Epitaxial growth of (BaxSr1−x)SnO3 films with 0 ≤ x ≤ 1 using molecular beam epitaxy is reported. It is shown that SrSnO3 films can be grown coherently strained on closely lattice and symmetry matched PrScO3 substrates. The evolution of the optical band gap as a function of composition is determined by spectroscopic ellipsometry. The direct band gap monotonously decreases with x from to 4.46 eV (x = 0) to 3.36 eV (x = 1). A large Burnstein-Moss shift is observed with La-doping of BaSnO3 films. The shift corresponds approximately to the increase in Fermi level and is consistent with the low conduction band mass.
Alkaline Earth stannates (ASnO3 where A = Ca, Sr, or Ba) have attracted significant interest for use as transparent conductors1,2 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.
(BaxSr1−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 × 10−5 Torr. 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 SnOx flux was set to a constant value of ∼1.5 × 10−6 Torr, and the (Ba + Sr) flux to ∼5.0 × 10−8 Torr. The (Ba + Sr)/SnOx 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 Kα 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 (apc = 4.023 Å, where the subscript indicates pseudocubic notation), which has the same space group as SrSnO3 [apc = 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 002pc 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 103pc reflection were used to determine the in- and out-of-plane lattice parameters for all (BaxSr1−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 (aip) and out-of-plane (aoop) 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 BaxSr1−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 ( = 4.116 Å). The composition of the films was estimated by comparing a0, determined as described above, with bulk values from the literature.4
where h is Planck's constant, A a constant, υ is the frequency, Eg 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 (EF) above the conduction band minimum (ECBM) is given by
where m* is the effective mass (∼0.19 m0,18,m0 is the free electron mass) and n3D is the carrier density. For the two doping densities n3D = 2.9 × 1019 and 1.5 × 1020 cm−3, 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 ∼1020 cm−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 (BaxSr1−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.
The authors thank Tiffany Kaspar, Scott Chambers, David Singh, Stefan Zollner, and Jim Allen for very helpful discussions. The work was supported by the U.S. National Science Foundation (Grant No. DMR-1409985) and the Extreme Electron Concentration Devices (EXEDE) MURI of the Office of Naval Research (ONR) through Grant No. N00014-12-1-0976. The TEM experiments were supported by the U.S. Department of Energy (Grant No. DEFG02-02ER45994) and the UCSB MRL, which is supported by the MRSEC Program of the U.S. National Science Foundation under Award No. DMR 1121053.