Introduction

Over the last years, there has been a surge of interest in transparent conducting oxides (TCOs), which combine weak optical absorption with high electrical conductivity. This combination is possible when the bandgap remains wide (over 3 eV) while high doping is attained without affecting electron mobility, or in systems with a small bandgap but enhanced effective mass due to strong electron–electron interactions1. Perovskite alkaline earth stannates, such as BaSnO3 (BSO) and SrSnO3 (SSO), fulfill the requirements of the first and thus are promising candidates for realizing novel optoelectrical devices. In particular, BSO crystals with wide band gaps (~3.0–4.0 eV) have shown unusually high room temperature electron mobility of over 100 cm2 V−1 s−1(see ref. 2), while doped bulk BSO reaches mobility of 320 cm2 V−1 s−1 (see ref. 3). Therefore, BSO demonstrates a realistic potential to replace traditional transparent conductive oxides, such as indium-based systems4, in optoelectronic technology. Furthermore, both BSO and SSO in thin film form show further improvement in light transparency, electrical conductivity5,6, and electron mobility compared to the bulk compounds, which is generally attributed to a low electron-effective mass in the range of 0.2–0.4 me7,8,9,10,11. Significant theoretical and experimental efforts12,13,14 have been made to understand these unique electronic properties. Band structure calculations based on density functional theory (DFT) found a low effective mass for the conducting state of bulk BSO11, which was attributed to a substantial reduction in the electron–phonon scattering rate.

Perovskite oxides generally exhibit the emergence of novel phenomena at surfaces and interfaces, manifesting tremendous potential for technological applications15,16. Indeed, it was suggested that stannates could host an interfacial electron gas since they experience polar interfaces band bending near the surface17. Kim et al. reported that LaInO3/(Ba,La)SnO3 heterostructure shows enhancement of the conductance, suggesting that a 2-dimensional electron gas (2DEG) has been created at the interface6,18. Moreover, Feng et al. recently reported that 2DEG is generated at the interface between a thick BSO film and a thin LaAlO3 capping layer19 by the creation of oxygen vacancies. This result suggests that the 2DEG in BSO heterostructures is in some respects analogous to the one found in the LaAlO3/SrTiO3 (LAO/STO) system, which is likewise a transparent conducting system20. Numerous insights into the electronic structure of the LAO/STO system have been obtained from ARPES studies of a 2DEG found on the bare STO surface21,22,23. Investigating the surface structure of BSO using angle-resolved photoemission spectroscopy should likewise be beneficial for understanding the properties exhibited by BSO-based heterostructures.

In this article, we report the investigation of BSO’s surface electronic properties using a combination of angle-resolved photoemission spectroscopy (ARPES) on La-doped BaSnO3 (LBSO) films and ab initio calculations. Our spectroscopy measurements demonstrate the existence of a two-dimensional (2D) state at the surface of LBSO thin films with distinct properties from the bulk. Comparing the experimental data with the calculated band structure for BSO in both bulk and slab forms, we find that the observed 2D state resides on the SnO2-terminated surface and features a significantly smaller effective mass than found in the bulk bands.

Results and discussion

For this study, 30-nm-thick LBSO films were grown by hybrid molecular beam epitaxy (MBE) on Nb-doped STO (001) substrates. Figure 1a displays the X-ray diffraction pattern of an LBSO film. The out-of-plane lattice parameter of 4.140 ± 0.002 Å reveals that the studied LBSO film is mostly relaxed. A slightly higher out-of-plane lattice parameter compared to bulk LBSO is due to the small residual biaxial strain in the film. Fringes around the (002) X-ray diffraction (XRD) peak of LBSO (Fig. 1a) are due to the finite film thickness and indicative of a smooth surface (see Supplementary Note 1 for more details). Figure 1b shows the reflection high-energy electron diffraction (RHEED) pattern of an as-grown sample (measured at the University of Minnesota). The sample’s RHEED pattern after transport to the SIS beamline at the Swiss Light Source (Fig. 1c) was still well-defined, verifying the preservation of the surface’s crystallinity. However, a relatively high background visible in the RHEED data indicated some surface contamination, and therefore we performed high-temperature annealing at 600 °C in 1.0 × 10−4 mbar of O2. This procedure resulted in a significant improvement of the surface quality, as evidenced both by RHEED and low-energy electron diffraction (LEED) in Fig. 1d, e, respectively (see Supplementary Note 2 for more details). The RHEED pattern (Fig. 1d) exhibits a weak sign of surface reconstruction, which might be related to the \(\sqrt{2}\times \sqrt{2}R4{5}^{\circ }\) reconstruction reported to occur after annealing up to 600–700 °C in ultrahigh vacuum13. The samples were then transferred in situ (pressure better than 5.0 × 10−10 mbar) to the main experimental chamber, where the measured LEED pattern and ARPES data showed a 1 × 1-ordered surface.

Fig. 1: X-ray diffraction, reflection high-energy electron diffraction (RHEED), and low-energy electron diffraction (LEED) of La-doped BaSnO3.
figure 1

a Angle X-ray diffraction of a 30-nm-thick La-doped BaSnO3 film grown on (001) oriented Nb-doped SrTiO3 substrate. RHEED pattern taken along the [100] azimuth after (b) growth (in situ at 14 keV), c ex situ transfer and exposure to air, and d high-temperature oxygen annealing to remove surface contamination. e LEED pattern at 147 eV, acquired from the surface after oxygen annealing.

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ARPES is a powerful tool to directly determine the electronic band structures of materials and hence also the dimensionalities of their electronic states. In Fig. 2, we present the electronic band structure obtained from the LBSO films. The kz momentum is perpendicular to the sample surface and thus orthogonal to the kx and ky momenta, which lie on the surface plane along the (100) and (010) cubic axes, respectively. By varying the incoming photon energy from 20 to 145 eV, we measured band dispersions along kx at various kz values. Figure 2a displays the deep valence band structure along cuts parallel to Γ-X passing through the different kz values marked by white curves in Fig. 2b. To better visualize the bands, the spectra have been processed using the 2D curvature method24.

Fig. 2: Surface and bulk electronic structure of La-doped BaSnO3.
figure 2

a Valence band dispersion parallel to Γ-X, acquired with incoming photon energies of 80, 122, and 132 eV, corresponding to different perpendicular momentum kz values as indicated by the white curves in (b). The measured band structure is overlaid with the LQSGW band structure calculated for bulk BaSnO3. The measured and calculated bands show good agreement, with a clear dispersion along kz. b Intensity map at the Fermi energy in the plane perpendicular to the sample surface (kx–kz), measured with incoming photon energies ranging from 20 to 145 eV. No clear periodicity is evident along kz. The black squares indicate the Brillouin zone boundaries as inferred by the periodicity of the valence bands shown in panel (a), using the LQSGW calculations as a reference. The red circumferences mark the expected bulk Fermi surface centered at the Γ points (c) Sketch illustrating the difference between the measured and calculated Fermi surfaces. The calculated 3D sphere-like Fermi surface with Fermi momentum kF based on the nominal doping of the film is shown in red, while the measured 2D cylinder-like Fermi surface with kF based on the measurements results is shown in green. ARPES intensity follows the attached color scale bar.

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In Fig. 2a, we also compare the measured band structure to linearized quasiparticle self-consistent GW (LQSGW) calculations for bulk BSO using the experimental lattice constant of a = 4.14 Å (see Supplementary Note 3 for more details). For each spectrum image, we overlay the data with the calculated band structures at the corresponding kz value. The agreement between the experimental data and the calculations is overall very good, and a clear dispersion along kz is observed, thus verifying the three-dimensional (3D) nature of the bulk bands. The calculated indirect bandgap (between Γ and R points) of 2.9 eV compares well to the experimental value of ~3 eV obtained from optical measurements7,25 and is lower than the reported 3.7 eV obtained by ARPES14. Compared with other theoretical approaches, band gaps calculated by LQSGW tend to be larger than those predicted with LDA and GGA calculations26, and similar to the band gaps obtained using hybrid exchange-correlation functionals, such as PBE027 and HSE0628,29.

From the analysis of the ARPES data, we find the conduction band effective masses in the Γ-X direction to be 0.17 me. Our results are in good agreement with the values of 0.20 and 0.22 me reported in refs. 11,30, where the authors employed HSE06 and PBE0 hybrid functionals, respectively, as well as with the experimental value of 0.19 me reported in ref. 9.

When Ba is substituted with La, the conduction band, which is mainly composed of Sn 5s states (see Supplementary Note 2 for more details), becomes occupied by the donated electrons, turning LBSO into a metal. Previous studies showed that thin films of LBSO could exhibit high conductivity exceeding 104 Scm−1, and it can be enhanced dramatically at the interface of BSO with another insulator6. Indeed, the properties of BSO-based heterostructures strongly depend on the electronic structure of the interface region, which might bear similarities with the BSO film surface. Using vacuum ultraviolet energies for ARPES ensures a short probing depth and thus high sensitivity to the surface electronic structure.

For metallic bulk LBSO, the Fermi surface (FS) is expected to be 3D and isotropic in momentum space, with symmetry inherited from the Sn 5s states, as shown by the red sphere in the sketch of Fig. 2c. Nevertheless, the measured FS lying on the perpendicular kx–kz plane at the Fermi energy (presented in Fig. 2b) shows no clear dispersing bands along kz. Occasionally, such behavior can be attributed to the kz broadening effect that occurs in ARPES measurements31. However, this possibility is unlikely in this case, because the broadening would need to be enormous to stretch the expected small Fermi surface of LBSO to the Brillouin zone boundary. Moreover, the states at EF reach the Brillouin zone boundary at the Z point, as indicated by the black squares in Fig. 2b, and their intensity varies with no clear periodicity. The variations in the band’s intensity are thus evidently related to the photoemission cross-section, rather than kz dispersion. Finally, the values of the Fermi momentum kF and bandwidth are similar at different kz values (see Fig. 3d). Thus, the measured Fermi surface is cylindrical (sketched in green in Fig. 2c) rather than spherical (shown by the red sphere), indicating the 2D nature of this electronic state.

Fig. 3: Photoemission spectrum near the Fermi energy.
figure 3

a Spectra acquired with different photon energies corresponding to different perpendicular momentum kz values, as indicated by black stars in Fig. 2b. For all the acquired bands, the bandwidth and Fermi momentum is similar, as shown by the momentum distribution curves (MDCs) at Fermi energy EF (red) and the matched band (black). The vertical dashed lines indicate Fermi momentum kF. b Intensity map at the Fermi energy assembled from several cuts at different ky values. c Spectrum image obtained along a cut parallel to the Γ-X direction, as indicated by the dashed white line in (b). The spectra in (b) and (c) were measured with an incoming photon energy of 28 eV, providing a higher resolution than in previously shown spectra. d Momentum distribution curve (MDC) extracted from panel (c) at Fermi energy EF, and fitted to two Lorentzian profiles to determine the position of Fermi momentum kF. e Second derivative along the energy axis for the spectrum image in (c), providing an enhanced view of the dispersing band.

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To obtain more quantitative information about this 2D band, we performed detailed ARPES measurements using a photon energy of 28 eV, which provides the best energy and momentum resolution among all photon energies used in this work. The intensity map at the Fermi energy (Fig. 3b), which is built from several cuts acquired along the direction parallel to Γ-X (see Fig. 3a), confirms the circular shape formed from the electron-like band shown in Fig. 3b, d. According to the Luttinger theorem32, the carrier density is proportional to the volume enclosed by the Fermi surface. We extracted the value of the Fermi momentum, kF, by fitting the MDC at EF to two Lorentzian curves (Fig. 3d). The measured kF of the 2D Fermi surface is found to be smaller than the expected value for bulk (kF ~0.067 Å−1), and amounts to a charge carrier density of n\({}_{2D}^{ARPES}\) = 1.2 × 10−2 e− per a2 (where a is the lattice parameter of BSO), which corresponds to 7 × 1012 e− per cm2. The carrier density measured by transport for this film5 is n3D = 1.7 × 1020 e− per cm3. Considering the 2D band to extend over 1–3 unit cells, the bulk carrier density corresponds to a planar density n2D between 7 × 1012 and 2 × 1013 e− per cm2. The similar electron concentrations of the surface state and the bulk suggests homogeneous doping of La across the whole film and imply that the conduction states show an altered dimensionality at the surface. These surface states are reminiscent of Shockley states since they have features of nearly free electron states and occur essentially due to the SnO2 termination33.

Tracking the band dispersion in Fig. 3b, d reveals other unique properties of this 2D state. Keeping kF fixed, as determined by Fig. 3c, the experimental spectrum can be well-described by a parabola with the minimum around 0.15 eV and effective mass around 0.12 me. The observed value of m* is smaller than previously reported values from bulk optical measurements9 and bulk DFT calculations8. Interestingly, the spectra presented in Fig. 3, although with only a moderate background, are rather broad. This broadening can be a sign of many-body interactions, such as electron–phonon coupling. Indeed, it was reported that strong electron–phonon coupling of the conduction electrons with the longitudinal optical LO1, 2, 3 phonon modes is present in BSO34. It is also important to note the strong incoherent spectral weight around the Γ point, which is also found in low-doped STO, where it is originates from strong electron–phonon coupling35,36,37.

The above results suggest the existence of a 2D state at the LBSO surface, which can be related to the observed 2DEG-like electrical properties in LaInO3/BaSnO3 bilayers6. A downward band bending scenario has been proposed to explain the formation of the 2DEG at oxide surfaces, for instance, in the case of STO21,22,23. Indeed, it was experimentally observed that doped BSO films undergo an upward band bending, consequently reducing the conduction band’s occupation12. Another possible cause of the observed 2D electronic structure can be that breaking translation symmetry on the surface results in a new state whose wave function is localized with different properties than the bulk band33. Our ARPES experiments alone cannot disclose the origin of such a state; therefore, we performed the first principle calculations.

To investigate the origin of these 2D states, we simulated 1 × 1 × 8 BSO (001) slabs with both SnO2 and BaO terminations. Since LQSGW calculations are computationally too demanding, we performed the electronic structure calculations using the Heyd–Scuseria–Ernzerhof (HSE06)38 hybrid exchange-correlation functional, which has been shown to provide a good description of the electronic structure and phonon dispersion of bulk BSO28,29. The optimized crystal structures, along with their orbital-resolved band structures highlighting the contribution from both surface and bulk Sn 5s orbitals, are shown in Fig. 4a, b for the SnO2- and BaO-terminated slabs, respectively. It is interesting to note that the bandgap is, in general, smaller than its bulk counterpart. For the SnO2-termination, we found an indirect bandgap of 1.2 eV between the Γ and M points, while for the BaO-termination it is 2.1 eV. For comparison, we also performed calculations using the PBE39 exchange-correlation functional for the SnO2-terminated slab. Although both calculation methods provided very similar band structures (details about the method employed in our calculations and our experimental procedures are available in Supplementary Note 3), the bandgap with PBE is severely underestimated, leading to a spurious metallic solution that is not observed experimentally (details about the method employed in our calculations and our experimental procedures are available in Supplementary Note 3).

Fig. 4: Comparison of the calculated electronic structure of BaSnO3 slab with different terminations.
figure 4

a Optimized SnO2-terminated slab structure and corresponding orbital-resolved density functional theory band structure along X-Γ-X. The valence band is dominated by O 2p states, while the conduction band is dominated by Sn 5s states. Bands originating from the surface Sn atoms are highlighted in gold, while bands originating from the Sn atoms in the central layers of the slab, which represent the bulk, are highlighted in pink. b Equivalent data for a BaO-terminated slab. The crystal structures were generated with the VESTA software41, and the band structures were plotted with PyProcar42.

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Furthermore, our calculations show that the lowest-lying unoccupied states are mainly derived from Sn 5s orbitals from the surface atoms, while the Sn 5s states from the bulk region of the slab appear around 0.5 eV above. In contrast, for the BaO-terminated slab, the lowest-lying unoccupied states have predominantly bulk character. The calculated effective masses of both the surface- and bulk-derived state of the SnO2-terminated slab, within HSE06, are around 0.21 me and 0.22 me, respectively. The discrepancy between the effective masses of the 2D state obtained by ARPES (0.12 me) and calculated with DFT may originate from the in-plane size of the slab and details of the surface structure used in our simulations.

Combining angle-resolved photoemission spectroscopy (ARPES) with ab initio calculations, we revealed the existence of a two-dimensional metallic state at the surface of 1% LBSO thin film, its origin, and characteristics. The comparison between the experimental data and the calculated band structure for BSO slabs indicates that only the SnO2-terminated surface hosts this 2D state. The surface state exhibits unique behavior, with an extraordinarily low effective mass of about 0.12 me, significantly different from the bulk value. This surface state’s particular property, combined with light transparency, warrants BSO a relevant standing among constituent materials of heterostructures for optoelectrical devices.

Methods

Sample preparation and characterization

The LBSO thin films were grown by hybrid molecular beam epitaxy (MBE) at the University of Minnesota on Nb-doped STO (001) substrates. Details of the growth can be found in the report by Prakash et al.40. After the growth, the samples were transferred ex situ and loaded into the ARPES system at the SIS beamline of the Swiss Light Source. RHEED patterns were recorded after the ex situ transfer and after each annealing procedure (UHV annealing and annealing at pressure 1.0 × 10−4 mbar of O2 and temperature 600 °C). All ARPES data presented in the manuscript were obtained from O2-annealed samples. The XPS spectra were acquired in the APRES chamber by integrating the angle axis of the spectra images.