Structure and optical band gaps of (Ba,Sr)SnO₃ films grown by molecular beam epitaxy

Alkaline Earth stannates (ASnO₃ where A = Ca, Sr, or Ba) have attracted significant interest for use as transparent conductors^1,2 and as high-mobility, wide band gap channel materials in electronic devices,³ where they can be integrated epitaxially with functional oxides that possess the same perovskite crystal structure. Room temperature electron mobilities in BaSnO₃ single crystals exceed 300 cm²/V s,¹ which is much higher than the carrier mobility of most perovskite oxides. For electronic devices, high-mobility epitaxial films with low defect concentrations and a range of band gaps are needed. The band gap and lattice parameters can be tuned by alloying SrSnO₃ and BaSnO₃,^4,5 thus presenting opportunities for the growth of lattice-matched films on different substrates, strain engineering, and tuning of heterojunction band offsets in this class of materials.

BaSnO₃ is cubic and has an indirect band gap, corresponding to transitions from the valence band maximum at the R point to the conduction band minimum at Γ.^6,7 A direct band gap is relatively close in energy.^6,7 SrSnO₃, which is orthorhombic (Pbnm space group⁸) is believed to either possess a direct gap (valence band maximum at Γ)⁷ or the two band gaps are very close in energy.⁹ The reported experimental band gap values for BaSnO₃ and SrSnO₃ range between 2.9 and 4.0 eV (Refs. 2, 7, and 10–13) and 4.1 eV to 4.27 eV,^7,10 respectively. Density functional theory (DFT) values also differ greatly.^6,13–16 Several factors affect the measured band gaps. Optical absorption is likely dominated by the direct band gap. For example, no significant changes in the optical absorption edge occur across the (Ba,Sr)SnO₃ series despite the presumed change in the nature of the band gap.⁵ Doped samples² are expected to exhibit a large Burstein–Moss shift due to the small conduction band mass.^12,17,18 Recently, it was suggested that doped samples also undergo a strong band gap renormalization.¹⁹ 

BaSnO₃ films have been grown by several techniques,^1,20–22 including molecular beam epitaxy (MBE),^19,23,24 which results in the highest mobility films,²⁴ whereas (Ba,Sr)SnO₃ and SrSnO₃ films have so far only been grown by high-energetic pulsed laser deposition.¹⁹ Here, we demonstrate MBE of (Ba,Sr)SnO₃ and SrSnO₃ for systematic tuning of band gaps and film strain in epitaxial heterostructures.

(Ba_xSr_1−x)SnO₃ films were grown using an MBE approach developed for BaSnO₃, where a SnO₂ source is used instead of elemental Sn, which addresses issues related to SnO volatility at low oxygen pressures typical in MBE.²⁴ SnO₂, Ba, Sr, and the La-dopant were supplied from effusion cells. Beam fluxes were calibrated using an ionization gauge and are given as beam equivalent pressure (BEP). Oxygen was provided by an RF-plasma source and the oxygen BEP was kept at 1.5 × 10⁻⁵Torr. Prior to growth, the substrates were annealed at the growth temperature (800 °C, monitored via an optical pyrometer) under plasma exposure for 20 min. The SnO_x flux was set to a constant value of ∼1.5 × 10⁻⁶Torr, and the (Ba + Sr) flux to ∼5.0 × 10⁻⁸Torr. The (Ba + Sr)/SnO_x flux ratio was varied to optimize film stoichiometry. Unless stated otherwise, films were doped with La (0.2%–0.3%). Only the most Ba-rich films (x = 1 and x = 0.8) became electrically conductive when doped with La. The reason for the inability to dope Sr-rich films will be a subject of future investigations.

In situ reflection high-energy electron diffraction (RHEED) patterns were streaky throughout all growths, indicating smooth films. Post-growth characterization methods included high-resolution x-ray diffraction (XRD) with a Cu K^α x-ray source. The film thicknesses were determined from x-ray reflectivity. For (scanning) transmission electron microscopy (S/TEM) studies, cross-sectional samples were prepared by wedge polishing with a 2° angle and imaged using a field emission FEI Titan S/TEM operated at 300 keV. The direct band gap was analyzed using spectroscopy ellipsometry performed with a Wollam ellipsometer at incident angles of 60°–75° and photon energies from 0.7 to 6.5 eV.²⁵ 

SrSnO₃ films were grown on (001) SrTiO₃ (lattice parameter a = 3.905 Å) and on closely lattice matched orthorhombic (110) PrScO₃ (a_pc = 4.023 Å, where the subscript indicates pseudocubic notation), which has the same space group as SrSnO₃ [a_pc = 4.034 Å (Ref. 8)]. The lattice mismatch between SrSnO₃ and PrScO₃ is thus very small, −0.27%. Out-of-plane high resolution XRD scans around the 002_pc reflections are shown in Fig. 1(a). Thickness fringes are much more pronounced for the film on PrScO₃, consistent with a coherently strained film and smoother interfaces/surfaces. (S)TEM images of the SrSnO₃ films are shown in Fig. 2. No misfit dislocations were detected in the film on PrScO₃, consistent with a coherently strained film, whereas the film on SrTiO₃ relaxes by incorporation of periodically spaced misfit dislocations.

Reciprocal space maps (RSM) around the 103_pc reflection were used to determine the in- and out-of-plane lattice parameters for all (Ba_xSr_1−x)SnO₃ films. Examples are shown for SrSnO₃ in Figs. 1(c) and 1(d). On PrScO₃, the in-plane reciprocal lattice vectors of film and substrate align, indicating that the film is fully strained [Fig. 1(c)]. On SrTiO₃, the film is mostly relaxed, with a small residual compressive strain (−0.4%). The in-plane (a_ip) and out-of-plane (a_oop) lattice parameters were used to calculate the unstrained film lattice parameter (a₀) as a function of composition²⁶ 

where c₁₁ and c₁₂ are the film elastic constants and c₁₂/c₁₁∼ 0.24.^27,28a₀ is 4.041 ± 0.002 Å on PrScO₃ and 4.039± 0.006 Å on SrTiO₃, in close agreement with bulk SrSnO₃. Errors in a₀ (and thus also the errors for the composition in Fig. 3) were estimated from the standard deviation of two-dimensional Gaussian curves fitted to the diffraction peaks.

Out-of-plane x-ray diffraction scans of the 002 reflection of the Ba_xSr_1−xSnO₃ alloys are shown in Fig. 1(b). The shifts to lower angles with increasing x (Ba content) are consistent with the expected increase in lattice parameter (⁠$aBaSnO3$ = 4.116 Å). The composition of the films was estimated by comparing a₀, determined as described above, with bulk values from the literature.⁴ 

Ellipsometry measurements of (Ba_xSr_1−x)SnO₃ films were used to extract the optical absorption coefficient α.²⁵ Optical band gaps were then estimated from Tauc plots, i.e., the relation²⁹ 

where h is Planck's constant, A a constant, υ is the frequency, E_g the band gap, and n a constant that indicates the nature of the transition (i.e., direct/indirect, allowed/forbidden). Here, we use n = 2, corresponding to a direct allowed band gap. Although undoped BaSnO₃ could also be fit to an indirect model (n = 0.5), similar to Ref. 11, the absorption is orders of magnitude too high for a typical indirect band gap in a thin film.³⁰ Therefore, only the direct band gap should be extracted. Tauc plots for differently doped BaSnO₃ films and for SrSnO₃ are shown in Fig. 3(a). Figure 3(b) shows the extracted band gap values for all compositions. The band gap monotonously increases with decreasing x but does not follow a linear Vegard's law. Since the films on SrTiO₃ are (almost) completely relaxed, we expect no large strain effects on the measured band gaps. The measured band gap values can be compared with those reported in the literature; most data are for BaSnO₃. The measured band gap (3.36 eV) for the undoped MBE BaSnO₃ film is somewhat smaller than values reported for single crystals from ellipsometry (∼3.5 eV),¹³ thin films in ellipsometry and optical absorption,^10,11 and slightly larger than that of ceramics and single crystals characterized by optical absorption (∼3.1 eV).^7,12

Doping increases the measured optical band gap (Fig. 3), due to a pronounced Burstein–Moss shift, which is due to the increase in Fermi level. For a single, parabolic conduction band minimum, which is a good approximation for BaSnO₃, the position of the Fermi level (E_F) above the conduction band minimum (E_CBM) is given by

where m* is the effective mass (∼0.19 m₀,^18,m₀ is the free electron mass) and n_3D is the carrier density. For the two doping densities n_3D = 2.9 × 10¹⁹ and 1.5 × 10²⁰cm⁻³, $EF−ECBM$ is 0.18 and 0.55 eV, respectively. The fraction of ionized dopants was previously estimated to be ∼90%.¹⁸ These values are in close agreement with the increase in the optical band gap for these two samples, of 0.15 and 0.47 eV, respectively, relative to the undoped sample (see Fig. 3). In Ref. 19, a band gap renormalization (shrinking) of ∼0.4 eV is suggested for a sample doped to ∼10²⁰cm⁻³, which should have almost completely eliminated the Burstein–Moss shift. Thus the data reported here do not support a strong band gap normalization. This experimental result is also consistent with predictions from DFT.¹⁷ 

In summary, high-quality, MBE grown (Ba_xSr_1−x)SnO₃ films allow for developing band gap and strain engineered heterostructures with the perovskite stannates. They also provide a consistent picture of the relationship between their composition and optical properties. In particular, the band gap measurements of doped BaSnO₃ films are consistent with the light conduction band mass resulting in a strong Burstein–Moss shift, but only a small band gap renormalization. The much improved structural quality of SrSnO₃ films on a nearly lattice matched substrate, PrScO₃, as evidenced by XRD and TEM, augurs well for future improvements in mobility for BaSnO₃, if more closely lattice matched substrates that allow for similar reductions in extended defect densities, could be obtained.