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[Andrei Novitskii](https://orcid.org/0000-0002-7304-806X), Michael Y. Toriyama, [Illia Serhiienko](https://orcid.org/0000-0002-3072-9412), [Takao Mori](https://orcid.org/0000-0003-2682-1846), G. Jeffrey Snyder, Prashun Gorai

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 This is the peer reviewed version of the following article: Andrei Novitskii, Michael Y. Toriyama, Illia Serhiienko, Takao Mori, G. Jeffrey Snyder, Prashun Gorai. Defect Engineering of Bi2SeO2 Thermoelectrics. Advanced Functional Materials. 2024, 35 (10), 2416509, which has been published in final form at https://doi.org/10.1002/adfm.202416509. This article may be used for non-commercial purposes in accordance with Wiley Terms and Conditions for Use of Self-Archived Versions. This article may not be enhanced, enriched or otherwise transformed into a derivative work, without express permission from Wiley or by statutory rights under applicable legislation. Copyright notices must not be removed, obscured or modified. The article must be linked to Wiley’s version of record on Wiley Online Library and any embedding, framing or otherwise making available the article or pages thereof by third parties from platforms, services and websites other than Wiley Online Library must be prohibited.[In Copyright](http://rightsstatements.org/vocab/InC/1.0/)

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[Defect Engineering of Bi<sub>2</sub>SeO<sub>2</sub> Thermoelectrics](https://mdr.nims.go.jp/datasets/68364e10-199b-49de-9751-f05c07b3ef3e)

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Defect Engineering of n-Type Bi2SeO2 ThermoelectricsAndrei Novitskii,a,† Michael Y. Toriyama,b,† Illia Serhiienko,a,c Takao Mori,a,c,∗ G. Jeffrey Snyder,b Prashun Goraid,e,∗Bi2SeO2 is a promising n-type semiconductor to pair with p-type BiCuSeO in a thermoelectric (TE) device. The TE figure of meritzT and, therefore, the device efficiency must be optimized by tuning the carrier concentration. However, electron concentrations inself-doped n-type Bi2SeO2 span several orders of magnitude, even in samples with same nominal compositions. Such unsystem-atic variations in the electron concentration has a thermodynamic origin related to the variations in native defect concentrations.In this study, we use first-principles calculations to show that the selenium vacancy, which is the source of n-type conductivityin Bi2SeO2, varies by 1–2 orders of magnitude depending on the thermodynamic conditions. We predict that the electron con-centration can be enhanced by synthesizing under more Se-poor conditions and/or at higher temperatures (TSSR), which promotethe formation of selenium vacancies without introducing extrinsic dopants. We validate our computational predictions throughsolid-state synthesis of Bi2SeO2. We observe more than two orders of magnitude increase in the electron concentration by solelyadjusting the synthesis conditions. Additionally, we reveal the significant effect of grain boundary scattering on electron transportin Bi2SeO2, which is controlled by adjusting TSSR. By simultaneously optimizing the electron concentration and mobility, we achievea zT of ∼0.2 at 773 K for self-doped n-type Bi2SeO2. Our study highlights the need for careful control of thermodynamic growthconditions and demonstrates TE performance improvement by varying synthesis parameters.1 IntroductionThermoelectric (TE) materials utilize the Seebeck effect for solid-state conversion of heat to electricity.1 The figure of merit (zT )is a measure of the TE performance of a material and is givenby zT = α2σT/κtot , where α, σ , κtot and T are the Seebeck co-efficient, electrical conductivity, total thermal conductivity, andtemperature, respectively. κtot is the sum of the electronic andlattice (phonon) contributions (κtot = κel + κlat). Layered oxy-chalcogenides are promising TE materials2–4 due to their high-temperature chemical and structural stability, relatively high See-beck coefficient, and intrinsically low κlat .5 p-type BiCuSeO, isa well-known mid-temperature TE material,6 with zT reaching amaximum of 1.5 at 873 K.7,8 We need both p-type and n-type legsto build a TE device. It would be ideal to use the same materialas the p- and n-type legs to avoid device failure due to differentcoefficients of thermal expansion and other issues. While p-typeBiCuSeO exhibits relatively high TE performance, it is challengingto obtain n-type BiCuSeO.9 Attempts to dope BiCuSeO n-type withhalogens,10–12 and transition metals,8,13 have resulted in eitherlow power factors and/or anomalous p-n-p transitions in the con-ductivity type with T . Therefore, an alternative n-type material isneeded to pair with p-type BiCuSeO in a TE device.Bi2SeO2 has emerged as a potential n-type material to pair withp-type BiCuSeO in TE devices. The crystal structure of Bi2SeO2can be thought of as BiCuSeO-derived with missing Cu. Bi2SeO2is known to be natively self-doped n-type.14 Pan, et al., demon-strated a TE module of p-type BiCuSeO and n-type Bi2SeO2 witha maximum device ZT of 0.8 at 793 K.15 The material zT of n-type Bi2SeO2 is lower than p-type BiCuSeO. To improve deviceefficiency, zT of each leg must be optimized, particularly throughaWPI-MANA, National Institute for Materials Science (NIMS), Tsukuba, Ibaraki 305-0044, Japan. bNorthwestern University, Evanston, IL 60208, USA. cGraduate Schoolof Pure and Applied Sciences, University of Tsukuba, Tsukuba, Ibaraki 305-8573,Japan. dColorado School of Mines, Golden, CO 80401, USA. eRensselaer Poly-technic Institute, NY 12180, USA. †These authors contributed equally. ∗E-mail:MORI.Takao@nims.go.jp, goraip@rpi.edu.charge carrier optimization. Although the electron concentrationin Bi2SeO2 in the aforementioned device was optimized througha mechanical shear exfoliation method,15 other routes have alsobeen adopted. Substituting Bi with Sb16 and La,17 Ge,18,19 Sn,20Ti,21 Ce,22 Nb23,24 and Ta,25 has been successful to various de-grees, either due to an increase in the electron concentration,change in the effective mass, or a combination of both. Substi-tuting Se or O with S,26 Te,27,28 and Cl29 has increased zT com-pared to self-doped Bi2SeO2. The highest zT of 0.69 at 773 Kwas achieved by Te substitution obtained through a mechanicalshear exfoliation technique,15,28 which was claimed to increasethe concentration of donor-like Se vacancies (VSe) leading to asixfold enhancement in the power factor.TE materials are often optimized through defect engineering,which can increase (or decrease) the concentration of charge car-riers and decrease κlat through increased phonon scattering. Theformation of point defects is strongly influenced by the synthe-sis conditions, including the reaction temperature. As a result,the reported electron concentrations in self-doped n-type Bi2SeO2span several orders of magnitude (1015 – 1019 cm−3) even in ma-terials with the same nominal composition. Bi2SeO2 synthesistypically involves a solid-state reaction step, where one procedureuses a two-step method with different reaction temperatures andholding times,18,25,30 while another uses a single solid-state reac-tion step at a fixed temperature.26 A fundamental question arises:are these different synthesis procedures responsible for the widevariations in the reported electron concentrations and therefore,the TE performance of Bi2SeO2? For practical purposes, how dowe systematically tune the electron concentration and improvethe TE performance?First-principles defect modeling can reveal the thermodynamicorigin of the variations in defect-dependent material properties,including doping preference,31 ionic conductivity,32 dielectricproperties,33 etc. In this work, we combine density functionaltheory (DFT) calculations and solid-state synthesis to show thatthe wide variations in the reported electron concentrations of n-type Bi2SeO2 are due to unsystematic changes in the point defect1–10 | 1MORI TAKAO取り消し線Bi2Se3Se-poorSe-richBi SeOBi2O3Bi2SeO2Bi2SeO5Figure 1 (a) Calculated phase diagram of the Bi-Se-O ternary composition space. Bi2SeO2 phase equilibria corresponding to the most Se-rich andmost Se-poor thermodynamic conditions are highlighted. The calculated formation energy (∆ED,q) of vacancy and antisite defects in Bi2SeO2 areshown for (b) most Se-poor condition, where Bi2SeO2 is in equilibrium with Bi and Bi2O3, and (c) most Se-rich condition, where Bi2SeO2 is inequilibrium with Se and Bi2SeO5. ∆ED,q of VSe is lowest and highest under the most Se-poor and Se-rich conditions, respectively.concentrations and grain boundary scattering of charge carriers.We show that the solid-state reaction temperature (TSSR) and el-emental chemical potential (Se concentration) are accessible ex-perimental knobs for controlling defect formation, grain bound-ary scattering, and TE performance of Bi2SeO2. Ultimately, byadjusting only the synthesis parameters, we achieved zT of 0.2 at773 K for n-type self-doped Bi2SeO2.2 Results and Discussion2.1 Defect Chemistry of Bi2SeO2Charged defects are the source of electronic carriers (electrons,holes) in semiconductors, and their concentrations directly affectthe electronic carrier concentrations. The defect concentrationdepends on two parameters – formation energy (∆ED,q) and tem-perature. Here, the temperature is typically the synthesis temper-ature at which the defects are sufficiently mobile to allow equi-libration. Among other factors, ∆ED,q also depends on the ther-modynamic phase equilibrium.31,32 In principle, both the tem-perature and phase equilibrium can be tuned by adjusting thesynthesis conditions, enabling control over defect formation, andconsequently, the electronic carrier concentration. To guide theoptimization of the TE properties of Bi2SeO2, we computed theformation energetics of native defects using first-principles defectcalculations. The computational methodology is discussed in Sec-tion 4. The goal is to identify experimental synthesis conditionsthat maximize electron concentration in n-type Bi2SeO2.Figure 1(a) shows the calculated equilibrium phase diagramin the ternary Bi-Se-O chemical space. There are 5 distinctphase equilibria regions of Bi2SeO2, corresponding to the trian-gles around Bi2SeO2. ∆µi are determined by the phase stabilityof Bi2SeO2 in the grand potential phase diagram and it capturesthe synthesis conditions, e.g., Se-rich and Se-poor growth condi-tions. The elemental chemical potentials (∆µi) in each of thesethree-phase equilibria are listed in Table S1.∆ED,q depends on ∆µi (Eq. 5). Figure 1 shows ∆ED,q plotted asa function of the Fermi energy (EF) under two limiting synthesisconditions – Se-poor (equilibrium with elemental Bi and Bi2O3)and Se-rich (equilibrium with elemental Se and Bi2SeO5). We findthat under both conditions, selenium vacancies (VSe) are the dom-inant defects with lowest ∆ED,q, followed by oxygen vacancies(VO). Both VSe and VO are shallow donors, i.e., they donate freeelectrons and are responsible for the n-type conduction in self-doped Bi2SeO2. ∆ED,q of VSe is the lowest under Se-poor synthesisconditions (Figure 1b) and the highest under Se-rich conditions(Figure 1c), but regardless of the synthesis conditions, Bi2SeO2remains an n-type material. The low ∆ED,q of the donor VSe andVO imply that Bi2SeO2 cannot be doped p-type because the holesgenerated by the acceptor dopant will be charge-compensated bythe electrons produced by the native donor defects.The free electron concentration (n) in Bi2SeO2 is principallydetermined by the formation energy of donor-like VSe, which isdifferent for each phase equilibrium condition. Therefore, wepredict a range of n at a given synthesis temperature (Figure 2).The upper bound of n is determined by the most Se-poor condi-tion (lowest VSe formation energy) and the lower bound by themost Se-rich condition (highest VSe formation energy). The mea-sured n for single-crystal Bi2SeO2 are within the range calculatedwith DFT. However, the measured n in polycrystalline samplesvary between 1015 and 1019 cm−3, and in many cases, fall outsidethe DFT calculated range. We attribute this discrepancy to thepresence of grain boundaries in polycrystalline samples, whichcan act as sources or sinks of electronic carriers. For example,atom probe tomography showed evidence that Mg-deficient grainboundaries in Mg3Sb2 can deplete free electrons from the mate-rial, thus lowering its concentration relative to the grains.34 Ourpredictive defect model does not account for extended defectssuch as grain boundaries, which could explain the discrepancybetween the measured and calculated n.The large variations in n for polycrystalline samples are pre-sumably due to the differences in the microstructure arisingfrom different processing conditions , e.g., ball milling, shear ex-foliation, different atmospheres during the solid-state reaction,2 | 1–10600 800 1000 1200Synthesis temperature (K)10151016101710181019Carrier concentration (cm3 )Se-poorSe-richPredictedrangeBi2SeO2Bi2SeO2-OSBi2Se0.95O2773773773873873873973973973107310731073117311731173Drasar et al.Chen et al.Mao et al.Wang et al.Xu et al.Liu et al.Hong et al.Tan et al.Pan et al.Zheng et al.Figure 2 The charge carrier concentration of Bi2SeO2 as a function ofsynthesis temperature. The upper and lower bounds (black dashedlines) of the free electron concentration are predicted from DFT defectcalculations under Se-poor and Se-rich conditions, respectively.Experimentally measured n values obtained in this work are shown asopen (Bi2SeO2), solid (Bi2SeO2 fabricated by one-step solid-statereaction), and filled (Bi2Se0.95O2) symbols, respectively. Literature datafor single crystals (filled gray symbols) and polycrystals (open graysymbols) is also shown for comparison (Drasar et al., 35 Chen et al., 36Mao et al., 37 Wang et al., 38 Xu et al., 39 Liu et al., 18 Hong et al., 22 Tanet al., 25 Pan et al., 15 Zheng et al. 30).etc.15,25,30 For example, Pan et al. increased n from ∼ 1016 cm−3to ∼ 1019 cm−3 using a shear exfoliation technique,15 which isclaimed to form a high concentration of VSe, even higher than theequilibrium concentrations predicted by our defect calculations.Similarly, synthesis conditions that allow more Se evaporation(vs. conditions with limited Se ventilation) will create Se-poorenvironments that promote the formation of VSe and increase n.For example, Zheng et al. conducted solid-state synthesis on pow-ders of Bi2SeO2 rather than cold-pressed pellets, which caused Seevaporation due to relatively poor mixing.30In order to engineer the TE properties of Bi2SeO2 rationally,defects must be controlled systematically. The VSe concentrationand, therefore, n can be controlled by (1) tuning the synthesistemperature, and (2) changing the synthesis condition (Se-richvs. Se-poor). Since many recipes for Bi2SeO2 involve a solid-state reaction step, an accessible experimental knob for tuningn is the solid-state reaction temperature (TSSR). Moreover, thenominal composition can be varied to explore TE properties un-der Se-rich and Se-poor conditions. In the following sections, weshow the effects of modifying thermodynamic conditions on themicrostructure, n, and TE properties.2.2 Structural and Microstructural PropertiesWe synthesize two series of samples, one with a nominally sto-ichiometric composition of Bi2SeO2, and another with a nominalcomposition of Bi2Se0.95O2. Both series were synthesized througha two-step solid-state reaction followed by spark plasma sintering(SPS), as detailed in Section 4. To reveal the effect of processingconditions during the solid-state reaction, samples with a nomi-nal composition of Bi2SeO2 were also obtained using a one-stepprocedure (see Section 4 for details). Since the data obtained forthis series of samples are similar to those for Bi2SeO2 obtained bya two-step solid-state reaction, it is mainly presented in the Sup-porting Information. To explore the effects of synthesis temper-ature, we vary the solid-state reaction temperature (TSSR) from773 K to 1173 K for each series.The room-temperature X-ray powder diffraction (XRD) pat-terns of all samples are displayed in Figure 3 and Figure S1. Allthe main diffraction peaks correspond to the Bi2SeO2 phase withthe tetragonal (Na0.25Bi0.75)2O2Cl-type structure and I4/mmmspace group.40 In nominally stoichiometric samples, no sec-ondary phases are discernible (Figures 3a, S1). Thus, within thedetection limit of XRD, we can confirm that all specimens, regard-less of TSSR and number of steps during reaction, exhibit a pristineBi2SeO2 phase. The actual composition and the distribution of el-ements examined by energy-dispersive X-ray spectroscopy (EDS)indicate that all the elements are homogeneously distributed, andthe actual compositions are similar to the nominal ones for all thesamples among both the one-step and two-step series of Bi2SeO2(Figures S2 – S6).In the relatively Se-poor samples synthesized with a nomi-nal composition of Bi2Se0.95O2, however, peaks corresponding toBi2O3 impurities are evident near 27◦ in the XRD patterns (Fig-ure 3c). In fact, trace amounts of both Bi2O3 and elemental Bican be found in EDS measurements (Figures S2 – S6), indicatingthat these samples exist in the three-phase equilibrium region la-beled “Se-poor” in Figure 1a. However, while remaining in thethree-phase region, it seems that the ratio of secondary phases inthese samples changes with increasing TSSR, as indicated by thevariations in intensities in the XRD patterns (Figure 3c). Whilethe intensities of monoclinic Bi2O3 decrease with increasing TSSR,for the sample with TSSR = 1173 K, reflections from cubic and/ortetragonal Bi2O3 also become visible near 28◦, as can be expectedwhen Bi2O3 is heated above 1030 K.41As TSSR increases, there is a noticeable increase in the rela-tive intensities of (00l) peaks shown in the XRD patterns (Fig-ures 3a, b, S7). This suggests a preferential orientation of thecrystallites, which is commonly observed in layered oxyselenidesfollowing a uniaxial densification process.42,43 Indeed, in con-trast to the samples obtained at TSSR = 773 K with randomlyarranged platelet grains (Figure 3d), the grains of the samplessynthesized at TSSR = 1173 K are more aligned along a singledirection (Figure 3e). The degree of ab orientation for the (00l)crystal planes, termed as F(00l) and determined using the Lotger-ing method, rises from slightly less than 0.05 at TSSR = 773 K tojust over 0.25 at TSSR = 1173 K (Figure S7), further supportingpreferential grain orientation in the samples. Interestingly, along1–10 | 320 40 60 802  (degree)Intensity (arb. units)Bi2SeO2Bi2SeO2 (a)(101)(004)(103)(110) (006)(200)(008)(0010)20 40 60 802  (degree)Bi2Se0.95O2 (b)(101)(004)(103)(110) (006)(200)(008)Bi2SeO2, Bi2O3773 K873 K973 K1073 K1173 K25 30 352  (degree)(c) (d)TSSR = 773 K10 m(e)TSSR = 1173 K10 mFigure 3 Room temperature X-ray diffraction patterns of (a) Bi2SeO2 and (b) Bi2Se0.95O2 samples prepared by two-step solid-state reaction.(c) Magnified section of (b) in a 2θ range from 25◦ to 35◦ to show the most intensive reflections corresponding to Bi2O3. In (c), the main diffractionpeak of the Bi phase is also indicated by a black triangle (▼). SEM micrographs of the fracture surface for Bi2SeO2 obtained at (d) TSSR = 773 K and(e) TSSR = 1173 K, respectively.with a more pronounced preferred orientation, the grain size alsoproportionally increases with rising TSSR, but only in the in-planedirection; meanwhile, the thickness of platelet-like grains slightlydecreases from 400 – 600 nm (TSSR = 773 K) to 200 – 400 nm(TSSR = 1173 K), as shown in Figures 3d and 3e. Note that thestronger intensities of the (00l) peaks with increasing TSSR (Fig-ures 3a, b) may also suggest an increase in the concentration ofVSe, as the I(004)/I(101) ratio is dependent on the Se content.442.3 Experimental Carrier ConcentrationIn the nominally stoichiometric series synthesized using thetwo-step solid-state reaction procedure, we observe a gradualincrease in carrier concentration (n) with increasing TSSR, from∼ 6× 1015 cm−3 at TSSR = 773 K to ∼ 4× 1017 cm−3 at TSSR =1173 K (Figure 2). This is consistent with the DFT prediction thatincreasing the synthesis temperature will increase n, suggestingthat more VSe defects are being generated with increasing TSSR. Asimilar increase in n with TSSR is observed in Bi2SeO2 synthesizedusing the one-step solid-state reaction process (Figure 2).Interestingly, n of the one-step sub-series are slightly higherthan those of the two-step sub-series, and this difference dimin-ishes as TSSR increases (Figure 2). The difference in n can be at-tributed to the thermodynamic conditions established by the tworeaction series. Se does not have sufficient time to react with Biduring the one-step solid-state reaction,30 whereas most Se re-acts with Bi and forms an intermediate Bi2Se3 phase during theinitial heating stage at 573 K in the two-step process. Bi2SeO2 istherefore in a slightly more Se-rich state when synthesized with atwo-step solid-state reaction than with a one-step process, whichlowers n. At higher TSSR, the difference in n between the one-stepand two-step sub-series reduces because Se can evaporate fromBi2SeO2 more readily. At the same time, n for the samples ob-tained at TSSR = 1173 K is slightly lower compared to that at TSSR= 1073 K. This could be attributed to the Se-rich environmentformed in the sealed tubes during the solid-state reaction at highTSSR.The Bi2Se0.95O2 samples exhibit higher n than the stoichiomet-ric samples (Figure 2). This observation is consistent with thehigher concentration of VSe defects, arising from the lower forma-tion energy of VSe under Se-poor conditions (Figure 1b) comparedto Se-rich conditions (Figure 1c). Despite the larger concentrationof VSe in the Bi2Se0.95O2 samples, we find that n decreases slightlywith TSSR, contrary to the stoichiometric series where n increaseswith TSSR. It is unclear what is causing the inverse trend betweenn and TSSR in the Bi2Se0.95O2 samples, as it can arise from nu-merous factors such as defect equilibration during the SPS stepof the synthesis instead of the solid-state reaction step, the tem-perature dependence of the elemental chemical potentials ∆µi, orfree carriers from the impurity phases Bi2O3 and elemental Bi.Nonetheless, our results confirm that synthesizing Bi2SeO2 underslightly Se-poor conditions (in this case, nominally Bi2Se0.95O2)can raise n compared to a stoichiometric composition, especiallyat lower solid-state reaction temperatures (Figure 2).2.4 Electrical Transport PropertiesWe analyze the evolution of electrical transport properties inour samples using a single parabolic band transport model, whichis appropriate for Bi2SeO2 given the nearly parabolic conductionband obtained from DFT (Figure S8). We studied the Seebeck co-efficient (α) as a function of electrical conductivity (σ) and car-rier concentration (n) as shown in Figure 4. For semiconductorswith a chemical potential η ≤ 1 (|α| ≥ 150 µV K−1), the relation-ship between α and n (or σ) can be described by the Pisarenkoformula:1α =±kBer+52+ ln(2(2πm∗dkBT )3/2h3n) (1)orα =±kBer+52+ ln(Γ(r+52)σE0)− lnσ , (2)4 | 1–10where kB is the Boltzmann constant, e is the electron charge, r isthe scattering factor (r = −1/2 for acoustic phonon scattering),m∗d is the density-of-states effective mass, h is the Planck’s con-stant, Γ is the gamma function, and σE0 is the transport coeffi-cient, which is merely a function of the weighted mobility:45σE0 =8πe(2πmekBT )3/23h3 µw. (3)Here, µw is the weighted mobility given by µw = µ0(m∗d/me)3/2,where µ0 represents the intrinsic carrier mobility, and me is theelectron mass.Figure 4 shows the Pisarenko (Figure 4a) and Jonker (Fig-ure 4b) plots for Bi2SeO2 samples from the literature as wellas those studied in the present work. In agreement with sin-gle parabolic band transport and previous reports,14 the effectivemass is estimated to be m∗d ≈ 0.2 for all the samples (Figure 4a).At the same time, the electrical transport properties of Bi2SeO2and Bi2Se0.95O2 are clearly modified by tuning TSSR (Figures 4,5). The negative α confirms the n-type conduction, i.e., electronsare the majority charge carriers. At room temperature, there is atwofold decrease in α of the Bi2SeO2 samples as TSSR and, conse-quently, n increases (Figures 4, S9a). Simultaneously, the room-temperature σ increases by nearly three orders of magnitude byelevating TSSR from 773 K to 1173 K (Figures 4b, S9b), consistentwith the increase in n (Figure 2). The optimized balance betweenσ and α leads to a nearly two order of magnitude improvementin the power factor (α2σ) as the solid-state reaction temperatureincreases from 773 K to 1173 K (Figure S9c).The weighted mobility of Bi2SeO2 samples also increases withTSSR (Figure 4b), which are at odds with the single parabolic bandmodel. Typically, charge carrier mobility decreases when carrierdensity increases in semiconductors. The weighted mobility (µw)and Hall mobility (µH), however, both unexpectedly increase byover an order of magnitude with elevated TSSR (Figure S10). In-deed, µw of Bi2SeO2 varies from less than 10−1 cm2 V−1 s−1 forfine-grained polycrystalline samples to almost 102 cm2 V−1 s−1for single crystals despite comparable carrier density level (Fig-ure 4b). The temperature dependence of µw can be used to re-veal the main charge carrier scattering mechanism, in a similarway to the analysis of µH(T ).45 A closer look at µw(T ) indeedindicates changes in electron scattering (Figure S11). Similarto Mg3Sb2 and SrTiO3,46,47 it seems that grain boundary scat-tering plays an important role in the charge carrier transport ofBi2SeO2. Grain boundary resistance is also evident from the in-crease in σ with measurement temperature (not to be confusedwith TSSR) at T < 500 K for samples obtained at TSSR below973 K (Figure 5a). Se-poor Bi2Se0.95O2 samples, in turn, showfar less thermally-activated conductivity near room temperature(Figure 5a). Moreover, samples synthesized at higher TSSR ex-hibit reduced grain boundary scattering (Figure S11). This re-duction allows µw and µH to approach values similar to those ofsingle crystals (Figures 4b, S10). All of the aforementioned makecharge carrier mobility the main reason behind the increase in σof Bi2Se0.95O2 from 14 Ω−1 cm−1 (TSSR = 773 K) to 36 Ω−1 cm−1(TSSR = 1073 K) at room temperature (Figure S9b), while α is10 2 100 102 ( 1 cm 1)0200400600 (V K1 )(b)10 010 1 w =10 2 (cm 2 V1 s1)10 310 41015 1016 1017 1018 1019n (cm 3)0200400600 (V K1 )(a)m*d =0.2Bi2SeO2Bi2SeO2-OSBi2Se0.95O2773773773873873873973973973107310731073117311731173Drasar et al.Wang et al.Liu et al.Tan et al.Hong et al.Pan et al.Zheng et al.Figure 4 Room temperature Seebeck coefficient versus (a) carrierconcentration (Pisarenko plot) and (b) electrical conductivity (Jonkerplot) for Bi2SeO2 (open symbols) and Bi2Se0.95O2 (filled solid symbols)samples fabricated by a two-step solid-state reaction at differenttemperatures. Data for Bi2SeO2 fabricated by a one-step solid-statereaction is also presented (solid symbols). The solid line in (a)represents the Seebeck coefficient calculated in the framework of thesingle parabolic band model, assuming acoustic phonon scattering(r =−1/2) and m∗d = 0.2. The dashed lines in (b) represent thePisarenko formula (Eq. 2) for different weighted mobility values (µw incm2 V−1 s−1), each labeled next to its corresponding curve at the toppart of the figure. For comparison, literature data for both single crystals(filled gray symbols) and polycrystals (open gray symbols) are alsoshown (Drasar et al., 35 Wang et al., 38 Liu et al., 18 Hong et al., 22 Tan etal., 25 Pan et al., 15 Zheng et al. 30).only slightly affected by changes in TSSR (Figures 5b, S9a). Inter-estingly, similar changes in the temperature dependence of elec-trical conductivity were also observed in the study of Pan et al.,15where the activated behavior of σ(T ) was suppressed with an in-crease in shear-exfoliation time. The authors did not discuss thisin detail, but the reduction in grain boundary scattering mightbe another reason for shear-exfoliated Bi2SeO2 to exhibit higherzT values, in addition to the significant increase in VSe concentra-tion.15,28Overall, there are noticeable difference in the transport prop-1–10 | 5erties between Se-poor Bi2Se0.95O2 samples and nominally stoi-chiometric Bi2SeO2 samples. Our results demonstrate that care-fully controlling thermodynamic conditions (chemical potential,temperature) during the synthesis of Bi2SeO2 allows independentcontrol of both charge carrier concentration (n) and mobility (µ).Simultaneous optimization of n and reduction of grain boundaryscattering by shifting synthesis conditions to Se-poor and increas-ing TSSR have resulted in a sizeable improvement of the powerfactor across the entire temperature range studied (Figure S12).2.5 Thermal Transport and Thermoelectric EfficiencyThe total thermal conductivity (κtot) monotonically de-creases with temperature for all the samples, reaching nearly1 W m−1 K−1 or below at 773 K (Figure 5c). For the Bi2SeO2sample obtained at TSSR = 1173 K, κtot reaches its lowest values,approaching the glassy limit (≈ 0.55 W m−1 K−1)48 at 773 K. Tofurther understand the thermal transport in Bi2SeO2, we exam-ine both the lattice (κlat) and electronic (κel) contributions to κtotusing the Wiedemann-Franz law, as described in Section 4. Theelectronic contribution does not exceed 3% even for Bi2Se0.95O2samples (which have high σ), indicating that the κtot is predom-inantly determined by the lattice contribution. Furthermore, ouranalysis reveals that point defects are the dominant phonon scat-tering mechanism as κlat(T ) follows a T−0.6 dependence for allsamples (Figure S12).In Bi2SeO2 samples in particular, a considerable drop in κtot bymore than 30% upon increasing TSSR is observed (Figure S9d),which can be attributed to the increase in VSe concentration.This substantial reduction in κtot is comparable to, and even sur-passes, the reported reduction in κtot for conventionally-dopedBi2SeO2.17,18,22,25,27 This becomes possible due to the high effi-cacy of vacancy defects as scattering centers in contrast to sub-stitutional atoms. The formation of vacancies involves the com-plete removal of bonds to the neighboring atoms, which intro-duces strong mass and strain fluctuations and decreases κlat .49,50On the other hand, κtot of Se-poor Bi2Se0.95O2 samples slightly in-creases with increase in TSSR (Figure S9d). This is consistent withthe discussion presented in Sections 2.3 and 2.4, suggesting thatthe VSe concentration does not vary significantly in Bi2Se0.95O2samples upon increasing TSSR. In the Se-poor samples, the maineffect of increasing TSSR is the corresponding grain growth, whichis most likely the origin of the observed increase in κtot .We achieve a peak zT of 0.15 – 0.2 at 773 K for Bi2SeO2 sam-ples obtained at TSSR = 1073 K and 1173 K, as well as Se-poorBi2Se0.95O2 samples obtained at TSSR below 1173 K (Figure 5d).These are some of the highest zT values reported thus far forundoped Bi2SeO2 obtained with solid-state reaction synthesis,which typically reaches zT ≤ 0.1.15,17,18,22,25,27 The improvementin zT can be understood through the quality factor β ∝ µw/κlat ,which determines the maximum zT achievable for a given car-rier concentration at a specific temperature.1,51 In Bi2SeO2, in-creasing TSSR generates more VSe, resulting in a higher weightedmobility (Figure S9e) and lower lattice thermal conductivity (Fig-ure S9d). As a result, the quality factor β is enhanced with TSSR(Figure S9f), and a higher zT is achieved (Figure S14). Such a10 210 1100101 (1  cm1 )(a)Bi2SeO2Bi2Se0.95O27737738738739739731073107311731173T (K)600400200 (V K1 )(b)0.61.01.41.8tot (W m1  K1 )(c)300 400 500 600 700 800T (K)0.00.10.2zT(d)Figure 5 Temperature dependence of the (a) electrical conductivity σ ,(b) Seebeck coefficient α, (c) total thermal conductivity κtot , and (d) thefigure of merit zT for Bi2SeO2 samples fabricated by one-step (solidsymbols) and two-step (open symbols) solid-state reactions.noticeable improvement of µw is possible due to the simultaneousoptimization of charge carrier concentration and the reduction ofgrain boundary scattering, as discussed in detail in Section 2.4.In turn, even more pronounced suppression of grain boundaryscattering in Se-poor samples correspondingly leads to a moresubstantial increase in µw (Figure 4b). Consequently, β is also sig-nificantly improved despite a slight increase in κlat of Bi2Se0.95O2with TSSR (Figure S9d). Although this does not lead to a signifi-cantly higher zTmax value, it still improves zT at low temperatures6 | 1–10(Figure 5d), thereby leading to higher ZTav in Bi2Se0.95O2.3 ConclusionsThe development of efficient n-type oxyselenide-based TE ma-terials requires precise control of native defects. In this work,we combine theory and experiment to demonstrate that TE prop-erties and performance in n-type Bi2SeO2 can be improved bysystematically controlling defect formation with synthesis condi-tions. We predict that VSe is the main source of n-type conductiv-ity, and that the free electron concentration can be increased withthe synthesis temperature and/or shifting thermodynamic condi-tions from Se-rich to Se-poor. Experiments largely confirm thesepredictions. When the solid-state reaction temperature (TSSR)is elevated, nominally stoichiometric samples of Bi2SeO2 exhibitenhanced electron concentration n and reduced grain boundaryscattering, thus improving the power factor. A suppression inthermal conductivity is also observed, consistent with the higherVSe content at higher TSSR. Relatively Se-poor samples (with nom-inal composition of Bi2Se0.95O2), on the other hand, exhibit nabout two orders of magnitude larger than nominally stoichio-metric samples for TSSR at or below 873 K. However, n and theVSe concentration are not significantly affected by TSSR; instead,a reduction in grain boundary scattering explains the increase incarrier mobility and enhancement in power factor. The thermalconductivity increases slightly with TSSR due to grain size growth.Cumulatively, simultaneous charge carrier concentration and mo-bility improvement yield a fourfold enhancement of the zT in self-doped Bi2SeO2, ultimately reaching ∼0.2 at 773 K. This studyunderscores the importance of systematically controlling synthe-sis parameters to regulate defect formation and carrier scatteringin Bi2SeO2.4 MethodsExperimental detailsSample preparation. Samples with the nominal composi-tion of Bi2SeO2 and Bi2Se0.95O2 were synthesized using two-stepsolid-state reaction. Commercial powders of Bi2O3 (Strem Chem-icals, 99.9998%), Bi (Sigma-Aldrich, ≥99.99%), and Se (Sigma-Aldrich, 99.99%) were used as starting materials. The powderswere weighed according to the stoichiometric ratio and subse-quently mixed in a stainless-steel jar without milling media, us-ing a high-energy ball mill (8000D Mixer/Mill, SPEX SamplePrep,USA) for 5 min. The obtained mixture was then cold pressed intopellets and sealed in evacuated quartz tubes. The tubes wereheated to 573 K and held for 6 h, followed by subsequent heat-ing to the temperature range from 773 K to 1173 K and held foranother 12 h. Another series of samples with the nominal com-position Bi2SeO2 was also prepared by a one-step solid-state reac-tion, where the sealed tubes were directly heated to temperaturesranging from 773 K to 1173 K and held for 10 h. All the obtainedsamples were ground to powders by hand and consolidated usingspark plasma sintering (SPS; Dr. Sinter-1080, Fuji-SPS, Japan)at 903 K for 5 min in a graphite die under uniaxial pressure of50 MPa in an Ar atmosphere. After SPS, the sintered pellets wereannealed at 803 K for 6 h in an evacuated quartz tube.Structural and morphological characterization. X-raydiffraction (XRD) patterns were collected at room temperatureusing a MiniFlex diffractometer (Rigaku, Japan) with a Cu-Kα ra-diation. The ab orientation degree for the (00l) crystal planes ofthe bulk samples was estimated by the Lotgering method asF(00l) =P−P01−P0, withP =∑ I(00l)∑ I(hkl), and P0 =∑ I0(00l)∑ I0(hkl),(4)where P and P0 are the ratios of the integrated intensities ofall (00l) crystal planes to those of all (hkl) planes for preferen-tially and randomly oriented samples. F(00l) = 0 and F(00l) = 1refer to completely disordered and ordered cases, respectively.52The morphology of the sintered samples was examined by fieldemission scanning electron microscopy (FESEM; Hitachi SU8230,Japan). The actual chemical composition of the samples was ob-tained with the aid of energy-dispersive X-ray spectroscopy (EDS;X-MaxN EDS detector, Horiba Scientific, Japan).Transport properties characterization. The bulk sampleswere cut and polished into the required shapes and dimensionsfor various measurements. The Seebeck coefficient α and electri-cal conductivity σ were simultaneously measured on rectangularbars with dimensions of 1× 3× 8 mm3 using a commercial ap-paratus (ZEM-3, Advance Riko Inc., Japan) under a partial Hepressure. The total thermal conductivity κtot was determined us-ing the formula κtot = χ ·Cp ·d, where χ is the thermal diffusivity,Cp is the specific heat capacity, and d is the volume density mea-sured through the Archimedes method. The thermal diffusivity χwas measured on graphite-coated disc-shaped samples of 10 mmdiameter and ∼1 mm thickness using the laser flash technique(LFA 467 Hyperflash, Netzsch, Germany) and analyzed using amodified Cape-Lehman model53 with pulse correction. Simulta-neously, the Cp was estimated using the comparison method witha standard sample (pyroceram-9606). The obtained Cp valueswere found to be in good agreement with those calculated usingthe Debye model. The lattice thermal conductivity κlat was calcu-lated from κtot by subtracting the electronic contribution κel esti-mated according to the Wiedemann–Franz law where κel = σLT .L is the Lorenz number derived from the Seebeck coefficient inthe framework of the single parabolic band model with acous-tic phonon scattering.54 All transport properties were measuredalong the direction perpendicular to the sintering pressure. TheHall measurements were performed at room temperature using aphysical properties measurement system (PPMS9T, Quantum De-sign Inc, USA). Electrical contacts were made with a 0.025-mmplatinum wire and silver paste (Ted Pella, Inc., USA). To improveelectrical contact, a thin layer of silver was pre-deposited onto thecontact area. The Hall coefficient RH was obtained from the lin-ear fit of the Hall resistivity versus magnetic field between −5 and5 T. The Hall carrier concentration was calculated by nH = 1/eRH,where e is the electronic charge. In principle, the Hall carrier con-centration is related to the carrier concentration through n= nHrHwith rH representing the Hall factor, which depends on the chem-ical potential and on the carrier scattering mechanism (see Sup-1–10 | 7porting Information). Thus, free electron concentration n wasestimated in the framework of the single parabolic band model,assuming acoustic phonon scattering as the main scattering mech-anism for carriers. The Hall carrier mobility µH was calculated byµH = σRH, where σ is the electrical conductivity. The uncertaintyof the Hall measurements was estimated to be 5 – 10%, whilefor the Seebeck coefficient, it was estimated to be 6%, 8% for theelectrical conductivity, 11% for the thermal conductivity, and 16%for the figure of merit zT .55Computational detailsDensity functional theory (DFT) calculations were performedusing the Vienna Ab initio Simulation Package (VASP)56,57 underthe projector-augmented wave formalism.58,59 An energy cutoffof 340 eV was used in all calculations.Since Bi2SeO2 has a layered structure with space groupI4/mmm, the generalized gradient approximation (GGA) ofPerdew-Burke-Ernzerhof (PBE) overestimates the c axis by 1.2%(Table S2) due to the underbinding of layers in quasi-2D struc-tures by GGA.60 We therefore use the vdW-corrected optB86(vdW) functional61 to relax all structures related to Bi2SeO2(bulk, defects, etc.). As shown in Table S2, the lattice constantsare in much better agreement with experiments with the vdWfunctional. The electronic structure of Bi2SeO2 was calculatedusing the HSE06 functional with spin-orbit coupling on the vdW-relaxed structure, as suggested by Marom et al.62 The density ofstates was calculated using the tetrahedron method63 and a Γ-centered 8× 8× 4 grid for k-point integration.64 The calculatedband gap is Eg = 0.857 eV, in agreement with the experimentalband gap of 0.8 – 0.9 eV.36,65,66All point defect calculations were performed on a 3×3×2 su-percell of Bi2SeO2 (containing 90 atoms total). A two-step com-putational process was undertaken, where structural relaxationswere performed using the vdW functional and, subsequently, thetotal energies were calculated using HSE06. A similar approachwas taken in a previous study of point defect chemistry in layeredBiCuSeO,9 where fair agreement with experimental carrier con-centrations was observed. The formation energy ∆EDq of a defectD with charge state q was calculated using the formula67∆EDq = EDq −Ehost −∑iniµi +qEF +Ecorr (5)where EDq and Ehost are the total energies of the supercell withand without the defect, respectively, µi is the chemical poten-tial of an atom that is either added (ni > 0) or removed (ni < 0)to created defect D, EF is the Fermi energy, and Ecorr is a cor-rection to the formation energy arising from finite-size effectsof the supercell approach. We represent the chemical poten-tial of each element as a deviation from a reference state, i.e.,µi = µ0i +∆µi, where the elemental reference energy µ0i was fit toa set of experimentally-measured formation enthalpies of severalcompounds under standard conditions (Table S3).68 The devia-tion from the reference energy, ∆µi, is determined by the thermo-dynamic conditions of the system. Since Bi2SeO2 is in thermo-dynamic equilibrium with different secondary phases dependingon the initial synthesis conditions of the sample, ∆µi of each el-ements will also differ (Table S1); for example, if Bi2SeO2 is inequilibrium with Bi2O3 and elemental Bi (i.e., the most Se-poorcondition), then the chemical potentials ∆µi are determined bythe following set of equations:2∆µBi +2∆µO +∆µSe = ∆HBi2SeO2f∆µBi = ∆HBif (= 0)2∆µBi +3∆µO = ∆HBi2O3f(6)Since we assumed a dilute-limit model, corrections arising fromfinite-size effects, i.e., Ecorr, were also considered.69 Due to thefinite supercell size used in our defect calculations, we consid-ered energy corrections arising from three factors: (i) long-rangeinteractions between image charges across periodic boundaries,(ii) misalignment of the average electrostatic potential betweenthe system with and without the defect, and (iii) Moss-Burstein-type band filling of shallow defects.70The free charge carrier concentrations were calculated follow-ing the charge neutrality condition∑Dq[qNDe−∆EDq/kBT]+ p−n = 0 (7)where ND is the site concentration, kB is the Boltzmann constant,and T is the synthesis temperature. The free hole (p) and electron(n) concentrations are calculated using the density-of-states g(E)and the Fermi-Dirac distribution f (E) asp =∫ VBM−∞g(E)[1− f (E)]dE,n =∫∞CBMg(E) f (E)dE.(8)AcknowledgementsT.M., A.N., and I.S. acknowledge JST Mirai JPMJMI19A1 andJST SPRING JPMJSP2124. M.Y.T. is funded by the United StatesDepartment of Energy through the Computational Science Gradu-ate Fellowship (DOE CSGF) under grant number DE-SC0020347.M.Y.T. also acknowledges support from the Johannes and JuliaRandall Weertman Graduate Fellowship. M.Y.T. and G.J.S. ac-knowledges the support of award 70NANB19H005 from U.S. De-partment of Commerce, National Institute of Standards and Tech-nology as part of the Center for Hierarchical Materials Design(CHiMaD). P.G. acknowledges support from NSF through awardDMR-2102409. The research was performed using computationalresources sponsored by DOE’s Office of Energy Efficiency and Re-newable Energy and located at the NREL. A part of this work wassupported by “Advanced Research Infrastructure for Materials andNanotechnology in Japan (ARIM)” of the Ministry of Education,Culture, Sports, Science and Technology (MEXT); proposal num-ber JPMXP1224NM5121.CRediT StatementAndrei Novitskii: Conceptualization, Methodology, Investiga-tion, Data Curation, Writing (Original Draft). Michael Toriyama:8 | 1–10Conceptualization, Investigation, Data Curation, Writing (Orig-inal Draft). Illia Serhiienko: Investigation, Writing (Editing).Takao Mori: Writing (Editing), Resources, Supervision, FundingAcquisition. G. Jeffrey Snyder: Writing (Editing), Supervision.Prashun Gorai: Conceptualization, Writing (Editing), Supervi-sion, Project Administration.Conflicts of InterestThere are no conflicts to declare.Data Availability StatementThe data that supports the findings of this study are availablewithin the article and its supplementary material.References1 A. F. 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