Structural characterization of the LaInO₃/BaSnO₃ interface via synchrotron scattering Open Access

The alkaline earth stannates are perovskite oxides with chemical formula ASnO₃, where A denotes an alkaline earth metal.¹ When electron doped, they display high carrier mobility at room temperature,^2,3 which can be leveraged in all-epitaxial oxide heterostructures as the foundation of novel multifunctional devices. Of particular interest is barium stannate, BaSnO₃, which, in addition to its high mobility, is a transparent conducting oxide (or TCO) and possesses excellent thermal stability, maintaining highly stable oxygen stoichiometry and conduction behavior against annealing in various atmospheres at temperatures up to 1000 °C.^2,3 These properties make BaSnO₃ useful for devices such as high-temperature sensors⁴ and solar cells.⁵ 

Bulk single crystal lanthanum-doped barium stannate Ba_0.93La_0.07SnO₃ (or LBSO) has a mobility of 100 to 320 cm²/(Vs),^2,3,6 a factor of 10 better than the mobility of strontium titanate (SrTiO₃ or STO), which is the current standard for perovskite oxide-based devices. Thin film BSO^7,8 has been demonstrated to have a mobility as high as 150 cm²/(Vs) on PrScO₃ (110)⁹ and 183 cm²/(Vs) on DyScO₃ (001).¹⁰ LBSO on STO (001)¹¹ has a measured mobility of 70–120 cm²/(Vs).^2,12–14

Researchers have demonstrated an all-oxide field effect transistor (or FET) using BaSnO₃ as the conducting channel¹⁵ and either aluminum oxide (Al₂O₃),¹⁶ hafnium oxide (HfO₂),^17,18 or lanthanum indate (LaInO₃)^19–21 as the gate dielectric. We investigate the all-perovskite LaInO₃/BaSnO₃/SrTiO₃ FET, which has a large on/off ratio, I_on⁄I_off = 10⁷, and high field effect mobility, μ ∼ 90 cm²/(Vs).¹⁹ This high mobility may be due to the polar LaInO₃ gate dielectric remotely doping²² the BaSnO₃ conducting channel, resulting in an electronic reconstruction at the interface. Interfacial electronic reconstruction and its creation of high mobility carriers has been observed and studied in similar polar/nonpolar structures, such as LaAlO₃/SrTiO₃^23,24 and RTiO₃/SrTiO₃^25–27 materials.²⁸ 

Nonpolar BaSnO₃ (or BSO) is cubic in structure, with lattice parameter a = 4.116 Å, and is well lattice-matched to polar LaInO₃ (or LIO), which has lattice parameters a = 4.124 Å and b = c = 4.108 Å.²⁹ LIO possesses strong octahedral rotations, displacement of the oxygen anions from their face-centered positions, and displacement of the La³⁺ cations from their corner positions in large anti-parallel shifts. Owing to these distortions, the crystalline structure of LIO is best described by an orthorhombic unit cell consisting of 2 La³⁺ cations, 2 In³⁺ cations, and 6 O²⁻ anions with lattice parameters a = 5.940 Å, b = 8.216 Å, and c = 5.723 Å.²⁹ 

In Glazer notation, the LIO octahedral tilt pattern is a⁺b⁻b⁻ (i.e., space group Pnma), where a⁺ denotes in-phase rotation by angle α around the x-axis and b⁻b⁻ denotes anti-phase rotation by angle $β=γ$ around the y and z axes.³⁰ For in-phase rotation [see Fig. 1(a)], octahedra in adjacent perovskite layers along the rotational axis rotate in the same direction, while for anti-phase rotation [see Figs. 1(b) and 1(c)], octahedra in adjacent perovskite layers along the rotational axis rotate in opposing directions. Octahedral rotation around each of the 3 axes creates a unique set of half-order Bragg peaks:

• in-phase rotation along the x-axis creates peaks at 1 2(eoo) for k ≠ l,

• anti-phase rotation along the y-axis creates peaks at 1 2(ooo) for h ≠ l,

• and anti-phase rotation along the z-axis creates peaks at 1 2(ooo) for h ≠ k,

where o denotes an odd number and e denotes an even number. In response to these octahedral rotations, the La³⁺ cations are displaced along the [011] direction by vectors of magnitude d₁ and d₂, [see Fig. 1(d)], resulting in strong reflections at 1 2(oee). These cation shifts also contribute to 1 2(ooo) reflections due to anti-phase oxygen octahedral rotation, as discussed above.

Epitaxial thin films of LaInO₃/BaSnO₃ are grown on SrTiO₃ (001) substrates by pulsed laser deposition (or PLD). LIO film thicknesses range from 1.2 to 10.0 nm [i.e., 3–24 unit cells (uc)], and the BSO thickness is held constant at 120 nm (∼290 uc).

The crystalline structure of the LaInO₃/BaSnO₃ thin films is investigated using synchrotron x-ray diffraction. Data are collected on the X-ray Science Division beamline 33-ID at the Advanced Photon Source, Argonne National Laboratory. Diffraction measurements are taken at room temperature using an x-ray energy of 12.6 keV (λ = 0.984 Å). During measurement, the samples are mounted inside a dome of flowing helium gas to minimize background scattering. The diffracted intensity is measured using a solid state area detector at 300 K for each sample. Measurements are taken at half-order Bragg peaks (i.e., at half-integer values of h,k,l) of the BaSnO₃ film. At a thickness of 120 nm, the BaSnO₃ film is relaxed relative to the SrTiO₃ substrate and cubic with lattice parameter a = 4.11 Å, allowing us to isolate the BaSnO₃ Bragg peaks at multiples of the SrTiO₃ in-plane indices h = k = 3.905 Å/4.11 Å = 0.95. The LIO is tetragonally strained to the BSO, with c/a = 4.15 Å/4.11 Å = 1.01.

From the presence and absence of specific half-order peaks, we find that for films as thin as 3 uc, the LIO film has one domain with the same Glazer tilt pattern as bulk LIO, (i.e., a⁺b⁻b⁻) and that the film also includes a second domain rotated 90° in-plane from the first, with rotation pattern b⁻a⁺b⁻. Octahedral rotations of the second domain result in peaks 1 2(oeo) for h ≠ l and 1 2(ooo) for k ≠ l. Anti-parallel cation displacements along the [101] direction for this second domain, as shown in Fig. 1(e), result in peaks 1 2(eoe). Half-order peaks from a potential third domain b⁻b⁻a⁺, which would create peaks 1 2(ooe) for h ≠ k and 1 2(eeo), are not observed.

A comparison of the diffraction from 5 films with LIO thickness ranging from 1.2 to 10.0 nm shows that, beginning at 3.6 nm thickness, the LIO film begins to relax relative to the BSO. As shown in Fig. 2(a), while peaks 1 2(302) and 1 2(315) increase in intensity and decrease in width, as expected for the increasing film thickness, peak 1 2(218) achieves its maximum intensity for thickness 3.6 nm. The intensity of peak 1 2(218) is decreased above this thickness as the intensity is then divided between two peaks as the film relaxes to two orthorhombic domains. Because in-plane lattice parameters a ≠ b, in the LIO 2 × 2 unit cell, the scattering from domains which would appear at the same location under the standard fourfold geometric symmetry is distinctly separated in reciprocal space once the film relaxes. As shown in the reciprocal space maps in Fig. 2(b), these two 1 2(218) peaks become distinct by thickness 10.0 nm.

We fit the diffraction to the function

where n is the number of non-primitive LIO unit cells, and calculate a scaled integrated intensity I_data ∼ height × width = A/n, where FWHM = 0.4428/n. From the good agreement of the mean peak width n with the actual LIO thickness, we determine that the octahedral rotation and cation shifts occur throughout the film. Because of relaxation, for films of LIO thickness greater than 3.6 nm, the mean peak width n is decreased with a larger error. Table I shows the integrated intensities I_data, sorted into groups 1 2(eol), 1 2(oel), and 1 2(ooo), for our 5 films. The mean peak width n as a function of film thickness is shown in Table II.

To determine the rotation angles α, β, and γ and the magnitude of the cation displacements d₁ and d₂, we fit the half-order Bragg peak integrated intensities to a kinematic model of x-ray diffraction with a non-primitive c(2 × 2) unit cell,^31,32 allowing rotations of oxygen octahedra as well as anti-parallel La³⁺ cation displacements in the LIO film. Because LIO and BSO have cations of similar scattering strength, our x-ray measurements are not sensitive to any possible interfacial cation intermixing. We focus our analysis instead on the system’s distortion from the cubic structure.

The integrated intensities are fit to a model with incoherent scattering between four domains,^33,34

where the first two domains are a⁺b⁻b⁻ and b⁻a⁺b⁻, discussed above, the third domain has tilt pattern a⁺b⁻b⁻ and is rotated 180° in-plane from domain 1, and the fourth domain has tilt pattern b⁻a⁺b⁻ and is rotated 180° in-plane from domain 2. The La³⁺ cations are displaced according to the configurations shown in Figs. 1(d) and 1(e), respectively, for the first two domains, and in those same configurations rotated by 180° for the third and fourth domains.³⁴ n is the number of non-primitive LIO unit cells previously calculated from our fits to the peak width. The domains possess equal occupation D_j = 1/4, and the structure factor for each Bragg peak is

where the energy-dependent atomic scattering factor f is approximately equal to the atomic number Z, $fO2−≈8$⁠, and $fLa3+≈57$⁠.

The integrated intensities of the half-order Bragg peaks are shown with their best fits in Table I. Because $fLa3+>fO2−$⁠, peaks 1 2(hke), which are due to cation shifts, possess higher intensity than peaks 1 2(hko), which are primarily due to octahedral rotation. Cation shifts are also the dominant scattering contribution for peaks 1 2(ooo), and therefore our data are not sufficiently sensitive to the out-of-phase rotation angles $β=γ$⁠, which thus converge to their bulk value 12.2°. We note that these values have not been refined and expect them to be different, $β≠γ$⁠, owing to the inequivalent in-plane and out-of-plane pseudocubic lattice parameters b ≠ c induced by biaxial strain. With the relaxation of the $β=γ$ constraint, the two LIO domains are then more aptly characterized as a⁺b⁻c⁻ and b⁻a⁺c⁻.

We determine best fit values for in-phase rotation angle α and cation shift displacements d₁ and d₂ and find that there is no clear thickness dependence for these values. From the rotation angles α, β, and γ, we calculate the bond angle distortion θ_In−O−In along the x, y, and z axes, as shown in Table III. Within our model, we assume that the LIO structure is uniform across the film; reported values are therefore averages across all layers. Error bars represent the standard deviation of the refined values of all the samples.

While the larger of the two cation displacements d₂ is in good agreement with its bulk value, the smaller cation displacement d₁ is increased and the in-phase rotation angle α is decreased from the bulk. The slight decrease in angle α can be understood as a result of the LIO film being clamped to the cubic BSO and its rotation therefore being suppressed.³⁵ Of greater interest is the robustness of the cation displacements d₁ and d₂, which continues all the way to the LIO/BSO interface. This abrupt discontinuity in cation displacement across the interface should have interesting implications for interfacial polarization, which is critical to the system’s transport properties.

In particular, we expect the out-of-plane cation displacements in the interfacial layer to play an important role in the confinement of electrons in the LIO/BSO interface. For example, in the polar catastrophe model, each LIO unit cell donates half an electron to the BSO, with net charge flowing from the polar (LaO)⁺ to the nonpolar (SnO₂)⁰. At a basic level, this flow is boosted by cation shift away from the interface and impeded by cation shift toward the interface. Because the cations are displaced in alternating directions over the xy plane, these two effects should cancel each other out. However, due to the large size of the cation shifts, with d₂ = 0.08c, the interatomic potential between the La³⁺ and O²⁻ ions across the LIO/BSO interface can be modeled by an anharmonic potential, such as the Lennard-Jones potential. In such a model, the alternating cation displacements create a nonzero, net positive potential. This potential and the corresponding interfacial polarization are intrinsic to the crystalline structure and distinct from those created by charge imbalance in the polar catastrophe model. Such interfacial polarization may be behind the 2DEG-like behavior in the LIO/BSO interface.

In summary, we have reported on the crystalline structure of epitaxial LaInO₃/BaSnO₃ thin films, which have been used in a high mobility field effect device, where polar LaInO₃ remotely dopes the stannate with electrons. Using synchrotron x-ray diffraction, we have characterized half-order Bragg peaks of LaInO₃ to examine the role of the large oxygen octahedral rotations found in bulk LaInO₃ in influencing the polarization of this system. We observe two orientational domains in the LaInO₃ and find that for films as thin as 3 uc, the LaInO₃ has bulk-like rotations and enhanced cation displacements right up to the BaSnO₃ interface and believe these distortions strongly influence the polarization and transport.

Work at Yale is supported by the Office of Naval Research under Grant Nos. N00014-18-1-2704 and N00014-12-1-0976. Use of the Advanced Photon Source was supported by the U. S. Department of Energy, Office of Science, Office of Basic Energy Sciences, under Contract No. DE-AC02-06CH11357. Work at SNU was supported in part by the Samsung Science and Technology Foundation under Project No. SSTF-BA1402-09.