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Thermoelectric properties of GeSe

Xinyue Zhang, Jiawen Shen, Siqi Lin, Juan Li, Zhiwei Chen, Wen Li, Yanzhong Pei*

Key Laboratory of Advanced Civil Engineering Materials of Ministry of Education, School of Materials Science and Engineering, Tongji Univ., 4800 Caoan Rd.,

Shanghai 201804, China

Received 27 July 2016; revised 29 August 2016; accepted 5 September 2016

Available online 13 September 2016

Abstract

The recently reported superior thermoelectric performance of SnSe, motivates the current work on the thermoelectric properties of poly-crystalline GeSe, an analog compound with the same crystal structure. Due to the extremely low carrier concentration in intrinsic GeSe, variousdopants are utilized to substitute either Ge or Se for increasing the carrier concentration and therefore for optimizing the thermoelectric powerfactor. It is shown that Ag-substitution on Ge site is the most effective, which enables a hole concentration up to ~1018 cm�3. A further isovalentsubstitution by Pb and Sn leads to an effective reduction in the lattice thermal conductivity. A peak figure of merit, zT of ~0.2 at 700 K can beachieved in Ag0.01Ge0.79Sn0.2Se, a composition with the highest carrier concentration. The transport properties can be well described by a singleparabolic band model with a dominant carrier scattering by acoustic phonons at high temperatures (>500 K). This further enables a prediction onthe maximal zT of ~0.6 at 700 K and the corresponding carrier concentration of ~5 � 1019 cm�3.© 2016 The Chinese Ceramic Society. Production and hosting by Elsevier B.V. This is an open access article under the CC BY-NC-ND license(http://creativecommons.org/licenses/by-nc-nd/4.0/).

Keywords: Thermoelectric; GeSe

1. Introduction

Thermoelectric materials, which can directly convert heatinto electricity based on either Seebeck or Peltier effect, hasdrawn increasing attention in the research community con-cerning the energy crisis [1]. The thermoelectric performanceof a material depends on the dimensionless figure of merit,zT ¼ S2T/r(kE þ kL), where S, r, T, kE, and kL represent theSeebeck coefficient, electrical resistivity, absolute tempera-ture, electronic thermal conductivity and lattice thermal con-ductivity, respectively. Materials possessing a high zT require ahigh power factor (S2/r) and a low thermal conductivity(kE þ kL). However, the strongly coupled S, r, and kE, lead tothe difficulty for obtaining high zT value [2].

Since S, r, and kE mentioned above are all closely related tothe carrier concentration (n), an optimization of n is

* Corresponding author.

E-mail address: yanzhong@tongji.edu.cn (Y. Pei).

Peer review under responsibility of The Chinese Ceramic Society.

http://dx.doi.org/10.1016/j.jmat.2016.09.001

2352-8478/© 2016 The Chinese Ceramic Society. Production and hosting by Elsevi

creativecommons.org/licenses/by-nc-nd/4.0/).

fundamentally required for realizing the maximal available zTin a given material [3e5]. To further enhance the maximal zT,proven strategies are typified either by enhancing the powerfactor (S2/r) through band engineering [6] including bandconvergence [7e11], band nestification [12], band effectivemass [13], or by minimizing the lattice thermal conductivity(kL), the only one independent material property. Several ap-proaches have been taken to reduce the lattice thermal con-ductivity, through alloying [9,14], nanostructuring [15e18],lattice anharmonicity [19,20], liquid-like transport behaviorscompounds [21] and more recently a low sound velocity [22].Providing the carrier concentration is optimized, these strate-gies have been demonstrated to be effective for advancing thethermoelectric performance in many materials.

As a new thermoelectric material, single-crystal SnSe hasrecently been reported to show an extraordinarily high ther-moelectric figure of merit at high temperatures (zT of 2.6 at973 K along the b axis), due to the ultralow thermal conduc-tivity [20]. With a further optimization in the carrier concen-tration by sodium doping on Sn site, single-crystal SnSe was

er B.V. This is an open access article under the CC BY-NC-ND license (http://

Table 1

Room temperature transport properties of GeSe doped with Cu, Na, La, and

As.

p-Type doping r (mU$cm) S (mV$K�1) k (W$m�1 K�1)

Ge1-xCuxSe x ¼ 2% 1.51 � 108 591.25 1.54

Ge1-xNaxSe x ¼ 2% 6.81 � 105 626.93 1.48

x ¼ 4% 2.99 � 107 631.24 1.40

x ¼ 6% 3.39 � 107 500.80 1.43

n-Type doping r (mU$cm) S (mV$K�1) k (W$m�1 K�1)

Ge1-xLaxSe x ¼ 2% 2.03 � 108 668.85 1.52

x ¼ 6% 4.24 � 108 441.10 1.03

GeSe1-xAsx x ¼ 2% 3.25 � 108 670.66 1.63

x ¼ 4% 3.99 � 107 614.29 1.55

332 X. Zhang et al. / J Materiomics 2 (2016) 331e337

reported to show a large increase in zT at moderate tempera-tures and therefore a high average zT (zTave) of ~1.3, ascompared with the zTave of only ~0.2 for pristine single-crystalSnSe [23,24]. Afterward, polycrystalline SnSe has also beenreported to have a low lattice thermal conductivity and a highzT (~0.8) [25e28].

These literatures send a message that high zT value can beprobably realized in the same orthorhombic bulk materials. Itis therefore important to explore new thermoelectric materialshaving the same or similar crystal structure with SnSe, sinceits low lattice thermal conductivity and high zT are probablyinherent to materials with this type of crystal structure orsimilar, particularly for those having constituent elements withsimilar chemical properties to SnSe.

Actually, all the layer-like IVeVI compounds, such asGeS, GeSe, SnS, and SnSe, crystallize in the GeS-typestructure at room temperature. This structure belongs to theorthorhombic family with a space group of D16

2h (Pnma)[29,30]. Among these IVeVI compounds, SnS and GeSeshow not only the same crystal structure but also very similarchemical composition with SnSe. The thermoelectric prop-erties of SnS have recently reported to show a decent zT of0.6 [31]. However, thermoelectric properties of GeSe have sofar been rarely reported, and most of the available workfocused on the theoretical calculations [32,33]. A minimumlattice thermal conductivity of 0.39 W m�1 K�1 is predictedfor GeSe, which is lower than that of SnS and GeS [33].Meanwhile, a large value of Seebeck coefficient and powerfactor can be achieved by proper p-type or n-type doping[33]. In another work [32], the predicted peak zT of 2.5 at800 K for GeSe along b axis due to a multiband effect, iseven higher than that of SnSe. All these finding indicatesGeSe should potentially be a superior thermoelectricmaterial.

This motivates the current work focusing on the measuredtransport properties of GeSe. The chemical doping for tuningthe carrier concentration, the transport properties and therelevant physics of polycrystalline of GeSe are discussed. Theresistivity of undoped GeSe is very large due to the extremelylow carrier concentration, as compared with conventionalthermoelectric materials [14,34]. This leaves a primary pur-pose to improving its electrical properties by increasing itscarrier concentration by doping. Therefore, various elements(Cu, Ag and Na for p-type, and Bi, Sb, La, As and I for n-type)are used to achieve a high enough carrier concentration. Itturns out that, among the above mentioned elements, only Agenables a carrier concentration up to ~1018 cm�3. Addition-ally, isovalent alloying with Sn and Pb on Ge site, is found toachieve an effectively reduction in the lattice thermal con-ductivity approaching the theoretical minimal estimated by theCahill model [35]. As a result of both doping and alloying, themeasured maximal zT is about 0.2 at 700 K. The transportproperties can be well described by a single parabolic bandmodel with a dominant carrier scattering of acoustic scatteringat high temperatures. This predicts a maximal zT of 0.6 at700 K for polycrystalline GeSe with an optimize carrier con-centration of ~5 � 1019 cm�3.

2. Experiment

Various dopants, including sodium (Na), iodine (I), anti-mony (Sb), lanthanum (La), arsenic (As), copper (Cu) andsilver (Ag), were used to dope GeSe to tune the carrier con-centration. Polycrystalline GeSe samples and alloys with PbSeand SnSe, with and without doping, were synthesized bymelting the stoichiometric quantities of high purity elements(>99.99%) sealed in silica ampoule at 1123 K for 7 h,quenching in cold water and then annealing at 853 K for 3days. The obtained ingots were hand ground into fine powdersfor X-ray diffraction (XRD) to identify the phase composition,and for hot press by induction heating at 800 K for 30 minunder a uniaxial pressure of ~70 MPa. The resulting pelletswith a density higher than 96% of the theoretical densityvalue, were ~12.0 mm in diameter and ~1 mm in thickness.

The electrical transport properties including resistivity,Seebeck coefficient and Hall coefficient of the pellet sampleswere simultaneously measured, under vacuum in the temper-ature range of 300e700 K. The resistivity and Hall coefficientwere measured using the van der Pauw technique under areversible magnetic field of 1.5 T. The Seebeck coefficient wasobtained from the slope of the thermopower versus tempera-ture gradients [36]. Thermal diffusivity (l) measured by a laserflash technique (the Netzsch LFA457 system) was used tocalculate the thermal conductivity, k ¼ dlCp, where d is thedensity measured by a mass/volume method and Cp isassumed to be a DulongePetit limit of heat capacity and to betemperature independent as well. The measurement uncer-tainty for S, r and k is 5% approximately.

Sound velocities were measured on the pellet samples atroom temperature, using pulse-receiver (Olympus-NDT)equipped with an oscilloscope (Keysight). Water and Shear gel(Olympus) were used as couplant during the measurements oflongitudinal and transverse sound velocity (vL and vS)respectively.

3. Results and discussion

The room temperature transport properties for dopedpolycrystalline GeSe with various dopants, excluding Ag, arelisted in Table 1. These elements are considered as ineffective

333X. Zhang et al. / J Materiomics 2 (2016) 331e337

dopants since the resistivity and Seebeck coefficient are toolarge to enable a high thermoelectric performance. It is foundthat Ag is the most effective dopant enabling a carrier con-centration up to ~1018 cm�3, probably due to the small elec-tronegative and atomic size differences between Ag and Ge.Therefore Ag-doped samples are focused on for the followingdiscussion.

The crystal structure of orthorhombic GeSe has been wellinvestigated previously [30]. The crystal structure of GeSe inthe room-temperature phase (Pnma) is shown in Fig. 1a, whichis a distorted NaCl-type structure. The primitive cell containseight atoms and two adjacent double layers. Each atom isconnected with three nearest neighbors through covalent bondin a single layer, creating zigzag chains along the b axis. It isknown that GeSe undergoes a first-order phase transition fromorthorhombic structure to NaCl-type structure at ~920e930 Kand remains cubic up to the melting point [37].

The XRD patterns for Ge1-xAgxSe (x ¼ 0%, 0.2%, 0.5%,1%, 1.5%, 3%) samples and Ge1-xAgxSe alloyed with PbSeand SnSe (x ¼ 1%) are shown in Fig. 1b. All the peaks can bewell indexed to orthorhombic GeSe structure without anyobservable peaks of impurities. The diffraction peaks of PbSe-and SnSe-alloyed samples shift toward the lower angle, indi-cating the increase of lattice constant.

Fig. 2 shows the temperature dependent Hall carrier con-centration (a) and Hall mobility (b) for Ge1-xAgxSe. It can beseen that Ag-doping can effectively increase the Hall carrierconcentration (nH) up to ~1018 cm�3. It is also shown that theHall carrier concentration of Ge1-xAgxSe quickly saturates atx ~0.002, meaning that nH does not increase with a furtherincrease in high nominal doping levels. It is seen thatalloying with Sn on Ge site can still enable a hall carrierconcentration of ~1018 cm�3 while alloying with Pb signifi-cantly reduces nH.

The Hall mobility (mH) for all Ag-doped samples show avery similar decrease with increasing temperature viamHfT�1.5 when temperature is above 500 K, indicating a

Fig. 1. (a) Crystal structure of orthorhombic GeSe, in which the blue and red at

Ge0.99Ag0.01Se-based alloys with PbSe and SnSe.

dominant mechanism of charge carriers scattering by acousticphonons at these temperatures. However, at lower tempera-tures (300e500 K), the Hall mobility rises with increasingtemperature via mHfT2.5 approximately, revealing additionalscattering mechanism which is believed to be due to grain-boundary potential barrier scattering. This observed increasein the Hall mobility with increasing temperature has been seenin SnSe, SnS and PbTe based materials [31,38,39].

According to the recent band structure calculation for GeSe[32], the energy difference between the first and secondvalence band maximum is small. Therefore it is in principleeasy to achieve a two-band conduction behavior for enhancingthe thermoelectric performance. It should keep in mind thatthe Fermi level needs to be deep in the valence band, in orderto involve the beneficial contribution from the second valenceband. This usually means that a heavily doping is required,which is unfortunately not achieved in this work due to lowdoping effectiveness of the dopants considered. In fact, theobtainable carrier concentration by Ag-doping is not highenough to position the Fermi level deep enough into thevalence band to enable a two-band conduction.

The band gap of 1.1 eV in GeSe [40,41] is much larger thanthat of conventional thermoelectric materials (0.2e0.5 eV forBi2Te3, PbTe and PbSe) [42e44], leading to a much weakerinteraction between the valence and conduction bands.Therefore, it is reasonable to approximate the band as para-bolic [45].

Therefore, the Seebeck coefficient at 700 K can be verywell described by a single parabolic band (SPB) model in theHall carrier concentration range obtained in this work(1017~1018 cm�3) as shown in Fig. 3a. It should be noted thatthe SPB model here assumes a dominant acoustic scattering,as evident from Fig. 2b. In other words, polycrystalline GeSein this work can be effectively approximated as a single bandconduction due to its low carrier concentration (only up to~1018 cm�3), although the band calculation indeed shows amultiband structure.

oms represent Ge and Se respectively. (b) XRD patterns for Ge1-xAgxSe and

Fig. 2. (a) Temperature dependent Hall carrier concentration for Ge1-xAgxSe and Ge0.99Ag0.01Se-based alloys with PbSe and SnSe. (b) Temperature dependent Hall

mobility for Ge1-xAgxSe.

Fig. 3. Hall carrier concentration dependent Seebeck coefficient (a) and Hall mobility (b) for Ge1-xAgxSe and its alloys at 700 K. The curves represent the

prediction based on the SPB model with a constant density-of-states effective mass (m*) of 1.04 me and a deformation potential coefficient (Edef) of ~17 eV.

334 X. Zhang et al. / J Materiomics 2 (2016) 331e337

The approximation of a single parabolic band conductioncan be further supported by the carrier concentrationdependent Hall mobility as shown in Fig. 3b. It is seen thatthe Hall mobility can be nicely predicted by the same SPBmodel as well, for all the Ag-doped GeSe samples obtainedin this work. When GeSe is further alloyed with PbSe (bluesymbols, concentrations of 8%, 10% and 14%) or SnSe (olivesymbols, concentrations of 10% and 20%), the mobility de-creases due to the additional scattering by substitutionaldefects.

The measured temperature Seebeck coefficient and elec-trical resistivity for Ge1-xAgxSe are shown in Fig. 4a and b,respectively. Seebeck coefficient for all the samples is posi-tive, indicating a p-type conduction. Seebeck coefficient de-creases with the increasing Ag content. Due to the low carrierconcentration, resistivity of the samples here is high, ascompared with traditional thermoelectrics. With increasingAg-doping level, the resistivity decreases by orders ofmagnitude. When further alloying with PbSe, both resistivityand Seebeck coefficient increase, because of the reduced Hallcarrier concentration as shown in Fig. 2a. The decrease inSeebeck coefficient and resistivity at T > 600 K is believed tobe due to the bipolar conduction.

The DulongePetit limit of heat capacity (Cp) and density(d ) of all samples are listed in Table 2.

Temperature dependent total thermal conductivity and itslattice component for Ge1-xAgxSe and its alloys are shown inFig. 4c and d. The lattice thermal conductivity (kL) is obtainedby subtracting the electronic thermal conductivity (kE) fromthe total thermal conductivity. The electronic thermal con-ductivity is estimated by kE ¼ LT/r according to the Wiede-manneFranz law, where L is the Lorenz factor determined bythe single parabolic band (SPB) model discussed above. Bothk and kL of all the samples decline as temperature rises. Itshould be noted that the electronic contribution to the totalthermal conductivity is less than 1% for all the samples in thiswork, even at temperatures that the bipolar conduction hap-pens. This is again due to the low carrier concentration.

The lattice thermal conductivity decreases as 1/T approxi-mately, indicating a dominant phonon scattering by Umklappprocesses in intrinsic GeSe and Ag-doped compounds. Ascompared with polycrystalline SnSe [27], GeSe obtained hereshows a very similar lattice thermal conductivity in theimportant temperature range of 500e700 K for thermoelectricapplications, which can be understood by the same crystalstructure between these two compounds.

Fig. 4. Temperature dependent Seebeck coefficient (a), resistivity (b), total thermal conductivity (c), thermal diffusivity (inset) and lattice thermal conductivity (d)

for Ge1-xAgxSe and its alloys. The thermal conductivity of polycrystalline SnSe [27] is also included for comparison.

Table 2

DulongePetit limit of heat capacity (Cp) and density (d ) of Ge1-xAgxSe and

Ge0.99Ag0.01Se-based alloys with PbSe and SnSe.

Samples Cp(J$g�1 K�1) d (g$cm�3)

x ¼ 0 0.3291 5.52

x ¼ 0.2% 0.3290 5.47

x ¼ 0.5% 0.3287 5.6

x ¼ 1% 0.3284 5.58

x ¼ 1.5% 0.3280 5.56

x ¼ 3% 0.3268 5.62

Ge0.89Ag0.01Pb0.1Se 0.3016 5.77

Ge0.79Ag0.01Sn0.2Se 0.3096 5.69

335X. Zhang et al. / J Materiomics 2 (2016) 331e337

The lattice thermal conductivity decreases with increasingconcentration of Ag-doping in the whole temperature range.Through a further alloying with PbSe or SnSe, the latticethermal conductivity is significantly reduced down to ~0.4 W/m-K at 700 K. With the measured average longitudinal(vL ¼ 3210 m/s) and transverse (vS ¼ 1952 m/s) sound ve-locities for polycrystalline samples obtained in this work, thetheoretical minimal lattice thermal conductivity (kL

min) is esti-mated to be ~0.4 W/m-K at high temperatures, based on theCahill model [35]:

kminL ¼�p6

�1 =

3

kBn2 =

3ð3vDÞ�

T

QD

�2 ZQD=T

0

x3ex

ðex � 1Þ2 dx ð1Þ

where kB is Boltzmann constant, n is the number density ofatoms and QD is the Debye temperature, QD ¼ vD (ħ/kB)(6p2n)1/3. And vD is average sound velocity determined by

vD ¼

0BBBB@

11

13

�1

v3L

þ 2

v3S

�

1CCCCA

1=3

ð2Þ

Noted that the sound velocity measurements here show wellagreement with previous calculations for single crystal GeSe[33].

This estimation on minimal lattice thermal conductivityshows an excellent agreement with the calculations [33]. Mostimportantly, the samples obtained here show a very compa-rable lattice thermal conductivity with the theoretical minimalvalue.

Fig. 5. Temperature dependent figure of merit, zT (a) for Ge1-xAgxSe and its alloys, and the predicted Hall carrier concentration dependent zT at 700 K (b).

336 X. Zhang et al. / J Materiomics 2 (2016) 331e337

Temperature-dependent figure ofmerit, zT is shown in Fig. 5a.Amaximal zTof 0.2 is achieved in Ge0.79Ag0.01Sn0.2Se.With themeasured average lattice thermal conductivity for these mate-rials, the SPB model enables a prediction on the carrier con-centration dependent zTat a given temperature. Shown in Fig. 5bis a case for 700 K. First of all, the model prediction agrees wellwith the experimental data. It is shown that a maximal zTof ~0.6is predicted, if the carrier concentration can be further increasedto ~5 � 1019 cm�3.

zT achieved so far in this compound is low, however, theband calculation [32] indicated a multiband structure, whichshould in principle enable a significantly enhanced zT if thematerial can be doped to have a carrier concentration of~1020 cm�3. It should be, once again, noted that such amultiband effect has not been taken into account in the pre-diction here, because it is unnecessary to include thiscomplexity in the carrier concentration range studied here.However, it is still believed that GeSe has a potential as apromising thermoelectric material, through a further carrierconcentration increase and/or band engineering.

4. Summary

In summary, Ag acts as an effective dopant on Ge site forincreasing the hole concentration, which results in anenhancement on power factor and therefore figure of merit, zT.A further alloying with Pb and Sn on Ge site can reduce thethermal conductivity effectively in the entire temperaturerange. The obtained lattice thermal conductivity is actuallyapproaching the theoretical minimum as estimated by theCahill model. The combined approach of both doping andalloying leads to a maximal zT of 0.2 at 700 K for GeSe. Thehigh temperature carrier concentration dependent transportproperties here can be well understood by a single parabolicband conduction with acoustic scattering, which further en-ables a prediction of a peak zT of 0.6 at 700 K. According tothe model prediction, the carrier concentration obtained in thiswork stays not fully optimized, suggesting available room forfurther improvements, especially by doping and band engi-neering approaches.

Acknowledgment

This work is supported by the National Natural ScienceFoundation of China (Grant No. 51422208, 11474219 and51401147) and the national Recruitment Program of GlobalYouth Experts (1000 Plan).

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3088.

Professor Yanzhong Pei, Tongji University, Email:

yanzhong@tongji.edu.cn, Yanzhong Pei is a profes-

sor at Tongji University, China. He has been working

on advanced thermoelectric semiconductors for

about a decade, from synthesizing the materials to

understanding the underlying physics and chemistry.

He holds a B.E. from Central South University in

China, a Ph. D from Shanghai Institute of Ceramics,

CAS and postdoctoral research experience from

Michigan State University and the California Insti-

tute of Technology.