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[Yukari Katsura](https://orcid.org/0000-0002-8905-2995), Masaya Kumagai, Takushi Kodani, Mitsunori Kaneshige, Yuki Ando, Sakiko Gunji, Yoji Imai, Hideyasu Ouchi, Kazuki Tobita, Kaoru Kimura, [Koji Tsuda](https://orcid.org/0000-0002-4288-1606)

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[Data-driven analysis of electron relaxation times in PbTe-type thermoelectric materials](https://mdr.nims.go.jp/datasets/ea8104f9-bcc6-4cfb-b6fb-b85cf0ecee66)

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Data-driven analysis of electron relaxation times in PbTe-type thermoelectric materialsFull Terms & Conditions of access and use can be found athttps://www.tandfonline.com/action/journalInformation?journalCode=tsta20Science and Technology of Advanced MaterialsISSN: (Print) (Online) Journal homepage: https://www.tandfonline.com/loi/tsta20Data-driven analysis of electron relaxation timesin PbTe-type thermoelectric materialsYukari Katsura, Masaya Kumagai, Takushi Kodani, Mitsunori Kaneshige, YukiAndo, Sakiko Gunji, Yoji Imai, Hideyasu Ouchi, Kazuki Tobita, Kaoru Kimura& Koji TsudaTo cite this article: Yukari Katsura, Masaya Kumagai, Takushi Kodani, Mitsunori Kaneshige, YukiAndo, Sakiko Gunji, Yoji Imai, Hideyasu Ouchi, Kazuki Tobita, Kaoru Kimura & Koji Tsuda (2019)Data-driven analysis of electron relaxation times in PbTe-type thermoelectric materials, Scienceand Technology of Advanced Materials, 20:1, 511-520, DOI: 10.1080/14686996.2019.1603885To link to this article:  https://doi.org/10.1080/14686996.2019.1603885© 2019 The Author(s). Published by NationalInstitute for Materials Science in partnershipwith Taylor & Francis Group.Published online: 04 Jun 2019.Submit your article to this journal Article views: 4441View related articles View Crossmark dataCiting articles: 18 View citing articles https://www.tandfonline.com/action/journalInformation?journalCode=tsta20https://www.tandfonline.com/loi/tsta20https://www.tandfonline.com/action/showCitFormats?doi=10.1080/14686996.2019.1603885https://doi.org/10.1080/14686996.2019.1603885https://www.tandfonline.com/action/authorSubmission?journalCode=tsta20&show=instructionshttps://www.tandfonline.com/action/authorSubmission?journalCode=tsta20&show=instructionshttps://www.tandfonline.com/doi/mlt/10.1080/14686996.2019.1603885https://www.tandfonline.com/doi/mlt/10.1080/14686996.2019.1603885http://crossmark.crossref.org/dialog/?doi=10.1080/14686996.2019.1603885&domain=pdf&date_stamp=2019-06-04http://crossmark.crossref.org/dialog/?doi=10.1080/14686996.2019.1603885&domain=pdf&date_stamp=2019-06-04https://www.tandfonline.com/doi/citedby/10.1080/14686996.2019.1603885#tabModulehttps://www.tandfonline.com/doi/citedby/10.1080/14686996.2019.1603885#tabModuleData-driven analysis of electron relaxation times in PbTe-type thermoelectricmaterialsYukari Katsuraa,b, Masaya Kumagaic,d, Takushi Kodania,b, Mitsunori Kaneshigee, Yuki Andob, Sakiko Gunjia,b,Yoji Imaib,c, Hideyasu Ouchia,b,c, Kazuki Tobitaa,b, Kaoru Kimuraa and Koji Tsudaa,b,caDepartment of Advanced Materials Science, Graduate School of Frontier Sciences, SAKURA Research Center, The University of Tokyo,Chiba, Japan;bResearch and Services Division of Materials Data and Integrated System (MaDIS), National Institute for Materials Science (NIMS),Tsukuba, Ibaraki, Japan;cMolecular Informatics Team, Center for Advanced Intelligence Project, RIKEN, Tokyo, Japan;dSAKURA Research Center, SAKURA Internet Inc., Osaka, Japan;eScientific Computing Division, X-Ability Co. Ltd, Tokyo, JapanABSTRACTData mining from published papers can generate large experimental datasets that have beenoverlooked in computational materials informatics. We developed an open web systemStarrydata2 to accelerate a comprehensive digitization of data of materials from as-reportedplot images in published papers, without sample selection based on performance. By plottingresults obtained from our dataset on experimental thermoelectric properties of 434 samplesof rock-salt-type (PbTe-type) thermoelectric materials, we revealed differences in electronicstructure of parent compounds PbTe, PbSe, PbS, and SnTe from just experimental data. Weobserved that the calculated Seebeck coefficients were fairly consistent with experimentaldata for n-type PbTe but not for p-type PbTe, indicating possible modifications in its valence-band electronic structure. We evaluated the electron relaxation time τel from 207 reportedsamples of n-type PbTe by combining calculations and experimental data. We found that τel isnot a constant but varies by at least two orders of magnitude. Achieving long τel wassuggested to be critical in increasing the thermoelectric figure of merit ZT.Reproduced with permission from Thermoelectrics Society of Japan.ARTICLE HISTORYReceived 22 January 2019Revised 8 March 2019Accepted 1 April 2019KEYWORDSMaterials informatics;database; data curation;thermoelectric materials;first-principles calculation;electron relaxation timeCLASSIFICATION40 Optical, magnetic andelectronic device materials;210 Thermoelectronics /Thermal transport /insulators; 404 Materialsinformatics / Genomics; 4011st principle calculationsIntroductionMaterials informatics based on large-scale first-principles calculations is rapidly developing in func-tional materials science [1]. However, the propertiesof functional materials are not only determined bythe electronic structures of the parent compounds butalso determined by various experimental factors suchas impurity doping and microstructural control. ToCONTACT Yukari Katsura katsura@phys.mm.t.u-tokyo.ac.jp Graduate School of Frontier Sciences, The University of Tokyo, Chiba, Japan; MasayaKumagai masaya.kumagai@riken.jp Center for Advanced Intelligence Project, RIKEN, Tokyo, JapanSCIENCE AND TECHNOLOGY OF ADVANCED MATERIALS2019, VOL. 20, NO. 1, 511–520https://doi.org/10.1080/14686996.2019.1603885© 2019 The Author(s). Published by National Institute for Materials Science in partnership with Taylor & Francis Group.This is an Open Access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0/), which permitsunrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.http://www.tandfonline.comhttps://crossmark.crossref.org/dialog/?doi=10.1080/14686996.2019.1603885&domain=pdf&date_stamp=2020-02-04include these effects in materials informatics, we needto use a large number of digitized experimental data.Thermoelectric materials are an example of suchfunctional materials [2–4]. They are studied for appli-cations in compact cooling and power-generationdevices that interconvert heat and electricity. Formore than a century, experimental searches for effi-cient thermoelectric materials have been conducted.Because there are many material families, the max-imum reported value of the thermoelectric figure ofmeritZT ¼ S2σTκ¼ S2σTκel þ κph(1)is widely used in selecting a good material family.Thermoelectric conversion efficiency increases withincreasing ZT, and ZT>1 has been considered as thecriterion for applications. Equation (1) implies thatSeebeck coefficient S and electrical conductivity σneed to be increased to increase ZT; thermal conduc-tivity κ, comprising electron thermal conductivity κeland phonon (lattice) thermal conductivity κph, needsto be decreased to increase ZT. However, S, σ, and κelhave strong dependence on the carrier doping densityn. As a result, these parameters cannot be controlledindependently, and a balance is needed to maximizeZT. Introducing impurities and defects of variousscales [2–5] is effective in decreasing κph. The pho-non-glass-electron-crystal (PGEC) is a concept thatdescribes the best materials for high ZT, in whichphonons are scattered as in amorphous glass whereaselectrons pass freely as in crystals [6].Although first-principles calculation is a powerfultool to select many candidate thermoelectric materi-als [7,8], various kinds of uncertainties arise in pre-dicting actual thermoelectric properties [9].Calculations usually examine idealistically clean crys-tals, whereas experimental high-ZT samples are muchdirtier. The errors in band gap values create hugeerrors in calculating Seebeck coefficients in manyhigh-ZT compounds, which are narrow-gap semicon-ductors. Calculations employing Boltzmann’s trans-port equation cannot calculate σ and κel directly; theycan only evaluate σ/τel and κel/τel, where τel is anunknown variable called the electron relaxationtime. As τel is the time between electron scattering,long τel is expected in PGEC materials. Althoughmany studies assume constant τel (often at 10−14 s),a large sample dependence of τel is reported in a fewstudies [9,10].Recently, by combining first-principles calcula-tions and experimental data, materials informaticshas emerged. The leading example is Citrination ther-moelectrics recommendation engine [11], which bymachine learning assists the users in the selection ofgood parent compounds of thermoelectric materials.As calculation data, they used the TE Design Labdatabase [7], which contains electronic structureparameters of over 2300 parent compounds. Asexperimental data, they used several experimentaldatabases including UCSB Thermoelectrics Data(MRL Datamining Chart/Energy MaterialsDatamining) [12], which contains experimental dataof about 300 samples (over 1000 data points at 4different T) of thermoelectric materials reported inover 100 publications.To empower such experimental materials infor-matics, we attempted to collect experimental dataon a greater scale. During the history of thermoelec-tric materials, thousands of experimental sampleswere fabricated, and their properties were publishedas papers. Unfortunately, most of the precious data isburied in plot images, and not accessible in digitalform. We attempted to recycle such experimentaldata by plot digitization, termed ‘plot mining’.Unlike text and images, digitized scientific dataextracted from plot images can be shared withoutviolating the copyrights of publishers [13], if thenecessary citation is indicated. Plot mining is a high-speed and costless way to obtain experimental data,rather than repeating similar experiments.In this study, we developed a web system namedStarrydata2, which can efficiently collect and sharedigital experimental data, extracted from plot imagesin published papers. We developed this web systemfrom scratch, employing a completely different archi-tecture and user interface from our prototype websystem [14]. By embedding the plot digitization anddata upload interface in a typical reference managerlike Mendeley [15], we attempted to speed up thehuman-based comprehensive data collection. Thisweb system enables community-based collections ofpublished data by worldwide researchers, and thecollected data can be downloaded freely.A classical approach in theoretical materialsscience have been to use a state-of-the-art calculationderived from theory, and supporting it with a fewexperimental data of selected samples. However, inthis approach, it was difficult to know what are thecritical factors that determine the properties of themajority samples, which may be dirty or low inperformance or missing some information. We pre-sent an alternative approach to use a large dataset pfexperimental samples, and test for guiding principlesthat work for most of the experimental data. Thename of our web system reflects our concept totreat every datum as important as top data, likea starry sky that contains numerous dwarf stars.As an example, we used our dataset for experi-mental samples of rock-salt-type thermoelectricmaterials. Rock-salt-type thermoelectric materials,which are often referred as PbTe-type thermoelectricmaterials, are a family of thermoelectric materialsSci. Technol. Adv. Mater. 20 (2019) 512 Y. KATSURA et al.that crystallize in NaCl-type crystal structure. Thetypical parent compounds are PbTe, PbSe, PbS, andSnTe. Various other metals can substitute the cationsites, and non-metals can substitute the anion sites.Some samples in this family have been reported topossess high ZT values over 2 [16,17].The phonon properties of the real samples of rock-salt-type thermoelectric materials is difficult to predictfrom first-principles. Large atomic mass and weakbonding results in low phonon velocity, and strongphonon anharmonicity related to the lone pairs of thedivalent cations are related to the high phonon scatter-ing rate in intrinsic PbTe [18,19]. The chemical proper-ties of the parent compounds accept doping of non-stoichiometry, various elements and solid solutioningin wide ranges of compositions. Such site vacancies,impurity elements, intra-grain nanoprecipitates andgrain boundaries in the polycrystalline samples all scat-ter phonons of various wavelengths [16] to achieve lowκph [17,20,21] around 1 Wm−1K−1.The electronic structures of rock-salt-type thermo-electric materials are also complex, making theoreticalprediction of transport properties extremely difficult.The valence bands are composed of the p-bands of theanions have hole pockets along at Σ and L points[22,23], requiring complex treatment of inter-bandscattering for transport properties. The calculated holeFermi surfaces of PbTe are complex in shapes hardlyexpressed in parabolic band model [22,23]. The banddegeneracy changes with T and lattice parameters[16,24]. Spin-orbit interaction splits the bands to recon-struct the band structure around the Fermi level. Thewidth of this splitting increases in the order Sn<Pb andS<Se<Te, and further variation in band structure isexpected when these elements are randomly mixed.The conduction band, which is composed of the sp-bands of the cation, is relatively simpler than the valenceband. There are electron pockets at L-point, forminga direct band gap at L. The site vacancies and impurityelementsmay further modify the band structure aroundFermi level. The calculation results strongly depend onthe selection of exchange-correlation potentials [23,25].In such a complex material family, it is importantto reveal the trend that is applicable for most of theexperimental samples. We plotted the thermoelectricproperties of 434 reported samples in single plots, toreveal the common trends across the samples. Asa candidate parameter to enable prediction of ZT,we evaluated τel for constant relaxation time approx-imation by combination with a first-principles calcu-lation for 207 samples of PbTe.MethodsA list of papers with keyword ‘thermoelectric’ wasretrieved from the Scopus web system [26]. Fromthis list, we collated possible papers on materialproperties, by automatically detecting characteristicwords of material names in the titles. We manuallydownloaded the full-text PDF (Portable DocumentFormat) files for these selected papers from the pub-lisher’s web sites. Then we manually checked each forcontent and classified them into categories based onthe parent compounds. The papers on bulk samplescomposed of PbTe, PbSe, PbS, and SnTe with lessthan 10% impurity elements were classified as rock-salt-type thermoelectric materials.From each full-text PDF, we manually captured theplot images on the experimental T-dependence of thethermoelectric properties S, σ (or electrical resistivityρ = 1/σ), κ = κel+κph, power factor P = S2σ, and ZT. Weopened these images in WebPlotDigitizer [27], andextracted the original numerical data by semi-automaticcolour detection or by manual mouse-clicking. Thenumerical data were fit using polynomial functions ofup to 5th order, to evaluate the thermoelectric propertiesat T = 300, 400, . . ., 800 K. The missing parameters wereestimated by mathematical operations between knownparameters. If reported, the experimental Hall carrierdensity nH,exp at room temperature was also recorded.The possible chemical composition of each sample wasextracted by comprehending the text and identifying thestarting compositions.To make the above data collection process moreefficient, we developed a web system namedStarrydata2 on a cloud server at http://www.starrydata2.org. When a Digital Object Identifier (DOI) issupplied by a user, the web system automaticallyretrieves bibliographic information such as authornames and journal names from CrossRef.org [28],and records those to our database. The web systemautomatically generates links to the publisher’s web-site, the data-collection page, and the data-browsingpage. The data-collection page contains the interface ofWebPlotDigitizer [27], and a data-upload text boxwith an automatic unit convertor. The collected data-sets can be freely downloaded as text files in CommaSeparated Variables (CSV) and JavaScript ObjectNotation (JSON) formats. This web system is accessi-ble to the public free of charge.The example first-principles calculations of PbTe wasperformed using the Full-potential LinearizedAugmented Plane Wave (FLAPW) method implemen-ted in the WIEN2k code [29]. We employed theGeneralized Gradient Approximation (GGA) correla-tion-exchange potential [30] with spin-orbit interaction.Core/valence cut-off energy was set at −6.0 Ry, and thecalculation was performed on a 50 × 50 × 50 k-mesh.Thermoelectric properties were calculated from theBoltzmann transport equations, using the BoltzTraPcode [31], which was modified [9] to include second-order terms for κel. The chemical potential (μ) depen-dences of additional charges per unit cell N, S, σ/τel, andκel/τel, at T = 300, 400, 500, 600, 700, and 800 K wereSci. Technol. Adv. Mater. 20 (2019) 513 Y. KATSURA et al.http://www.starrydata2.orghttp://www.starrydata2.orgobtained from output files generated by BoltzTraP. Thevalues of μ were converted to carrier doping densitiesn = -N/Vcell [cm−3], where Vcell is the unit cell volume.We evaluated τel for each T in each sample usingexperimental Seebeck coefficient Sexp and experimen-tal electrical conductivity σexp. From the calculated S–n curve, we estimated n, the carrier doping densitythat corresponds to Sexp. If the S–n curve is bell-shaped due to the bipolar effect, we selected thesolution with higher n, unless bipolar effects wereobvious in the experimental data. From the n andthe calculated n-dependence of σ/τel, we evaluated(σ/τel)calc to estimate τel fromτel ¼ σexpσ=τelð Þcalc: (2)With this τel, we estimated κph usingκph ¼ κexp � τel κel=τelð Þcalc: (3)Results and discussionFrom Scopus [26], we retrieved with the keyword‘thermoelectric’ a list of 47,936 papers publishedbetween 1875 and 2015. Our original material-namedetection script selected 18,585 papers from the list,and among them we accessed the full-text of 14,835papers to select those that contain plots of interestand to classify them into material families.The screenshot of our original web systemStarrydata2 is shown in Figure 1. For each record ofa paper, Starrydata2 stores the bibliographic informa-tion, the numerical data extracted from the plots, andthe chemical compositions of the corresponding sam-ples. The system only shows the numerical data andthe replots, without storing the original full-text andthe plot images, which are often protected by publish-er’s copyright. The users can generate lists of pub-lications of interest, and browse the data collected byall users. They can download them as a data file,either in spreadsheet-like format (CSV and JSON)or in a relational-database-like format (JSON only).Our data visualization system can display the datafiles in various formats including line plots, heatmaps, and multiple scatter plots.Using Starrydata2, we succeeded in attaininga considerable improvement in the speed of manualdata collection. We rejected the selection of papersand samples in previous data collections to increaseboth the number of recorded samples and the speedof data collection. Currently, we have collected thedata for 11,506 samples in 9509 figures published in1957 papers. About 500–1000 samples are added eachmonth. Since the experimental data for a sampleusually appear in multiple figures, we manuallyrelated these data from an identical sample by com-prehension of the paper. By using the recent versionof our web system, a single data collector succeededto process 166 papers (806 plots, 1148 samples, 3251datasets and 89,210 data points) in 25 working days.On average, 1.03 papers (5.00 plots, 7.12 samples,20.2 datasets, 553 data points) were processedper hour. This time includes the time to read thetext to identify the chemical composition of eachsample. By increasing the number of data collectors,much more experimental data on other materialfamilies will be uploaded in our database.Figure 2 shows a part of our experimental dataseton rock-salt-type thermoelectric materials ina comparison with the UCSB Thermoelectric data[12], the largest literature-based experimental dataseton thermoelectric properties. Each data point, whichcorresponds to one experimental sample, is enteredin a plot of P against κ. Our dataset contained 434samples of PbTe, PbSe, PbS, SnTe and their solidsolutions from 64 publications [33–86], whereasUCSB Thermoelectric data contained 8 such samples.The large diversity of the scatter plot is a result of thenon-selective character of our dataset, which acceptedmany samples with bad properties. In contrast, theFigure 1. Concept of plot mining in the Starrydata2 web system. An example paper [32] and the screenshots of Starrydata2 websystem are presented. Reproduced with permission from Thermoelectrics Society of Japan.Sci. Technol. Adv. Mater. 20 (2019) 514 Y. KATSURA et al.samples from UCSB thermoelectric data were distrib-uted in the right-bottom corner of Figure 2(c), imply-ing that the UCSB Thermoelectric data selectivelycollected the samples that possess high ZT.Figure 3 shows the raw data of temperature depen-dences of S, σ, and κ of the 434 samples of rock-salt-type thermoelectric material. The colours indicate themaximum ZT of each sample. We observed thatsamples with wide ranges of S, σ, and κ can befabricated in this type of thermoelectric material.Simultaneously, it can be said that it is difficult toselect a single sample to represent the overall proper-ties of rock-salt-type thermoelectric materials. Mostof the samples possessed S values between ±300 μV/Kthat monotonically increased with T. Two samplesundergoing sign changes in S were typical of low-n (bipolar) samples. Most of the samples underwentmonotonic decreases in σ and κ with increasing T.The range of σ was between 103 and 106 S/m, and thehigh-ZT samples were distributed in the middle. Therange for κ was below 10 W/mK, and the high-ZTsamples were observed near the bottom of the dis-tribution. Such a direct comparison of many experi-mental data is helpful to reveal the non-calculablecharacteristics of each material family from the con-fusion inherent in strong sample dependences ofthermoelectric properties.The diversity of our dataset enabled us to revealthe characteristics of the parent compounds, fromonly simple scatter plots. Figure 4 is a Jonker plotshowing the relationship between S and log σ. Amongp-type samples, the Jonker curve of p-type PbTe washigher than those of PbSe and PbS. In contrast, theJonker curve of n-type PbTe was not distinguishablefrom those of PbSe and PbS. These differences areconsistent with calculated electronic structures, wherethe valence bands are composed of p-bands of Te, Se,and S, and the conduction bands are composed of Pb/Sn sp-bands. From the plot, all reported samples ofSnTe were seen to be p-type and high in σ, suggestingthe presence of a strong hole-doping mechanism.Figure 5 shows a comparison of theoretical S–n curves obtained from a typical first-principlesFigure 2. Scatter plot of the power factor P and thermal conductivity κ of rock-salt-type thermoelectric materials including PbTe,PbSe, PbS, SnTe, and their solid solutions, recorded in Starrydata2 and UCSB Thermoelectric data (displayed as UCSB), at (a)300 K, (b) 400 K, and (c) 700 K.Figure 3. Experimental transport properties of 434 experimental samples of rock-salt-type thermoelectric materials includingPbTe, PbSe, PbS, SnTe, and their solid solutions. Temperature dependences of (a) the Seebeck coefficient S, (b) electricalconductivity σ, and (c) the total thermal conductivity κ. Colours indicate the maximum ZT of each sample.Figure 4. A Jonker plot of rock-salt-type thermoelectric mate-rials with experimental values of the Seebeck coefficientS against electrical resistivity σ for PbTe, PbSe, PbS, andSnTe at T = 300, 400, 500, 600, 700, and 800 K. The parentcompounds of the samples are displayed in different colours.Sci. Technol. Adv. Mater. 20 (2019) 515 Y. KATSURA et al.calculation, to the experimental S–n curve of PbTesamples. Only 38 samples out of 207 samples of PbTeare shown in this plot, because the values of experi-mental n above room temperature were not reportedfor the other samples. Our transport calculation forn-type PbTe were close to the experimental data atfor each T, especially in high-n region over 1019 cm−3.In contrast, the S-n curve of our calculation was farfrom the most of reported p-type samples, especiallyat high T. This showed that the model of our trans-port calculation is not valid for most samples ofp-type PbTe. Several other theoretical papers [38,87]have successfully reproduced the experimentalS-n curve of n-type PbTe, however, they did notshow S-n curve for p-type PbTe. These implied thepossible difficulty in the modelling of transport prop-erties of p-type PbTe, despite the high ZT valuescompared to n-type PbTe.By combining first-principles calculations and ourexperimental data of Sexp, σexp, and κexp, weattempted to evaluate τel, an unknown parameter infirst-principles calculations of σ and κel. During theevaluation of τel, we need the value of calculated σ/τel.As this value is given as a function of n, this analysiscould be done only for samples with known experi-mental n. However, for most of the reported samplesof thermoelectric materials, Hall measurement todetermine experimental n has not been carried out.So in this study, we attempted to estimate n by usingthe reported values of experimental S and a calculatedS-n curve. Since this analysis is applicable only whenthere is a consistency between calculated and experi-mental S–n curves, we carried out this analysis onlyfor n-type samples.Figure 6(a) shows the values of n and τel of the 207samples of n-type PbTe, estimated from Sexp and σexp.The values of τel were between 10−15 s and 10−13 s,exhibiting a two-orders-of-magnitude variation. Theseτel values are composite values of intrinsic τel and extrin-sic τel, which can be expressed by Matthiesen’s rule suchthat fel,total = fel,intrinsic + fel,extrinsic, by using electronscattering rate fel = τel−1. The intrinsic fel due to electron-phonon interaction of PbTe has been calculated to bearound 1012–1013 Hz by a DFPT calculation consideringscreening effects by electrons [87]. Our total fel were ina range between 1013–1015 Hz. The samples with fel~1013 Hz (τel ~10–13 s) are expected to be clean samples,in which intrinsic electron-phonon interaction is one ofthe dominant electron scattering mechanisms. The sam-ples with fel ~1015 Hz (τel ~10–15 s) were expected to bedirty samples, where extrinsic electron scatteringmechanisms are dominant. The candidates of suchextrinsic electron scattering centers in n-type PbTeinclude atomic vacancies, impurity atoms, intra-grainnanoprecipitates, dislocations, grain boundaries andimpurity phases. The trend that short τel is observedmore frequently in high-n samples was consistent withthe expectation that the carrier-doping vacancies andimpurities also scatter electrons. The trend that τeldecreases with increasing T is observed especially inlow-n samples, and this was consistent with the thatphonon scattering rate increases with increasing T.Our analysis also revealed that the popular trans-port calculations that use a fixed value of τel = 10−14 sfor constant relaxation time approximation is not validfor most of the reported samples of n-type PbTe.Figure 6(b) shows the relationship between τel andZT. For each T, we observed a trend whereby anincrease in τel results in a monotonic increase inZT. The surprising thing here is not that ZT increasedwith τel, but that the τel of almost all the reportedexperimental samples clearly followed a commonFigure 5. Calculated carrier doping level (n) dependences ofthe Seebeck coefficient (S) from first-principles calculationusing Boltzmann transport equations, in the range 300–800 K,against the experimental Hall carrier concentration at roomtemperature, for 38 samples of n-type and p-type PbTe.Experimental data of S are also plotted against n.Figure 6. Relationship between (a) carrier doping level n and electron relaxation time τel, (b) τel and thermoelectric figure ofmerit ZT, and (c) τel and phonon thermal conductivity κph, estimated for 207 experimental samples of n-type PbTe.Sci. Technol. Adv. Mater. 20 (2019) 516 Y. KATSURA et al.curve, which can be drawn for each T = 300, 400, . . .,800 K. This showed that the ZT values can beexpected only from T and τel, for these real samplesof PbTe-type thermoelectric materials. In researchesof thermoelectric materials, this is quite a rare casethat ZT values can be predicted only from one phy-sical parameter other than T. This result givesresearchers a strong guiding principle that anincrease in τel directly enhance ZT of n-type PbTe.Figure 6(c) shows the relationship between τel andκph. If the dominant electron scattering centers actedas the dominant phonon scattering centers, we wouldhave seen a correlation in this plot. However, wecould not observe any correlation between τel andκph. This indicated that in most samples of n-typePbTe, there are dominant phonon scattering mechan-isms other than electrons, or there are dominantelectron scattering mechanisms other than phonons.Even though electrons in ideal PbTe crystals arereported to be scattered mainly by phonons [87],this does not mean that phonons are mainly scatteredby electrons. The advantage of n-type PbTe may bethe availability of the phonon scattering mechanismswithout heavy electron scattering, as to realize theconcept of PGEC.ConclusionWe developed an original web system Starrydata2 asan open database, to let researchers gather and shareexperimental data from published plot images. So far,we have succeeded to collect experimental data frommore than 11,500 samples of thermoelectric materi-als. Our web system enabled collective analysis ofpublished samples, to discover the guiding principlesthat work for most of the published samples.By combining our partial dataset on rock-salt-typethermoelectric materials with first-principles calcula-tions, we analysed thermoelectric properties of rock-salt-type thermoelectric materials. The differences invalence band electronic structures of PbTe, PbSe,PbS, and SnTe were revealed in the Jonker plots.For n-type PbTe, we found that the effective τel forconstant relaxation time approximation varied bymore than two orders of magnitude, indicating thatτel is not a constant but a very important determinantof ZT. This analysis is applicable for other thermo-electric materials, whose S-n curves were successfullyreproduced by first-principles calculations and trans-port calculations. As our database is growing to covermore and more families of thermoelectric materials,evaluation of τel of various experimental samples ofthermoelectric materials will be a strong guide forexperimental researchers to design high-ZT samplesof thermoelectric materials.AcknowledgmentsWe thank all the people who gave us valuable suggestions toimprove our system and our data collection project. Wethank the members of MI2I, the members of‘Thermoelectric Database Working Group’ and the commit-tees of Thermoelectrics Society of Japan, and the members ofSAKURA Internet Inc. for supports of our project. We thankShinji Nagashiro from X-Ability Co. Ltd. for technical adviceon the development of the data visualizer. We thank RichardHaase, Ph.D, from Edanz Group (www.edanzediting.com/ac)for editing the first draft of this manuscript.Data AvailabilityThe experimental data obtained from the publications can befreely downloaded from our Starrydata2 web system at http://www.starrydata2.org. The datasets generated in this study areavailable at GitHub repository, https://github.com/starrydata.Disclosure statementNo potential conflict of interest was reported by theauthors.FundingThis work was financially supported by a KAKENHI grant[No. 16K14379] from the Ministry of Education, Culture,Sports, Science and Technology Japan, Watanabe memorialfoundation for the advancement of new technology, and‘Materials Research by Information Integration’ Initiative(MI2I) project of the Support Program for Starting UpInnovation Hub from the Japan Science and TechnologyAgency (JST).References[1] Jain A, Hautier G, Ong SP, et al. New opportunitiesfor materials informatics: resources and data miningtechniques for uncovering hidden relationships.J Mater Res. 2016;31:977–994.[2] Snyder GJ, Toberer ES. Complex thermoelectricmaterials. Nat Mater. 2008;7:105–114.[3] Liu W, Yan X, Chen G, et al. Recent advances inthermoelectric nanocomposites. Nano Energy.2012;1:42–56.[4] Gayner C, Kar KK. 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