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## Creator

Xinyi He, Takehito Komatsu, [Takayoshi Katase](https://orcid.org/0000-0002-2593-7487), [Terumasa Tadano](https://orcid.org/0000-0002-8132-2161), [Takashi Honda](https://orcid.org/0000-0003-4121-8957), [Masayoshi Miyazaki](https://orcid.org/0000-0003-4343-1137), Masaaki Kitano, Hidenori Hiramatsu, Hideo Hosono, Toshio Kamiya

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This document is the Accepted Manuscript version of a Published Work that appeared in final form in 
ACS Applied Energy Materials, copyright © 2025 American Chemical Society after peer review and technical editing by the publisher. To access the final edited and published work see https://doi.org/10.1021/acsaem.5c01610.[In Copyright](http://rightsstatements.org/vocab/InC/1.0/)

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[Strong Phonon Scattering and Enhanced Thermoelectric Performance in SrTiO<sub>3</sub> Polycrystals by Simultaneous Hydrogen Substitution and Oxygen Vacancy Formation](https://mdr.nims.go.jp/datasets/65090121-3f26-4fa2-8904-8f02ea9da779)

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1 Strong phonon scattering and enhanced thermoelectric performance in SrTiO3 polycrystals by simultaneous hydrogen substitution and oxygen vacancy formation  Xinyi He1,2, Takehito Komatsu1, Takayoshi Katase1,3,*, Terumasa Tadano4, Takashi Honda5, Masayoshi Miyazaki1, Masaaki Kitano1, Hidenori Hiramatsu1,3, Hideo Hosono1, and Toshio Kamiya1,3,* 1 MDX Research Center for Element Strategy, Institute of Integrated Research, Institute of Science Tokyo, 4259 Nagatsuta, Midori, Yokohama 226-8501, Japan 2 Kanagawa Institute of Industrial Science and Technology, 705-1 Shimoimaizumi, Ebina, Kanagawa 243-0435, Japan 3 Materials and Structures Laboratory, Institute of Integrated Research, Institute of Science Tokyo, 4259 Nagatsuta, Midori, Yokohama, 226-8501, Japan 4 Research Center for Magnetic and Spintronic Materials, National Institute for Materials Science, 1-2-1 Sengen, Tsukuba, Ibaraki 305-0047, Japan 5 Institute of Materials Structure Science, High Energy Accelerator Research Organization, Tsukuba, Ibaraki 305-0801, Japan  * Correspondence to: katase.t.aa@m.titech.ac.jp, kamiya.t.aa@m.titech.ac.jp     2 ABSTRACT: Reduction of lattice thermal conductivity (klat) is one of the most critical strategies for achieving high thermoelectric energy conversion efficiency (ZT). SrTiO3 is regarded as an environmentally benign thermoelectric material. Complex cation-site defects in SrTiO3, such as those produced by heavy-mass rare-earth cation substitution and the formation of Sr vacancies, have been proven effective in reducing klat. In this paper, we synthesized SrTiO3−x−dHxVOd bulk polycrystals with complex anion-site defects, incorporating large amounts of both hydrogen anions (H-) and oxygen vacancies (VO), with the total concentration of x + d controlled over a wide range from 0.13 to 0.40. As increasing x + d values, klat at 300 K largely decreased from 8.22 W/(mK) for pure SrTiO3 to 4.02 W/(mK) for SrTiO2.60H0.27VO0.13. Both H and VO were found to contribute almost equally to phonon scattering, attributed to local structure distortions in Ti−O6 octahedra. In contrast, while the carrier activation rate of H- was nearly 100%, that of VO was only 23-27% in SrTiO3-x-dHxVOd bulks, allowing the realization of low klat and a high power factor (PF) even at high x + d values. The highest ZT value of ~0.1 was obtained at 300 K for SrTiO2.87H0.06VO0.07, and further increased to 0.21 at 673 K for SrTiO2.73H0.16VO0.11. These findings demonstrate that anion-site defect engineering via mixed-anion substitution and vacancy formation is a promising strategy for further reducing klat and enhancing the performance of thermoelectric oxides.  KEYWORDS. Thermoelectric material; Transition metal oxide; Hydrogen; Phonon transport; Carrier transport   3    4 1. INTRODUCTION Thermoelectric effect, that enables direct and reversible conversion between thermal and electrical energy, has been expected to provide a viable route for power generation from waste heat.1-3 The efficiency of thermoelectric energy conversion of the thermoelectric materials is defined by the dimensionless figure of merit, ZT = S2·s·T·κ-1, where S is the Seebeck coefficient, s is the electronic conductivity, T is the absolute temperature, κ is the sum of electronic (κele) and lattice thermal conductivities (κlat).4-6 Therefore, the large S and high s (leads to the high power factor, PF = S2s) coupled with the low k are required for high ZT. The high ZT has been demonstrated mainly in heavy metal chalcogenides, such as Bi2Te3, PbTe, and GeTe,4,7-9 due to their intrinsic low klat. However, the use of toxic elements, such as Pb and Te, is not preferred for wide applications of thermoelectricity. Recently, various effective strategies for reducing klat have been proposed for the development of eco-friendly thermoelectric materials, including point defect engineering, nano-structuring, and introduction of local bonding heterogeneity.10-12 A perovskite-type oxide SrTiO3 has been regarded as one of the potential candidates for environmentally benign thermoelectric materials due to their earth abundance, nontoxic nature, and high chemical stability.13-15 SrTiO3 is an n-type semiconductor with the bandgap of ~ 3.2 eV. The aliovalent cation substitution, such as La3+ for the Sr2+ site and Nb5+ for the Ti4+ site can increase its s value by the large increase of carrier concentration.16 Moreover, the triple degeneracy of the conduction bands formed by Ti 3d t2g orbitals and its large electron effective mass 6-8 me15 lead to a large S even at high carrier concentrations. Owing to the promising electronic transport characteristic, the electron-doped SrTiO3 single crystal possesses high PF = 20-30 µW/(cmK2), comparable to that of Bi2Te3 at room temperature (RT).13-15 However, ZT of the electron-doped SrTiO3 has been limited to as low as 0.05-0.08 at RT in single crystals because of its high κlat  5 value of ~10 W/(mK),17 which is 10 times higher than ~1 W/(mK) of Bi2Te3 at RT.18 To date, most efforts to reduce κlat in SrTiO3 have focused on cation-site defect engineering. For example, cation-site defects have been introduced by substituting heavy rare-earth cations and creating Sr cation vacancies, and the double substitution of rare-earth and transition metal cations at the Sr and the Ti sites, respectively.19-23 On the other hand, we have recently proposed a new approach to reduce κlat and demonstrated ZT enhancement in SrTiO3 bulk polycrystal by hydrogen anion (H-) substitution at the oxygen ion (O2-) sites, i.e., SrTiO3-xHx.24-26 Heavy-mass element substitution has been a conventional approach to reduce κlat, while we showed that the substitution of light-mass H- at the O2- site is very effective to reduce κlat of SrTiO3. Only the 1.9% addition of H- at the O2- site reduces κlat from 8 W/(mK) of SrTiO3 to 6.5 W/(mK) at x = 0.057 and further reduces it to 3.6 W/(mK) at maximum x = 0.216 for SrTiO3-xHx at RT. The H- substitution introduces distorted local coordination structures in the Ti-(O,H)6 octahedra due to the heterogeneity of chemical bonding structures with the weak Ti−H bonds and the strong Ti-O bonds, which strongly enhances the phonon scattering in the SrTiO3-xHx.24 Note that a recent study has demonstrated that isotope substitution of O16 with O18 in SrTiO3 effectively reduces the klat by nearly 20%, due to mass-difference-induced phonon scattering.27 In addition, H- substitution generates high carrier concentrations and achieves high carrier mobility with much less grain boundary (GB) scattering than the conventional La-doped SrTiO3 polycrystals. The H- substitution does not form a GB potential barrier and thus suppresses electron scattering despite their polycrystalline nature. As a result, SrTiO3-xHx bulk polycrystals exhibit a high PF comparable to the La-doped SrTiO3 single crystal.25 As a consequence, the SrTiO3-xHx bulk with optimal x = 0.068 exhibits a ZT = 0.11 at  6 RT and the ZT value increases continuously up to 0.22 at T = 657 K. It is possible to reduce κlat by increasing x in SrTiO3-xHx, but the PF reaches its maximum at low x (i.e., low carrier concentrations) due to the high carrier activation rate of H- at O2- site,24 which limits ZT enhancement to the low x region. Further improvement of ZT requires increasing anion-site defects to reduce κlat, while simultaneously controlling the carrier concentration to remain within the optimal range. Excessive anion-site defects lead to too high carrier densities, which deteriorate the PF due to reduced Seebeck coefficient. In addition, the SrTiO3−xHx bulk polycrystals require the complex and time-consuming synthesis processes: first, the SrTiO3−xHx powders were prepared through low-T topochemical reaction between parent SrTiO3 precursors and calcium hydride (CaH2),28,29 and then densified into bulk polycrystals by spark plasma sintering (SPS). The topochemical reaction of SrTiO3 with CaH2 needs heat treatment for a long time (~7 days). Moreover, the washing process for the obtained SrTiO3−xHx powders is necessary to remove the residual CaH2 and byproduct CaO. Such complex and time-consuming process is unsuitable for future thermoelectric applications. In addition, since the CaH2 is a strong reductant, the topochemical reaction of SrTiO3-xHx at T ≥ 500 °C results in the decomposition, observed by increasing amounts of TiH2 impurity. On the other hand, after the high-T sintering by SPS, the oxidized TiOx impurities are formed in bulk polycrystal, and their volume fractions increase up to 12 mol% for SrTiO3-xHx bulks.24 Moreover, due to the loss of H during high-T SPS process, oxygen vacancies (VO) should be formed in the SrTiO3-xHx bulks, and the VO formation provide strong phonon scattering. However, the presence of impurities made it difficult to quantify both H- and VO concentrations, hindering an understanding of their respective contributions to the klat reduction in the SrTiO3-xHx. The  7 preparation of high phase-purity SrTiO3-xHx powders and bulk polycrystals with controlled x and the amounts of VO is still a challenge to clarify the effect of the H substitution and VO formation on electronic and thermoelectric properties.  In this paper, we demonstrate the synthesis of high phase-purity, heavily H-doped SrTiO3-xHx powders by the solid-state reaction of SrO, SrH2, and TiO2 as the starting materials. We previously reported the direct synthesis of heavily H-doped hexagonal BaTiO3−xHx (x ~ 1) powders through the solid-state reaction of BaH2 with TiO2 at a relatively low T = 800 °C under H2 gas flow.30 SrTiO3-xHx powders were synthesized in a similar manner to hexagonal BaTiO3−xHx, but the samples contained many impurity phases. In this work, we applied solid-state reaction at much higher T > 1000 oC in a H2-filled silica-glass tube. The amount of impurity phase was largely decreased at higher T, and single phase SrTiO3-xHx powders with x = 0.17-0.37 were obtained at T = 1100 oC. On the other hand, subsequent SPS sintering yielded highly dense SrTiO3−x−dHxVOd bulk polycrystals containing large amounts of both H and VO, where the total concentration of x + d was controlled over a wide range from 0.13 to 0.40. The carrier activation rate of H- was nearly 100%, while that of VO was only 23-27% in SrTiO3-x-dHxVOd bulks, enabling the low klat and high PF even at high x + d values. We investigated the electronic and phonon transport properties of SrTiO3−x−dHxVOd bulks, and discussed the effects of H- and VO on phonon scattering with assistance of first-principles calculations.  2. EXPERIMENTAL SECTION 2.1. Bulk synthesis. SrTiO3-xHx powders were synthesized by high-T solid-state reactions of (1-x)SrO + xSrH2 + TiO2 → SrTiO3-xHx + 0.5xH2. First, fresh Sr metal (99.9%, Aldrich) was  8 finely cut into small pieces of grains,31 and the Sr grain was annealed in H2 gas at 400 °C for 20 h to prepare SrH2 powder. The SrO powder was obtained by decarbonization of SrCO3 powder (99.5%, Kojundo kagaku) at 1200 oC in air. Then the powders of SrH2, SrO, and TiO2 (99.999%, Kojundo Kagaku) were mixed and pressed into pellets in 10-mm diameter. The handling of starting materials was performed in a glovebox with a dry inert Ar gas (the dew point <−100 °C, the oxygen concentration < 1 ppm). The obtained pellet was wrapped in Mo foil and then sealed with H2-filled silica-glass tube (the inside of the silica-glass ampule was vacuumed, and then, H2 gas was filled at ~1 atm at RT before sealing the glass tube). The sealed tube was heated at 1000-1100 °C for 20 h. The obtained SrTiO3-xHx powders were reground and pressed into 10-mmf pellets. The SrTiO3-xHx pellet was sealed with a stainless capsule. The sealed pellet was densified rapidly by SPS under 80 MPa at T = 1150 °C in vacuum, resulting in the SrTiO3−x−dHxVOd bulks. After that, the stuck Mo foil and stainless capsule were peeled off, and the sample surface was polished. For comparison, a SrTiO3 polycrystal was prepared by the SPS in vacuum, where the SrTiO3 bulk was annealed in air to reduce VO fomed during the SPS process. 2.2. Crystal structure and chemical composition analysis. Crystalline phases for SrTiO3-xHx powders and SrTiO3−x−dHxVOd bulks were examined by X-ray diffraction (XRD) with the Bragg−Brentano geometry with a Cu Kα radiation source. The lattice parameters were determined by the Pawley method using the TOPAS ver. 4.2 program (Karlsruhe, Germany: Bruker AXS GmbH). Time-of-flight neutron powder diffraction (NPD) measurements were carried out using a NOVA neutron total scattering instrument (BL21 beamline) at the Japan Proton Accelerator Research Complex (J-PARC). The measurement was performed for fine powders by crushing the sintered SrTiO3−x−dHxVOd bulks. The white neutron beam intensity at J-PARC was 800 kW. The  9 crystal structures were analyzed by Rietveld refinement using the computer program Z-Rietveld (Ver. 1.1.3).32,33 Microstructures and chemical composition mappings of the SrTiO3−x−dHxVOd bulks were observed by electron probe microanalyzer (EPMA). The H concentration (x) was measured by the thermal desorption spectroscopy (TDS), and the VO concentration (d) was estimated by thermogravimetric analysis (TGA) for SrTiO3-xHx powders and SrTiO3-x-yHxVOy bulks. The measurements for SrTiO3-x-yHxVOy were performed by crushing the sintered bulks to fine powders. TDS measurement was performed under ultra-high vacuum condition, in order to detect the H release from the samples at high T. TGA measurement was performed in air to oxidize the samples, where they exhibited a weight gain with increasing temperature due to the replacement of H and VO with oxygen from the atmosphere. Therefore, the total concentration of H and VO can be estimated from TGA data. 2.3. Electronic and thermal transport properties. Electronic and thermal transport properties were characterized for the SrTiO3−x−dHxVOd bulks. s and S were simultaneously measured by four-probe method with a ZEM-3 (ADVANCE-RIKO, Inc.) under a Helium atmosphere. The k was obtained from k = D·C·d, where the thermal diffusivity (D) along out-of-plane direction in the bulk was measured in an Argon atmosphere by a laser flash diffusivity method (LFA 457, NETZSCH) and the heat capacity (C) was measured by differential scanning calorimetry (DSCvesta, Rigaku Corp.), and the sample density (d) was determined by the dimensions and mass of the samples. Low-T Hall effect was measured under applied magnetic field up to ± 5 T with a physical property measurement system (PPMS, Quantum Design). The carrier concentration was calculated by n = 1/e|RH| and Hall mobility was calculated by μ = s/(en), where RH is Hall coefficient and e is the elementary charge.  10 2.4. Phonon transport calculations. Density functional theory (DFT) calculations were conducted using the projector augmented wave (PAW) method as implemented in the Vienna Ab initio Simulation Package (VASP) code34,35 with the generalized gradient approximation (GGA) Perdew–Burke–Ernzerhof (PBE) functional.36 Crystal structures were optimized with a plane wave cutoff energy of 600 eV. A 2 × 2 × 2 supercell of the fully-relaxed SrTiO3 primitive cell was constructed containing 8 Sr atoms, 8 Ti atoms, and 24 O atoms. Then, two O atoms were substituted with H atoms to create SrTiO2.75H0.25 model. Subsequently, these H atoms were removed from the substituted O sites to create the oxygen-deficient SrTiO2.75VO0.25 model. Phonon transport properties for SrTiO3, SrTiO2.75H0.25, and SrTiO2.75VO0.25 were calculated using the ALAMODE code,37,38 with detailed settings referring to our previous work.24   3. RESULTS AND DISCUSSION 3.1. Synthesis. First, we optimized the annealing temperatures (TA) from 1000 oC to 1100 oC for the synthesis of high-purity SrTiO3-xHx powders with a nominal x = 0.2 (Figure 1a). At TA = 1000 oC, the diffraction peaks corresponding to the cubic SrTiO3 phase (space group: Pm3-m) was observed, as indicated by the vertical black lines. On the other hand, several diffraction peaks that could not be assigned to the cubic SrTiO3 phase were observed and were identified as impurity phases, including Sr2TiO4, Sr3Ti2O7, Sr(OH)2, Ti2O3. With increase of TA, the formation of the impurity phases was suppressed at TA = 1050 oC, and then single phase SrTiO3-xHx powder was obtained at TA = 1100 oC. Figure 1b summarizes the XRD patterns at RT for SrTiO3-xHx powders with nominal x = 0.2-0.4, synthesized at the optimized TA = 1100 oC. For comparison, the XRD pattern of pure SrTiO3 powder is also shown. All diffraction peaks are assigned to the cubic SrTiO3  11 phase without any impurity phases. The cubic lattice parameters (a), refined by Rietveld analysis of XRD patterns, increases proportionally from 3.905 Å for pure SrTiO3 to 3.911 Å for SrTiO3-xHx with nominal x = 0.4 (Figure 1c). Consequently, the lattice volume (V) expands from 59.547 to 59.836 Å3. The lattice expansion is attributed to the larger ion radius of H- (1.54 Å) compared to O2- (1.38 Å),29 as well as the larger ion radius of Ti3+ (0.67 Å) than compared to Ti4+ (0.61 Å).39,40 In addition to these ion size differences, the lattice expansion may also result from the longer and weaker Ti-H and Sr-H bonds than Ti-O and Sr-O bonds in the Ti-(O,H)6 octahedra and Sr-(O,H)12 polyhedra (See ref 24). Figure 1d shows the relationship between the nominal x and the measured x for H concentration, as well as d for VO concentration in SrTiO3−x−dHxVOd. The TDS and TGA spectra are summarized in Figure S1 of Supporting Information. The measured x increased from 0.17 to 0.37, and there is a good agreement between the nominal and measured x values, indicating that H was incorporated almost exactly as designed. Additionally, the VO concentration (d) is less than 0.005 for all samples and remains nearly unchanged across the range of nominal x. Therefore, the high-purity SrTiO3-xHx powders with measured x = 0.17 to 0.37 were successfully synthesized via the high-T solid-state reaction without significant H loss, i.e., VO formation.  Next, we performed SPS for the single-phase SrTiO3-xHx powders to obtain dense SrTiO3−x−dHxVOd bulks at a sintering temperature of 1050 oC. For all nominal x compositions, single-phase, high-purity bulk samples were obtained without the formation of any impurity phases (Figure 2a), and the a increases monotonically with nominal x (Figure 2b), similarly observed in SrTiO3-xHx powders. The TDS and TGA spectra for SrTiO3−x−dHxVOd bulks are summarized in Figure S2 of Supporting Information. The measured x values for the bulk samples  12 increased from 0.06 to 0.27 but became smaller than the corresponding nominal x values (Figure 2c). Meanwhile, the VO concentration (d) increased with increase of nominal x, yielding the compositions of SrTiO2.87H0.06VO0.07 for the nominal x = 0.2 sample, SrTiO2.73H0.16VO0.11 for x = 0.3, and SrTiO2.60H0.27VO0.13 for x = 0.4, respectively. The sintered SrTiO3-xHx bulks contained both H and VO, with x controlled in the range of 0.06 to 0.27 and d in the range of 0.07 to 0.13. The sum of the measured x and d values closely matched the nominal x values, suggesting the formation of VO during the high-T SPS process. The sintered density for all samples was ~93%, and the average grain sizes ranged from 200 to 500 nm (Figure S3 of Supporting Information). We performed NPD measurements for the SrTiO3−x−dHxVOd bulk samples to estimate the amount of H and VO at O sites. For comparison, the NPD measurement was also performed for SrTiO3 bulk. The NPD patterns and Rietveld analyses are summarized in Figure S4 and Tables S1, S2 of Supporting Information. The chemical composition for pure SrTiO3 bulk was estimated to be SrTi0.99O3.00 with negligible formation of VO. On the other hand, the chemical compositions for SrTiO3−x−dHxVOd bulks were estimated to be Sr0.99Ti0.99O2.88H0.09VO0.03 for the nominal x = 0.2 sample and SrTi0.97O2.72H0.23VO0.05 for x = 0.4. It should be noted that the H substitution and VO formation at O site induce the local structure distortion in Ti-O6 octahedra, resulting in distributions in the bond length of Ti-O and the bond angles of O-Ti-O and Ti-O-Ti, as discussed later. Although the local structure is expected to exhibit lower symmetry, the NPD data were analyzed assuming a high-symmetric cubic structure that represents the averaged global structures. As a result of the refinement, it was found that the atomic displacement parameters (Table S1) obtained from Rietveld refinement for SrTiO3−x−dHxVOd are larger than that of the pure SrTiO3 with the ideal cubic structure, presumably  13 reflecting the spatial distribution of local distortions in the Ti-O6 octahedra. Although the absolute values of measured x and d obtained from TDS and TGA spectra differ slightly from the NPD results, their increasing trends with respect to nominal x are almost consistent. The incorporated H is predominantly substituted at the O site. It is known that VO can be formed in SrTiO3 by heating in highly reducing condition (H2 gas) at high T. The reported VO concentration (d) is only 0.06 in SrTiO3−δ polycrystal.41 It can be considered that by using SrTiO3-xHx powder samples with high x, bulk samples containing not only a large amount of H but also significant numbers of VO can be fabricated, which should be expected to provide strong phonon scattering and reduce klat.  3.2. Thermal transport properties. Figure 3a show the T dependence of total k and electronic k (kele) of SrTiO3−x−dHxVOd bulks. The T dependences of heat capacity and thermal diffusivity are summarized in Figure S5 of Supporting Information. The kele was calculated by Wiedemann-Franz law as kele = LTs, where the Lorenz number L is calculated by the single parabolic band model using the Fermi level estimated from the measured S.42 The s and S will be shown later. The κ of all SrTiO3−x−dHxVOd bulks showed monotonic decrease with the increase of T. The k at T = 300 K decreased from 6.45 W/(mK) to 5.26 W/(mK) with the increase of x from 0.06 to 0.27 and d from 0.07 to 0.13. The kele at T = 300 K increased from 0.67 W/(mK) to 1.49 W/(mK) due to the increase of s by the increase of H- and VO donors, as will be discussed later. Then, the lattice k (klat) was calculated by subtracting the electronic contribution from the total k, i.e., klat = k -kele (Figure 3b). The klat of pure SrTiO3 bulk and reported klat of SrTiO2.94VO0.06 bulk41 are also shown to discuss the effect of H- substitution and VO formation on klat of the present SrTiO3−x−dHxVOd  14 bulks. The klat at T = 300 K largely decreased from 8.22 W/(mK) of pure SrTiO3 bulk to 5.78 W/(mK) for SrTiO2.87H0.06VO0.07 bulk, and κlat was further reduced to 4.17 W/(mK) for SrTiO2.73H0.16VO0.11 bulk, which is 49% lower than that of pure SrTiO3. The klat at high T = 673 K was also reduced from 4.58 W/(mK) of SrTiO3 bulk to 3.46 W/(mK) of SrTiO2.73H0.16VO0.11 bulk, indicating that the H substitution and VO formation enhanced the phonon scattering in the wide T range. On the other hand, even if the x and d was further increased, the κlat reduction was saturated at 4.02 W/(mK) for SrTiO2.60H0.27VO0.13 bulk and the κlat showed an almost negligible T dependence. This result suggests that phonon scattering induced by H⁻ substitution and VO formation reaches an upper limit. As shown in Fig. 4(e), since O vibrations primarily contribute to high-frequency optical phonon modes, the phonon scattering induced by H⁻ substitution and VO formation predominantly affects the high-frequency phonons. However, thermal transport in SrTiO3 is also governed by low-frequency phonons mainly from Sr atomic vibrations. Therefore, further reduction in κlat would require scattering mechanisms for low-frequency phonons for example, through defect engineering at the Sr site.19-22 Compared to the κlat of 6.5 W/(mK) at T = 322 K for the reported SrTiO2.94VO0.06 bulk, the klat was significantly reduced due to the large amount of H- and VO in present SrTiO3−x−dHxVOd bulks. As discussed later, H⁻ substitution and VO formation introduce local structure distortions in the Ti-O6 octahedra, which result in strong phonon scattering. As the concentrations of H⁻ and VO increase, the phonon scattering becomes stronger, leading to a significant reduction in κlat.  3.3. Phonon transport calculations. To understand the effect of the H substitution and VO formation on the reduction of κlat, we performed anharmonic phonon calculations using SrTiO3, SrTiO2.75VO0.25, and SrTiO2.75H0.25 models. To create the SrTiO2.75H0.25 model, two O atoms of  15 cubic SrTiO3 model were replaced with H atoms. Owing to the crystalline symmetry, seven different configurations are possible for placing the two H atoms at O sites.See Ref. 24 for the detailed H positions in the SrTiO2.75H0.25 models. The difference in total energy of the SrTiO2.75H0.25 models with different H positions is as small as 14 meV/atom, indicating that all models can coexist in the experimental samples synthesized at finite temperatures, which is consistent with the random distribution of O and H at the anion sites (Table S1). To simplify, among them, we used the H configuration yielding the lowest klat in SrTiO2.75H0.25 model, where the two H atoms are substituted at O site on the Sr-O plane in diagonally opposite (cater-cornered) Ti-O6 octahedra (Figure S6a of Supporting Information). By removing the two H atoms from the substituted O sites, we constructed the SrTiO2.75VO0.25 model. Figures 4a-c compare the phonon dispersion and partial phonon density of states (DOSs) of cubic SrTiO3, SrTiO2.75VO0.25, and SrTiO2.75H0.25 models. The corresponding harmonic phonon dispersions are provided in Figure S7 of Supporting Information. For cubic SrTiO3, the optical phonon bands, dominated by Ti and O atomic vibrations, are highly dispersive at high frequencies of 4−15 THz (Figure 4a). The dispersion is much larger than the low-frequency acoustic phonon bands (< 4 THz), arising from Sr atomic vibrations. In contrast, SrTiO2.75H0.25 and SrTiO2.75VO0.25 models similarly exhibit nondegenerate phonon bands than cubic SrTiO3 (Figures 4b,c), due to the local structure distortion with distributions in the bond length of Ti-O and the bond angles of O-Ti-O and Ti-O-Ti caused by the H substitution and VO formation (Figure S6b of Supporting Information), resulting in the splitting of degenerated phonon bands. Particularly, the optical phonon bands become flatter due to fluctuations in the Ti–(O,H) bonding environment, and the slopes of the acoustic phonon branches decrease along the Γ–X and Γ–M directions. Notably, the substituted H in SrTiO2.75H0.25 introduces localized phonon modes at high frequencies of ~24 THz and ~37 THz (Figure 4b),  16 but due to their low group velocity and isolation from lower-frequency modes, they contribute negligibly to phonon transport and anharmonic phonon scattering in SrTiO2.75H0.25. Note that cubic SrTiO3 shows a low-frequency soft-phonon mode at R point (Figure 4a), which primarily originates from the antiferrodistortive (AFD) rotation of Ti-O6 octahedra and is closely related to the instability of the cubic structure.43 A similar low-frequency phonon mode appears at G point (corresponding to the symmetry-transferred R point) in both SrTiO2.75H0.25 and SrTiO2.75VO0.25 models (Figures S7b,c). Figure 4d compares the T dependence of calculated klat for SrTiO3, SrTiO2.75VO0.25, and SrTiO2.75H0.25 models. The calculated klat at T = 300 K largely decreases from 9.18 W/(mK) for SrTiO3 to 2.85 W/(mK) for SrTiO2.75H0.25 and 2.24 W/(mK) for SrTiO2.75VO0.25. Note that the calculated klat for SrTiO2.75H0.25 and SrTiO2.75VO0.25 is lower than the experimental values, likely due to the dependence of klat on the H substitution and VO formation sites.24 Figure 4e shows the klat spectra at T = 300 K as a function of the phonon frequency. In SrTiO3, the major contribution to the total klat arises from phonons with frequencies below 15 THz. Both the H substitution and VO formation significantly reduce klat by suppressing the contribution from the low-frequency phonons. Figure 4f shows the cumulative klat with respect to the phonon mean free path (lph). The klat of SrTiO3 is dominated by phonons with the lph shorter than 10 nm, while their phonon transport is significantly suppressed by the H substitution and VO formation. Figures 4g-i compare the lph, the phonon group velocity (νph), and the phonon lifetime (τph) in terms of the phonon frequency. For SrTiO3, the τph is small at frequencies > 4 THz (Figure 4i), but the νph is large in wide phonon frequency range (Figure 4h), reflecting the widely spread optical phonon bands. The H substitution and VO formation reduce both the τph and νph of SrTiO3, resulting in the shorter lph  17 in the wide frequency range (Figure 4g). The reduction of νph originates from the flatter optical phonon bands and the downward shift of acoustic phonon branches associated with Sr atomic vibrations around ~3 THz, suggesting the enhanced Umklapp scattering due to the acoustic and optical phonon interaction (Figures 4b,c). These results indicate that the H substitution and VO formation have comparable effects on phonon transport properties. The underlying origin of the similar behaviors of  H⁻ substitution and VO formation is further discussed in the following section. We previously reported that the reduction in klat for SrTiO2.75H0.25 originates from local structure distortion, specifically the heterogeneity of Ti−(O,H) bond lengths induced by the H substitution.24 The relationship between the calculated klat and the distortion of Ti−(O,H) bond lengths for the SrTiO3, SrTiO2.75VO0.25, and SrTiO2.75H0.25 models is shown in Figure S8 of Supporting Information. Both the H substitution and VO formation cause similar distortions in the Ti−O6 octahedra, resulting in the comparable klat values. The H substitution and VO formation break the local structural symmetry and induce additional modulation of the force constants, leading to splitting of degenerate phonon modes and the observed reduction in phonon dispersion. These broad frequency shifts enhance the phonon-phonon scattering, which results in large tph reduction in SrTiO3. We analyzed the chemical bonding characteristics of the Ti-O and Ti-H bonds in SrTiO2.75H0.25 model using the crystal orbital Hamiltonian overlap (COHP),44 calculated by the LOBSTER codes.45 The −COHP for the Ti-O and Ti-H bonds is shown in Figure S9 of Supporting Information. The averaged −iCOHP value of the Ti–O bonds is 3.58 eV/bond, indicating a strong covalent interaction between the Ti and O atoms, while that of the Ti–H bond is only 0.96 eV/bond, suggesting a more ionic nature of the Ti and H atom interaction. Due to the  18 significantly weaker Ti-H bonds, H behaves similarly to VO in the Ti-O6 octahedra, as VO effectively removes a Ti–O bond entirely.   3.4. Thermoelectric properties. s and S for the SrTiO3-x-dHxVOd bulks as a function of T are summarized in Figures 5a,b. We confirmed that the s and S for all SrTiO3-x-dHxVOd bulks were reversibly reproduced during heating and cooling cycles in the T range between 300 K (RT) and 673 K (400 °C), indicating that H does not desorb from bulks at this T range. All SrTiO3-x-dHxVOd bulks exhibited metallic T dependence of s (Figure 5a). The s at T = 300 K increased from 1260 S/cm to 2350 S/cm with the increase of H and VO concentrations (x + d) from 0.13 to 0.27, but it decreased to 1850 S/cm for higher x + d values of 0.40. All the samples showed negative S in the whole T range (Figure 5b), indicating the majority carrier is electron, consistent with the fact that H- and VO act as donor. The absolute values of S (|S|) at T = 300 K monotonically decreased from 129 µV/K to 47 µV/K with the increase of x + d from 0.13 to 0.40, and the |S| values for all samples increased with increasing T. Figures 5c,d show the low-T carrier mobility (µ) and carrier concentration (n). The n for all samples exhibited almost no T dependence, indicating degenerated electron conduction. The n at T = 300 K increased from 1.7×1021 cm-3 for x + d = 0.13 to 5.8×1021 cm-3 for x + d = 0.40 (Figure 5d). The dotted lines indicate the nH+VO, estimated by considering that all H- at O2- site provides one electron and VO gives two electrons in the SrTiO3-x-dHxVOd. The nH+VO is larger than measured n for all samples regardless of x + d. It is reported that the carrier activation rate of H- in SrTiO3-xHx thin films is almost 100%,46 while the carrier activation rate of VO in SrTiO3-d single crystal is as low as 25-53%.47 By considering the 100% activation rate of H-, we estimated the carrier activation rate of VO to be 23-27% in SrTiO3-x-dHxVOd bulks. The µ  19 at T = 300 K decreased from 4.6 cm2/(Vs) for x + d = 0.13 to 1.9 cm2/(Vs) for x + d = 0.40, but all samples exhibited a trend of increasing µ at lower T. Detailed µ analyses at low T ≤ 300 K as well as high T ≥ 300 K are summarized in Figure S10 of Supporting Information. The µ of the SrTiO3−x−dHxVOd bulks is limited mainly by impurity scattering and electron-electron scattering at low T and that is limited by optical phonon scattering at high T. The higher concentration of H and VO results in the increase of impurity scattering and electron-electron scattering due to increase of n. On the other hand, grain boundary scattering is negligible across the entire T range in SrTiO3−x−dHxVOd bulks even with its polycrystalline form. Figures 5e,f summarize PF (= S2s) and ZT of the SrTiO3−x−dHxVOd bulks. PF at T = 300 K decreased from 20.9 to 4.1 µW/(cmK2) with the increase of x + d from 0.13 to 0.40 due to the decease of  S (Figure 5e). However, for SrTiO2.73H0.16VO0.11 and SrTiO2.60H0.27VO0.13 bulks, the PF increased to 8.1 and 12.8 µW/(cmK2) with increasing T up to 648 K, respectively. On the other hand, the PF for SrTiO2.87H0.06VO0.07 decreased to 12.0 µW/(cmK2) at T = 673 K. The SrTiO2.87H0.06VO0.07 bulk with x + d = 0.13 exhibited the highest ZT = ~0.1 at T = 300 K (Figure 5f) and ZT value increased continuously up to 0.18 at T = 673 K. On the other hand, SrTiO2.73H0.16VO0.11 bulk with x + d = 0.27 showed the highest ZT = 0.21 at T = 673 K. Owing to the significant reduction in the klat, the ZT of SrTiO3−x−dHxVOd bulk at T = 300 K is more than 5-times higher than 0.01-0.02 reported for La-doped SrTiO3 polycrystals,48 and exceeds the ZT values of 0.07-0.08 for the La-doped SrTiO3 single crystals.13,15,49  4. CONCLUSIONS  20 We reported the synthesis and thermoelectric properties of SrTiO3−x−dHxVOd bulk polycrystals with complex anion-site defects, containing large amounts of both H and VO, with the total concentration of x + d controlled over a wide range from 0.13 to 0.40. The SrTiO3−x−dHxVOd bulks were prepared by a high-T solid-state reaction (SrH2+SrO+TiO2→SrTiO3-xHx with x = 0.17-0.37), followed by high-T SPS, during which partial H loss occurred. This process enables large-scale synthesis in a shorter time and simpler process compared to conventional topochemical reaction methods. As increasing x + d values, klat at T = 300 K largely decreased from 8.22 W/(mK) for pure SrTiO3 to 4.02 W/(mK) for SrTiO2.60H0.27VO0.13. It was found that both H and VO contribute almost equally to phonon scattering, attributed to local structure distortions in Ti−O6 octahedra. On the other hand, while the carrier activation rate of H- was nearly 100%, that of VO was only 23-27% in SrTiO3-x-dHxVOd bulks. This enabled decoupled control of electronic and phonon transport, achieving both low klat and high PF even at high x + d values. The highest ZT value of ~0.1 was obtained at T = 300 K for SrTiO2.87H0.06VO0.07, while it increased to 0.21 at T = 673 K for SrTiO2.73H0.16VO0.11. These results highlight that anion-site defect engineering via mixed anion substitution and vacancy formation is a promising strategy for further reducing klat and enhancing the performance of thermoelectric oxides. For example, incorporating H, VO, and other anions such as nitrogen, which acts as an acceptor,50 is expected to achieve even lower klat and higher ZT. In addition, the combination of cation-site and anion-site defects could offer an even more powerful strategy. Note that direct mechanochemical reactions have been reported for synthesizing fine powders of hydride-substituted perovskite oxides without the need of  21 heat treatment.51 The combination of mechanochemical synthesis and subsequent sintering represents a promising approach with a simpler and more scalable process.  ASSOCIATE CONTENT Supporting Information  Supporting Information is available free of charge. Crystal structure, microstructure, and chemical composition analyses of SrTiO3-xHx powders and SrTiO3−x−dHxVOd bulks. Temperature dependence of heat capacity and thermal diffusivity, as well as carrier mobility analyses of SrTiO3−x−dHxVOd bulks. Phonon transport, crystal structure, and chemical bonding analyses of SrTiO3, SrTiO2.75H0.25, and SrTiO2.75VO0.25 models by DFT calculations.  AUTHOR INFORMATION Corresponding Authors Takayoshi Katase; katase.t.aa@m.titech.ac.jp Toshio Kamiya; kamiya.t.aa@m.titech.ac.jp  Author contributions X. H., T. Komatsu, T. Katase, T.T., T.H., M.M., and T. Kamiya contributed to the synthesis and characterization of samples, as well as DFT calculations. All authors discussed the results and commented on the study. X. H., T. Katase., and T. Kamiya co-wrote the manuscript. T. Katase and T. Kamiya proposed the idea and supervised the entire project.  22 Note The authors declare no conflict of interest.  ACKNOWLEDGMENT This work was supported by MEXT Program: Data Creation and Utilization Type Material Research and Development Project (Grant No. JPMXP1122683430), and also by Design and Engineering by Joint Inverse Innovation for Materials Architecture. X. He and T. Katase was supported by a project of Kanagawa Institute of Industrial Science and Technology (KISTEC). T. Katase was also supported by Special Award for Science Tokyo Advanced Researchers (STAR) funded by Institute of Science Tokyo, Murata Science and Education Foundation, and Japan Society for the Promotion of Science (JSPS) through Grant-in-Aids for Scientific Research (B) (Grant No. JP22H01766), Scientific Research (S) (Grant No. JP22H04964), and Challenging Research (Exploratory) (Grant No. 24K21671). H.Hi. was supported by JSPS through Grants-in-Aid for Scientific Research (A) (Grant Nos. JP20H00302, JP21H04612, and JP24H00376). The neutron total scattering experiments were approved by the Neutron Scattering Program Advisory Committee of IMSS, KEK (Proposal Nos. 2019S06, 2024S06). 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Direct synthesis of barium titanium oxyhydride for use as a hydrogen permeable electrode. J. Mater. Chem. A 2021, 9, 20371–20374.    28 Figures   Figure 1. (a) XRD patterns of SrTiO3-xHx powders with a nominal x = 0.2 synthesized by solid-state reaction at various temperatures of TA = 1000-1100 °C. Black vertical bars indicate the diffraction peak positions for cubic perovskite SrTiO3 phase (space group Pm3-m). Red, blue, green, and orange arrows denote the diffraction peaks from impurity phases of Sr2TiO4, Sr3Ti2O7, Sr(OH)2, and Ti2O3, respectively. (b) Wide-range XRD patterns for SrTiO3-xHx powders with nominal x = 0.2-0.4. (c) Lattice parameter (a) as a function of nominal x for SrTiO3-xHx powders. For comparison, XRD pattern and lattice parameter of pure SrTiO3 powder are also shown in (b,c). (d) Relationship between the nominal x and the measured x for H concentration, as well as d for VO concentration in SrTiO3−x−dHxVOd.    29    Figure 2. (a) XRD patterns of SrTiO3−x−dHxVOd bulks obtained by sintering SrTiO3-xHx powders with nominal x = 0.2-0.4. The black vertical bars denote the diffraction angles of the cubic perovskite structure (space group: Pm3-m). (b) Lattice parameter (a) as a function of nominal x. For comparison, XRD pattern and lattice parameter of SrTiO3 bulk are also shown in (a,b). (c) Measured x and d in SrTiO3-x-dHxVOd bulks as a function of nominal x. The yellow plots are the sum of x and d.      30     Figure 3. T dependences of (a) total thermal conductivity (k) and electronic k (kele), (b) lattice k (klat) for SrTiO3−x−dHxVOd bulks. The klat of pure SrTiO3 bulk and the reported klat of SrTiO2.94VO0.06 bulk37 are shown in (b) for comparison.    31   Figure 4. (a-c) Phonon dispersion (left panel) and partial phonon density of states (DOSs) projected on each element (right panel) at T = 300 K for (a) cubic SrTiO3, (b) SrTiO2.75H0.25, and (c) SrTiO2.75VO0.25 models. (d) T dependences of calculated klat. (e) klat spectra at T = 300 K. (f) Cumulative klat as a function of phonon mean free path (lph). (g) lph, (h) phonon group velocity (νph), and (i) phonon lifetime (τph) as a function of the phonon frequency.    32  Figure 5. Thermoelectric properties for SrTiO3−x−dHxVOd bulks. (a,b) T dependences of (a) electrical conductivity (s) and (b) Seebeck coefficient (S) at T ≥ 300 K. The measurements were initially performed during the heating process (closed symbols), and then swiched to the cooling process (open symbols). (c,d) T dependences of (c) Hall mobility (µ) and (d) carrier concentration (n) at T ≤ 300 K. The dotted lines in (d) indicate the carrier concentration (nH+VO) estimated by considering that all H− provides one electron and VO provides two electrons in SrTiO3−x−dHxVOd. (e,f) T dependences of (e) power factor (PF) and (f) dimension-less figure of merit (ZT).   33  For Table of Contents Only    34 Supporting Information Strong phonon scattering and enhanced thermoelectric performance in SrTiO3 polycrystals by simultaneous hydrogen substitution and oxygen vacancy formation Xinyi He1,2, Takehito Komatsu1, Takayoshi Katase1,3,*, Terumasa Tadano4, Takashi Honda5, Masayoshi Miyazaki1, Masaaki Kitano1, Hidenori Hiramatsu1,3, Hideo Hosono1, and Toshio Kamiya1,3,* 1 MDX Research Center for Element Strategy, Institute of Integrated Research, Institute of Science Tokyo, 4259 Nagatsuta, Midori, Yokohama 226-8501, Japan 2 Kanagawa Institute of Industrial Science and Technology, 705-1 Shimoimaizumi, Ebina, Kanagawa 243-0435, Japan 3 Materials and Structures Laboratory, Institute of Integrated Research, Institute of Science Tokyo, 4259 Nagatsuta, Midori, Yokohama, 226-8501, Japan 4 Research Center for Magnetic and Spintronic Materials, National Institute for Materials Science, 1-2-1 Sengen, Tsukuba, Ibaraki 305-0047, Japan 5 Institute of Materials Structure Science, High Energy Accelerator Research Organization, Tsukuba, Ibaraki 305-0801, Japan  * Correspondence to: katase.t.aa@m.titech.ac.jp, kamiya.t.aa@m.titech.ac.jp     35 Contents Figure S1. TDS and TGA spectra of SrTiO3-xHx powders. Figure S2. TDS and TGA spectra of SrTiO3−x−dHxVOd bulks. Figure S3. Microstructure and chemical composition mappings of SrTiO3−x−dHxVOd bulks. Figure S4. NPD patterns and Rietveld refinements for SrTiO3−x−dHxVOd bulks and SrTiO3 bulk. Figure S5. Temperature dependence of heat capacity and thermal diffusivity of SrTiO3−x−dHxVOd bulks. Figure S6. Relaxed crystal structures and local structure analyses of SrTiO3, SrTiO2.75H0.25, and SrTiO2.75VO0.25 models. Figure S7. Harmonic phonon dispersions for SrTiO3, SrTiO2.75H0.25, and SrTiO2.75VO0.25 models. Figure S8. Relationship between calculated lattice thermal conductivity at 300 K and the deviation index of Ti−(O,H,VO) lengths for SrTiO3, SrTiO2.75H0.25, and SrTiO2.75VO0.25 models. Figure S9. Calculated −COHPs for Ti-O and Ti–H bonds in SrTiO2.75H0.25 model. Figure S10. Analysis of carrier mobility as a function of temperature for SrTiO3−x−dHxVOd bulks. Table S1. Crystallographic data obtained by Rietveld refinement results of NPD patterns for SrTiO3−x−dHxVOd bulks. Table S2. Crystallographic data obtained by Rietveld refinement results of NPD patterns for SrTiO3 bulk.      36 Microstructure and chemical composition analysis  Figure S1. Thermal desorption spectroscopy (TDS) spectra for H (m/z = 1), H2 (m/z = 2), H2O (m/z = 18) and thermogravimetric analysis (TGA) spectra for SrTiO3-xHx powders with nominal x = (a) 0.2, (b) 0.3, and (c) 0.4.    Figure S2. TDS spectra for H (m/z = 1), H2 (m/z = 2), H2O (m/z = 18) and TGA spectra for SrTiO3−x−dHxVOd bulks obtained by sintering SrTiO3-xHx powders with nominal x = (a) 0.2, (b) 0.3, and (c) 0.4.    37   Figure S3. (a) Microstructure of broken-out surface and (b) chemical composition mappings of Sr, Ti, and O elements for the polished surface for SrTiO2.73H0.16VO0.11 bulk.      38 Neutron diffraction measurements    Figure S4. (a,b) Neutron powder diffraction (NPD) patterns for SrTiO3−x−dHxVOd bulks obtained by sintering SrTiO3-xHx powders with nominal x = (a) 0.2 and (b) 0.4, and (c) NPD pattern for SrTiO3 bulk. The green tick marks and blue lines denote the Bragg peak positions from cubic SrTiO3 structure (Space group: Pm3-m) and the difference curves, respectively.     39 Table S1. Crystallographic data obtained by Rietveld refinement results of NPD patterns for SrTiO3−x−dHxVOd bulks obtained by sintering SrTiO3-xHx powders with nominal x = 0.2 and 0.4. a, Occ., B (B11 and B33) are the lattice parameter, the site occupancy, and anisotropic displacement parameters, respectively. SrTiO3-x-dHxVOd Nominal x = 0.2 Nominal x = 0.4 Crystal system Cubic Cubic Space group Pm3-m Pm3-m a (nm) 0.3908204(4) 0.3908404(4)  Nominal x = 0.2  x y z Occ. B11(Å2) B33(Å2) Sr 0 0 0 0.994(1) 0.612(7)  Ti 1/2 1/2 1/2 0.992(1) 0.412(9)  O 0 1/2 1/2 0.9599(2) 0.884(8) 0.282(13) H 0 1/2 1/2 0.0286(2) = B11(O) = B33(O) Nominal x = 0.4  x y z Occ. B11(Å2) B33(Å2) Sr 0 0 0 1.000 0.693(7)  Ti 1/2 1/2 1/2 0.973(2) 0.353(8)  O 0 1/2 1/2 0.9069(4) 1.010(8) 0.230(12) H 0 1/2 1/2 0.0759(6) = B11(O) = B33(O)  Table S2. Crystallographic data obtained by Rietveld refinement results of NPD patterns for SrTiO3 bulk. SrTiO3  Crystal system Cubic Space group Pm3-m a (nm) 0.3905431(2)   x y z Occ. B11(Å2) B33(Å2) Sr 0 0 0 1 0.502(3)  Ti 1/2 1/2 1/2 0.985(1) 0.208(4)  O 0 1/2 1/2 0.9998(4) 0.796(3) 0.161(5)    40 Phonon transport measurements    Figure S5. Temperature (T) dependence of heat capacity (C) and thermal diffusivity (D) for bulk samples of SrTiO2.87H0.06VO0.07, SrTiO2.73H0.16VO0.11, and SrTiO2.60H0.27VO0.13. The black dotted line in C vs. T data indicates the polynomial fitting with C = aT3+bT2+cT+d, where a, b, c, and d are fitting parameters.     41 DFT calculations  Figure S6. (a) Fully-relaxed crystal structures of cubic SrTiO3, SrTiO2.75H0.25, and SrTiO2.75VO0.25 models, drawn by VESTA.1 Sr, Ti, O, H atoms are depicted by blue, orange, yellow, and red spheres, respectively. VO position is indicated by dotted circles. (b) Ti−(O,H,VO) and Sr−(O,H,VO) lengths (the circle, square, and diamond markers represent the lengths of Ti–O, Ti–H, and Ti–VO, respectively), as well as (O,H,VO)−Ti−(O,H,VO) angles (α) in each Ti−(O,H,VO)6 octahedron and Ti−(O,H,VO)−Ti angles (β) between two Ti−(O,H,VO)6 octahedra. The Ti-VO length is determined by the distance between Ti and the center of VO.   Figure S7. Comparison of harmonic phonon dispersion (black dot lines) and finite-temperature phonon dispersion at T = 300 K (blue solid lines) for (a) cubic SrTiO3, (b) SrTiO2.75H0.25, and (c) SrTiO2.75VO0.25 models. When transferring the cubic SrTiO3 (5 atoms) to tetragonal SrTiO2.75H0.25 and SrTiO2.75Vo0.25 cell (20 atoms), R(0.5 0.5 0.5) is transfered to G(0 0 0). The unstable phonon  42 mode originating from AFD rotation of Ti-O6 octahedra is observed at R point for cubic SrTiO3, while it is observed at G point for SrTiO2.75H0.25, and SrTiO2.75VO0.25. Note that the additional unstable phonon mode is observed at A point for SrTiO2.75VO0.25.    43    Figure S8. Relationship between the calculated klat at T = 300 K and the deviation index (D) of Ti−(O,H,VO) lengths for SrTiO3, SrTiO2.75H0.25, and SrTiO2.75VO0.25 models. The distortion index D of perovskite oxides ABO3 is evaluated by 𝐷 = !"∑ $𝑑# − 𝑑̅$"#$! , where n is the number of B-O bonds, 𝑑# is each B-O bond length and 𝑑̅ is the average bond length in the B-O6 polyhedra.2-4 The Ti-VO length is determined by the distance between Ti and the center of VO.       Figure S9.  Calculated −COHPs for Ti-O and Ti–H bonds in SrTiO2.75H0.25 model. In SrTiO2.75H0.25 model, there are 5 different Ti-O bonds due to the distortion. Therefore, we plot –COHPs for all 5 Ti-O bonds. The positive value of -COHP indicates the bonding state, while the negative value is the anti-bonding state. The −iCOHP values were calculated by integrating −COHP up to Fermi level (EF) to estimate the bonding strength per bond. The averaged −iCOHP value of Ti–O bond is 3.58 eV/bond, while that of Ti–H bond is only 0.96 eV/bond.     44 Carrier mobility analysis Carrier mobility analyses were performed for SrTiO2.87H0.06VO0.07, SrTiO2.73H0.16VO0.11, and SrTiO2.60H0.27VO0.13 bulk samples. It is known that for electron-doped SrTiO3 with n > 1019 cm–3, μ at T below 300 K is mainly dominated by electron–electron scattering.5 This is because the high carrier density effectively screens the contribution of optical phonon scattering. However, at higher T, the μ is primarily limited by scattering from longitudinal (LO) optical phonons.6-8 We then analyzed the contribution of each scattering on µ in SrTiO3−x−dHxVOd bulks. As shown in Figures S10a-c, we fitted the low-T Hall mobility (µHall) using Matthiessen’s rule: 𝜇%&%.(!  = 𝜇)*+.(! +𝜇,(,(! + 𝜇&+%(! . Here, µimp. is the low-T limit of the µ determined by ionized impurity scattering, µe-e is the electron-electron scattering limited mobility, and µopt. is the optical phonon scattering limited mobility. Each mobility component is described as follows: 𝜇)*+.(! = A (constant),  𝜇,(,(! =  𝛼𝑇- (a is a measure of the strength of electron-electron scattering), and 𝜇&+%.(! = 1/ (B(exp 5ℏ/!016 − 1)), where B is constant, in the degenerate regime. The LO optical phonon energy (ℏ𝜔2) was fixed at 100 meV, which is typical for cubic SrTiO3.9 The calculated µtot. (shown as red line) based on the Matthiessen’s rule matched experimental µHall over a wide T range. The estimated µimp. decreases from 31 cm2/(Vs) for SrTiO2.87H0.06VO0.07 to 3.8 cm2/(Vs) for SrTiO2.60H0.27VO0.13. The decrease of µ with increasing T is mainly due to stronger electron-electron scattering. The estimated a for electron-electron scattering increases from 2.30×10-6 Vs/cm2K2 for SrTiO2.87H0.06VO0.07 and 4.52×10-6 Vs/cm2K2 for SrTiO2.60H0.27VO0.13. Figure S10d summarizes the H and VO concentration (x+d) dependence of the µimp. (triangles) and µe-e (pentagons) calculated using the extracted fitting parameters, and µtot. (circles) at T = 300 K. The higher concentration of H- and VO result in the  45 reduction both of µimp. and µe-e because of their contribution to the impurity scattering and increase of carrier concentrations.  We also estimated weighted carrier mobility (µw) at high T ≥ 300 K using the equation: 𝜇3 =45"678(-:#0$1)"/&:<=>? |(|)$/#(-@!A<=>?(BC |(|)$/#(!D@+"*&  |(|)$/#!A<=>?BC |(|)$/#(!D@; . Here, h is the Planck constant, kB is the Boltzmann constant, e is the elementary electric charge, and me is the free electron mass.10 µw is related to the drift mobility µ by 𝜇F ≈ 𝜇 5:∗:#64/-, where m* is the density of states effective mass. Figures S10e-g show the high-T µw fitted using the Matthiessen’s rule: 𝜇%&%.(!  = 𝜇)*+.(! + 𝜇&+%.(!  The calculated µtot. (shown as red line) agrees well with the measured µw, indicating the µ is mainly limited by the scattering from optical phonons at high T. Figure S10f shows the H and VO concentration (x+d) dependence of the µimp. (triangles) and µopt. (diamonds) calculated using the extracted fitting parameters, and µtot. (circles) at T = 673 K. Both µimp. and µopt. decrease with increase of x+d, indicating that higher impurity scattering and optical phonon scattering reduce the µtot. From these results, the µ of the SrTiO3−x−dHxVOd bulks is limited mainly by impurity scattering and electron-electron scattering at low T and that is limited by optical phonon scattering at high T, similar to the Sr1-xLaxTiO3 single crystal.1 On the other hand, it is known that μ of conventional La-doped SrTiO3 polycrystals is often limited by strong grain boundary (GB) scattering.11,12 The GBs act as a potential barrier for electron transport, reducing the σ across the GBs. In contrast, the present samples exhibit significantly higher µ with minimal GB scattering across the entire T range. This results in high PF by the single-crystal-like electron transport in SrTiO3−x−dHxVOd bulks even with its polycrystal form.   46  Figure S10. Analysis of carrier mobility (µ) as a function of temperature (T) for SrTiO2.87H0.06VO0.07, SrTiO2.73H0.16VO0.11, and SrTiO2.60H0.27VO0.13 bulks. (a-c) Low-T Hall mobility (µHall) vs. T (gray triangles). The red line shows the total mobility (µtot.) calculated by Matthiessen’s rule, 𝜇%&%.(!  = 𝜇)*+.(! + 𝜇,(,(! + 𝜇&+%.(! . The dark yellow, green, purple lines show the ionized impurity scattering limited mobility (µimp.), the electron-electron scattering limited mobility (µe-e), and the optical phonon scattering limited mobility (µopt.), respectively. (d) H and VO concentration (x+d) dependence of the µimp. (triangles) and µe-e (pentagons) calculated using the extracted fitting parameters, and µtot. (circles) at T = 300 K. (e-f) High-T weighted mobility (µw) vs. T (gray triangles). (h) H and VO concentration (x+d) dependence of the µimp. (triangles) and µopt. (diamonds) calculated using the extracted fitting parameters, and µtot. (circles) at T = 673 K.   47 References (1) K. Momma, F. 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