Phase-transition temperature suppression to achievecubic GeTe and high thermoelectric performanceby Bi and Mn codopingZihang Liua,b,c, Jifeng Sund, Jun Maob,c, Hangtian Zhub,c, Wuyang Renb,c,e, Jingchao Zhoua,b,c, Zhiming Wange,David J. Singhd, Jiehe Suia,1, Ching-Wu Chub,c,1, and Zhifeng Renb,c,1

aState Key Laboratory of Advanced Welding and Joining, Harbin Institute of Technology, 150001 Harbin, China; bDepartment of Physics, University ofHouston, Houston, TX 77204-5005; cTexas Center for Superconductivity, University of Houston, Houston, TX 77204-5002; dDepartment of Physics andAstronomy, University of Missouri-Columbia, Columbia, MO 65211; and eInstitute of Fundamental and Frontier Sciences, University of Electronic Science andTechnology of China, 610054 Chengdu, China

Contributed by Ching-Wu Chu, April 6, 2018 (sent for review February 5, 2018; reviewed by Austin J. Minnich and Li-Dong Zhao)

Germanium telluride (GeTe)-based materials, which display in-triguing functionalities, have been intensively studied from bothfundamental and technological perspectives. As a thermoelectricmaterial, though, the phase transition in GeTe from a rhombohe-dral structure to a cubic structure at ∼700 K is a major obstacleimpeding applications for energy harvesting. In this work, we dis-covered that the phase-transition temperature can be suppressedto below 300 K by a simple Bi and Mn codoping, resulting in thehigh performance of cubic GeTe from 300 to 773 K. Bi doping onthe Ge site was found to reduce the hole concentration and thus toenhance the thermoelectric properties. Mn alloying on the Ge sitesimultaneously increased the hole effective mass and the Seebeckcoefficient through modification of the valence bands. With the Biand Mn codoping, the lattice thermal conductivity was also largelyreduced due to the strong point-defect scattering for phonons,resulting in a peak thermoelectric figure of merit (ZT) of ∼1.5at 773 K and an average ZT of ∼1.1 from 300 to 773 K in cubicGe0.81Mn0.15Bi0.04Te. Our results open the door for further studiesof this exciting material for thermoelectric and other applications.

thermoelectric | phase transition | germanium telluride | Mn alloying |band-structure engineering

Thermoelectric power generation (TEG), capable of directlyconverting heat into electricity, has reliably provided powerfor spacecraft explorations (1), but the low efficiency has im-peded broader application. Due to the significantly improvedperformance realized in the last decade (2–4), TEG has drawnwide attention for energy harvesting from waste heat and naturalheat that would provide an alternative approach to tackle thechallenges of energy sustainability (5). The conversion efficiencyof TEG is mainly determined by the material’s dimensionlessthermoelectric figure of merit (ZT), ZT = [S2σ/(κlat + κele)]T,where S, σ, κlat, κele, and T are the Seebeck coefficient, electricalconductivity, lattice thermal conductivity, electronic thermalconductivity, and absolute temperature, respectively. Conven-tional methods to enhance the ZT mainly include optimizingcarrier concentration and strengthening point-defect phononscattering (6, 7), but peak ZT was limited to around unity fromthe 1950s to the 1990s (8). Recently proposed effective conceptsor strategies, including ‘‘phonon glass electron crystal’’ to designnew compounds (6), band-structure engineering to maximize thepower factor (PF = S2σ) (9–13), microstructure engineering tosuppress the κlat (14–17), and point-defect engineering to opti-mize performance (18–21), have led to the remarkable progressin the thermoelectric area (22–26). It should be noted that PbTe,one of the oldest and most-studied thermoelectric materials (27),plays a major role in evoking enthusiasm for current thermo-electric study since most conceptual breakthroughs have comefrom the recent study of the PbTe system (11, 15, 28, 29).However, the toxicity of Pb largely hinders applications for

energy harvesting and therefore much scientific interest hasshifted to Pb-free systems.GeTe, one of the analogs of PbTe, has recently received in-

tense attention from the thermoelectric community in its aim toreplace traditional PbTe (30–36). GeTe undergoes a ferroelec-tric phase transition from the low-temperature rhombohedralstructure α-GeTe (space group R3m) to cubic structure β-GeTe(space group Fm�3m) at the critical temperature (Tc) around 700 K(37). Due to the presence of a high concentration of Ge vacancies(38), undoped rhombohedral GeTe is a typical degenerate p-typesemiconductor with intrinsically high hole concentration,which results in relatively low ZT. To overcome this short-coming, In, Bi, or Sb doping as well as Pb alloying on the Gesite and Se alloying on the Te site have been proven to beeffective in reducing the hole concentration and further en-hancing ZT (30–36). However, the thermoelectric properties ofall compositions previously investigated show the evident fea-ture of phase transition in the measured temperature range. It iswell known that phase-transition behavior is detrimental forapplications because the sudden change in the thermal expan-sion coefficient would induce high internal stress between thematerials and the contacts in the device that would lead tocrack generation and consequently to deteriorating perfor-mance or failure under high thermal stress. Therefore, developing

Significance

Phase-transition behavior in thermoelectric materials is detri-mental for their application in thermoelectric devices. Here wedesigned, and experimentally realized the high thermoelectricperformance of cubic GeTe-based material by suppressing thephase transition from a cubic to a rhombohedral structure tobelow room temperature through a simple Bi and Mn codopingon the Ge site. Bi doping reduced the hole concentration whileMn alloying largely suppressed the phase-transition tempera-ture and also induced modification of the valence bands. Ourwork provides the basis for studying phase transitions inother thermoelectric materials to optimize these materials forapplications.

Author contributions: Z.L., J. Sun, J. Sui, C.-W.C., and Z.R. designed research; Z.L. and J. Sunperformed research; J.M., H.Z., W.R., J.Z., Z.W., and D.J.S. analyzed data; and Z.L., J. Sun,J. Sui, C.-W.C., and Z.R. wrote the paper.

Reviewers: A.J.M., California Institute of Technology; and L.-D.Z., Beihang University.

The authors declare no conflict of interest.

Published under the PNAS license.1To whom correspondence may be addressed. Email: suijiehe@hit.edu.cn, cwchu@uh.edu,or zren@uh.edu.

This article contains supporting information online at www.pnas.org/lookup/suppl/doi:10.1073/pnas.1802020115/-/DCSupplemental.

Published online May 7, 2018.

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high-performance GeTe-based materials without the detri-mental phase transition from α-GeTe to β-GeTe remains asignificant challenge to be addressed. Based on the pseudo-binary phase diagram of GeTe–MnTe solid solution (39), it ispossible that Mn alloying on the Ge site would be an effectivemethod to reduce the phase-transition temperature. AlthoughGe1−xMnxTe systems have been reported (40, 41), the primaryfocus of these studies was on the low-temperature magneticproperties of the systems.Here we successfully achieved suppression of the phase-transition

temperature from around 700 K to below 300 K, resulting inthe high thermoelectric performance of cubic GeTe, by a simpleBi and Mn codoping on the Ge site using mechanical alloyingand hot pressing. Bi doping reduced the hole concentration whileMn alloying induced significant valence band modification inaddition to the large suppression of the phase-transition tem-perature. A peak ZT of ∼1.5 at 773 K and a corresponding av-erage ZT of ∼1.1 from 300 to 773 K were achieved in cubicGe0.81Mn0.15Bi0.04Te.

Results and DiscussionThe room-temperature X-ray diffraction (XRD) patterns ofGe1−xBixTe samples closely match that of α-GeTe (SI Appendix,Fig. S1), confirming their room-temperature crystal structure asrhombohedral (37), but the phase-transition temperature fromα-GeTe to β-GeTe decreases from 700 K (x = 0) to 585 K (x =0.08) (SI Appendix, Fig. S2). Benefiting from the reduced holeconcentration nH upon Bi doping (Table 1), the electrical re-sistivity ρ shows an obvious increase to the desired value forgood thermoelectric performance over the entire temperaturerange (Fig. 1A). As expected, Seebeck coefficient S increasesupon Bi doping (Fig. 1B), in accordance with the tendency of ρ.Assuming the single parabolic band (SPB) model with acousticphonon scattering as the dominant mechanism for carriers (6,42), the calculated total density of states (DOS) effective massm* continuously increases with Bi doping concentration (Table1). Therefore, the enhancement of S could be ascribed to thecombination of reduced nH and band modification upon Bi dop-ing. Compared with the pristine α-GeTe, Bi doping decreases PF,especially in the high-temperature range (Fig. 1C). The totalthermal conductivity κtot shows a significant suppression upon Bidoping due to the decreased lattice thermal conductivity κlat, aswell as the electronic thermal conductivity κele. The κlat is obtainedby subtracting κele from κtot (Fig. 1D), where κele is calculated usingthe Wiedemann–Franz relationship, κele = LσT, in which L is thecalculated Lorenz number. There is an obvious reduction of κlatafter Bi doping, e.g., room-temperature κlat decreased from2.4 W m−1·K−1 for α-GeTe to 1.0 W m−1·K−1 for α-Ge0.92Bi0.08Te(Fig. 1E). Bi doping on the Ge site introduces large mass fluctu-ations and surrounding local strain-field fluctuations due to thesignificant difference in the atomic mass and ionic radius betweenBi and Ge atoms (43). In the low-temperature range from 300 to523 K, α-GeTe shows the typical feature of Umklapp scatteringwith T−1.2 dependence (Fig. 1E), basically consistent with thetheoretical value T−1. In contrast, κlat of α-Ge0.92Bi0.08Te is almosttemperature independent, which may be related to the induced highdegree of disorder and stronger anharmonicity by Bi doping (44,45). The possibly incomplete subtraction of the electronic contri-bution may also have some effects because of the complex bandstructure. Due to the significantly suppressed κlat, Bi doping largelyenhances the ZT over the whole temperature range. A peak ZT of∼1.4 was achieved for α-Ge0.96Bi0.04Te, more than 50% higher thanthat of the pristine α-GeTe (Fig. 1F). It should also be noted thatthe pristine α-GeTe in our work exhibits a higher PF and ZT due toits relatively lower nH in comparison with the previously reportedsamples that were synthesized by the method of melting andannealing (31, 32, 36). In general, the mechanical alloying method isable to fabricate materials with the needed chemical constituents,resulting in the lower carrier concentration in our current work.This result indicates that the combination of mechanical alloyingand hot pressing is a more appropriate method to fabricate high-performance GeTe-based thermoelectric materials.

Table 1. Electrical transport properties of α-Ge1−xBixTe and α-Ge0.96−xMnxBi0.04Te samples

Composition nH, 1020 cm−3 μH, cm

2 V−1·s−1 rH m*, m0 μW, cm

2 V−1·s−1

GeTe 4.2 95.3 1.0 1.6 197.9Ge0.96Bi0.04Te 2.4 64.2 1.06 1.9 168.5Ge0.92Bi0.08Te 1.0 51.3 1.10 2.1 159.7Ge0.91Mn0.05Bi0.04Te 3.2 30.6 1.07 2.6 130.6Ge0.86Mn0.1Bi0.04Te 4.1 16.9 1.08 3.9 123.0Ge0.81Mn0.15Bi0.04Te 5.5 9.4 1.1 5.6 124.7Ge0.76Mn0.2Bi0.04Te 10.0 4.4 1.11 9.9 136.7Ge0.66Mn0.3Bi0.04Te 56.4 0.5 1.12 36.7 122.0

nH is Hall carrier concentration (or hole concentration); μH is Hall carrier mobility (or hole mobility); rH is Hallfactor; m* is total DOS effective mass; m0 is the electron rest mass; and μW is weighted mobility.

FE

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10 GeTe Ge0.96Bi0.04TeGe0.92Bi0.08Te

Temperature (K)

(10-5Ohm

m)

300 400 500 600 700 8000

200

400

Temperature (K)

S(VK-1)

A

Fig. 1. Temperature-dependent thermoelectric properties of α-Ge1−xBixTesamples (x = 0, 0.04, and 0.08). (A) ρ, (B) S, (C ) PF, (D) κtot, (E ) κlat, and(F ) ZT.

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Although Bi doping effectively reduces nH and thus enhancesZT, the obvious phase-transition phenomenon remains. Basedon the pseudobinary phase diagram of GeTe–MnTe solid so-lution (SI Appendix, Fig. S3) (39), Mn alloying on the Ge site isemployed to possibly reduce the phase-transition temperatureand obtain the cubic structure even at room temperature. XRDpatterns of Ge0.96−xMnxBi0.04Te samples are shown in Fig. 2A.Samples with low Mn alloying concentration (x ≤ 0.1) continueto crystallize in rhombohedral structure while samples with highMn alloying concentration (x ≥ 0.15) crystallize in cubic struc-ture (37, 39). In the literature, the reported critical Mn alloyingcomposition in the pseudobinary phase diagram of GeTe–MnTeis about x = 0.18 (39). This discrepancy can be attributed to thecontribution of Bi doping, which also decreases the phase-transition temperature to a certain extent. Fig. 2B shows thecalculated lattice parameter and interaxial angle dependence onMn alloying concentration. It is apparent that Mn alloying leadsto an almost linear decrease of lattice parameters in solid so-lution. Since α-GeTe is a slightly distorted rock-salt latticealong the (111) direction (37), the interaxial angle change fromnon-−90° to 90° after Mn alloying is consistent with XRDmeasurement. Heat capacity measurements are displayed inFig. 2C, which clearly show that Mn alloying gradually de-creases the phase-transition temperature. However, it is diffi-cult to detect the phase-transition temperature for x ≥ 0.1 bydifferential scanning calorimetry (DSC) measurement due to thevery small or perhaps zero latent heat. Additionally, the XRDmeasurements of Ge0.66Mn0.3Bi0.04Te sample when heating upto 473 K and cooling down to 300 K in air are performed, asshown in Fig. 2D. It is obvious that all of the obtained XRDpatterns well match the cubic GeTe structure without the ap-pearance of phase transition within the XRD detection limit. Thebroad peaks in the DSC measurements may be due to the highheating rate during the DSC measurements causing an incompletephase transition.Mn element is well known for its complex oxidation state,

spanning from +2 to +7, and the most common and stable oxi-dation state is +2 (46). It was previously reported that Mn inGeTe–MnTe solid solution also showed the +2 that is identicalto that of the host atom Ge (40, 47), but Mn alloying gradually

increased the nH of Ge0.96−yMnyBi0.04Te (Table 1). Lewis et al.(38) found that the nH of GeTe–MnTe solid solution increaseswith Mn concentration as a result of the increased Ge vacancies(38). The number of Ge vacancies in the GeTe system is directlyrelated to the nH because each Ge vacancy, acting as an acceptorcenter, donates one or two carriers to the valence band (38). Inour first-principles calculations (addressed below) we indeed findthat Mn is divalent in GeTe and that it adopts a high spin state.Mn alloying intensifies the scattering of holes, leading to thesignificantly decreased Hall mobility μH (Table 1). Thus, ρgradually increases over the entire temperature range with in-creasing Mn concentration (Fig. 3A). Despite the increased nH, Scontinuously increases with increasing Mn concentration (Fig.3B), which will be addressed in detail below. It should be notedthat the reduction of both ρ and S at high temperature for x ≥0.1 is caused by the bipolar effect, rather than the phase transi-tion, while both the bipolar effect and phase transition contrib-ute to those reductions for x ≤ 0.05. After Mn alloying, PFdecreased somewhat due to the increased ρ (Fig. 3C). Basically,weighted mobility μW = μH(m*/m0)

3/2, where m0 is the free-electron mass, determines the maximum PF assuming that thecarrier concentration is optimal (48). The calculated room-temperature μW displays the same variation trend as that of PF(Fig. 3D), both of which indicating that Mn alloying is not a validmethod to enhance PF in this system.To understand and quantify the abnormal behavior of the

concurrently increased nH and S of Ge0.96−xMnxBi0.04Te withincreasing Mn concentration, the corresponding m* were cal-culated based on the SPB model, shown in Table 1. Obviously,Mn alloying leads to the significant enhancement of m*, which isalso demonstrated by the calculated Pisarenko plots displayedas dashed lines in Fig. 4A. This is consistent with the measuredlow μH of Mn alloyed samples, because heavy carriers generallydiffuse with low velocities in a semiconductor. Experimentaldata of previously studied compositions, including Ge1+xTe,Ge1−xSbxTe, and GeTe1−xSex, fall on the solid black line (33),which is calculated by the modified two-band model (33), whileat the same nH, Ge0.96−xMnxBi0.04Te samples exhibit a muchhigher S than the theoretical prediction. As a result of the highS, our PFs were observably higher than those of the previousreports (Fig. 4B).First-principles calculations, including electronic DOS and

band-structure calculations, were performed to shed light on the

DC

B

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Temperature (K)

0.00 0.05 0.10 0.15 0.20 0.25 0.305.915.925.935.945.955.965.975.985.99

Mn concentration (x)

Latticeparameter(Å)

88.288.488.688.889.089.289.489.689.890.0

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2 (Degree)

-GeTe-GeTex=0x=0.05

x=0.1x=0.15

x=0.2x=0.3

A

Fig. 2. (A) XRD patterns of Ge0.96−xMnxBi0.04Te samples (x = 0, 0.05, 0.1,0.15, 0.2, and 0.3). (B) Lattice parameter and interaxial angle dependenceon Mn concentration. (C ) Temperature-dependent heat capacity ofGe0.96−xMnxBi0.04Te samples (x = 0, 0.01, 0.05, 0.1, 0.15, 0.2, and 0.3). (D) XRDpatterns of Ge0.66Mn0.3Bi0.04Te sample after heating up to 473 K and coolingdown to 300 K in air.

0.0 0.1 0.2 0.3

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24

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10

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Temperature (K)

(10-5Ohm

m)

A

Fig. 3. Temperature-dependent (A) ρ, (B) S, and (C) PF of Ge0.96−xMnxBi0.04Tesamples (x = 0, 0.05, 0.1, 0.15, 0.2, and 0.3). (D) PF and weighted mobility μWdependence on Mn concentration at room temperature. The solid and dashedlines in D are included as guides for the eye.

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role of Mn alloying in the significantly higher m* of rhombohe-dral and cubic GeTe. Fig. 5 compares the difference of the cal-culated DOS between pure GeTe and after Mn alloying inrhombohedral and cubic GeTe, respectively. Introducing Mnmade the DOS steeper in both rhombohedral and cubic GeTe,especially near the valence band edge (e.g., from −0.05 to−0.2 eV for α-GeTe and from −0.25 to −0.3 eV for β-GeTe).This sharper DOS feature corresponds to the higher mass and isbeneficial for enhancing the Seebeck coefficients, which is alsoconsistent with the increased effective SPB m* after Mn alloying.Fig. 6 shows the calculated electronic band structures for boththe pure and Mn-doped GeTe supercell with spin-orbital cou-pling (SOC). The primitive band structure of both the rhombo-hedral and cubic GeTe are essentially similar to the previouslyreported ones (34). For rhombohedral and cubic pristine GeTe(Fig. 6 A and C), the most beneficial feature is the multiple va-lence bands with relatively small band offset. Mn doping signif-icantly increases the nH and the corresponding Fermi level ispushed downward into the multiple valence band, resulting inthe multiple valence band contribution to carrier conducting.Moreover, Mn alloying in rhombohedral GeTe realigns thebands, resulting in the contribution of the multiple band at dif-ferent points (Fig. 6B). This underlines the higher DOS, which isalso beneficial for achieving high S (49), as demonstrated invarious systems, such as PbTe (11), SnTe (50), Mg2Si (10, 13),etc. The calculated band structure without SOC can also supportthis conclusion (SI Appendix, Fig. S4). We have also shown thespin-polarized band structure in SI Appendix, Fig. S4 since theMn alloying leads to a magnetic system (magnetic moment =5 μB/Mn) corresponding to the high spin state of Mn2+, which isconsistent with the previously measured electron paramagneticresonance result (47). It should be noted that magnetic Mn2+

will introduce spin scattering, which is detrimental to the mobility.Thus, it will be promising and also challenging to investigateother alloying elements in the future to find nonmagnetic orweakly magnetic element ions that similarly allow carrier con-centration optimization and stabilization of the cubic phase,perhaps with even higher ZT.The κtot shows a significant reduction upon Mn alloying (Fig.

7A), as a result of both the decreased κlat and κele. Heavy Mnalloying leads to the obvious suppression of κlat due to the in-creased point-defect scattering. For example, room-temperatureκlat decreases from 1.6 W m

−1·K−1 for α-Ge0.96Bi0.04Te to1.2 W m−1·K−1 for α-Ge0.86Mn0.1Bi0.04Te and to 1.1 W m−1·K−1for β-Ge0.76Mn0.2Bi0.04Te (Fig. 7B). Additionally, the Debye–Callaway model, shown as the solid line in Fig. 7B (Inset), basi-cally explains the decreasing trend of κlat with increasing Mnconcentration (43, 51), in which the longitudinal (3,400 m/s) andtransverse (1,890 m/s) sound velocities of pure GeTe are obtainedfrom ref. 36. To confirm the origin of the reduction of κlatupon Mn alloying, phonon dispersion and phonon density ofstates (PDOS) of both α-GeTe and α-Ge0.875Mn0.125Te werecalculated. Mn alloying in α-GeTe does not significantly alterthe phonon dispersion (Fig. 7C), including acoustic modesand optical modes with low frequency. In addition, the PDOSat the low-frequency range from acoustic phonons is almostunchanged upon Mn alloying. Computational results showthat Mn alloying does not significantly change the acousticphonon properties of rhombohedral GeTe despite the in-duced substantial structure disorder. Furthermore, theoreticalcalculations of κlat based on the Debye–Callaway model arebasically consistent with the experimental observations, whichin turn indicates that Mn alloying can simply be regarded asthe point-defect scattering centers. In contrast, Murphy et al.argued that soft optical mode transitions in Pb1−xGexTemaximize the anharmonic acoustic–optical coupling and re-sult in low κlat (52). Due to the presence of imaginary fre-quencies in the phonon dispersion of β-GeTe (SI Appendix, Fig.S5), it cannot provide a qualitative picture of the effect of Mnalloying on phonon transport in β-GeTe.

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m* = 2.5 m0

m* = 4 m0

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m* = 10 m0

Ge1+xTeGeTe1-xSex

Ge0.96-yMnyBi0.04Te

S(VK-1)

nH (1020 cm-3)

A

Fig. 4. Hall carrier-concentration-dependent (A) S and (B) PF of Ge0.96−xMnxBi0.04Te and previously studied compositions, including Ge1+xTe, Ge1−xSbxTe, and GeTe1−xSex (33). The dashed lines in A were calculated by theSPB model with m* = 1.5, 2.5, 4, 5.5, and 10 m0, respectively, while the redsolid black line was obtained based on the modified two-valence-bandmodel. The dashed line in B is included as a guide for the eye.

B

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Energy (eV)

β-GeTe-scβ-Ge0.875Mn0.125Te

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2

4

6

8

10

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Energy (eV)

α-GeTe-scα-Ge0.875Mn0.125Te

A

Fig. 5. Comparison of the difference of the calculated DOS between pureGeTe and Mn-alloyed GeTe for (A) rhombohedral structure and (B) cubicstructure. Black and red lines represent the pristine GeTe and Ge0.875Mn0.125Te,respectively.

Fig. 6. The calculated electronic band structures with SOC of (A) rhom-bohedral structure α-GeTe, (B) α-Ge0.875Mn0.125Te, (C ) cubic struc-ture β-GeTe, and (D) β-Ge0.875Mn0.125Te. The dashed line represents theFermi level.

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Due to the balance between the decreased PF and the sup-pressed κtot, the highest peak ZT at 773 K is almost unchangedafter Mn alloying—they are all about 1.5 for α-Ge0.96Bi0.04Te,α-Ge0.86Mn0.1Bi0.04Te, and β-Ge0.81Mn0.15Bi0.04Te—but the low-temperature ZT is enhanced somewhat (Fig. 8A). In appli-cations, the average ZT over the working temperature rangedetermines the conversion efficiency of a device (53, 54). Forrhombohedral GeTe-based materials, the highest average ZTfrom 300 to 773 K in our work is comparable with those ofprevious reports (Fig. 8B) (31, 33). It should be highlighted thatthe highest average ZT of cubic Mn-doped GeTe is higher thanthat of the current state-of-the-art p-type PbTe- (0.9) and SnTe-(0.4) based materials (Fig. 8B) (9, 50). Therefore, we havedemonstrated the high performance of bulk cubic GeTe-basedmaterials, for which there is no phase transition over the wholetemperature range from 300 to 773 K. Additionally, Mn alloyingin the GeTe system also reduces the cost of raw materials sinceless Ge is used. Both characteristics are beneficial for promotingthe GeTe system for energy harvesting.

ConclusionsIn summary, we succeeded in suppressing the phase-transitiontemperature from ∼700 K to below ∼300 K to achieve cubicGeTe without phase transition from 300 to 773 K by a simple Bidoping and Mn alloying on the Ge site. The suppression of thephase transition to below room temperature is significant for anythermoelectric applications. Bi doping reduces the hole con-centration and thus enhances ZT of the rhombohedral GeTe.Mn alloying induced significant valence band modification andincreases the hole effective mass for both the rhombohedral andcubic GeTe, leading to a much higher Seebeck coefficient. Thestrong point-defect scattering for phonons caused by Bi and Mnlargely reduces the lattice thermal conductivity, which leads to apeak ZT ∼1.5 at 773 K for cubic Ge0.81Mn0.15Bi0.04Te. Our workopens the door for further studies of phase transition in otherthermoelectric materials.

Experimental SectionSynthesis. Appropriate raw materials, including Ge disks, Mn disks, Bi chunks,and Te chunks from Alfa Aesar, were weighed according to the nominalcompositions Ge1−xBixTe (x = 0, 0.04, and 0.08) and Ge0.96−xMnxBi0.04Te (x =

0, 0.01, 0.05, 0.1, 0.15, 0.2, and 0.3), loaded into a stainless-steel jar in a glovebox under argon atmosphere, and then subjected to ball milling for 5 h. Theball-milled powder was loaded into a die and hot pressed at 773 K for 2 minunder a pressure of 90 MPa.

Phase and Property Characterizations. XRD analysis was performed using aPANalytical multipurpose diffractometer with an X’celerator detector(PANalytical X’Pert Pro). Bar samples were cut from the pressed disksand used for simultaneous measurement of electrical resistivity (ρ) andSeebeck coefficient (S) on a commercial system (ULVAC ZEM-3). Thethermal conductivity was calculated using κ = DCpd, where D, Cp, and d arethe thermal diffusivity, specific heat capacity, and density, respectively.The thermal diffusivity coefficient (D) was measured on a laser flash sys-tem (Netzsch LFA 457). The specific heat capacity (Cp) was measured ona DSC thermal analyzer (Netzsch DSC 404 C). The density (d ) around6.2 g cm−3 was determined by the Archimedes method. The room-tem-perature Hall coefficient RH was measured using the Physical PropertiesMeasurement System (Quantum Design). The Hall carrier concentration(nH) was obtained by nH = 1/eRH and the Hall carrier mobility (μH) wascalculated by σ = eμHnH, where e is the electronic charge and σ is the electricalconductivity. The uncertainty for the electrical conductivity is 3%, the Seebeckcoefficient is 5%, and the thermal conductivity is 7%, so the combined un-certainty for the PF is 13% and that for ZT value is 20%. To increase thereadability of the curves, error bars were not shown in the figures.

First-Principles Calculations. The electronic band-structure calculations wereperformed by adopting the generalized gradient approximation of thePerdew–Burke–Ernzerhof functional for the exchange-correlation poten-tial and the projector augmented wave method as implemented in theVienna Ab initio Simulation Package (VASP) (55–57). The valence electronsincluded for Ge, Te, and Mn are 4s24p2, 5s25p4, and 3p64s23d5, respectively.The electron wave function was expanded in a plane-wave basis set with anenergy cutoff of 400 eV. The convergence of the calculations were testedwith dense k-point meshes. The structures were fully relaxed until the forceon each atom was less than 10−5 eV Å−1 for both pure and Mn-doped GeTe.The effects of Mn doping were considered through a substitution of oneMn with one Ge atom in a 2 × 2 × 2 supercell that was built based on theoriginal primitive cell in both cubic and rhombohedral phases. This yields acomposition of Ge0.875Mn0.125Te. The spin polarization was included withan initial magnetic moment of 5 μB on Mn. The supercell band structureswere unfolded to the primitive Brillouin zone high-symmetry path usingthe BandUP code (58, 59).

Phonons calculations were obtained within the harmonic approximationand using the finite displacement method based on the forces calculated viathe Hellmann–Feynman theorem (60). A 2 × 2 × 2 supercell was set up forboth pristine and Mn-doped rhombohedral phases, which consists of128 atoms. The nonanalytical correction is applied by including the Borneffective charges and dielectric constants calculated using the densityfunctional perturbation theory.

ACKNOWLEDGMENTS. The work performed at the University of Houstonand the University of Missouri is supported by the US Department of Energyunder Award DE-SC0010831, as well as by US Air Force Office of ScientificResearch Grant FA9550-15-1-0236, the T. L. L. Temple Foundation, the John J.and Rebecca Moores Endowment, and the State of Texas through the TexasCenter for Superconductivity at the University of Houston. J. Sui acknowl-edges support from the National Natural Science Foundation of China(Grant 51622101).

B

0.0

0.4

0.8

1.2

1.6 This work

Ref. 9 Ref. 50

Ref. 33Ref. 31

Sn 0.91Mn 0.09Te

PbTe 0.95Se 0.05

β-Ge 0.81Mn 0.15Bi 0.04Te

α-Ge 0.87Pb 0.13Te/Bi 2Te 3

α-Ge 0.9Sb

0.1Te 0.88Se 0.12

(ZT)

ave

α-Ge 0.86Mn 0.1Bi 0.04Te

This work

300 400 500 600 700 8000.0

0.5

1.0

1.5

2.0x=0 x=0.05x=0.1 x=0.15x=0.2 x=0.3

Temperature (K)

ZT

A

Fig. 8. (A) Temperature-dependent ZT of Ge0.96−xMnxBi0.04Te and (B) com-parison of average ZT (from 300 to 773 K) of rhombohedral and cubicMn-doped GeTe as well as the state-of-the-art p-type rhombohedral GeTe,cubic PbTe, and SnTe (9, 31, 33, 50).

DC

BA

Fig. 7. Temperature-dependent (A) κtot and (B) κlat of Ge0.96−xMnxBi0.04Tesamples. (B, Inset) Room-temperature κlat dependence on Mn concen-tration, where the solid line is calculated by the Debye–Callawaymodel (43, 51). (C ) Phonon dispersions and (D) PDOS of α-GeTe andα-Ge0.875Mn0.125Te.

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