic rearrangement of the surface, the distance between the dopants is caused by the dopant size mismatch and epitaxial strain. Particularly, for both the use of tensile epitaxial strain and smaller cation as dopant (Ca versus Sr), the width of the observed periodicity on the surface is 4a instead of 5a, despite optimal doping (x = 0.16). At this point, one can argue that the concentration of the dopants in the case of Ca and Sr and in the case of the tensile strain will be different by a factor of 5/4 according to the difference in the corresponding surface reconstruction patterns. At the same time, the dopant concentration is the same within flux calibration error in both cases, which is less than 5%. The possible deviation of the surface structure from the ideal arrangement and possible dopantfree areas will not affect the resulted RHEED images drastically.

Our plan-view model of the distribution of Sr in one LCO unit cell (two molecular layers) [Fig. 6(a)] presents the checkerboardlike structure with well-ordered Sr dopants. The distance between Sr dopants in a single La/Sr-O atomic layer is 5a; the Sr doping in the La/Sr-O layer not only distorts the lattice but also creates oxygen vacancies in the upper, CuO_2−δ terminated layer. The polar discontinuity⁴⁵ of the upper CuO₂ layer is compensated by the in-plane oxygen vacancies. The inferred surface motif is a consequence of dopant-distribution induced oxygen vacancy decoration in the CuO_2−δ planes with characteristic 5a length. The oxygen vacancy forms close to the topmost Sr position in Cu–O plane induced by the Sr positions in the atomic layer below. Since oxygen vacancy formation is a random process and it is not required to form at particular Cu–O bonds, we anticipate irregular 5a-length orthogonal “stripes” to be formed in the CuO_2−δ planes instead of a well-ordered checkerboard motif. This results in intrinsic heterogeneity. Given it is not possible to directly detect an oxygen vacancy position, our model displaying the stripes is depicted for the optimal condition in Fig. 6. The direct influence of the oxygen vacancies is supported by “vacuum” versus “ozone-assisted” experiments, as the 5a distance shrinks to 4a after the deposition of Cu in vacuum and again recovers to 5a after the delivery of ozone to the growth chamber (as it is shown Fig. 3). Another example indicating the dopant-distribution-induced surface reconstruction is the “vacuum” versus “ozone-assisted” experiment conducted during the growth of an undoped LCO film, where the surface reconstruction after Cu deposition in vacuum (a 7a reconstruction) remains unchanged after the subsequent delivery of ozone. The absence of dopants changes the surface kinetics, and different surface ordering occurs. The results are presented in Fig. S4.⁵⁴ 

The random distribution of Sr dopants in La(Sr)O layers above and below CuO₂ planes breaks the inversion symmetry in LSCO films as reported using surface x-ray diffraction experiments analyzed by the Coherent Bragg Rod Analysis (COBRA) method.⁵¹ In contrast to our optimally doped LSCO films, in overdoped LSCO layers, the concentration of Sr above the CuO_2−δ layers is greater than the concentration below the layers irrespective of the deposition sequences. We, therefore, think that a direct comparison of optimally doped and overdoped systems is not applicable. Other evidence for the presence of oxygen vacancies in the overdoped LSCO epitaxial films grown by using ozone-assisted MBE was reported in Ref. 52. For higher doping levels, one can even expect the formation of defect associates, for instance, the formation of oxygen vacancies together with hole doping.^41,52

Finally, these oxygen vacancies form in the top molecular layer due to the polar origin of single atomic layers and can be filled in the bulk crystal structure, while the ordered distribution of dopants is maintained. Each ordered dopant is associated with a local charge carrier and thus can be associated with the modulation of the charge.⁵³ One can further speculate that with increasing dopant concentration from x = 0.06, the superconducting state becomes more and more homogeneous and reaches the most favorable dopant distribution (Fig. 5) at optimal doping (x = 0.16). The optimally doped LSCO film has an extraordinary sharp superconducting transition measured by using mutual inductance setup, while as the doping concentration increases the transition width becomes broader, indicating the presence of disorder and inhomogeneities. For the overdoped regime (x > 0.16), one needs to consider not only the overlapping of the 5a periodic dopant distribution but also the increase in the oxygen vacancy concentration and the associated defects.^41,52

In conclusion, we demonstrate the in situ control and engineering of high-T_c La₂CuO₄ surfaces during layer-by-layer MBE growth. Real-time RHEED imaging of the specific surface reconstructions provides clues of the active role of oxygen vacancy decoration on the surface induced by dopant ordering. Different parameters, e.g., dopant size, the epitaxial strain (i.e., the choice of the substrate), the doping concentration, and the oxygen pressure, directly affect the surface motif. They determine the intrinsically heterogeneous structure characterized by distorted checkerboard patterns on the surfaces. Optimally doped LSCO epitaxial films accommodate characteristic orthogonal {5 × 1} in-plane surface stripes jointly generated by the oxygen vacancies at the surface and the dopant decoration, where the well-ordered dopant distribution can be correlated with the charge distribution at the surfaces. The controlled in situ engineering of oxide surfaces may further improve the specific customizing of the surface and also the interface profiles of oxide heterostructures.

The project was conceived by Y.E.S. and G.L. RHEED measurements are performed by Y.E.S., G.C., and G.L. PCA and k-means clustering analyses of RHEED images are performed and evaluated by P.T.G. and R.B.C. including Y.E.S. and G.L. Superconductivity measurements were performed by G.C. and G.L. Electron microscopy and spectroscopy measurements were performed by Y.E.S. and interpreted together with P.A.v.A. The initial draft was prepared by Y.E.S. and G.L. All authors contributed to the interpretation and the discussion of the experimental data and to editing the draft. The authors thank Minu Kim for careful reading of the manuscript and helpful comments, and Gideok Kim, Ulrich Starke, Philipp Rosenzweig, Hrag Karakachian, and Felix V. E. Hensling for fruitful discussions; Peter Specht for the technical support on the oxide MBE and LEED systems; and Ute Salzberger for TEM specimen preparation. This project has received funding from the European Union’s Horizon 2020 research and innovation program under Grant Agreement No. 823717—ESTEEM3. P.T.G., S.R.P., and R.B.C. gratefully acknowledge funding from the Air Force Office of Scientific Research under Award No. FA9550–20-1-0034.

The data that support the findings of this study are available from the corresponding author upon reasonable request.