SrNbO3 as a transparent conductor in the visible and ultraviolet spectra

Few materials have been identified as high-performance transparent conductors in the visible regime (400–700 nm). Even fewer conductors are known to be transparent in ultraviolet (UV) spectrum, especially at wavelengths below 320 nm. Doped wide-bandgap semiconductors employed currently as UV transparent conductors have insufficient electrical conductivities, posing a significant challenge for achieving low resistance electrodes. Here, we propose SrNbO3 as an alternative transparent conductor material with excellent performance not only in the visible, but also in the UV spectrum. The high transparency to UV light originates from energetic isolation of the conduction band, which shifts the absorption edge into the UV regime. The standard figure of merit measured for SrNbO3 in the UV spectral range of 260–320 nm is on par with indium tin oxide in the visible, making SrNbO3 an ideal electrode material in high-performance UV light emitting diodes relevant in sanitation application, food packaging, UV photochemotherapy, and biomolecule sensing. Optically transparent electrodes with high electrical conductance are essential for the implementation of optoelectronics, but current technology performs poorly in the ultraviolet regime. Here, SrNbO3 is proposed as an alternative material due to its high figure of merit in the ultraviolet range.

T he demand for high performance transparent conductor materials has significantly increased because the unique combination of electrical and optical properties-allowing light to effectively cross the path of electric conduction-is needed for top electrodes used in light emitting diodes (LEDs), photovoltaic cells and optical detectors. Up until now, the focus has been on high optical transparency in the visible spectrum while maintaining a high electrical conductivity. Many applications require shorter wavelength light, such as solar blind detection in the range of 240-280 nm 1 , ultraviolet (UV) curing (260-320 nm) 2 , biomolecule sensing (250-400 nm) 3 , UV germicidal irradiation in the upper UV range (260-280 nm) 4 , UV lithography (248 nm) 5 , UV phototherapy (ultraviolet B (UVB), 280-315 nm) 6 , photochemotherapy (ultraviolet A (UVA), 315-400 nm) 7 , and light sources for plant growth stimulating the secondary metabolism by exposure to radiation in UVB 8 . This wide application space has driven research in the area of UV LEDs as environmentally benign alternative over conventional UV light sources, such as low-pressure mercury lamps, offering higher efficiency, longer lifetime, and fast switching 9,10 .
In contrast to the high external quantum efficiencies (EQEs) of 45-96% achieved for LEDs emitting in the visible (400-700 nm) and UVA spectrum [11][12][13][14][15] , LEDs emitting deeper in the UV have significantly lower EQEs of only around 1% [16][17][18][19] , attributed to poor hole injection 20 , and high defect densities of the wide band gap semiconductor in the active region 21 . Another roadblock towards a higher EQE is the lack of a transparent electrode material with high electrical conductivity and high optical transparency in the deeper UV range that has similar performance to transparent conductors in the visible 22 . Indium-tin oxide (ITO), which is the most widely used transparent electrode, has a strong absorption edge near 360 nm rendering it unsuitable as a UV transparent electrode 23,24 . Currently proposed visible transparent conductors, such as oxide-metal-oxide heterostructures, e.g. ITO/Cu/ITO or indium zinc oxide (IZO)/Ag/ IZO 25,26 , transparent conducting oxide (TCOs), such as Zn-In-Sn-O multicomponent oxides and indium-free Al and Ga-doped ZnO films 27,28 , and ultrathin metallic films, such as Ag, Ni and Cr [29][30][31] , lack high transmittance in the deep UV region. Considerable efforts have been undertaken to synthesize deep UV transparent conductor thin films by utilizing ultrawide bandgap semiconductors, such as β-Ga 2 O 3 32,33 and ZnGa 2 O 4 34,35 . Although these materials possess high transmittance in the UV range due to their large band gaps of about 4.5 36 and 5.0 eV 37 , respectively, their electrical conductivities are orders of magnitude lower than degenerately doped ITO. Given the lack of high performance UV transparent conductors, recent improvements of UV LEDs have been achieved utilizing costly flip-chip designs 38 , in which a metal reflector enhances the light extraction by guiding the emission towards transparent sapphire substrate, resulting in increased EQEs typically ranging between 3% and 10% [39][40][41] , and up to 20% EQE at a wavelength of 275 nm 42 . Ultimately, alternative materials options for UV transparent electrodes are needed to enhance EQEs of UV LEDs 43,44 .
We propose the correlated metal SrNbO 3 as an alternative UV transparent conductor that shows excellent performance in both the visible and the UV regime from 260 to 320 nm. The design rule of this UV transparent conductor is based on taking advantage of the energetically isolated conduction band originating from the Nb 4d orbitals, and a sizeable electron correlation present in SrNbO 3 , as first proposed by Zhang et al for the vanadates in the visible spectrum 45 . In correlated metals, manybody effects arising from strong electron-electron interactions affect transport properties and optical response of the carriers and are quantified by the renormalization constant Z k . If the electron interaction strength is negligible (Z k = 1), itinerant carriers respond like a free electron gas; if Z k = 0 as a consequence of a strong electron interaction, all free carriers are localized at lattice sites (Mott insulator); and if the renormalization constant is between these limiting cases (0 < Z k < 1) electrons maintain their itinerant character but their dynamic properties, such as the carrier effective mass m*, have to be renormalized 46 . For correlated metals the effective mass m * ¼ m * b =Z k is increased relative to the band effective mass m * b by the inverse of the renormalization constant. As a consequence, the reduced plasma frequency is shifted towards the IR despite a metal-like carrier concentration n, with ε 0 and ε r the vacuum and relative permittivity, and e the elemental charge. Although the increase in effective mass somewhat reduces the electrical conductivity σ ¼ enμ ¼ e 2 τ n=m * À Á , with carrier mobility μ and electron scattering time τ, typical electrical conductivities 45,47 of correlated metals were found to be about one order of magnitude higher than that of ITO and more than three orders of magnitude higher than those of doped β-Ga 2 O 3 33,48 and ZnGa 2 O 4 34,35 .
While correlated oxides with perovskite structure, like SrVO 3 , were experimentally verified as an excellent alternative to conventional transparent conductors, the absorption edge was located at about 2.9 eV (427 nm), causing a sizeable loss in the average optical transparency in the visible range. The large absorption was identified to originate from an interband transition from oxygen 2p bands forming the valence band to the unoccupied states of the conduction band derived from the t 2g orbitals of the transition metal element vanadium. This interband absorption edge could be potentially shifted to higher energy if the electronegativity difference (Δχ) between the transition metal cation and oxygen anion would be larger. Choosing a less electronegative transition metal with larger Δχ to oxygen and similar electronic configuration would increase the energy difference between O 2p and transition metal t 2g bands, causing the absorption edge to occur at higher photon energies. Replacing the vanadium cation (V 4+ ) by the isoelectronic niobium (Nb 4+ ) with a smaller electronegativity of niobium (1.690 for Nb 4+ compared to 1.795 for V 4+ ) 49 , Δχ becomes larger by~6% and the transparent window can potentially be widened by pushing the absorption edge beyond the visible and into the UV regime. Upon substituting vanadium by niobium not only a blue-shift of the absorption edge, but also a reduction of the electron correlation strength is expected. The size of d-orbitals is larger for Nb 4+ compared to V 4+ , so that the orbital overlap and thus the bandwidth W of the conduction band is larger for SrNbO 3 despite its larger lattice parameter of a = 4.02 Å, compared to SrVO 3 with a = 3.84 Å. The consequence of a smaller electron correlation strength is a renormalization constant closer to unity, and thus a smaller m*. This in turn decreases the correlation induced red-shift of the reduced plasma frequency and might reduce optical transparency of SrNbO 3 at long wavelengths of the visible spectrum.
Here we present a combined first principles calculation and experimental study to demonstrate the potential of SrNbO 3 as UV transparent conductor material. A thickness series of SrNbO 3 films was grown and electrical properties were determined from Hall effect and conductivity measurements. The dielectric function of SrNbO 3 was measured using spectroscopic ellipsometry and electron correlation strength was extracted applying the extended Drude model. Good agreement between experiment and theoretical prediction was obtained. The figure of merit for transparent conductors was determined for SrNbO 3 in the visible and UV spectral range from 260 to 320 nm to be in the range of mid and low 10 −3 Ω −1 , respectively. These values are comparable with indium-tin oxide in the visible, but one order of magnitude higher in the UV, rendering SrNbO 3 as superior transparent conductor in this spectral range.

Results
Density functional theory and dynamical mean field theory. Motivated by these trends we performed density functional theory (DFT) and dynamical mean-field theory (DMFT) calculations to quantify the potential of SrNbO 3 as a visible and UV transparent conductor 50,51 , Fig. 1a shows the calculated band structure of SrNbO 3 , which is found to be qualitatively similar to isoelectronic SrVO 3 seen in Fig. 1b. Three bands originated from the t 2g manifold of the Nb 4d orbital were intersected by the Fermi level, giving rise to metallic conduction. The valence bands derived from the O 2p orbitals were well below the Nb 4d bands. An energy gap between the valence band maximum and the conduction band minimum of about 2.3 eV was obtained, considerably larger than the energy gap calculated for SrVO 3 of about 1 eV. The interband absorption edge originated from a strong interband transition, either from occupied states of the O 2p bands to unoccupied states of Nb 4d t 2g bands or from occupied states of Nb 4d t 2g bands below the Fermi level to higher lying unoccupied bands derived from the Nb 4d e g and Sr 5s orbitals. For electrons to transition between occupied O 2p and unoccupied Nb 4d t 2g states photon energies larger than 4 eV were needed, while interband transition energies from occupied Nb 4d t 2g to unoccupied Nb 4d e g and Sr 5s states were~2.5-3 eV. The energy separation between the individual bands was considerably larger compared to SrVO 3 , where transitions from occupied O 2p to unoccupied V 3d t 2g states already occurred at about 2.7 eV, while interband transition energies from occupied V 3d t 2g to unoccupied V 3d e g already occurred at about 2.2 eV, albeit with a small dipole matrix element 45 . The direct comparison of DFT results with DMFT calculations for SrNbO 3 (Fig. 1a, c) and SrVO 3 (Fig. 1b, d) also confirmed the reduced correlation strength of SrNbO 3 , resulting in a larger renormalization constant (Z k ∼ 0.72) and thus a smaller overall reduction of the conduction band width W compared to SrVO 3 (Z k ∼ 0.55) 52 . This is seen by comparing the conduction band widths obtained from DFT and DMFT for both materials shown in Fig. 1. For clarity the 1 st Brillouin zone of tetragonally distorted perovskite crystals is shown in Fig. 1e. The reduced correlation strength in SrNbO 3 was attributed to the increased size of the 4d orbitals compared to 3d orbitals in SrVO 3 , giving rise to a larger orbital overlap despite a larger lattice parameter. The correlation induced red-shift of the reduced plasma frequency marking the reflection edge of carriers is therefore somewhat smaller for SrNbO 3 .
Electrical Characterization of SrNbO 3 Thin Films. After confirming the potential of SrNbO 3 as a transparent conductor using first principle calculations, we experimentally investigated the electrical and optical properties of SrNbO 3 by growing a series of films with varying thickness on KTaO 3 substrates. The sheet resistance (R s ) as a function of thickness is shown in Fig. 2a. The line fitted through the data takes into account the Fuchs-Sondheimer effect 53,54 for electron surface scattering (see Supplementary Note 1). The SrNbO 3 films with thicknesses in the range of 10-60 nm had sheet resistance values between 67.5 Ω/sq and 7.3 Ω/sq and the films' electrical resistivities varied between 6.9 × 10 −5 Ω cm and 3.8 × 10 −5 Ω cm. The variation was attributed to a larger surface scattering contribution for thinner films. Note that the residual resistivity ratios (RRR) were relatively small, as can be seen from the temperature dependent resistivity curves for SrNbO 3 films with 23 nm and 37 nm thickness, shown in the inset of Fig. 2a. The RRR values were 1.6 and 3.2, respectively, indicating that temperature independent scattering from defects significantly affected the electric conductivity. Nevertheless the sheet resistance values measured for SrNbO 3 thin films are comparable to sheet resistance values of other high-performance transparent conductors in the visible spectrum 28,29,45,55,56 and were about three orders of magnitude lower compared to current UV transparent conductor materials 32,35 . Figure 2b show thickness dependence of carrier mobility μ and carrier concentration n for the SrNbO 3 thin films. An average mobility value of~8 cm 2 V −1 s −1 was determined at room temperature, comparable to values of other correlated metals, such as SrVO 3 and CaVO 3 45 , and about an order of magnitude lower than those of ITO and conventional TCOs 28 . Typical carrier concentrations were around 1 × 10 22 cm −3 , about a factor of two smaller than carrier concentration measured for SrVO 3 , but over one order of magnitude higher than conventional TCOs, and UV transparent conductor in particular. While the highest carrier concentration reported for Ga 2 O 3 was on the order of low 10 20 cm −3 with a carrier mobility of 50 cm 2 V −1 s −1 57,58 , typical values for ZnGa 2 O 4 were similar with carrier concentrations not higher than 10 20 cm −3 and carrier mobilities of~80 cm2 V −1 s −1 59 . The much lower carrier mobility of SrNbO 3 was overcompensated by the high carrier concentration present, giving rise to superior electrical properties compared to conventional UV transparent conductors. The relatively small effect of resistivity increase arising from surface scattering in SrNbO 3 is attributed to the short electron mean-free path (EMFP) Λ, which was estimated using the Sommerfeld model and experimental values for carrier mobility and carrier concentration: Λ ¼ hÁμ e 3π 2 n ð Þ 1=3 (see Supplementary Note 1) 60 . For the films investigated an average EMFP of (3.5 ± 0.7) nm was found, which was comparable to those of transparent correlated metals SrVO 3 (Λ = 5.6 nm) and CaVO 3 (Λ = 3.9 nm) 45 , but much lower than those of conventional metals, such as silver (Λ = 52 nm) 61 . This small EMFP allows for more aggressive thickness scaling.
Optical characterization of SrNbO 3 thin films. Optical properties of SrNbO 3 films were characterized by spectroscopic ellipsometry at room temperature. Figure 2c-f show the complex dielectric function (ε = ε 1 + iε 2 ) measured for three SrNbO 3 films with thicknesses of 10, 23 and 29 nm. In addition, the dielectric function calculated from DFT is shown for comparison as well. Fig. 2c, e show the real and imaginary part of the dielectric function in the infrared (IR) range from 20 μm down to 800 nm, Fig. 2d and f show ε 1 and ε 2 from 800 nm down to 200 nm across the entire visible range all the way into the UV. The IR range from 20 μm to 800 nm was dominated by a Drude peak. The screened plasma energy (ħω p ) extracted from the experiment at ε 1 (ω) = 0 was (1.98 ± 0.03) eV. This value was smaller than the reduced plasma energy of 2.15 eV 52 found from DFT. Taking the mass renormalization due to electron correlation effects into account from the comparison of band widths of SrNbO 3 calculated by DFT and DMFT, the theoretical value of the reduced plasma frequency is corrected to a smaller value of 1.82 eV. The experimental determination of renormalization constant Z k from electron correlation effects extracted from the extended Drude model 62,63 was somewhat higher (Z k = 0.89 ± 0.02) than the theoretically prediced value of 0.72 (see Supplementary Note 2 and 3). Using the Z k value extracted from experiment gave a corrected reduced plasma frequency of (1.91 ± 0.04) eV, which was in better agreement to the measured screened plasma frequency, indicating that the calculated correlation strenght might be slighlty overestimated. In the case of SrNbO 3 films the correlation induced red-shift was not sufficient to push the carrier reflection edge completely into the IR range, but it helped increasing the transparency within the visbible spectrum at long wavelengths. It is shown in Fig. 2f that the main interband absoption edge was experimentally found at around 4.8 eV (∼260 nm), in very good agreement with DFT predictions. Compared to SrVO 3 , the interband absorption of SrNbO 3 was blue-shifted by over 1.5 eV into the UV range. The real and imaginary part of the dielectric function experimentally determined for the SrNbO 3 films were small in the visible and UV region up to the absorption edge near 4.8 eV, indicating a relatively low optical absorption coefficient. The small absorption peak at~2.7 eV obtained in the DFT calculation was originated by a weak interband transition from the t 2g to the e g band. A similar peak was also predicted for SrVO 3 , but was not experimentally found in either material system. It is not clear why this absorption peak was not measured for SrNbO 3 films, and we speculate that the sizeable defect concentration present in the films, which gave rise to relatively low RRR values, also affected the optical properties.

Discussion
The performance of SrNbO 3 as transparent conductor was evaluated using the Figure of Merit (Φ TC ) proposed by Haacke 64 Φ TC = T 10 /R s with optical transmittance T and sheet resistance R s . Figure 3a shows the film thickness dependence of Φ TC calculated in the visible range (400-700 nm), and for the UV spectrum from 260 to 320 nm, encompassing the entire UVB range (280-315 nm), along with results from SrVO 3 and ITO 45 .
The transmittance of the films were calculated from the dielectric function by assuming normal incidence and a freestanding film including surface reflections and multiple interference effects (see Supplementary Note 4). Since the transmittance varied with wavelength the values used were averaged over the spectrum of interest. Thickness-dependent effects on sheet resistance, such as surface and grain boundary scattering were considered in the calculation as well (see Supplementary Note 5). First, the discussion is focused on the performance of SrNbO 3 in this visible spectrum. Maximum Φ TC values of 5 × 10 −3 Ω −1 were found at a film thickness of 10 nm, about a factor of two higher than SrVO 3 at similar thickness, and a factor of three higher than the best ITO with Φ TC of about 1.6 × 10 −3 Ω −1 at a thickness of 150 nm 45 . The pronounced minimum in Φ TC of ITO was due to constructive interference of light reflected at both surfaces of a freestanding film. The higher Φ TC values of SrNbO 3 and the shift of the maximum of the Φ TC curve toward larger thickness compared to SrVO 3 was indicative that the optical properties of SrNbO 3 were better. Figure 3b shows a direct comparison of the transmission calculated from the dielectric function for 10-nmthick SrNbO 3 and SrVO 3 films. While SrNbO 3 has a lower transmission in the visible spectrum at longer wavelengths, much higher transmission in the blue spectrum led to an overall higher optical transmission in the visible range. This improvement in optical properties even compensated for the somewhat higher sheet resistance of SrNbO 3 (68 Ω/sq.) at a film thickness of 10 nm compared to SrVO 3 (R s = 45 Ω/sq.). This shows that SrNbO 3 is a competitive transparent conductor material in the visible range. The transmission curve further shows that SrNbO 3 has acceptable transmission values in the UV spectrum from 320 to 260 nm. Fig. 3a shows the thickness dependence of Φ TC for SrNbO 3 , SrVO 3 and ITO determined for this UV range. For all transparent conductor materials considered the figure of merits were smaller and the maximum of the Φ TC curves shifted towards smaller film thickness, indicating a reduced optical performance in the UV compared to the visible spectrum. The effect was much less for SrNbO 3 films, specifically the Φ TC value for 10-nm-thick films were still above 10 −3 Ω −1 and thus comparable with ITO performance in the visible. In contrast, 10-nm-thick SrVO 3 the Φ TC was reduced by about two orders of magnitude, rendering it unsuitable for UV applications. ITO had a maximum Φ TC at a thickness of~60 nm, albeit an order of magnitude lower than the highest Φ TC measured for SrNbO 3 . The figure of merit for ultrawide band gap semiconductors like Ga 2 O 3 were estimated to be in the mid 10 −7 Ω −1 range due to their low electrical conductivity. Furthermore, large dopant concentration of Sn in β-Ga 2 O 3 on the order of 10% resulted in a room temperature resistivity of only about 10 −1 Ω cm with carrier mobilities of~50 cm 2 V −1 s −1 and a low carrier concentration of about 10 18 cm −348 . Increasing amounts of Sn caused a red-shift of the fundamental absorption edge from 266 to 298 nm in the material, which we attributed to a lattice expansion of the host semiconductor due to the larger size of Sn and an associated decrease of band gap.
In conclusion, SrNbO 3 thin films were proposed and experimentally confirmed as high-performance UV transparent  Nominal double counting is used, which is known to give reasonable agreement with experiment in the early d 1 transition metal oxides. The on-site self energy obtained from DMFT has vanishingly small imaginary part on the Fermi level, and its real part is linear, hence the Fermi liquid approach used in the text is valid.
Sample growth and X-ray diffraction. The SrNbO 3 films were grown on (100) plane of KTaO 3 single crystal substrate by pulsed laser deposition. Details of the film growth condition were reported elsewhere 68 . In short, a sintered pellet of Sr 2 Nb 2 O 7 placed in a vacuum chamber was irradiated by KrF excimer laser (λ = 248 nm). The KTaO 3 substrates were heated at 700°C by using an infrared lamp heater. SrNbO 3 films were grown by other groups with comparable properties when grown under oxygen deficient conditions 69 . Crystal structure and thicknesses of the thin films were examined by X-ray diffraction (XRD) and X-ray reflectivity using a four-axis diffractometer (Bruker AXS, D8 Discover) with a 2D area detector or a 1D array detector. Details of the XRD results are provided in Supplementary Note 6.
Optical and electrical characterization. Spectroscopic ellipsometry measurements were performed at room temperature to determine the optical properties of SrNbO 3 thin films. Ellipsometry spectra in (Ψ,Δ) were collected for KTaO 3 substrate, prior to measurements on SrNbO 3 films. The (Ψ,Δ) spectra were then collected for SrNbO 3 thin films with thicknesses of 10, 23, and 29 nm at incidence angles of 50°, 60°, and 70°using M-2000 Ellipsometer (J.A.Woollam Co., spectral range: 0.734-5.043 eV) and IR-VASE Ellipsometer (J.A.Woollam Co., spectral range: 0.044-0.814 eV), and at the incidence angle of 65.23°using M-2000F Focused Beam Ellipsometer (J.A.Woollam Co., spectral range: 1.242-6.458 eV). All the data collected was appended and modeled with Com-pleteEase software (J.A. Woollam Co.). Detailed information on ellipsometry modeling and table of oscillators are listed in Supplementary Note 7. Electrical transport measurements were performed at varying temperatures using van der Pauw (VdP) geometry in a Quantum Design Physical Properties Measurement System with a source current of 500 μA. Number of carriers and mobility were determined through Hall measurements in VdP geometry in magnetic field strengths of up to ±8 T applied perpenddicular to the film plane. Sample quality was verified by measuring resistivity from room temperature down to 2.2 K to determine the RRR.

Data availability
All relevant data are available from the corresponding author.