Strain-induced structural transition in DyBa₂Cu₃O_7−x films grown by atomic layer-by-layer molecular beam epitaxy

Copper-oxide superconductors with the “123” structure (chemical composition RBa₂Cu₃O_7−x with R = rare earth element) have long been at the forefront of fundamental and application-oriented research on high-temperature superconductivity, owing to their unique combination of properties. Their role as model materials in fundamental research¹ is rooted at the maximal superconducting transition temperature of T_c = 93 K, combined with the nearly stoichiometric crystal structure and low chemical disorder, which greatly facilitates the interpretation of experimental data. The high critical current density of 123 compounds and the availability of facile low-temperature synthesis methods further underpin their potency as a basis for superconducting technologies.² In particular, 123 thin films^3–5 have served as prominent components of superconducting heterostructures and devices.^6–12 Whereas it is widely recognized that defects such as dislocations, stacking faults, and twin boundaries often associated with thin-film deposition can substantially affect the electronic properties, systematic investigations of such structure-property relationships are rare. We have harnessed recent advances in oxide molecular-beam epitaxy (MBE)^13,14 combined with synchrotron-based x-ray reciprocal-space mapping to systematically explore the influence of the crystal structure on the normal-state resistivity and superconducting T_c of DyBa₂Cu₃O_7−x (DyBCO) films.

Compared to other techniques such as pulsed laser deposition (PLD) and reactive magnetron sputtering, the lower deposition energy of MBE tends to minimize the density of defects. Already shortly after the discovery of high-T_c superconductivity, MBE was used to grow DyBCO and NdBCO via co-deposition^15–17 or modulated co-deposition (where the Cu cell remains open, while Dy and Ba are alternated^18,19). The recently developed atomic layer-by-layer deposition method allows greater stoichiometry control and generates thin-film structures with atomically smooth interfaces and superior electron mobility.^13,14,20,21 Following the successful application of this technique to La-based cuprates with maximal $Tc∼40$ K,^22–24 we demonstrate layer-by-layer MBE growth of coherently strained DyBCO films with minimal defect density on different substrates. Using electron microscopy and x-ray reciprocal space mapping, we also report a comprehensive investigation of the lattice structure and morphology of these films and their influence on the transport properties. In particular, we show that the films exhibit transitions from tetragonal to different forms of twinned orthorhombic crystal structures as a function of thickness, doping level, and epitaxial relationship with the substrate. Films with more pronounced orthorhombicity exhibit systematically lower normal-state resistivity and higher T_c.

Thin films of c-axis-oriented DyBCO were grown on three different substrates to obtain a different lattice mismatch with the a- and b-axes of optimally doped DyBCO (3.85 and 3.89 Å): a (001) surface of cubic SrTiO₃ (STO) (+1.6% and +0.5% mismatches along a and b, respectively), cubic (LaAlO₃)_0.3(Sr₂AlTaO₆)_0.6 (LSAT) (+0.7/−0.4% mismatch), and a (110) surface of orthorhombic NdGaO₃ (NGO) (+0.5/-0.6% mismatch). The films were deposited in a sequential layer-by-layer manner in a custom-made ozone-assisted MBE setup. The flux of the effusion cells was calibrated prior to growth with a quartz crystal microbalance and monitored during growth by in situ reflection high-energy electron diffraction (RHEED). Films were grown at substrate temperatures of 650–700 °C in $1.8×10−5$ Torr ozone-oxygen background pressure and were cooled down after the growth in the same atmosphere. All as-grown films exhibit $Tc≥80$ K, determined by the onset of the transition, with a transition width of less than 4 K as probed by the Meissner effect measured in a mutual inductance setup. For selected films, the resistivity was measured in van-der-Pauw geometry. High resolution x-ray diffraction (XRD) measurements were performed on a four-circle diffractometer with a Cu $Kα$ source, and selected films were further investigated with a four-circle setup at the MPI beamline of the KARA synchrotron. Scanning transmission electron microscopy (STEM) investigations were performed using a JEOL JEM-ARM 200CF microscope operated at 200 kV.

In layer-by-layer MBE growth, the elements are deposited individually and the stoichiometry can be adjusted during the deposition. We found that the Ba–Cu step in the deposition sequence of Ba-Cu-Dy-Cu-Ba-Cu atomic layers is highly susceptible to the formation of BaCu_xO_y defects, which gives rise to a characteristic RHEED pattern and matches with BaCu₂O₂ in XRD d-spacing analysis. Therefore, we separated the Ba and Cu deposition by a Dy layer and adopted a 2Ba-Dy-3Cu sequence similar to Locquet et al.²⁵ In contrast to the co-deposition mode, sequential growth provides the correct element ratio only after the completion of a full unit cell (u.c.). In order to obtain the desired 123 structure, the elements have to rearrange from the provided deposition sequence, but at the given growth temperature, the diffusion of the elements proved to be sufficiently rapid.

In the initial growth stage, the RHEED intensity decreases fast, indicating the absence of coherent growth seeds. If stoichiometry offsets are not corrected, defects form and serve as seeds for the following layers. Surprisingly, for the first unit cell on the substrate, deposition of only two atomic layers of Cu leads to the 123 structure, while deposition in the stoichiometric 1:2:3 ratio leads to the formation of BaCu_xO_y. This observation is explained by the fact that the first atomic layer on the substrate surface is a BaO layer [see Fig. 1(c)]. Accordingly, the starting sequence is BaO-CuO₂-Dy-CuO₂-BaO-CuO. In contrast to PLD, where multiple interface sequences were observed,²⁶ the individual element control in MBE growth allowed us to obtain a unique stacking order over the entire substrate interface.

After the fourth unit cell, a distinct RHEED pattern emerges and repeats itself after Ba, Dy, and Cu deposition for every additional layer. By observing multiple diffraction spots simultaneously, it is possible to identify impurity formation and to adjust the stoichiometry accordingly. For the subsequent layers, the RHEED oscillations remain almost undamped, indicating optimal growth [Fig. 1(a)].

The formation of phase-pure c-axis-oriented DyBCO was confirmed by XRD for all substrates. The diffraction patterns of films below a thickness of 40 u.c. contain no additional peaks associated with an impurity phase, which would be expected in the case of off-stoichiometric growth.

Information about nanoscopic defects was collected by cross-sectional STEM imaging. A representative image is shown in Fig. 1(b) for a 20 u.c. thick film grown on LSAT (100). The sharp interface and the nearly complete absence of defects throughout the structure are remarkable since the decrease in the RHEED intensity observed during deposition of the initial layers suggested a surface reconstruction. These observations indicate that the reconstruction healed out in later phases of the growth. Only in the topmost layers, a few DyBa₂Cu₄O₈ (124) stacking faults arising from intercalation of additional CuO layers are visible in Z-contrast STEM images as a dark space between BaO–DyO–BaO blocks [arrows in Fig. 1(b)], as well as a shift of the following blocks by half a unit cell along the a-axis.^27,28 The near absence of stacking faults is a distinct advantage of layer-by-layer MBE growth with in situ stoichiometry control.

The epitaxial relationship with the three different substrates was investigated in a series of x-ray reciprocal space maps (RSMs). Figures 2(a)–2(c) show RSMs with momentum transfer Q in the DyBCO (a,c)-plane around the (4 0 4) reflection of the substrates. (To facilitate comparison of films grown on different substrates, we label the substrate reflections based on the pseudocubic perovskite unit cell.) For films grown on LSAT and NGO, the (4 0 10) and (4 0 11) DyBCO reflections are centered around the substrate (4 0 L) axis and at Q_H values that correspond to the planar lattice parameters of bulk DyBCO, indicating partial relaxation of the epitaxial strain imposed by the substrates. A cut in the (H, K)-plane reveals that the (4 0 10) DyBCO reflection consists of four peaks [Figs. 2(d) and 2(e)], which are associated with the formation of orthorhombic twin domains along the [110] and [1$1¯$0] mirror planes (MPs).^29–32 In films on LSAT, the peaks are sharper and more widely spaced than in films on NGO, indicating a more pronounced orthorhombic distortion with larger twin domains.

RSMs of the 20 u.c. film on STO show that the DyBCO in-plane lattice parameters match the bulk values, indicating almost complete strain relaxation [Figs. 2(c) and 2(f)]. The (H, K)-cut of the (4 0 10) film peak does not show a fourfold symmetry as observed for the other substrates but instead a strong and a weak peak separated along H. No splitting is observed along K, and the corresponding scans can be modeled with a single Lorentzian function. Conversely, a splitting along K (and none along H) was observed in scans around the (0 4 10) reflection. The twofold symmetry of this pattern indicates twinning along the [100] and [010] directions.

Having noted substantial differences between the structure and morphology of 20 u.c. thick films on different substrates, we now discuss the evolution of the structural parameters with the thickness (Fig. 3). The RSMs of 10 u.c. films on LSAT [Fig. 3(d)] and NGO (not shown) look qualitatively similar to the 20 u.c. films [Figs. 2(d) and 2(e)] with a smaller fourfold splitting, indicating reduced orthorhombicity. In addition, substantial intensity at the commensurate (4 0 10) position suggests a tetragonal structure matching the substrate lattice, most likely located directly at the substrate interface. Analogous observations were made for the 10 u.c. film on STO [Fig. 3(a)] where the orthorhombic splitting along [100] is almost entirely suppressed. The peak position corresponds to the in-plane lattice parameters of STO and implies a tetragonal, substrate-matched structure.

The increase in the orthorhombicity with the increasing thickness explains the elliptical elongation of the DyBCO peaks in 20 u.c. on LSAT and NGO [Figs. 2(d) and 2(e)], which indicates a distribution of the DyBCO a- and b-axes located close to the substrate-film interface. The Bragg reflections of films with thickness $≥40$ u.c. exhibit circular shapes [Fig. 3(e)], indicating that most of the film is fully relaxed with bulk-like lattice parameters. For films on STO, the formation of bulk-like orthorhombic domains proceeds in two steps. Thin films grow with twins along the [100] and [010] directions, which are manifested in the two-peak structure of the 20 u.c. film [Fig. 2(f)]. With increasing thickness, the twinning shifts toward the [110] and [1$1¯$0] directions. This transition is seen in the 40 u.c. film, where the two peaks extend strongly along K [Fig. 3(b)]. The corresponding scans along K are best described with two Lorentzian functions instead of one. By increasing the film thickness further to 60 u.c., well separated peaks along H and K are observed [Fig. 3(c)] similar to the twinning of films on LSAT and NGO. Note that our data disagree with the phase sequence of tetragonal-pseudotetragonal-orthorhombic previously reported for NdBCO films on STO.³³ 

We now discuss the relationship between the lattice structure and morphology determined by XRD and the normal-state transport and superconducting properties. We first note that the T_c of ultrathin films [thickness $≤7(10)$ u.c. for LSAT (STO)] degrades over time. Their lattice structure is strained to the cubic substrates and, hence, cannot accommodate as much oxygen as bulk DyBCO under ambient conditions. During deposition, the oxidation power of the ozone atmosphere sustains a high oxygen content, but after growth, excess oxygen diffuses out of the film, and T_c decreases slowly. Thicker films are stable in the time frame of our experiments although some T_c degradation (presumably attributable to oxygen loss) was observed in reduced films after the prolonged exposure to intense x-ray beams required for reciprocal space mapping.

Figure 3(f) shows the superconducting T_c and the width of the superconducting transition of films grown on LSAT and STO. Note that we are quoting the T_c measured by mutual inductance, which especially for ultrathin films more closely reflects the distribution of superconducting transitions throughout the film than resistivity measurements. All films with a thickness of 10 u.c. have T_c exceeding 70 K, albeit with somewhat broadened transitions due to the gradual strain relaxation already noted in our discussion of the lattice structure. The maximal T_c in thicker films is about 87 K. The slight residual difference with the maximal T_c of the highest-quality single crystals (93 K) might originate in the twinned structure that persists even in thick films and/or in slight differences in stoichiometry.

The transport parameters exhibit a striking correlation with the crystal structure determined by reciprocal-space mapping. Films on LSAT and NGO, which are twinned in the [110]/[1$1¯$0] directions, exhibit T_c values that are systematically $∼3−5$ K higher than those on STO, which cross over from [100]/[010] to [110]/[1$1¯$0] twinning as a function of thickness, resulting in additional microstructural disorder. Whereas there are only slight differences between the T_c of films grown on LSAT and NGO, there is a substantial difference in the normal-state resistivity. Notably, the resistivity of films grown on LSAT is systematically lower than the one of our films on NGO and STO, in line with the more pronounced orthorhombicity and larger twin domains indicated by the RSMs. Figure 3(i) shows representative data on three 20 u.c. films. The same trend holds for $∼20$ films of different thicknesses investigated for this study (with a single exception: a 10 u.c. film on NGO, which shows a resistivity comparable to an equally thick film on LSAT, perhaps due to a particularly favorable domain structure).

The substantial influence of the twin structure on the transport properties can be attributed to the electronic activity of the CuO chains, which act as a charge reservoir for the CuO₂ layers and cause the orthorhombic distortion of the 123 structure. The observed RSMs imply short-range chain segments extending in both in-plane directions (a and b).³⁴ Macroscopically tetragonal films accommodate excess oxygen in chain segments comprising only a few atomic sites, thus generating copious defects. Since CuO chain-derived bands are at the Fermi level and hybridize strongly with the bands derived from the CuO₂ layers, defects in the chains can act as efficient scattering centers for normal-state conduction electrons, thus explaining the different transport properties. In view of the short superconducting coherence length and the recently observed formation of charge density waves that compete with superconductivity,³⁵ defects may also be at least partially responsible for the reduction of T_c in films on STO with a more disordered twin-domain structure.

We finally address the structural and electronic properties of DyBCO films with a reduced oxygen content. To this end, we annealed as-grown 20 u.c. thin films on LSAT at the growth temperature of 650–700 °C at a low ozone background pressure of 3–5 $×10−9$ Torr to avoid complete reduction. The annealed films showed a decrease in T_c and a broadening of the transition with decreasing background pressure. Whereas twin domains with reduced orthorhombicity persist in films with a moderately reduced oxygen content [Fig. 3(g)], the lattice structure becomes fully tetragonal upon further reduction [Fig. 3(h)]. The tetragonal films retain a T_c exceeding 50 K, in contrast to bulk 123 compounds, where the onset of superconductivity coincides with the transition from tetragonal to orthorhombic structures with increasing oxygen content.³⁶ 

In conclusion, we have developed a sequential ozone MBE growth method that enables the synthesis of DyBCO films with sharp substrate-film interfaces, minimal defect density, and high superconducting T_c. A comprehensive series of x-ray RSMs provide a detailed picture of the crystalline structure and its evolution with the thickness, doping, and substrate epitaxy. The insight into the lattice structure and structure-property relations we have obtained provides perspectives for the synthesis of optimized superconducting heterostructures and devices. In view of their high T_c and low residual resistivity, DyBCO films on LSAT are particularly attractive targets for quantum device structures. Finally, the controlled synthesis of this archetypical compound in different lattice symmetries is an excellent basis for fundamental investigations of the influence of the crystal lattice on electronic ordering phenomena such as charge density waves and their competition with superconductivity.

See the supplementary material for additional information on the sample growth, additional XRD data, surface morphology, and transport properties.

We thank Hans Boschker for fruitful discussions. We acknowledge funding from the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation), Projekt No. 107745057 TRR 80 and from the European Union's Horizon 2020 research and innovation programme under Grant Agreement No. 823717-ESTEEM3. The KIT Institute for Beam Physics and Technology (IBPT) is acknowledged for the operation of the storage ring, the Karlsruhe Research Accelerator (KARA), and provision of beamtime at the KIT light source.