Band alignment at epitaxial BaSnO₃/SrTiO₃(001) and BaSnO₃/LaAlO₃(001) heterojunctions

BaSnO₃ (BSO) is an attractive wide-bandgap semiconductor in the field of oxide electronics. When doped n-type, BSO exhibits considerably higher room-temperature electron mobility than SrTiO₃ (STO), which has traditionally been taken to be the leading perovskite oxide semiconductor. Bulk single crystals of BSO have been shown to exhibit room-temperature mobility values as high as 320 cm²/V s,¹ whereas epitaxial films typically yield lower values thus far, ranging between 10 and 150 cm²/V s.^2–6 Additionally, BSO has high optical transparency, rendering it of considerable interest for transparent electronic technologies.^7–10 While there is potential to increase room-temperature electron mobility in doped-BSO films through defect minimization, heterostructure engineering also provides a promising route to this end. Heterostructure engineering provides pathways to isolate the carriers from scattering centers such as the dopants from whence they come. This can be done by either modulation doping (introducing dopants in a different material across an interface from BSO) or polarization doping (inducing charge transfer into non-polar BSO via electronic reconstruction at the interface with a polar oxide). In either scheme, the conduction band minimum in the BSO should be of lower electron energy than that of the oxide to which the BSO is joined in order to confine carriers in the BSO. Under this condition, free carriers will readily spill over into and remain in the BSO layer, provided the conduction band offset is sufficiently large. Doped STO is a good choice as an electron source for the modulation doping scheme, and LaAlO₃ (LAO) is suitable to test the polarization doping approach.

To these ends, we have deposited epitaxial undoped BSO films on undoped STO(001) and LAO(001) substrates using hybrid molecular beam epitaxy (MBE) and have measured the band offsets and BSO band gap using ex situ x-ray photoelectron spectroscopy (XPS) and spectroscopic ellipsometry (SE), respectively. Details of our hybrid MBE method for BaSnO₃ heteroepitaxy are discussed elsewhere.^11,12 All films were insulating, establishing that our growth process does not unintentionally dope the BSO with O vacancies.

Figures 1(a) and 1(b) show out-of-plane, wide-angle x-ray diffraction (XRD) scans for 28 ± 1 unit cell (u.c.) BSO films on STO(001) and LAO(001), respectively. A single Bragg peak, indicating epitaxy, is observed for BSO films on both substrates for which the in-plane lattice mismatches (a_BSO – a_sub)/a_BSO) are +5.1% (STO) and +7.9% (LAO). Finite thickness fringes are also evident, indicating excellent crystallinity, as well as smooth surfaces and buried interfaces. Contact mode AFM images of the film surfaces are shown as insets. These images reveal atomically smooth surface morphology for both films, thereby corroborating the XRD results. The c lattice parameters were determined to be 4.137(5) Å and 4.122(5) Å for films on STO and LAO, respectively. These values are larger than the bulk value of 4.116 Å, which we attribute to incomplete strain relaxation in the 28 u.c. films. A much thicker (82 u.c.) film on LAO(001) grown under the same conditions yielded lattice parameters identical to those of bulk BSO, suggesting that the expanded c lattice parameters in our 28 u.c. films are not due to cation non-stoichiometry or oxygen vacancy defects, but rather to incomplete strain relaxation.¹¹ We show in Figure 1(c) Rutherford backscattering spectrometry (RBS) data for a 134 u.c. BSO film on STO(001), along with a SIMNRA¹³ simulation yielding a Ba/Sn ratio of 0.996 ± 0.010. The agreement is very good, providing direct evidence for correct stoichiometry in our BSO films.

Valence band offsets (VBO) were determined by high-energy resolution XPS from measurements taken for the as-received samples after a through-air transfer from the hybrid MBE system and then again after a UV/ozone treatment to remove adventitious carbon.¹² We use a straightforward method for measuring VBOs in which the valence band maximum (VBM) for each material in a heterostructure is referenced to select core-level (CL) photoelectron peaks uniquely associated with that material.^14–17 The binding energy differences between appropriate CL peaks are then used to determine the VBO. Figure 2 shows the spectra used to obtain the VBOs for heterojunctions of 5 u.c. BSO on STO and LAO. This BSO thickness was chosen to be large enough that the electronic structure of the BSO is likely to be fully developed, yet thin enough to yield sufficient photoemission signal from the substrate core peaks that their binding energies can be accurately measured. The Ba 4d spin-orbit features are asymmetric and require a second pair of peaks shifted ∼1 eV to higher binding energy in order to obtain a good fit. We assign these to Ba ions at the surface that are either oxidized to form BaO₂¹⁸ or are hydroxylated upon air exposure. The more intense peaks at lower binding energies are assigned to A-site cations in the pure BSO lattice. The La 4d spectrum also shows considerable structure, but this is due to many-body, charge–transfer effects rather than surface over-oxidation or hydroxylation.¹⁹ The high degree of symmetry in the Sn 3d_5/2 peaks is consistent with the undoped character of the films.¹¹ 

We show in Table I the resulting VBO values for the thin-film heterojunctions, each based on a different pair of core levels.¹² For BSO on both STO and LAO, the BSO VBM is at lower electron energy than that of the substrate for seven out of the eight measurements. The Sn 3d/Ti 2p CL pair yields a slightly positive value for the as-received BSO/STO heterojunction. As an independent test of the CL method applied to BSO/STO, we determined the VBO directly using VB spectra. We did so by simulating the VB for the 5 u.c. BSO/STO heterojunction by taking a linear combination of spectra for the STO substrate and the thick BSO film after weighting the intensities to account for film thickness, and shifting the BSO spectrum 0.28 eV (the average VBO from the CL pair measurements excluding the +0.04 eV outlier) to higher binding energy. This simulated spectrum matches well the measured spectrum with regard to overall shape and width, as seen in Figure 4, thereby corroborating the CL results.

In order to obtain the CB offset (CBO), we need an accurate value of the indirect band gap for 5 u.c. films of BSO. To this end, we used SE to measure the indirect and direct gaps for the 28 u.c. BSO films on LAO and STO and then correct for strain differences between the two thicknesses, since SE is not reliable for films as thin as 5 u.c. Figure 3(a) shows the refractive indices (n) and extinction coefficients (k) for the two 28 u.c. films. These results are in reasonable agreement with the dielectric function measured by Luo et al.⁸ on a single-crystal BSO specimen by SE. (Note that (n + ik)²= ε₁ + iε₂, where ε₁ and ε₂ are the real and imaginary components of the dielectric function, respectively.) The absorption coefficients (α) for the two films are shown in Figure 3(b). Because the films are rather thin (11–12 nm), the sensitivity of the ellipsometric measurement is low at lower photon energies (i.e., below the band edge),²⁰ and thus the absorption observed below ∼3 eV may not accurately reflect the optical properties of BaSnO₃. The indirect gaps were determined by constructing Tauc plots of (αhν)ⁿ vs hν with α = 4πk/λ and n = $12$⁠,²¹ and the resulting indirect gaps are 2.91(5) eV and 2.95(5) eV for growth on STO and LAO, respectively, as seen in Figures 3(c) and 3(d). The associated direct gaps obtained from Tauc plots with n = 2²² were found to be 3.55(5) eV and 3.57(5) eV for these films on LAO and STO, respectively.¹² Our indirect gap values are in good agreement with the bandgap values reported by Lebens-Higgins et al.⁴ based on hard x-ray XPS at hν = 4 keV. These authors measured the difference between the VBM and CB minimum (CBM) to be ∼3.07 eV for La-doped BSO epitaxial films with very low doping levels grown by MBE. Likewise, Kim et al.⁷ reported indirect and direct bandgap values of 2.95 and 3.10 eV, respectively, for an undoped single-crystal BSO specimen. Our indirect bandgap value agrees well with that reported by Kim et al.⁷ but agreement is not as good for the direct gap. This disagreement is likely due to the broader spectral range of our absorption data (up to 6 eV), which allowed us to identify a linear region inaccessible to Kim et al.⁷ 

The optical and electronic properties in Figure 3 are also in quantitative agreement with those obtained by recent density functional theory (DFT) calculations using the modified Becke-Johnson type potential functional of Tran and Blaha, which predicted an indirect bandgap of 2.82 eV, an index of refraction in the range of ∼1.85–2, and a similar dependence of the absorption coefficient on photon energy for unstrained, undoped BSO.^9,10 In contrast, the experimental bandgap values reported for BSO powder samples range from 3.1 eV (Ref. 23) to 3.4 eV,²⁴ likely due to a strong Burstein-Moss shift arising from unintentional defect- or impurity-induced carrier doping. The lack of a Burstein-Moss shift in the bandgap values reported here confirms the insulating nature of the thick epitaxial films.

Although we cannot reliably measure the band gaps of the 5 u.c. films by SE, we can estimate how the bandgaps might differ from those of the 28 u.c. films. DFT calculations by Singh et al.⁹ reveal that the BSO gap is strongly dependent on u.c. volume. This dependence is driven by the Sn 4s character of the conduction band. Thus, changes in the bandgap with strain are most likely manifested by movement of the CB edge energy, with the VB edge energy remaining approximately unchanged. It was not possible to obtain accurate lattice parameters from the XRD reciprocal space maps for the 5 u.c. BSO films. However, the out-of-plane lattice parameter can be estimated from a θ-2θ scan and was found to be 4.14 Å for 5 u.c. BSO/STO. Using Poisson's ratio for BSO (0.247),¹¹ the in-plane lattice parameter was estimated to be 4.07 Å, leading to a u.c. volume of 68.8 ų compared to 69.9 ų for bulk BSO. Using Singh's calculations, we estimate that the bandgap for 5 u.c. BSO/STO is ∼3.1(1) eV. The strain-based correction is smaller for BSO/LAO because the 5 u.c. films are more relaxed due to larger lattice mismatch. We estimate that the band gap for 5 u.c. BSO/LAO is ∼3.0(1) eV.

Having determined the indirect bandgap for BSO, the CBO is readily determined from the VBO and the difference in indirect gap values for the film and substrate materials as $ΔEC=ΔEg−ΔEV$⁠. As with $ΔEV$⁠, the sign convention is such that ΔE_C is negative if the CB minimum (CBM) in the BSO is at a lower electron energy than that of the substrate. The resulting CBOs, along with the VBOs and indirect gaps, are summarized in Figure 4. Here, we average over the two CL pairs summarized in Table I to obtain the VBO values for each kind of heterojunction. Our VBO for BSO/STO (−0.28 eV) is in excellent agreement with that calculated from DFT using the HSE06 hybrid functional by Krishnaswamy et al.²⁵ (−0.27 eV). However, these authors also calculate an indirect gap of 2.40 eV, which differs significantly from our measured values. This calculated value for the indirect gap stems from the use of a hybrid functional with 25% Hartree-Fock (HF) contribution, which was in turn based on satisfactory results for other oxides and a lack of closure on the band gap of BSO in the literature to date. However, based on our SE results, it appears that a larger HF contribution is required for better accuracy on BSO. This difference in indirect gap propagates into a similar discrepancy in the CBO between theory (−1.14 eV, using our sign convention), and experiment (−0.4 eV). Because of the relatively low CB density of states Krishnaswamy et al.²⁵ calculate for BSO, the CBO we measure (−0.4 eV) limits the carrier density that can be confined within BSO films using a modulation doped structure with STO to the low 10¹³cm⁻² range, as estimated from Fig. 5 of Ref. 25. However, based on the same figure, the BSO/LAO heterostructure with its larger CBO (−3.7 eV) should provide better carrier confinement up to ∼3–4 × 10¹⁴cm⁻².²⁵ Although these predicted extents of carrier confinement have yet to be experimentally verified, they show promise for the formation of confined quantum wells in BSO.

The experimental CBOs we report reveal that for both modulation doping with STO and polarization doping with LAO, the electrons should readily transfer into the BSO, thereby separating from their respective sources. The exact extent of confinement when in a heterojunction with STO depends on the strain, with the highest confinement occurring when the BSO is unstrained. These heterostructures should exhibit higher mobilities than would single films of La-doped BSO. BSO/STO and/or BSO/LAO interfaces may facilitate low-density, high-mobility electron gases, thereby paving the way for the investigation of integer/fractional quantum Hall effects. Such a high mobility channel at room temperature in an engineered complex oxide heterostructure may enable oxide-based, high-mobility, two-dimensional electron systems that can operate at ambient temperature. A material system of this kind would be highly useful for all-perovskite transistors in power electronics applications.

The thin film growth and characterization work at the University of Minnesota was supported primarily by the National Science Foundation through DMR-1410888 and, in part, by the MRSEC under Award No. # DMR-1420013. We also acknowledge use of facilities at the UMN Minnesota Nano Center. Parts of this work were carried out in the Characterization Facility, University of Minnesota, which receives partial support from NSF through the MRSEC program. The XPS and SE work at PNNL was supported by the U.S. Department of Energy, Office of Science, Division of Materials Sciences and Engineering under Award No. #10122. The PNNL work was performed in the Environmental Molecular Sciences Laboratory, a national scientific user facility sponsored by the Department of Energy's Office of Biological and Environmental Research and located at PNNL.