Electronic Structure and Defect Chemistry of Tin(II) Complex Oxide

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Electronic Structure and Defect Chemistry of Sn(II) Complex Oxide SnNbO Shota Katayama, Hiroyuki Hayashi, Yu Kumagai, Fumiyasu Oba, and Isao Tanaka J. Phys. Chem. C, Just Accepted Manuscript • DOI: 10.1021/acs.jpcc.6b01696 • Publication Date (Web): 20 Apr 2016 Downloaded from http://pubs.acs.org on April 27, 2016

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The Journal of Physical Chemistry

Electronic Structure and Defect Chemistry of Sn(II) Complex Oxide SnNb2O6

Shota Katayama*,†, Hiroyuki Hayashi**†, ‡,Yu Kumagaiǁ, Fumiyasu Oba†,ǁ, and Isao Tanaka† †

Department of Materials Science and Engineering, Kyoto University, Sakyo, Kyoto 606-8501, Japan

‡

Research Center for Low Temperature and Materials Science, Kyoto University, Sakyo, Kyoto 606-8501, Japan ǁ

Materials Research Center for Element Strategy, Tokyo Institute of Technology, Yokohama 226-8503, Japan

*E-mail: [email protected], TEL xx-81-75-753-5435 ** E-mail: [email protected], TEL xx-81-75-753-5435

ABSTRACT:

Sn(II) complex oxides have unique valence band structures due to the

contribution of the Sn-5sp orbitals. We investigate the fundamental electronic, optical, and defect properties of Sn(II) niobate (SnNb2O6) via first-principles calculations and the characterization of epitaxial thin films. The calculations reveal its characteristic valence band structure similar to that of SnO. SnNb2O6 is predicted to have an indirect-type band structure with an indirect gap of 2.41 eV and a direct gap of 2.55 eV. Epitaxial thin films of SnNb2O6 with smooth surfaces are fabricated on Al2O3 (0112)

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substrates using pulsed laser deposition. Experimental and theoretical absorption spectra consistently show an absorption threshold of ~2.5 eV. Both undoped thin films and doped sintered samples fabricated by a solid-state reaction show high electrical resistivities. Theoretical defect energetics suggests that the high resistivity is due to the charge compensation by oxygen vacancies and tin-on-niobium antisites.

Introduction Sn(II) oxides display unique electronic structures due to the presence of Sn-5sp electrons. Tin monoxide (SnO), a prototypical Sn(II) oxide with a litharge structure, exhibits p-type conductivity,1-3 which is partly due to the shallow valence band maximum (VBM) constructed from the hybridization of O-2p and Sn-5sp orbitals.4,5 First-principles calculations have predicted similar electronic structures for Sn(II) complex oxides (e.g., SnWO4, SnNb2O6, and Sn2Ta2O7).6,7 Although these compounds have been reported to show absorption thresholds in the visible light region and photocatalytic activities under visible light irradiation,8-10 little is known about their fundamental properties, including their absorption coefficients and electrical conductivity.

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The crystal structures of Sn(II) oxides are unique in many cases due to the presence of lone-pair electrons, similar to some Pb(II), Sb(III), and Bi(III) compounds.11-13 Among Sn(II) oxides, SnNb2O6 has an especially characteristic crystal structure.14 As shown in Figure 1a, SnNb2O6 is constructed by stacking Nb-O and Sn-O layers along the a axis; the Nb-O layers with a NbO6-octahedra network are similar to those of rutile (101), while the Sn-O layers have litharge (110)-like atomic arrangements (Figure 1b). Its valence band structure, which originates from the two-dimensional Sn-O structure, is of special interest. SnNb2O6 can be synthesized by calcining SnO and Nb2O5 in a vacuum or inert gas atmosphere.8,15,16 Mössbauer analyses indicate that samples fabricated by such methods contain a small amount of Sn(IV).15 This differs from other Sn(II) oxides such as SnWO4 and Sn2Nb2O7 in which partial oxidation of Sn(II) to Sn(IV) appears to be much more difficult to suppress.10,15 Recently, SnNb2O6 has attracted interest as a potential photocatalyst for water splitting. Hosogi et al. reported that SnNb2O6 has a photoabsorption threshold of 2.3 eV and a photocatalytic activity for H2 evolution from an aqueous methanol solution under visible light irradiation.8 They predicted that its VBM character is similar to that of SnO using first-principles calculations (i.e., the VBM composed of Sn-5sp and O-2p).7 However, their calculations were performed 3



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using the generalized gradient approximation (GGA), which tends to underestimate the band gaps of semiconductors and insulators, and the band structure around the band gap has not been discussed in detail. Additionally, the fundamental properties of SnNb2O6, including its electrical transport properties and optical absorption coefficient, have yet to be revealed. In this study, we investigate the electronic structure of SnNb2O6 using a combined computational and experimental approach. First-principles calculations using a hybrid density functional, which has been shown to describe the electronic structure of a variety of semiconductors more accurately than the local density approximation and GGA,17-22 are performed to predict the band structure, optical properties, and defect energetics. In addition, we report the epitaxial growth of highly oriented SnNb2O6 thin films for the first time and investigate their absorption coefficients and electrical conductivity. The possibility of carrier doping is discussed on the basis of the theoretical formation energies of relevant native point defects in SnNb2O6.

Methods Computational procedures. The calculations were conducted using the projector augmented-wave (PAW) method23 and the Heyd-Scuseria-Ernzerhof (HSE06) 4


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hybrid functional17-19 as implemented in the VASP code.24,25 A primitive cell with 18 atoms (Figure 2a) was taken from Ref. 14, which is registered in the Inorganic Crystal Structure Database26 (ICSD #202827). The lattice parameters and internal coordinates were relaxed within its symmetry of C2/c. A plane-wave cutoff energy of 550 eV and k-point sampling with a 2×2×3 mesh were used for geometry optimization. The Sn 5s, 5p, Nb 4p, 5s, 4d, O 2s, and 2p states were described as valence electrons. The path of the wave vectors in band structure diagrams was chosen using the method reported in Ref. 27. Optical absorption spectra were obtained via calculations of dielectric functions within the independent particle approximation. The electronic density of states (DOS) and dielectric functions were calculated using a 6×6×9 k-point mesh in combination with a reduced 2×2×3 mesh for the Fock exchange contribution. To calculate the defect formation energies, we constructed a 72-atom supercell (Figure 2b) by expanding a different primitive cell from the one shown in Figure 2a since an isotropic supercell shape is suitable to obtain a large distance between the defect and its periodic images in all directions. We considered the following defects: vacancies at the Sn, Nb, and three O sites (VSn, VNb, VO1, VO2, and VO3), cation antisites of Sn at the Nb sites (SnNb), and Nb at the Sn sites (NbSn), and interstitials at three kinds of sites with a large open space. We found that VO2 is the most energetically favorable 5



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among the three types of oxygen vacancies and, therefore, show only the results on VO2. Interstitials were excluded from investigation using the HSE06 hybrid functional because preliminary calculations using the Perdew-Burke-Ernzerhof (PBE) GGA28 indicated that their formation energies are much higher than the other defects. The defect charge states are set as follows; -2 to 0 for VSn, -5 to 0 for VNb, 0 to +2 for VOi (i=1, 2, and 3), -3 to 0 for SnNb, and 0 to +3 for NbSn. The internal atomic positions of the defect supercells were relaxed with cell shape and volume fixed. A plane-wave cutoff energy of 400 eV and a Γ-point centered 2×2×2 k-point sampling were employed for the relaxation. The formation energy of a defect is calculated as = { +

} − perfect − ∑ + ,

(1)

where is the total energy of a supercell with defect D in charge state q. perfect is the total energy of a perfect crystal supercell. is the number of atom i removed ( < 0) or added ( > 0) to form the defect, and is its chemical potential. The atomic chemical potential can vary in the range where the host SnNb2O6 phase is stable. Here we determine the chemical potentials using the calculated total energies. is the Fermi level, which can be treated as a variable that changes from the VBM (set to zero hereafter) to the conduction band minimum (CBM). For defects with occupied 6


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shallow donor states or unoccupied shallow acceptor states, band filling corrections were applied to recover the dilute defect and carrier concentration limit.29 In the calculations of charged defect supercells under three-dimensional periodic boundary conditions, large errors due to long-range Coulomb interactions between the defect charge, its periodic images, and background charge might make even qualitative predictions difficult. To reduce these errors, we consider the image-charge correction as

following Ref. 30. This correction is based on the scheme proposed by Freysoldt et al.31 but includes an extension so that the correction is effective even for crystals with anisotropy in the dielectric constants and defect supercells after atomic relaxation. We obtained a static dielectric tensor, namely the sum of the ion-clamped dielectric tensor (ϵele ) and ionic contribution (ϵion ) a finite electric field approach with HSE06 and density functional perturbation theory with PBE, respectively. The calculated ϵ11 , ϵ22, ϵ23 ( = ϵ32 ), and ϵ33 are 38.39, 126.73, 127.07, and 170.20, respectively. Using the theoretical defect formation energies, the defect concentration at absolute temperature T is obtained as = !exp (−

# $ % & '( )

),

7


(2)


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where ! is the concentration of the site for defect and *+ is the Boltzmann constant. The electron concentration in the conduction band and the hole concentration in the valence band are obtained following the Fermi-Dirac statistics as :

= ,;

= ,@: ()

-

9 ,

(3)

-

9 ,

(4)

2324 785( 6

2 32 ./01 4 785( 6

where () is the DOS, A+B is the energy level of the CBM, and VBM is that of the VBM. The concentrations of charged defects ( ) and carriers (> and ) are regulated by the charge neutrality condition as > − + ∑ = 0.

(5)

Solving equations (2)–(5) self-consistently determines the carrier concentrations, defect concentrations, and Fermi level.

Experimental procedures. SnNb2O6 thin films were fabricated by pulsed laser deposition (PLD) using a KrF excimer laser (λ = 248 nm, τ = 25 ns, Lambda Physik COMPex205). A sintered compact of an Sn-rich phase (Sn2Nb2O7) prepared by hot isostatic pressing was used as the target considering significant Sn evaporation from the growth front. A laser energy density of 1.5 J/cm2, a spot size of 2.0 mm2, and a pulse frequency of 5 Hz were used. The target-substrate distance was 65 mm. The pressure in 8


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the chamber was kept constant at 1.3 × 10-2 Pa by flowing oxygen gas during the deposition with a back pressure less than 5 × 10-4 Pa. The substrate temperature was 773 K. After the deposition, gas flow was terminated, and the samples were cooled to room temperature in the chamber. The selection of substrates is a crucial factor in epitaxial growth. Thus, a suitable substrate was explored from the viewpoint of the crystal structure of SnNb2O6. As mentioned above, SnNb2O6 exhibits a stacking structure along the a axis, where litharge (110)-like Sn-O layers and rutile (101)-like Nb-O layers are stacked. Although (110)-oriented SnO thin films have not been reported, epitaxial growth of rutile-TiO2 (101) on Al2O3 ( 0112 ) and rutile-SnO2 (101) on Al2O3 ( 0112 ) has been reported.32,33 Therefore, Al2O3 ( 0112 ) single crystals (Shinkosha, Co., Ltd.) were chosen as substrates, with which (100)-oriented epitaxial growth of SnNb2O6 is expected. Doped sintered samples [i.e., (Sn0.99A0.01)Nb2O6 (A = Li, Cu, Y, or Bi) and Sn(Nb0.99B0.01)2O6 (B = Ti, Ge, Zr, or W)] were synthesized at 1073 K by solid-state reaction between the powders of SnO, Nb2O5, and oxides of A or B in Ar atmosphere. The crystal structure and orientation of the films were investigated by five-axis X-ray diffraction (XRD) on a Rigaku SmartLab (Cu-Kα1, 40 kV, 30 mA) with an asymmetric Ge (111) two-crystal incidence monochromator. The film compositions 9



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were measured using a wavelength-dispersive X-ray spectrum (WDS) analyzer (Oxford instruments INCA Wave-500) on a scanning electron microscope (Hitachi S-3500H). The film thickness, surface roughness, and density were estimated by X-ray reflectivity analysis. The morphology of the film surface was observed using an atomic force microscope (AFM) (Shimadzu SPM-9700). The transmittance and reflectance spectra were obtained with a Shimadzu Solid Spec-3700DUV. The absorption coefficients (α) of the films were evaluated from the spectra in consideration of the light interference and multiple reflections at the surfaces and the film/substrate interface. The valence electronic structure was investigated by X-ray photoelectron spectroscopy using Al-Kα radiation (hν=1486 eV) on a JEOL JPS-9010TRX. Energy calibration was performed using the C-1s peak of a surface contaminant because the samples exhibited charging. The electrical resistivity of the film and sintered samples was measured by the van der Pauw method using a Resitest8300 (Toyo Corporation).

Results and Discussion Fundamental properties of SnNb2O6 from first-principles calculations. The optimized lattice constants and band gaps calculated with the PBE-GGA as well as the HSE06 hybrid functional are shown in Table 1. HSE06 reproduces the lattice parameters 10


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better than the PBE-GGA, although both tend to overestimate. While the direct band gap obtained using the PBE-GGA is significantly smaller than the experimentally reported optical absorption threshold of 2.3 eV,8 HSE06 reproduces it well; note that the electronic transition over the direct gap is predicted to be parity-allowed and, therefore, the absorption threshold energy corresponds to the direct gap value, as detailed later. Hereafter we discuss the electronic structures, optical spectra, and defect formation energies using the results of the HSE06 calculations. The calculated total and projected DOS of Sn, Nb, and O are shown in Figure 3. The VBM of SnNb2O6 is constructed from the hybridization of Sn-5sp and O-2p in contrast to that of typical oxides where the dominant component is O-2p. This electronic structure is a characteristic of Sn(II) oxides. On the other hand, the CBM is constructed mainly from Nb-4d. The band structure exhibits an indirect band gap of 2.41 eV with the VBM at the Y point and the CBM at a low symmetry point around the line connecting the X and Γ points (Figure 4a). The minimum direct gap of 2.55 eV is given at the Y point. The bands located between –1.7 eV and the VBM are isolated from the lower bands and are like intermediate states. Despite the layered crystal structure, the anisotropy in the curvature of this band is insignificant. Figure 4b shows the calculated absorption spectra assuming the light incident 11



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perpendicular and parallel to the a axis. The spectral threshold energies correspond to a direct band gap of 2.55 eV because the electronic transition over the direct gap is parity-allowed. Reflecting the layered crystal structure, the spectra show anisotropy. The absorption coefficient for the light incident with the electric field parallel to the a axis rises steeply than that for the electric field perpendicular to the a axis and reaches 105 cm-1 near the threshold.

Fabrication and characterization of SnNb2O6 epitaxial thin films. Optimizing the growth conditions is crucial to fabricate a single SnNb2O6 phase thin film. In particular, the substrate temperature and oxygen partial pressure during the growth largely affect the crystal phases. A substrate temperature below 673 K leads to non-crystalline films, while that above 973 K causes significant evaporation of Sn from the growth front. Too low oxygen pressure yields a Nb(IV) oxide phase of NbO2, whereas too high pressure gives SnO2. In addition, a small laser fluence near the ablation threshold is necessary to obtain a single phase of SnNb2O6. Figure 5a shows the XRD 2θ-θ profile of an SnNb2O6 thin film grown at the optimized conditions of 773 K and 1.3 × 10-2 Pa. All of the peaks are assigned to the diffraction from SnNb2O6 h00 and the substrate. Figure 5b is a magnification around the 12


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600 peak of SnNb2O6. A clear fringe structure forms around the peak, reflecting the high orientation of the film and the low dispersion of its out-of-plane lattice constant. The film thickness is estimated to be 20 nm from the oscillation cycles. The out-of-plane lattice constant is evaluated as 17.12 Å, which is close to the reported bulk value of 17.093 Å.14 Figure 5c shows the φ scans of the 620 diffraction of the film and 001 of Al2O3. The film is epitaxially grown on the substrate with an in-plane orientation relationship of SnNb2O6 [010] // Al2O3 1010 and the coexistence of 180-degree rotated domains. This in-plane orientation relationship is consistent with that predicted from the (101)-oriented rutile films (rutile-TiO2 // Al2O3, or SnO2 // Al2O3). The in-plane lattice parameters of the film evaluated from the XRD measurements for the 222, 311, 320, and 600 diffractions are b = 4.9 Å, c = 5.6 Å, and β = 90 degrees, which are also close to the bulk SnNb2O6 values of b = 4.877 Å, c = 5.558 Å, and β = 90.85 degrees.14 Figure 5d compares the atomic arrangements of SnNb2O6 (100) and Al2O3 (011 2). The mismatches between the film and the substrate are 2.7% along the b axis of SnNb2O6 and 8.9% along the c axis. The strain in epitaxial growth due to these mismatches is almost fully relaxed in the present case since the in-plane lattice parameters of the film are very close to those of the bulk.

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The film is approximately stoichiometric SnNb2O6 despite the use of an Sn2Nb2O7 target. The atomic fraction of Sn and Nb obtained by the SEM-WDX analysis are 36% and 64%, respectively, with a standard error of about ±3%. In our former study, deposition on yttria-stabilized-zirconia (100) substrates under the same conditions resulted in the growth of Sn2Nb2O7-related compounds in which the Sn/Nb ratio is close to unity.34 Thus, the substrate largely affects both crystal structure and composition of Sn-Nb-O films. Figure 6a shows the X-ray reflectivity of the SnNb2O6 film and a simulated profile. The simulation is based on the Parratt’s method,35 and the best fit is obtained with a film thickness of 20.5 nm, a density of 5.8 g/cm3, and a root mean square (RMS) surface roughness of 1.0 nm. The thickness is consistent with the value estimated from the XRD, and the density is coincident with the ideal one of 5.74 g/cm3. An AFM image of the film surface is shown in Figure. 6b. The surface exhibits a granular morphology, indicating crystal growth in the island mode. The RMS surface roughness is evaluated to be 0.9 nm from the AFM image, which is comparable to that from the X-ray reflectivity analysis. The optical property of SnNb2O6 was measured using a 10-nm thick epitaxial thin film. Figure 7a shows the transmittance and reflectance spectra of the SnNb2O6 14


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film with an Al2O3 substrate. There is a characteristic decrease in the transmittance around 500 nm, which is in a visible light region. The reflectance spectra were measured in two arrangements: light incident from the film side and the substrate side, respectively. The difference in the two reflectance spectra found at a shorter wavelength is ascribed to absorption by the film. Figure 7b presents the absorption coefficient evaluated from the transmittance and reflectance along with theoretical spectrum. The calculated absorption coefficient is for the light incident with the electric field perpendicular to the [100]. This comparison is reasonable because the experimental spectrum is measured for the (100)-oriented film with light incident from a direction almost perpendicular to the surface. The absorption threshold of the film is ~2.5 eV, which agrees well with that of the calculated spectrum of ~2.55 eV. Both the experimental and theoretical absorption coefficients reach 105 cm-1 at ~3 eV. Figure 8 shows the XPS spectrum of the SnNb2O6 film compared with that of an SnO film exhibiting p-type conductivity fabricated by PLD.3 It should be noted that the difference between the Fermi level and VBM is not exactly equal to that of bulk because of short escape depth of photoelectrons. In this study, the VBM positions are estimated by the thresholds of the XPS spectra. The Fermi level of the SnNb2O6 is

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higher than the VBM by approximately 1.3 eV. This differs from that of the p-type SnO, which is almost at the VBM. The SnNb2O6 film shows no measurable electrical conductivity, and the resistivity is estimated to be higher than 105 Ωcm, which is consistent with the Fermi level position by the XPS. In addition, doped sintered samples also show high resistivities. Considering the valence band structure with a large band dispersion near the VBM, the hole mobility should not be significantly low. Therefore, it is conceivable that the doped carriers are compensated by the formation of charged native point defects. The carrier compensation is discussed using theoretical defect formation energies and concentrations in the following section.

Native point defect formation in SnNb2O6. The defect formation energies depend on the atomic chemical potential as given in Eq. (1). However, SnNb2O6 shows a narrow stable region in the chemical potential space (Figure 9a); some relevant binary and ternary phases, such as SnO and Sn2Nb2O7, are calculated to be metastable using the HSE06 hybrid functional and do not appear in the diagram. The atomic chemical potentials are therefore represented by a condition of ∆EF = 0 eV, ∆GH = -1.30 eV, and ∆I = -2.63 eV hereafter. Figure 9b shows the defect formation energies 16


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calculated under these chemical potential conditions as a function of the Fermi level. The origin of the Fermi level is set at the VBM, and the upper limit of 2.41 eV corresponds to the CBM. Only the charge states that show the lowest formation energies against a given Fermi level position are presented. The slope of each line corresponds to the charge state of the defect, as represented in Eq. (1). Without carrier compensation by other defects, the formation of defects in positive charge states simultaneously provides electrons to the system (donor) and that of negatively charged defects gives holes (acceptor). On the other hand, these donor-like and acceptor-like defects may act to compensate holes and electrons, respectively. Figure 9(b) shows that some charged defects exhibit negative formation energies at a Fermi level position within the band gap. This means that the carrier compensation by charged defects, which spontaneously occurs in the case that the formation energies are negative, confines the Fermi level even when donor or acceptor impurities are doped36. The lower limit of the Fermi level (toward p-type doping) is 1.0 eV above the VBM, +2 which is pinned by the VO2 formation, and the upper limit (toward n-type doping) is

-1 0.3 eV below the CBM due to the SnNb formation. Thus, these defects should prevent a

high carrier concentration and consequently, a high conductivity, especially when aiming at p-type doping. This behavior is quite different from SnO that shows p-type 17



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conductivity even without intentional doping,1-3 where the sources of carriers have been attributed to VSn and complexes of H and VSn.5,37,38 Figure 10 shows temperature dependence of the equilibrium defect and carrier -1 concentrations. The dominant defects are V+2O and SnNb . As a result of the balance of

these defects, the equilibrium electron and hole concentrations are rather low. The temperature dependence of the Fermi level is found to be small, and the Fermi level is located at approximately 1.4 eV above the VBM through 300 K to 1200 K. This value is close to the estimated value of 1.3 eV for the SnNb2O6 film from the XPS measurement. Furthermore, as discussed above, the Fermi level control by doping should be limited within a narrow range around the middle of the band gap under thermal equilibria. Thus, the experimentally observed high resistivities of undoped and doped SnNb2O6 can be attributed to the charge compensation by native point defects. Although SnNb2O6 shows a characteristic valence band structure similar to that of SnO, the trend of defect formation is quite different from SnO and carrier doping is difficult under thermal equilibria.

Conclusions

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The electronic and defect structure of SnNb2O6 is investigated via first-principles calculations as well as the fabrication and characterization of epitaxial thin films. The calculations using the HSE06 hybrid functional well reproduce the lattice parameters and the photoabsorption threshold. The VBM of SnNb2O6 is composed of Sn-5sp and O-2p orbitals. SnNb2O6 is predicted to have an indirect-type band structure with an indirect gap of 2.41 eV and a direct gap of 2.55 eV, where the electronic transition over the direct gap is parity-allowed. Additionally, epitaxial SnNb2O6 thin films are fabricated on Al2O3 (0112) substrates by means of PLD. The XRD analyses reveal that the films grown under optimized conditions are composed of a single phase and highly oriented on the substrates. The absorption threshold of 2.5 eV is consistent with the calculated value, and the absorption coefficient reaches 105 cm-1 at 3.3 eV. The undoped films as well as the doped sintered SnNb2O6 samples show high resistivities. The theoretical analyses of -1 native point defects suggest that the formation of V+2O and SnNb confine the Fermi level

around the middle of the band gap, which is consistent with the XPS measurement. Although SnNb2O6 shows a characteristic valence band structure similar to that of SnO, the defect chemistry is quite different from SnO and carrier doping should be challenging under thermal equilibria. 19



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Acknowledgements This work was supported by Grants-in-Aid for JSPS fellows (Grant numbers 243018 and 242558), Scientific Research on Innovative Areas "Nano Informatics" (Grant number 25106005) from JSPS, and the MEXT Elements Strategy Initiative to Form Core Research Center. The crystal structures in Figs. 1, 2, and 5(d) were drawn using the VESTA code.39 The chemical potential diagram in Fig. 9(a) was plotted using the CHESTA code.40

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Figures

Figure 1. (a) Crystal structure of SnNb2O6. (b) Comparison of the atomic arrangements between the Sn-O layer and litharge (110) and between the Nb-O layer and rutile (101).

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Figure 2. (a) Primitive cell used in the calculations of fundamental bulk properties (solid line). (b) 72-atom supercell used in the defect calculations.

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Figure 3. Calculated total and projected electronic density of states of SnNb2O6. The origin of the energy is set at the VBM.

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Figure 4. (a) Calculated electronic band structure diagram of SnNb2O6 and (b) its absorption spectra. The light incident with the electric field parallel and perpendicular to the a axis is considered for the absorption spectra. The former corresponds to the stacking direction of the Sn-O and Nb-O layers.

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Figure 5. (a) XRD 2θ -θ profile of an SnNb2O6 thin film and (b) its magnification around the 600 diffraction of SnNb2O6. (c) XRD φ profile and (d) a comparison of the atomic arrangements of SnNb2O6 (100) and Al2O3 (011 2).

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Figure 6. (a) X-ray reflectivity profile of an SnNb2O6 thin film along with a simulated profile using a film thickness of 20.5 nm, a density of 5.8 g/cm3, and an RMS surface roughness of 1.0 nm. (b) AFM image of an SnNb2O6 thin film with a surface area of 3 µm × 3 µm.

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Figure 7. Optical properties of an SnNb2O6 thin film. (a) Experimental transmittance and reflectance spectra. (b) Experimental absorption spectrum compared with the theoretical spectrum.

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Figure 8. XPS spectrum of an SnNb2O6 thin film compared with that of a p-type SnO thin film.

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Figure 9. (a) Chemical potential diagram of the Sn-Nb-O system obtained using the calculated total energies. The chemical potentials are referenced to those at the standard states, which are taken to be the Sn and Nb metals and the O2 molecule. (b) Calculated formation energies of native point defects in SnNb2O6 as a function of the Fermi level. The slope corresponds to the charge state, and the most stable charge states with respect to the Fermi level are presented for each defect. The equilibrium Fermi level at 300 K is indicated by the dotted line. The positions of transition levels are depicted with filled black circles.

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Figure 10. Temperature dependence of defect and carrier concentrations simulated under thermal equilibrium.

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Table 1. Comparison of the lattice parameters and band gaps of SnNb2O6 calculated using the PBE-GGA and HSE06 hybrid functionals with the experimental values.8,14

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TOC figure of this manuscript.

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Electronic Structure and Defect Chemistry of Tin(II) Complex Oxide

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