-
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: [email protected], [email protected],or
[email protected].
This article contains supporting information online at
www.pnas.org/lookup/suppl/doi:10.1073/pnas.1802020115/-/DCSupplemental.
Published online May 7, 2018.
5332–5337 | PNAS | May 22, 2018 | vol. 115 | no. 21
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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
DC
B
300 400 500 600 700 8000.0
0.5
1.0
1.5
2.0
Temperature (K)
ZT
300 400 500 600 700 800
1
2
34
Temperature (K)
lat(W
m-1K-1)
T-1.2
300 400 500 600 700 8000
2
4
6
8
Temperature (K)
tot(W
m-1K-1)
300 400 500 600 700 80010
20
30
40
50
Temperature (K)
PF(Wcm
-1K-2)
300 400 500 600 700 8000.1
1
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.
Liu et al. PNAS | May 22, 2018 | vol. 115 | no. 21 | 5333
APP
LIED
PHYS
ICAL
SCIENCE
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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
20 30 40 50 60
Cooling
300 K
473 K
Intensity(a.u.)
300 K
2 (Degree)
Heating
-GeTe
300 400 500 600 700 8000.1
0.2
0.3
0.4
0.5
Heatcapacity(Jg-1K-1)
x=0 x=0.01x=0.05 x=0.1x=0.15 x=0.2x=0.3
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
Interaxialangle(Degree)
20 30 40 50 60 70
Intensity(a.u.)
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
12
16
20
24
w(Wcm
-1K-2)
PF(Wcm
-1K-2)
Mn concentration (x)
Power factor
100
120
140
160
180
Weighted mobility
DC
B
300 400 500 600 700 80010
20
30
40
50
Temperature (K)
PF(Wcm
-1K-2)
300 400 500 600 700 80050
100
150
200
250
300
Temperature (K)
S(VK-1)
300 400 500 600 700 8000.1
1
10
x=0 x=0.05x=0.1 x=0.15x=0.2 x=0.3
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.
B
1 10 100
5
10
15
20
25
nH (1020 cm-3)
PF(Wcm
-1K-2)
1 10 100
100
200
300
400
Ge1-xSbxTe
m* = 1.5 m0
m* = 2.5 m0
m* = 4 m0
m* = 5.5 m0
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
-0.4 -0.2 0.0 0.2 0.40
2
4
6
8
10
DOS(arb.units)
Energy (eV)
β-GeTe-scβ-Ge0.875Mn0.125Te
-0.4 -0.2 0.0 0.2 0.4 0.60
2
4
6
8
10
DOS(arb.units)
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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