Thermoelectric Materials Under Pressure

REVIEW@RRL High-Pressure Technology

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Thermoelectric Materials Under Pressure Najebah M. Alsaleh, Elvis Shoko, Muhammad Arsalan, and Udo Schwingenschlögl*

Recent advances in high-pressure technology provide access both to novel materials and to exotic properties of known materials, thus opening exciting opportunities for fundamental as well as applied research. This review summarizes for various classes of materials the existing knowledge on the thermoelectric behavior under hydrostatic pressure to identify promising directions for future developments.

generation technologies, see Figure 2 for a comparison.[7] Finally, the thermoelectric device efficiency is given by η¼

1

pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi TC 1 þ ZT 1 pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi TH 1 þ ZT þ TTHC

ð2Þ

where 1 TTHC is the Carnot efficiency and

ZT ¼

1. Introduction Thermoelectric devices can convert a temperature gradient into electrical energy (Seebeck effect) or can use electrical energy to create a temperature gradient (Peltier effect).[1] They typically combine the key properties of long lifetime, low operation cost, and scalability, which is difficult to achieve by other green technologies for power generation. Potential applications are found in many fields, as ellaborated in ref. [2], for example. A thermocouple, in general, consists of p-type (hole carriers) and ntype (electron carriers) semiconductors, see Figure 1. Several thermocouples may be connected in various configurations to meet the power requirements device.[3] The of a thermoelectric open circuit voltage ΔV ¼ Sp Sn ðT H T C Þ of a thermocouple is given by the Seebeck coefficients of the p-type (Sp ) and n-type (Sn ) semiconductors and the temperatures of the hot (T H ) and cold (T C ) sides.[4] The thermoelectric performance of a component material, on the other hand, is characterised by its dimensionless figure of merit, ZT ¼ S2 σT=κ

ð1Þ

with the electrical conductivity σ and thermal conductivity κ ¼ κe þ κl (sum of electronic and lattice contributions).[5] A high value of ZT is achieved when the power factor, S2 σ, is high and κ is low. While the best thermoelectric materials today realize ZT values close to 3,[6] ZT04 for both the p-type and n-type semiconductors is required for thermoelectricity to become competitive to other power

2 Sp Sn T 1 σ 1 κp þ κn p þ σn

ð3Þ

with T ¼ ðT H þ T C Þ=2. The search for well performing thermoelectric materials is a great challenge, see Figure 3, which illustrates the development of the maximal ZT values achieved in various classes of materials over time.[8] At elevated temperature, relatively high ZT values are provided by tellurides (e.g., Bi2Te3 and PbTe), perovskite oxides (e.g., SrTiO3[9]), other oxides (e.g., NaxCoO2[10]), half-Heusler alloys (e.g., (Ti,Zr,Hf)NiSn[11]), and Zintl compounds (e.g., Yb14MnSb11[12]), for example. A range of techniques, including nanostructuring, band alignment engineering, and hierarchical architecturing, continue to be combined in new ways in order to enhance the material properties, which is known as the panoscopic approach.[13] Nanostructuring is a particularly effective tool to boost ZT, because κl can be reduced by enhancing the phonon scattering without affecting S2 σ.[14] The fact that many of the leading thermoelectric materials have band gaps of 6–10 kB T,[15] where kB is the Boltzmann constant, indicates that the performance (in particular S2 σ) depends critically on this quantity. As hydrostatic pressure can strongly modify the size of the band gap, pressure engineering therefore has great potential in

N. M. Alsaleh, E. Shoko, Prof. U. Schwingenschlögl Physical Science and Engineering Divison (PSE) King Abdullah University of Science and Technology (KAUST) Thuwal 23955-6900, Saudi Arabia E-mail: [email protected] M. Arsalan Saudi Aramco Dhahran 31311, Saudi Arabia The ORCID identification number(s) for the author(s) of this article can be found under https://doi.org/10.1002/pssr.201800083.

DOI: 10.1002/pssr.201800083

Phys. Status Solidi RRL 2018, 1800083

Figure 1. Thermocouple consisting of p-type and n-type semiconductors.

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www.pss-rapid.com Table 1. Materials prepared by high-pressure synthesis together with the highest reported ZT value (ZT max ) and the temperature at that this value was measured (T max ). The materials are sorted from high to low ZT max . ZTmax

Tmax [K]

Ref.

(Sr0.09Ba0.11Yb0.05)Co4Sb12.3

1.90

835

[19]

In0.1Ge0.9Te

1.82

573

[20]

Pb0.98Na0.02Te

1.74

774

[21]

Mg2Si0.05Sn0.5

1.63

615

[22]

Material

Figure 2. Efficiency of electrical power generation (electrical power output relative to heat input) compared for different heat sources and conversion technologies. Competitivness of thermoelectric power generation requires materials (both p-type and n-type) with ZT04. Reproduced with permission.[7] Copyright 2009, Springer Nature.

Figure 3. Development of the maximal ZT values in various classes of materials from 1955 to 2016. Reproduced with permission.[8] Copyright 2015, Elsevier.

materials design. Recent advances in high pressure technology consequently open exciting (though rarely investigated) opportunities for achieving high performance thermoelectric materials. In the following chapters we will collect knowledge about the impact of hydrostatic pressure on the thermoelectric response, mainly focusing on high-ZT materials. Alternatively, materials can be synthesized in form of thin stressed films to obtain similar effects. High-pressure synthesis also has been used to create favorable thermoelectric properties. For example, it is known that SnSe benefits greatly from synthesis at 100 MPa (enhanced σ and reduced κ).[16] Similarly, due to modifications of the texture and preferred orientation, which enhance σ, the highest ZT values of BiSbTe3[17] and Bi2Te3[18] are achieved by synthesis at 2 and 2.5 GPa, respectively. Table 1 lists materials prepared by high-pressure synthesis together with the highest reported ZT value (ZT max ) and the temperature at that this value was measured (T max ).

2. Te Compounds The experimental band gap of Bi2Te3 (R3m symmetry) decreases under hydrostatic pressure[51] and the first-principles


BiSbTe3, p-type (no carrier concentration given)

1.40

432

[17]

Sr0.07Ba0.07Yb0.07Co4Sb12

1.40

800

[23]

Co4Sb11.5Te0.5 þ 0.25 vol% carbon nanotubes

1.32

773

[24]

Bi0.4Sb1.6Te3 þ 0.05 wt% graphene

1.26

423

[25]

Cu2Se, p-type (7.7 1020 cm3)

1.20

873

[26]

Bi0.5Sb1.5Te2.7Se0.3

1.16

300

[27]

Ba8Ga16Ge30

1.14

773

[28]

In0.1Co4Sb11Te0.8Ge0.2

1.12

773

[29]

Bi2Te2.95Se0.05

1.11

373

[30]

Cu2S, p-type (2.35 1020 cm3)

1.07

873

[26]

La0.29Co4Sb12

1.06

863

[31]

Co4Sb11.5Te0.5

1.03

710

[32]

Bi2Te2.73Se0.27

1.03

344

[33]

(AgSb)0.03Pb0.94Se

1.03

600

[34]

Ba0.25Pb0.05Co4Sb11.5Te0.5

1.00

720

[35]

Bi2Te3, p-type (no carrier concentration given)

0.97

365

[18]

In0.03Co4Sb11.5Te0.5

0.93

711

[36]

Bi2(Te0.9Se0.1)3

0.81

373

[37]

Yb13.7(Sc,Y)0.3MnSb11

0.80

950

[38]

Ag2Se, n-type (no carrier concentration given)

0.80

390

[39]

Bi2Te2.7Se0.3 þ Gd

0.74

423

[40]

PbTe0.9997I0.0003

0.71

600

[41]

SnSe, n-type (4.18 1017 cm3)

0.71

873

[16]

Ti0.2Co4Sb11.5Te0.5

0.70

706

[42]

BiCuTeO, n-type (1.16 1020 cm3)

0.65

650

[43]

Mg2Si0.995Sb0.005

0.62

800

[44]

Cu2Sn0.95In0.05Se3

0.62

773

[45]

CuAgSe, n-type (no carrier concentration given)

0.60

450

[39]

Mn0.98Te

0.59

773

[46]

Sm0.7Fe2.8Ni1.2Sb12.8

0.55

560

[47]

Ni0.15Co3.85Sb12

0.52

600

[48]

Ca2Si, p-type (1.16 1018 cm3)

0.52

1000

[49]

Mn34.6W1.8Si63.6

0.50

700

[50]

calculations of ref. [52], see Figure 4, show a phase transition into a metallic phase at 9 GPa. At 300 K, for n-type Bi2Te3 (3 1019 cm3 ) the predicted value of S2 σ increases up to the phase transition, while for p-type Bi2Te3 (2 1019 cm3 ) it decreases. At 298 K, the experiments of ref. [53] have found a maximum of S ¼ 170 mV K1 at 1 GPa and maxima of S2 σ ¼ 6:61 103 W m1 K2 and ZT ¼ 1:02 at 2.75 GPa.

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around 3 GPa, which can be attributed to band degeneracy.[52] Reference [52] also shows that S of p-type Bi0.6Sb1.4Te3 ( 4 1019 cm3 ) decreases by 20% and σ increases by a factor of 12 between 0 and 4 GPa. As S2 σ thus increases by a factor of 8, while κ simultaneously increases by a factor of 2, ZT approaches a value of 3. On the other hand, p-type Bi0.5Sb1.5Te3 (no carrier concentration given) shows experimentally a maximum of S ¼ 305 mV K1 at 1.7 GPa and, due to a simultaneous increase of σ, a high value of ZT ¼ 2:2.[56] The experimental S of p-type BaBiTe3 (no carrier concentration given) increases from 209 mV K1 at 0 GPa to a maximum of 315 mV K1 at 0.96 GPa, while simultaneously σ increases from 42 to 348 S cm1 and κ from 0.65 to 1.43 W m1 K.[57] As a result, S2 σ and ZT show pronounced maxima as function of hydrostatic pressure, see Figure 5. The experimental band gap of BiTeI decreases under hydrostatic pressure until the volume is reduced by 0.89% and then increases again.[58] The material undergoes structural phase transitions from P3m1 symmetry at 0 GPa to Pnma symmetry at 8.8 GPa and then to P4=nmm symmetry at 18.9 GPa.[59] In agreement with the behavior of the band gap, for a low hole concentration of 3 1018 cm3 at 300 K the calculated S exhibits a maximum of 150 mV K1 at a volume reduction of 1.00% and σ=τ a maximum of 6:2 1019 1/Ω m s at a volume reduction of 0.85%. As a consequence, S2 σ=τ can be significantly enhanced by hydrostatic pressure, for example, to 0:45 108 W m1 K2 s at 1000 K and a volume reduction of 0.85%. The first-principles results of ref. [60] show for the Fm3m phase of PbTe a minimum of the band gap at 5.2 GPa hydrostatic pressure. Concerning the behavior of S at 300 K, they agree qualitatively with the first-principles results of ref. [61], as given in Figure 6: In wide ranges of hole and electron concentrations, jSj first decreases as function of hydrostatic pressure (for low carrier concentrations approximately up to the point at that the band gap is minimal) and then increases toward a maximum. ZT roughly Figure 4. Band gap (top) and S2 σ (bottom) of Bi2x Sbx Te3x Sey at 300 K under hydrostatic pressure. Reproduced with permission.[52] Copyright 2017, Royal Society of Chemistry.

According to the all-electron first-principles calculations of ref. [54], the band gap of Sb2Te3 (which is isostructural to Bi2Te3) decreases under pressure perpendicular to the layers of the layered structure and reaches zero at 2.5 GPa, whereas there is little variation under hydrostatic pressure. The latter finding contradicts the pseudopotential first-principles result of ref. [52] that the band gap decreases from 0.28 eV at 0 GPa to 0.12 eV at 5 GPa (which comes along with a reduction of S2 σ). A phase transition from C2=m to R3m symmetry is found experimentally in As2Te3 between 6 and 8 GPa, with a continuously decreasing S of 250 mV K1 at 0 GPa, 100 mV K1 at 2 GPa, and 75 mV K1 at 6 GPa.[55] According to the first-principles calculations of ref. [52], see Figure 4, the band gaps of BiSbTe3 and Bi2Te2Se decrease under hydrostatic pressure. At 300 K, S2 σ tends to increase for n-type Bi2Te2Se (3 1019 cm3 ) and tends to decrease for p-type Bi2Te2Se (2 1019 cm3 ), whereas p-type BiSbTe3 (5 1019 cm3 ) shows a maximum of S2 σ ¼ 5:1 103 W m1 K2


Figure 5. ZT and S2 σ of BaBiTe3 under hydrostatic pressure. Reproduced with permission.[57] Copyright 2001, AIP Publishing.

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Figure 7. Experimental behavior of S for CoSb3 under hydrostatic pressure. Reproduced with permission.[67] Copyright 2014, Elsevier.

Figure 6. S (top) and ZT (bottom) of p-type (left) and n-type (right) PbTe at 300 K under hydrostatic pressure for carrier concentrations of 1 1018 cm3 (red), 1 1019 cm3 (blue), 5 1019 cm3 (green), and 1 1020 cm3 (brown). Reproduced with permission.[61] Copyright 2011, Springer Nature.

follows this trend. In contrast to the theoretical prediction, the experimental S included in Figure 6 for n-type PbTe (no carrier concentration given) declines almost monotonuously up to 12 GPa. According to the first-principles results of ref. [60] for the Pnma phase of PbTe, S at 300 K decreases under hydrostatic pressure monotonuously for a wide range of hole concentrations, because the band gap decreases from 0.48 at 0 GPa to 0.01 at 18 GPa, while ZT shows no clear trend. First-principles calculations for GeTe show that the band gap, S, S2 σ=τ, and ZT (1.0 at 0 GPa for a hole concentration of 1 1019 cm3 [61]) decrease under hydrostatic pressure for both the Fm3m and Pm3m phases.[62] According to ref. [63], p-doping is generally more efficient than n-doping to enhance the thermoelectric performance of SnTe. Under hydrostatic pressure the band gap shows a minimum at 1.5 GPa and ZT a maximum at 1 GPa (with a value of 1.5 for a hole concentration of 1 1019 cm3 , for example, as compared to 0.2 at 0 GPa). The structure type of ZnTe is zinc blende (F43m) up to 9.5 GPa, trigonal (P3121) between 9.5 and 11.5 GPa, and orthorhombic (Cmcm) between 11.5 and 13 GPa. Experimentally (no carrier concentration given), the value of S ¼ 400 mV K1 at 0 GPa decreases to almost zero at 11 GPa.[64] We note that calculated κl values of ZnTe and CdTe are constant under hydrostatic pressure up to 1.5 GPa, while a reduction is observed in the case of HgTe.[65]

3. Sb Compounds According to the first-principles calculations of ref. [66], under 3 GPa hydrostatic pressure the a, b, and c lattice constants of the Zintl compound Ca5Al2Sb6 decrease by 2.6, 2.4, and 1.8%,


respectively, and the volume decreases by 7.6%. However, these modifications cause no strong changes in the material’s thermoelectric performance. This is also true for the fact that the thermoelectric performance is much better in the c-direction than in the a and b-directions (because of stronger dispersion and higher band degeneracy). In the c-direction at 300 K and for the optimal electron concentration (6:91 1019 cm3 ) the value of ZT ¼ 2:0 at 0 GPa is slightly enhanced to ZT ¼ 2:1 at 2.6 GPa. Experimentally, the band gap of the skutterudite CoSb3 (no carrier concentration given) is direct with a size of 0.189 eV at 0 GPa but indirect with an increased size of 0.514 eV at 20 GPa.[67] Figure 7 shows that S increases rapidly under hydrostatic pressure and reaches a maximum of 375 mV K1 at 10 GPa, which is an increase by more than a factor of 7 as compared to the value at 0 GPa. While σ decreases simultaneously, because the band gap increases, S2 σ is still enhanced to a maximum of 15:8 106 W cm1 K2 at 10 GPa, that is, by a factor of 8 as compared to the value at 0 GPa. Total and partial densities of states show hybridization between the Co-3d and Sb-5s/5p states already at 0 GPa. Under hydrostatic pressure this hybridization becomes stronger, which explains why both the band gap and S are enhanced. For Zn4Sb3 (no carrier concentration given) the experimental value of S (118 mV K1 at 0 GPa and 297 K) decreases by 14% per GPa hydrostatic pressure (measured up to 1.2 GPa).[68] However, as σ is enhanced, S2 σ shows little pressure dependence.

4. Mg Compounds According to the first-principles calculations of ref. [69], in α-MgAgSb a phase transition from semimetallic to semiconducting behavior occurs at 5 GPa hydrostatic pressure and under higher pressure the band gap grows continuously. Therefore, S increases in the high pressure regime, for example, at 550 K and for a hole concentration of 2:7 1020 cm3 from 240 mV K1 at 7 GPa to 400 mV K1 at 17 GPa in the c-direction. Under the same conditions, S2 σ=τ mainly increases below 7 GPa, for example, from 0:26 103 W m1 K2 fs at 0 GPa to 0:56 103 W m1 K2 fs at 7 GPa in the c-direction. Using κ ¼ 0:8 W m1 K and τ ¼ 5 fs, the authors of ref. [69] find ZT ¼ 1:92.

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Experimentally, Mg2Si shows a phase transition from the antiflourite to the anticotunnite structure at 8.38 GPa.[70] The firstprinciples calculations of ref. [71] indicate that the band gap decreases under hydrostatic pressure from 0.21 eV at 0 GPa to 0.10 eVat 6 GPa. While σ=τ is thus enhanced, it turns out that S2 σ=τ is reduced in the temperature range 100 K T 1200 K (no carrier concentration given). The authors also find that κ is dominated by κl and that κe =τ shows virtually no dependence on hydrostatic pressure. Experiments on 1 at.% Al-doped Mg2Si at 300 K point to a significant decrease of S (120 mV K1 at 0 GPa) under hydrostatic pressure, while σ increases.[72] At 2 GPa, S2 σ and ZT show maxima of 8 103 W m1 K2 and 0.17, respectively. According to the firstprinciples calculations of ref. [73], the band gap of Mg2 Sn increases from 0.13 eVat 0 GPa to 0.28 eVat 5.6 GPa hydrostatic pressure and then decreases up to 50.7 GPa where a transition into a semimetallic phase occurs. In a wide temperature range, the calculated value of S2 σ=τ changes under hydrostatic pressure little in the case of p-doping but strongly in the case of n-doping (3 1020 cm3 ), following the trend of the band gap, such that the best thermoelectric performance is obtained at the critical pressure of 5.6 GPa. Rather surprisingly, it turns out that κl has a minimum around this pressure, while κe =τ shows a maximum.

strongly increases in all directions. Though κl increases (such that κ doubles at 6 GPa), ZT grows thanks to the strong response of σ. For example, S2 σ is enhanced by a factor of about 40 in the a-direction (600 K), 6 in the b-direction (700 K), and 5 in the c-direction (700 K). As a result, ZT is enhanced from 0.08 to 1.70 in the a-direction, from 0.74 to 2.50 in the b-direction, and from 0.65 to 1.70 in the c-direction. These values exceed the experimental maxima at 0 GPa (0.8 in the a-direction, 2.0 in the b-direction, and 1.5 in the c-direction), appearing for a hole concentration of 4 1019 cm3 .[76] While the first-principles calculations of ref. [77] show that the band gap of BiCuSeO increases under hydrostatic pressure, the authors argue that σ is enhanced. At 700 K and 0 GPa a value of S ¼ 375 mV K1 (S ¼ 500 mV K1) is obtained for low ndoping (p-doping) of 1 1018 cm3 , which increases slightly (decreases significantly) under hydrostatic pressure. According to Figure 9, S2 σ=τ is enhanced in both cases (due to the enhancement of σ). In the narrow band gap oxide semiconductors ZnO, Ti2O3, and Fe2O3 the experimental band gap and, therefore, S decrease under hydrostatic pressure.[78] The band structures of CePd3 and CeIn3 hardly vary under hydrostatic pressure, while CeSn3 shows a topological phase

5. Other Materials The space group of SnSe is Pnma below 11 GPa hydrostatic pressure, where a transition to space group Bbmm is encountered.[74] In both phases the lattice constants and band gap decrease continuously under hydrostatic pressure. Figure 8 summarizes results of first-principles calculations on the thermoelectric properties for a hole concentration of 1 1018 cm3 .[75] At 6 GPa, a p-type behavior of S is observed in the b and c-directions but an n-type behavior in the a-direction. In the b and c-directions, S is lower at 6 GPa than at 0 GPa, because the hydrostatic pressure reduces the density of states at the band edges. Due to reduction of the effective mass and enhancement of the carrier mobility, σ (and therefore κe )

Figure 8. Comparison of the thermoelectric properties of SnSe in the a, b, and c-directions at 0 GPa and 6 GPa. The circles represent experimental data at 0 GPa. Reproduced with permission.[75] Copyright 2016, Royal Society of Chemistry.


Figure 9. S2 σ/τ for n- and p-doped BiCuSeO at 700 K as function of the carrier concentration. Reproduced with permission.[77] Copyright 2014, Royal Society of Chemistry.

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Band gap (eV)

transition at 2.5 GPa.[79] The experimental S values at 0 GPa are 75 mV K1 for CePd3, 8 mV K1 for CeIn3, and 23 mV K1 for CeSn3. They increase for CePd3 and CeIn3 up to 5 GPa hydrostatic pressure, while for CeSn3 a minimum appears at 2.5 GPa. The first-principles calculations of ref. [80] show that hydrostatic pressure continuously reduces the band gap of MoS2 and even leads to a transition into a metallic phase at 25 GPa. While S is not subject to significant changes up to the phase transition (with similar values in the ab-plane and c-direction), both σ=τ and S2 σ=τ are enhanced, such that ZT reaches at 25 GPa

values of 0.05 in the ab-plane and 0.65 in the c-direction for an electron concentration of 1:5 1020 cm3 . Experimentally, S of Mn3Si (no carrier concentration given) increases under hydrostatic pressure, for example by about 10% from 0 to 22 GPa at 300 K.[81]

6. Summary Effects of hydrostatic pressure relevant for the thermoelectric properties have been collected for a variety of materials.

0.6 0.5 0.4 0.3 0.2 0.1

SnSe Bi2Te3 Bi0.5Sb1.5Te3 Bi2Te2Se Sb2Te3 Ca5Al2Sb6 CoSb3 Mg2Si Mg2Sn

0

10 5 Pressure (GPa)

15

600

Smax ( μV/K)

400 200 0

-200 0

10 5 Pressure (GPa)

15

SnSe (a-axis), 600 K SnSe (b-axis), 700 K Bi0.5Sb1.5Te3, 300 K BaBiTe3, 300 K PbTe (Fm3m), 300 K PbTe (Pnma), 300 K Ca5Al2Sb6 (c-axis), 300 K CoSb3, 300 K MgAgSb, 550 K Mg2Si, 300 K SnTe, 300 K ZnTe, 295 K

ZTmax

3 SnSe (a-axis), 600 K SnSe (b-axis), 700 K Bi2Te3, 300 K Bi0.5Sb1.5Te3, 300 K BaBiTe3, 300 K PbTe (Fm3m), 300 K PbTe (Pnma), 300 K Ca5Al2Sb6 (c-axis), 300 K SnTe, 300 K

2 1

0

10 5 Pressure (GPa)

15

Figure 10. Band gap, Smax , and ZT max of various materials under hydrostatic pressure. Dashed lines refer to experiments and solid lines to calculations.


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Wherever insight is available, the origin of the observed behavior has been discussed. It turns out that hydrostatic pressure can be a powerful tool for enhancing the thermoelectric response by modifying the electronic structure. In this sense, pressure engineering can complement the toolkit of the panoscopic approach. We summarize the insights from the foregoing discussions in Figure 10 to highlight the materials with strong dependence of the thermoelectric performance on hydrostatic pressure. The quantities Smax and ZT max refer to the highest reported values (not all carrier concentrations may have been studied) at specific hydrostatic pressure. For all materials included in Figure 10 the band gap tends to decrease under hydrostatic pressure, as expected, with the exceptions of CoSb3 and Mg2Sn. For S a variety of behaviors is observed, indicating that different mechanisms play a role in the pressure dependence. Finally, Bi0.5Sb1.5Te3 and SnTe show sharply enhanced values of ZT even under low hydrostatic pressure, at least at 300 K, which makes these materials interesting for future investigations.

Acknowledgements We thank Mohamed N. Noui-Mehidi for fruitful discussions. The research reported in this publication was supported by Saudi Aramco under the grant agreement number RGC/3/3158-02. It was also supported by funding from King Abdullah University of Science and Technology (KAUST).

Conflict of Interest The authors declare no conflict of interest.

Keywords figure of merit, hydrostatic pressure, thermoelectric materials Received: February 25, 2018 Revised: April 21, 2018 Published online:

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