University of Groningen Design of Advanced Thermoelectric Materials Shaabani, Laaya

Design of Advanced Thermoelectric Materials

Shaabani, Laaya

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Laaya Shaabani PhD thesis

University of Groningen, The Netherlands

Zernike Institute for Advanced Materials PhD thesis series 2018-14 ISSN: 1570-1530

ISBN: 978-94-034-0560-5 (printed version) ISBN: 978-94-034-0561-2 (electronic version)

The work described in this thesis was performed in the group “Solid State Materials for Electronics” (part of the Zernike Institute for Advanced Materials) at the University of Groningen, The Netherlands. This work was funded by the Dieptestrategie of the Zernike Institute for Advanced Materials.

Copyright © 2018 L. Shaabani. All rights reserved. No part of this thesis may be reproduced, stored in a retrieval system or transmitted in any form or be any means without prior written permission of the author.

Cover design by: Laaya Shaabani Layout by: Gildeprint

Proefschrift

ter verkrijging van de graad van doctor aan de Rijksuniversiteit Groningen

op gezag van de

rector magnificus prof. dr. E. Sterken, en volgens besluit van het College voor Promoties.

De openbare verdediging zal plaatsvinden op vrijdag 18 mei 2018 om 09:00 uur

door

Laaya Shaabani

geboren op 21 maart 1980 te Tabriz, Iran

Copromotor Dr. G. R. Blake Beoordelingscommissie Prof. dr. B. J. Kooi Prof. dr. O. Oeckler Prof. dr. M. Huijben

1 Introduction 9

1.1 Introduction to thermoelectric materials 11

1.2 Selection criteria for thermoelectric materials 12

1.3 Approaches for enhancing thermoelectric figure of merit 17

1.3.1 Reducing thermal conductivity 17

1.3.2 Improving the power factor 17

1.4 Motivation and outline of thesis 18

Bibliography 19

2 Experimental techniques 23

2.1 Synthesis details 25

2.1.1 Carbon coating 25

2.1.2 Spark plasma sintering 26

2.2 Structural and chemical characterization 27

2.2.1 Powder X-ray diffraction (PXRD) 27

2.2.2 Scanning electron microscopy and energy-dispersive X-ray spectroscopy 27

2.3 Magnetic properties measurement 28

2.4 Hall measurements 28

2.5 High temperature thermoelectric properties measurement 29 2.5.1 Seebeck coefficient and electrical resistivity measurement 29

2.5.2 Thermal conductivity measurement 32

3.2 Methods 41

3.2.1 Sample fabrication 41

3.2.2 Materials Characterization 41

3.3 Results and discussion 42

3.4 Conclusions 50

Bibliography 51

4 Thermoelectric performance of p-type single phase (PbTe)_0.55(PbS)_0.1(PbSe)_0.35 57

4.1 Introduction 59

4.2 Experimental 60

4.2.1 Sample fabrication 60

4.2.2 Transport properties measurements 61

4.2.3 Materials Characterization 61

4.3 Results and Discussion 62

4.4 Conclusions 68

Bibliography 69

5 Thermoelectric performance of Ce-doped PbSe 73

5.1 Introduction 75

5.2 Experimental section 76

5.2.1 Sample fabrication 76

5.2.2 Transport properties measurements 76

5.2.3 Materials Characterization 77

5.3 Results and Discussion 77

5.4 Conclusions 82

Bibliography 83

6 High temperature ferromagnetism in Ce-doped PbSe 87

6.1 Introduction 89

6.3 Results and discussion 91

6.3.1 PXRD patterns 91

6.3.2 Magnetic properties 92

6.3.3 Microstructural properties 95

6.3.4 Electrical resistivity, Seebeck coefficient and power factor 99

6.4 Conclusion 103

Bibliography 105

Summary 109

Samenvatting 113

Chapter

1

11

1

1.1

Introduction to thermoelectric materials

Thermoelectric technology is currently attracting attention as a green power source due to the global energy crisis and concern for the environment.1,2 _{Thermoelectric} devices can convert waste heat to electricity when a temperature gradient is applied across them according to the Seebeck effect, or can create a heat gradient in response to an electric current according to the Peltier effect.3-5 _{As a source of sustainable} and environmentally friendly energy, thermoelectric devices can use all kinds of energy in their surroundings such as waste heat, solar energy, radiant heat,2 _{etc. and} they have been used in many areas such as harvesting waste heat from automotive exhaust systems,6 _{powering deep space missions}7 _{and improving power efficiency} in other industrial processes. In addition, thermoelectric devices are reliable energy converters that generate no noise, have no mechanical moving parts and generate no pollution.2,8 _{The thermoelectric performance of a material is directly related to} the so-called dimensionless figure of merit, zT, defined as

zT = S2_{σT/κ =S}2_{σT/ (κ}

e + κl) (1.1)

where S is the Seebeck coefficient or thermopower (μVK-1_{), σ is the electrical} conductivity (Ω-1_m-1_{), κ is the total thermal conductivity (Wm}-1_K-1_{), and T is the absolute} temperature (K).3,9,10 _{The electrical properties determine the power factor, defined} as S2_{σ or S}2_{/ρ, where ρ is the electrical resistivity. The total thermal conductivity κ}

has two contributions, one from the electrical carriers κ_e, and the other from lattice vibrations κ_l.11 _{The conversion efficiency of a thermoelectric device, η, depends on a} combination of the Carnot efficiency and the figure of merit, and is defined as12

(1.2) Here, is the temperature difference across the thermoelectric module, is the Carnot efficiency, T_H is the temperature of the hot end, T_C is the temperature of the cold end of the thermoelectric module, and T_m is the average temperature. According to equation 1.2, the conversion efficiency of a thermoelectric

device depends not only on zT but also on the temperature difference of operation. It is evident that η can be increased by high values of zT and application of higher temperature gradients.

To obtain the maximum performance of a thermoelectric material, a high Seebeck coefficient, high electrical conductivity and low thermal conductivity are required. However, these three parameters depend on interrelated material properties. Therefore, optimizing these parameters together within the desired range of temperature is a challenge. Hence, a broad range of studies has been carried out to identify new materials with improved thermoelectric performance and to optimize existing materials. Several types of thermoelectric materials are currently under investigation including lead chalcogenides. Lead chalcogenide compounds have been investigated and considered as promising materials for thermoelectric applications for many years.13-21 _{They are typically used for thermoelectric generators} that function in an intermediate temperature region (400–800 K).22 _{The findings from} studies on lead chalcogenide based compounds have provided encouragement for the further improvement of thermoelectric technologies.23-33

1.2

Selection criteria for thermoelectric materials

Despite the advantages of thermoelectric materials described above, their applications have been limited because their energy conversion efficiency is low. Thus, current research in thermoelectric materials deals both with improving existing materials and discovering new systems to obtain the greatest efficiency possible. As the transport characteristics depend on interrelated material properties, the goal is to optimize a variety of conflicting properties.4

For metals and degenerate semiconductors with weak interactions the Seebeck coefficient is given by:4

13

1

electron, m* is the effective mass of the carriers, and n is the carrier concentration. The electrical conductivity (σ) and electrical resistivity (ρ) are related to n through the carrier mobility μ:

σ = 1/ρ = neµ (1.4)

The total thermal conductivity is given by:

κ = κ_e + κ_l (1.5)

Here κ_e (electronic thermal conductivity) is the thermal conductivity from electrons and holes transporting heat and κ_l (lattice thermal conductivity) originates from phonons travelling through the lattice. For many materials κ_e is directly related to the electrical conductivity through the Wiedemann–Franz law:

κ_e = LσT = neµLT (1.6)

where L, the Lorenz number, is given by π2_k

B2/9e2 = 2.4×10-8 V2K-2 for the degenerate limit (metals and heavily doped semiconductors), but it can vary depending on the material and temperature.34

Most of the materials investigated in thesis cannot be categorized as degenerate semiconductors as they exhibit strong electron-electron interactions. In this case equation 1.3 does not predict the Seebeck coefficient accurately, and the Lorenz number can deviate significantly from the value above. It is not straightforward to measure L experimentally because in order to do so the mobility should be higher than that generally found at thermoelectric operating temperatures. In such cases, and if the charge carrier conduction occurs within a single parabolic band, the following expression more accurately describes the Seebeck coefficient:35

Here λ is the charge carrier scattering parameter, which is zero for the approximation of acoustic phonon scattering, generally valid for most thermoelectric materials at high temperature. The functions F_j(η) are Fermi integrals expressed in terms of the reduced electrochemical potential η and the reduced carrier energy :

(1.8) Similarly, an expression can be obtained for the Lorenz number in the single parabolic band approximation:

(1.9) Kim et al. proposed a numerical solution to the above equations that directly relates

L to S measured experimentally as a function of temperature:36

(1.10)

Figure 1.1: Dependence of Lorenz number (L) on experimentally measured magnitude of

Seebeck coefficient (S) following equation 1.10 for the single parabolic conduction band model. Reproduced from ref. 36.

15

1

by Kim et al.36 _{to hold well for many common thermoelectric materials and to give a} much better prediction of L than the constant value in the degenerate limit. However, in materials with narrow direct band gaps such as the lead chalcogenides studied in this thesis, the valence and conduction bands can interact strongly, distorting their parabolic nature and causing the relation between L and S to deviate from that in figure 1.1. For materials with non-parabolic bands the Kane band model37 _{is more} appropriate, where the expressions for S and L in equations 1.7 and 1.9 are modified to include an additional non-parabolicity parameter α = k_BT/e_g (e_g is the band gap).36 In this model the band becomes more linear as e_g decreases, until a Dirac cone is obtained in the limit where e_g = 0. Non-parabolic bands in relation to thermoelectric properties are discussed in detail by Bhandari and Rowe.38

Improvement of the figure of merit, zT, of a thermoelectric material involves the optimization of the thermal conductivity, Seebeck coefficient and electrical conductivity together. However, all three parameters depend on the charge carrier concentration for a bulk material as presented in figure 1.2. According to this figure, the best performance occurs at carrier concentrations between 1019 _{and 10}21 _carriers per cm3_{, which corresponds to heavily doped semiconductors. The lattice thermal} conductivity, κ_l, is the only parameter that is not correlated with the electronic structure of the material, thus manipulating this parameter is an important strategy to enhance thermoelectric efficiency.16

Figure 1.2: Dependence of Seebeck coefficient (S), electrical conductivity (σ), and thermal

conductivity (κ) on the charge carrier concentration for metals and degenerate semiconductors. Reproduced from ref.39.

The lattice thermal conductivity of a semiconductor can be approximated by

κ_l = 1/3 (C_v V_s λ_ph) (1.11)

where C_v is the heat capacity V_s is the sound velocity and λ_ph is the mean free path of the phonons. Semiconductor materials often have favorably low thermal conductivity due to low sound velocity and short mean free paths (mfp), which make them appropriate candidates for achieving high zT.40

17

1

1.3

Approaches for enhancing thermoelectric figure of merit

1.3.1 Reducing thermal conductivity

The development of high performance thermoelectric materials therefore requires the optimization of related quantities as described above. A common strategy to enhance the efficiency of bulk materials is reduction of the lattice thermal conductivity. This can be achieved by:

- searching for phonon-glass electron-crystal (PGEC) materials. In this approach, suitable materials have high electronic conductivity associated with a highly periodic crystal structure, and the lattice thermal conductivity of a glass due to a complex structure. Such materials tend to have large unit cells and complex crystal structures,4,40 _{such as Zintl compounds and complex hybrid oxides.}41

- the use of materials containing heavy elements, which reduce the lattice thermal conductivity due to a low sound velocity, such as Bi₂Te₃, PbTe and BiSb.40

- designing alloys to create point defects such as interstitials and vacancies, or using materials that naturally contain atoms in cages or voids that scatter phonons, such as clathrates or filled skutterudites.41

- introducing a high density of interfaces to scatter phonons, for example by employing multiphase composites mixed on the nanometer scale.41

1.3.2 Improving the power factor

The improvement obtained in the zT by reducing the lattice thermal conductivity is usually limited, and this lower limit is reached when the phonon mean-free path becomes of the order of the interatomic distances. Therefore, another approach for enhancing zT is to maximize the power factor, S2_{/ρ, by achieving a balance between ρ}

and S. The optimization of carrier concentration is an approach that can enhance the electrical conductivity. Thus, the power factor can be improved through appropriate doping. Dopant elements can not only improve the electrical conductivity by changing the charge carrier density, but can also enhance the Seebeck coefficient by increasing the carrier effective mass. In the case of dopants with energy levels near the Fermi

level, the density of states (DOS) near the Fermi level will increase. This gives rise to an increase in the effective mass of the carriers without a significant change in their concentration. Since the thermopower is directly related to the carrier effective mass, it will be increased and zT will subsequently be improved.40,42

1.4

Motivation and outline of thesis

In this thesis, a series of experimental studies of ΙV-VI based thermoelectric materials is described. This thesis consists of the following chapters:

Chapter 2 presents the fabrication techniques used to prepare the samples and the different experimental characterization methods that were used. In chapter 3, a p-type wide band gap semiconductor, GeSe, is explored as a potential new thermoelectric material. Recently, excellent thermoelectric performance was theoretically predicted for GeSe, but experimental research on the thermoelectric properties of GeSe has received little attention thus far. Therefore, the main purpose was to obtain samples with the best possible quality and characterize their properties. Sodium was employed as a dopant in an attempt to improve the thermoelectric efficiency of the GeSe system. Chapter 4 describes the synthesis and investigation of single-phase quaternary (PbTe)_0.55(PbS)_0.1(PbSe)_0.35 compounds and the effect of sodium doping on the thermoelectric performance of this system. Single-phase quaternary compounds are very interesting thermoelectric systems, owning to their enhanced Seebeck coefficients originating from an enhanced DOS effective mass, and reduced lattice thermal conductivity by phonon scattering from solute atoms with high contrast atomic mass. In chapter 5, the effect of Ce doping on the thermoelectric properties of PbSe is reported. Chapter 6 describes the effect of Ce doping on the magnetic properties of PbSe by preparing a series of samples with various dopant concentrations. It is shown that Pb_0.99Ce_0.01Se exhibits ferromagnetic behavior to well above room temperature.

19

1

Bibliography

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2. E. Kh. Shokr, E. M. M. Ibrahim, A. M. Abdel Hakeem, and A. M. Adam, Structural, electrical, and thermoelectrical Properties of (Bi_1-xSb_x)₂Se₃ alloys prepared by a conventional melting technique. J. Experimental and Theoretical Physics 2013, 116, 1, 166.

3. D. M. Rowe, CRC Handbook of Thermoelectrics. CRC Press, 1995, Boca Raton, FL. 4. G. J. Snyder and E. S. Toberer, Complex thermoelectric materials. Nat. Mater.

2008, 7, 105.

5. J. Yang, H. –L. Yip, and A. K. -Y. Jen, Rational design of advanced thermoelectric materials. Adv. Energy Mater. 2013, 3, 549.

6. S. LeBlanc, Thermoelectric generators: Linking material properties and systems engineering for waste heat recovery applications. Sustainable Materials and

Technologies 2014, 1–2, 26.

7. Y. Pei, A. D. LaLonde, N. A. Heinz, and G. J. Snyder, High thermoelectric figure of merit in PbTe alloys demonstrated in PbTe–CdTe. Adv. Energy Mater. 2012, 2, 670.

8. Y. Z. Pei, A. D. Lalonde, N. A. Heinz, X. Shi, S. Iwanaga, H. Wang, L. D. Chen, and G. J. Snyder, Stabilizing the optimal carrier concentration for high thermoelectric efficiency. Adv. Mater. 2011, 23, 5674.

9. H. J. Goldsmid, Thermoelectric Refrigeration, 1964, Plenum, New York.

10. A. Minnich, M. Dresselhaus, Z. Ren, and G. Chen, Bulk nanostructured thermoelectric materials: current research and future prospects. Energy

Environ. Sci. 2009, 2, 466.

11. T. Sua, P. Zhua,c, H. Maa, G. Rend, J. Guoa, Y. Imai, and X. Jia, Electrical transport and thermoelectric properties of PbTe doped with Sb₂Te₃ prepared by high-pressure and high temperature. J. Alloys Compd. 2006, 422, 328.

12. H. S. Kim, W. Liu, G. Chen, C.W. Chu, and Z. Ren, Relationship between thermoelectric figure of merit and energy conversion efficiency. PNAS 2015, 112, 27, 8205.

13. D. M. Freik, R. I. Zapukhlyak, M. A. Lopjanka, G. D. Mateik, and R. Y. Mikhajlonka, Thermoelectric property features of PbTe monocrystalline and polycrystalline films. Semicond. Phys.: Quant. Electron. Optoelectron. 1999, 2, 62.

14. A. Hmood, A. Kadhim, and H. Abu Hassan, Influence of Yb-doping on the thermoelectric properties of Pb_1−xYb_xTe alloy synthesized using solid-state microwave. J. Alloys Compd. 2012, 520, 1.

15. J. Androulakis, Y. Lee, I. Todorov, D. Chung, and M. Kanatzidis, High-temperature thermoelectric properties of n-type PbSe doped with Ga, In, and Pb. Phys. Rev.

B 2011, 83, 195209.

16. J. R. Sootsman, D. Y. Chung, and M. G. Kanatzidis, New and old concepts in thermoelectric materials. Angew. Chem. Int. Ed. 2009, 48, 8616.

17. M. G. Kanatzidis, Nanostructured thermoelectrics: The new paradigm. Chem.

Mater. 2010, 22, 648.

18. J. P. Heremans, V. Jovovic, E. S. Toberer, A. Samarat, K. Kurosaki, A. Charoenphakdee, S. Yamanaka, and G. J. Snyder, Enhancement of thermoelectric efficiency in PbTe by distortion of the electronic density of states. Science 2008, 321, 554.

19. Y. Pei, H. Wang, Z. M. Gibbs, A. D. LaLonde, and G. J. Snyder, Thermopower enhancement in Pb_1−xMn_xTe alloys and its effect on thermoelectric efficiency.

NPG Asia Materials 2012, 4, e28.

20. H. Wang, Y. Pei, A. D. LaLonde, and G. J. Snyder, Weak electron–phonon coupling contributing to high thermoelectric performance in n-type PbSe. PNAS 2012, 109, 25, 9705.

21. D. Parker and D. J. Singh, High-temperature thermoelectric performance of heavily doped PbSe. Phys. Rev. B 2010, 82, 035204.

22. C. Wood, Materials for thermoelectric energy conversion. Rep. Prog. Phys. 1988, 51, 459.

23. Y. Pei, X. Shi, A. LaLonde, H. Wang, L. Chen, and G. J. Snyder, Convergence of electronic bands for high performance bulk thermoelectrics. Nature 2011, 473, 66.

24. Q. Zhang, F. Cao, W. Liu, K. Lukas, B. Yu, S. Chen, C. Opeil, D. Broido, G. Chen, and Z. Ren, Heavy doping and band engineering by potassium to improve the thermoelectric figure of merit in p-type PbTe, PbSe, and PbTe_1-ySe_y. J. Am. Chem.

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Kanatzidis, Nanostructures boost the thermoelectric performance of PbS. J. Am.

Chem. Soc. 2011, 133, 3460.

26. S. N. Girard, J. He, X. Zhou, D. P. Shoemaker, C. M. Jaworski, C. Uher, V. P. Dravid, J. P. Heremans, and M. G. Kanatzidis, High performance Na-doped PbTe–PbS thermoelectric materials: Electronic density of states modification and shape-controlled nanostructures. J. Am. Chem. Soc. 2011, 133, 16588.

27. S. N. Girard, J. He, C. Li, S. Moses, G. Wang, C. Uher, V. P. Dravid, and M. G. Kanatzidis, In situ nanostructure generation and evolution within a bulk thermoelectric material to reduce lattice thermal conductivity. Nano Lett. 2010, 10, 2825.

28. J. He, S. N. Girard, M. G. Kanatzidis, and V. P. Dravid. Microstructure-lattice thermal conductivity correlation in nanostructured PbTe_0.7S_0.3 thermoelectric materials. Adv. Funct. Mater. 2010, 20, 764.

29. R. J. Korkosz, T. C. Chasapis, S. H. Lo, J. W. Doak, Y. J. Kim, C. I. Wu, E. Hatzikraniotis, T. P. Hogan, D. N. Seidman, C. Wolverton, V. P. Dravid, and M. G. Kanatzidis, High ZT in p-type (PbTe)_1-2x(PbSe)_x(PbS)_x thermoelectric materials. J. Am. Chem. Soc.

2014, 136, 3225.

30. S. Aminorroaya Yamini, H. Wang, Z. M. Gibbs, Y. Pei, S. X. Dou, and G. J. Snyder, Chemical composition tuning in quaternary p-type Pb-chalcogenides-a promising strategy for enhanced thermoelectric performance. Phys.Chem.

Chem.Phys. 2014, 16, 1835.

31. S. Aminorroaya Yamini, H. Wang, Z. M. Gibbs, Y. Pei, D. R.G. Mitchell, S. Xue Dou, and G. J. Snyder, Thermoelectric performance of tellurium-reduced quaternary p-type lead-chalcogenide composites. Acta Materialia 2014, 80, 365.

32. S. Aminorroaya Yamini, D. R. G. Mitchell, Z. M. Gibbs, R. Santos, V. Patterson, S. Li, Y. Pei, S. X. Dou, and G. J. Snyder, Heterogeneous distribution of Sodium for high thermoelectric performance of p-type multiphase Lead-Chalcogenides.

Adv. Energy Mater. 2015, 5, 1501047.

33. S. Aminorroaya Yamini, H. Wang, D. Ginting, D. R. G. Mitchell, S. X. Dou, and G. J. Snyder, Thermoelectric performance of n-Type (PbTe)_0.75(PbS)_0.15(PbSe)_0.1 composites. ACS Appl. Mater. Interfaces 2014, 6, 11476.

34. G. S. Kumar, G. G. Prasad, and R. O. Pohl, Experimental determinations of the Lorenz number. J. Mater. Science 1993, 28, 4261.

35. A. F. May, E. S. Toberer, A. Saramat, and G. J. Snyder, Characterization and analysis of thermoelectric transport in n-type Ba₈Ga_16−xGe_30+x. Phys. Rev. B 2009, 80, 125205.

36. H.-S. Kim, Z. M. Gibbs, Y. Tang, H. Wang, and G. J. Snyder, Characterization of Lorenz number with Seebeck coefficient measurement. APL Mater. 2015, 3, 041506.

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38. C. M. Bhandari and D. M. Rowe, Electronic contribution to the thermal conductivity of narrow band gap semiconductors-effect of non-parabolicity of bands. J. Phys. D: Appl. Phys. 1985, 18, 873.

39. P. Vaqueiro and A. V. Powell, Recent developments in nanostructured materials for high-performance thermoelectrics. J. Mater. Chem. 2010, 20, 9577.

40. J. R. Szczech, J. M. Higgins, and S. Jin, Enhancement of the thermoelectric properties in nanoscale and nanostructured materials. J. Mater. Chem. 2011, 21, 4037.

41. C. S. Birkel, E. Mugnaioli, M. Panthöfer, U. Kolb, and W. Tremel, Solution synthesis of a new thermoelectric Zn_1+xSb nanophase and its structure determination using automated electron diffraction tomography. J. Am. Chem. Soc. 2010, 132, 9881.

42. G. D. Mahan and J. O. Sofo, The best thermoelectric. Proc. Natl. Acad. Sci. USA,

Chapter

2

25

2

2.1

Synthesis details

Polycrystalline Ge_1-xNa_xSe (Pb_1-xCe_xSe and Na_x(Pb_1-xTe)_0.55(Pb_1-xSe)_0.35(Pb_1-xS)_0.1) samples were prepared using a melt alloying technique. The elements used as starting materials were Ge (99.999%, Alfa Aesar), Se (99.999%, Alfa Aesar), Pb (99.999%, Alfa Aesar), Te (99.999%, Alfa Aesar), S (99.999%, Alfa Aesar), Ce (99.9%, Aldrich) and Na (99%, Aldrich). The elements were weighed in an argon atmosphere glove box according to stoichiometric amounts of each composition with a total mass of 10 g and transferred to a carbon-coated quartz tube (as described below) and sealed under vacuum (10-4 _{Torr). The sealed tube was heated to 1223 K (1323 K) over 12} hours and held at that temperature for 10 hours. The samples were then quenched in cold water, followed by annealing at 673 K (823 K) for 72 hours. The resulting ingots were taken out of the tubes and then hand ground thoroughly for 1 h using an agate mortar and pestle to obtain a fine powder. The powder was loaded into a 12 mm diameter graphite die. The powders were then sintered using Spark Plasma Sintering (SPS) at 623 K for 30 minutes (793 K for 1 hour) under an axial pressure of 40 MPa in vacuum.

2.1.1 Carbon coating

Carbon coating process requires the following steps:

1. Cleaning the inside of the quartz ampule using a series of rinses with water to minimize impurities

2. Heat treatment of the tubes to remove any possible organic residue 3. Coating the tube with carbon by heating the tube rinsed with acetone,

doing this step for 3 times

2.1.2 Spark plasma sintering

The SPS process is the method used to compact dense pellets from powders. This technique which is a fast sintering technique,1,2 _{results in achieving highly dense} samples at lower processing temperature compared to conventional sintering techniques.3 _{SPS can produce materials with nano size grains which is beneficial to} significantly enhance thermoelectric properties.4-10 _{It simultaneously applies electric} current and mechanical pressure to consolidate powders with desired density. The SPS container (punches, mould and spacers) is made of graphite. The SPS process and geometrical configuration of the punches, mould and powder are illustrated in figure 2.1. Powders to be consolidated, are placed in a die and heated by applying the electric current.

27

2

2.2

Structural and chemical characterization

2.2.1 Powder X-ray diffraction (PXRD)

Powder X-ray diffraction (PXRD) is a rapid analytical method for phase identification and structure characterization of powder polycrystalline materials. The measurements in this thesis were carried out with GBC Scientific X-ray diffractometer and Bruker D8 Advance diffractometer operating with Cu (Kα) radiation at room temperature. The 2θ scans were taken from 10 to 1000 _{with a step size of 0.02}0 _{and an integration} time of 1 s per step. Phase analysis and structural refinements were performed on the obtained XRD data by the Rietveld method using the GSAS (General Structure Analysis System) software package.11

2.2.2 Scanning electron microscopy and energy-dispersive X-ray spectroscopy

Scanning electron microscopy (SEM) is a technique to analyze surface morphology and chemical composition. It provides images based on the interaction of a focused beam of high-energy electrons with the sample surface. The interaction of the focused accelerated electrons with the exposed area of the sample gives rise to various electron signals. These signals include secondary electrons (SE), backscattered electrons (BSE) and diffracted backscattered electrons (EBSD). SEM most commonly uses the secondary electrons and backscattered electrons for imaging the sample. SEs are produced by atoms near the surface of a sample when the high energy electron beam excites an electron from one of the constituent atoms of the sample. Images of the surface morphology and topography can then be obtained. Backscattered electrons are elastically scattered electrons that are backscattered from the surface of the sample and they are sensitive to the atomic mass of the nuclei that they scatter from. These electrons are used for imaging contrast between different phases and chemical compositions in the sample. The inelastic collision of the incident electrons with the sample results in the emission of characteristic x-rays from the different elements present in the sample, which are used for elemental analysis. An energy dispersive x-ray (EDS) analyzer integrated with the SEM can be used for qualitative

and quantitative analysis of the different elements of the sample. The SEM images presented in this thesis were obtained using a JEOL JSM-7001 scanning electron microscope (SEM) combined with an energy-dispersive X-ray (EDS) spectrometer.

2.3

Magnetic properties measurement

The magnetic properties of the samples in this thesis were probed using a Quantum Design MPMS (magnetic properties measurement system) XL7 magnetometer. A SQUID (superconducting quantum interface device) is used to measure the magnetic dipole moment of a sample as a function of the temperature and the field. The operation temperature of the MPMS varies from 2 K to 350 K with a maximum magnetic field of ±7 T. Magnetic moments as low as 10-7 _{emu can be measured in the} MPMS. The temperature dependent magnetization measurements were conducted using zero field cooled (ZFC) and field cooled (FC) modes. In the ZFC mode, the studied sample was cooled to 5 K without an external magnetic field. Then, the magnetic field was applied and the magnetic moment as a function of temperature was measured while heating up the sample from 5 to 300 K (for high temperature measurements, the sample was heated from 300 K to 780 K). FC measurements were carried out in the same way, but the sample was first cooled down to 5 K in the presence of an applied magnetic field and measured on heating using the same applied field. Measurements of magnetization versus applied field were also carried out by applying field from 0.5 T to -0.5 T at constant temperature.

2.4

Hall measurements

The Hall coefficient (R_H) was measured using the Van der Pauw technique at Tongji University. The measurement was carried out in vacuum by sweeping the magnetic field between ±1.5 T.

The carrier concentration (n) was calculated from n = 1/eR

29

2

Hall mobility (μ) was calculated from:

μ = σ/ne = σR_H where σ is the electrical conductivity.

2.5

High temperature thermoelectric properties measurement

2.5.1 Seebeck coefficient and electrical resistivity measurement

The Seebeck coefficient is a fundamental electronic transport property of a material which describes the magnitude of a thermoelectric voltage built up when a temperature difference is applied across that material. This induced voltage can be measured, and with a known temperature gradient, the Seebeck coefficient is calculated. All high temperature Seebeck coefficient and electrical conductivity measurements were carried out simultaneously under helium atmosphere using a Linseis LSR-3 setup (figure 2.2a). The temperature dependence of the Seebeck coefficient and electrical conductivity can be measured on a cylindrical or bar shaped sample (at least 6 mm in length). Figure 2.2b shows the configuration of the thermocouples and sample.

Figure 2.2: (a) Picture of the Linseis LSR-3. (b) Configuration of thermocouples and sample,

labelled as follows. 1: differential thermocouple upper side (DTCU), 2: differential thermocouple lower side (DTCL), 3: probe thermocouple high side (PTCH), 4: probe thermocouple lower side (PTCL), 5: sample in a bar shape. A control thermocouple is attached to the susceptor (CTC) which surrounds this assembly (not shown in this figure). Picture 2.2b is adopted fromRef. 12.

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LSR-3. A sample is placed in a vertical position between the electrodes in the heating furnace. There are two source of heating in this setup. The primary furnace covers the entire measurement assembly and provides a specific temperature at which the measurement is taken. Once the sample has been heated and held at the desired temperature, a secondary heater placed in the lower electrode block generates a temperature gradient across the sample. The Seebeck coefficient is determined by measuring the upper and lower temperatures, T₁ and T₂, with the thermocouples in contact with the sample, and the electromotive force, dE, generated between the same wires in response to the temperature gradient. The multiple gradient method is implemented here. Based on the slope derived from the linear fitting of Seebeck voltage versus temperature gradient at a constant mean temperature, the absolute Seebeck coefficient of the sample is calculated as:

The electrical resistance at each specific temperature is measured using the dc 4-terminal method by applying a constant current between the ends of the sample and measuring the voltage drop, dV, between the same thermocouples connected to the sample by subtracting the thermo-electromotive force between leads. The electrical resistivity is then calculated from ρ = RA/l, where A is the area of the part of the sample in contact with the electrodes and l is the distance between the probe thermocouples.

Figure 2.3: Schematic illustration of measurement setup in Linseis LSR-3.12

2.5.2 Thermal conductivity measurement

Thermal conductivity is a property of a material that describes its ability to conduct heat. Here temperature dependent thermal conductivity was determined by the laser flash technique using a Linseis LFA 1000 (figure 2.4) and a Netzsch LFA at Tongji University and the University of New South Wales, respectively. The laser flash method a widely used technique for determining thermal conductivity by measuring thermal diffusivity at high temperatures. In this technique a short laser pulse or light pulse from a xenon flash lamp illuminates the bottom side of a disc-shaped sample and the temperature response on the top side of the sample is measured as a function of time (figure 2.5). The thermal diffusivity is calculated from the sample thickness and the time required to reach half of the maximum temperature increase. The thermal conductivity, κ, is then calculated by

κ = ρDC_p

where ρ is the density of the sample, calculated by measuring the mass and dimensions, and C_p is the specific heat capacity.

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Figure 2.4: The Linseis LFA 1000 system for high temperature thermal conductivity

measurement.13

Specific heat capacity can be estimated from 1. Experimental measurements 2. Dulong-Petit law

For this thesis study on Pb chalcogenides, heat capacity was estimated from the relation15,16

C_p (k_B per atom) = (3.07+4.7 ×10-4_(T-300))

based on experimental results that are consistent with theoretical calculated values within 2% error6 _{and is believed to be accurate for lead chalcogenides}17-19_{, where T is} the temperature in Kelvin and k_B is Boltzmann’s constant. Similarly, for the study of GeSe materials, this quantity was obtained from the relation20

C_p(GeSe, (298.15-940) K)=(46.777+15.099 ×10-3_{T-0.0316 ×10}-6_T2_{-1.231× 10}5 _T-2_)J.K-1_. mol-1

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Bibliography

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2. M. Omori, Sintering, consolidation, reaction and crystal growth by the spark plasma system (SPS). Mater. Sci. Eng. 2000, A287, 183.

3. K. Sairam, J. K. Sonber, C. Subramanian, R. K. Fotedar, P. Nanekar, and R. C. Hubli, Influence of spark plasma sintering parameters on densification and mechanical properties of boron carbide. International Journal of Refractory Metals and

Hard Materials 2014, 42, 185.

4. P. Roy, V. Pal, and T. Maiti, Effect of spark plasma sintering (SPS) on the thermoelectric properties of SrTiO₃: 15 at% Nb. Ceramics International 2017, 43, 12809.

5. H. Wang, J. F. Li, C. W. Nan, M. Zhou, W. S. Liu, B. P. Zhang, and T. Kita, High-performance Ag_0.8Pb_18+xSbTe₂₀ thermoelectric bulk materials fabricated by mechanical alloying and spark plasma sintering. Appl. Phys. Lett. 2006, 88, 092104.

6. L. D. Zhao, B. P. Zhang, J. F. Li, M. Zhou, W. S. Liu, and J. Liu, Thermoelectric and mechanical properties of nano-SiC-dispersed Bi₂Te₃ fabricated by mechanical alloying and spark plasma sintering. J. Alloys Compd. 2008, 455, 259.

7. C. Chen, D. W. Liu, B. P. Zhang, and J. F. Li, Enhanced thermoelectric properties obtained by compositional optimization in p-Type Bi_xSb_2−xTe₃ fabricated by mechanical alloying and spark plasma sintering. J. Electron. Mater. 2011, 40, 942.

8. S. I. Kim, K. H. Lee, H. A. Mun, H. S. Kim, S. W. Hwang, J. W. Roh, D. J. Yang, W. H. Shin, X. S. Li, Y. H. Lee, and G. J. Snyder, S. W. Kim, Thermoelectrics. Dense dislocation arrays embedded in grain boundaries for high-performance bulk thermoelectrics. Science 2015, 348, 109.

9. J. S. Son, M. K. Choi, M. K. Han, K. Park, J. Y. Kim, S. J. Lim, M. Oh, Y. Kuk, C. Park, S. J. Kim, and T. Hyeon, N-Type nanostructured thermoelectric materials prepared from chemically synthesized ultrathin Bi₂Te₃ nanoplates. Nano Lett.

2012, 12, 640.

10. S. Lim, J. Kim, B. Kwon, S. K. Kim, H. Park, K. Lee, J. M. Baik, W. J. Choi, D. Kim, D. Hyun, J. Kim, and S. Baek, Effect of spark plasma sintering conditions on the thermoelectric properties of (Bi_0.25Sb_0.75)₂Te₃ alloys. J. Alloys Compd. 2016, 678, 396.

11. B. H. Tobey, Expgui, a graphical user interface for GSAS. J. Applied Crystallography

2001, 34, 210.

12. Linseis, Instruction Manual LSR-3 Seebeck effect and electrical resistivity 2010. 13. Linseis, Instruction Manual LFA 1000 Laser Flash Thermal Constant Analyzer. 14. D. M. Rowe, Macro to Nano. CRC Handbook of Thermoelectrics. CRC Press, 2006,

Boca Raton, FL.

15. R. Blachnik and R. Igel, Thermodynamic properties of IV–VI compounds: Lead chalcogenides. Z.Naturforsch. B. 1974, 29, 625.

16. H. Wang, High temperature transport properties of Lead chalcogenides and their alloys. PhD thesis, California Institute of Technology, 2014.

17. H. Wang, Y. Pei, A. D. Lalonde, and G. J. Snyder, Heavily doped p-type PbSe with high thermoelectric performance: An alternative for PbTe. Adv. Mater. 2011, 23, 1366.

18. Y. Pei, A. D. LaLonde, H. Wang, and G. J. Snyder, Low effective mass leading to high thermoelectric performance. Energ. Environ. Sci. 2012, 5, 7963.

19. Y. Pei, X. Shi, A. LaLonde, H. Wang, L. Chen, and G. J. Snyder, Convergence of electronic bands for high performance bulk thermoelectrics. Nature 2011, 473, 66.

20. A. Olin, B. Noläng, E. G. Osadchii, L. O. Öhman, and E. Rosén, Chemical

Chapter

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Thermoelectric performance of

Na-doped GeSe

Abstract

Recently, hole-doped GeSe materials have been predicted to exhibit extraordinary thermoelectric performance owing largely to extremely low thermal conductivity. However, experimental research on the thermoelectric properties of GeSe has received less attention. Here, we have synthesized polycrystalline Na-doped GeSe compounds, characterized their crystal structure and measured their thermoelectric properties. The Seebeck coefficient decreases with increasing Na content up to x = 0.01, due to an increase in the hole carrier concentration, and remains roughly constant at higher concentrations of Na, consistent with the electrical resistivity variation. However, the electrical resistivity is large for all samples leading to low power factors. Powder X-ray diffraction and scanning electron microscopy (SEM)/energy-dispersive spectrometry (EDS) results show the presence of a ternary impurity phase within the GeSe matrix for all doped samples, which suggests that the optimal carrier concentration cannot be reached by doping with Na. Nevertheless, the lattice thermal conductivity and carrier mobility of GeSe are similar to those of polycrystalline samples of the leading thermoelectric material SnSe, leading to quality factors of comparable magnitude. This implies that GeSe shows promise as a thermoelectric material if a more suitable dopant can be found.

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3.1

Introduction

Thermoelectric materials (TE) have been intensively investigated over the past decades due to their ability to convert waste heat to electricity, especially in view of the energy crisis and concern for the environment.1-3 _{The performance of a TE} material is determined by its dimensionless figure of merit (zT), defined as zT = (S2_{σT)/κ, where S is the Seebeck coefficient, σ the electrical conductivity, κ the total} thermal conductivity and T the absolute temperature.4-6 _{There is an ongoing search} for new materials with high TE efficiency, especially using environmentally friendly and abundant elements, as well as the development of several approaches to improve the zT of existing materials via optimizing the parameters S, σ and κ.4,7-10 _Chalcogenide compounds have been extensively studied and their TE performance has shown significant enhancement in recent years.11,12 _{High thermoelectric performance has} recently been reported for single crystals of SnSe, largely due to their ultralow thermal conductivity.13 _{High zT values and low thermal conductivities are also reported in} polycrystalline SnSe, but their power factor values are significantly lower than single crystals.14-23 _{Germanium telluride (GeTe) based materials have also been widely} studied for their promising thermoelectric properties.24-28 _{However, germanium} selenide (GeSe) has received little attention for thermoelectric applications despite its use in other applications such as optoelectronics,29,30 _{resistive memory cells,}31 glass-forming materials for photonic devices with thin-film structures,32,33 _photovoltaic applications,29 _{and resistive switching materials.}31,34

GeSe is a p-type narrow band gap semiconductor (E_g=1.1-1.2 eV)35,36 which adopts a layered orthorhombic crystal structure (Figure 3.1a and b) at room temperature with space group Pnma, isostructural with GeS, SnS and SnSe.37 _{Only a} few reports have been published on the transport properties of GeSe; these mostly focus on the electrical conductivity35,36,38-42 _{with only two reports on the thermal} conductivity of GeSe.43,44 _{Recently, a theoretical study predicted the thermoelectric} performance of orthorhombic IV-VI compounds GeS, SnSe, SnS, and GeSe using density functional theory combined with Boltzmann transport theory.45 _{It is proposed that} GeS, SnS and GeSe show comparable thermoelectric properties to SnSe, which makes them promising candidates for high efficiency thermoelectric applications.45 _Another

Figure 3.1: (a) Crystal structure of Pnma phase along the a axis: grey, Ge atoms; red, Se atoms.

(b) Structure along the b axis. The block borders indicate the unit cell.13

modelling study using similar methods predicted extremely high thermoelectric performance in hole-doped GeSe crystals along the b- crystallographic direction, with a figure of merit ranging from 0.8 at 300 K to 2.5 at 800 K. This represents an even higher calculated figure of merit than that of hole-doped SnSe, which holds the current experimental record for high zT among bulk systems.46 _{Thus, it is highly} desired to experimentally explore the thermoelectric performance of GeSe-based materials. A recent study44 _{reports a maximum zT of 0.16 at 700K for Ag-doped} polycrystalline Ge_0.79Ag_0.01Sn_0.2Se by achieving carrier concentrations of ~1018 _cm -3_{. Better TE performance is predicted at higher carrier concentrations, which was} impossible to obtain by silver doping.

In this study, we have fabricated polycrystalline pristine and Na-doped GeSe samples and measured their thermoelectric properties. We have found that the lattice thermal conductivity of our samples is significantly higher than the ultralow values predicted theoretically,46 _{but at <0.8 W m}-1 _K-1 _{above 550 K for the pristine} sample is in good agreement with the previous experimental report in Ref. 44. Doping with 1% and 2% Na reduces κ to <0.7 W m-1 _K-1 _{and ~0.5 W m}-1 _K-1 _{respectively in}

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are low due to the formation of Na-rich precipitates, which prevents optimal carrier concentrations from being reached. Nevertheless, the measured carrier mobility of GeSe is comparable with that of SnSe, thus GeSe may be a promising thermoelectric material if a more suitable dopant is identified.

3.2 Methods

3.2.1 Sample fabrication

Synthesis. Polycrystalline Ge_1-xNa_xSe samples with x = 0.00, 0.01, 0.02 and 0.04 were synthesized using solid state reaction technique. Stoichiometric ratios of high purity elements, Ge (99.999%, Alfa Aesar), Se (99.999%, Alfa Aesar) and Na (99%, Aldrich), were weighed in an argon atmosphere glove box with a total mass of 10 g and loaded into carbon-coated quartz tubes. The tubes were sealed under vacuum, slowly heated to 1223 K and held at that temperature for 10 hours. The samples were then quenched in cold water, followed by annealing at 673 K for 72 hours. The ingots obtained were hand ground into fine powder using an agate mortar and pestle and loaded into a 12 mm diameter graphite die. The powders were then sintered using spark plasma sintering (SPS) at 623 K for 30 minutes under an axial pressure of 40 MPa in vacuum.

3.2.2 Materials Characterization

X-Ray diffraction. X-ray diffraction (XRD) measurements were performed using

a GBC Scientific X-ray diffractometer with Cu Kα radiation (λ= 1.5406 Å, 40 kV, 25 mA) at room temperature. The structural parameters were extracted from the X-ray diffraction patterns by the Rietveld refinement method using the GSAS software suite.47

Electron microscopy analysis. The microstructures of the samples were studied using

a high resolution scanning electron microscope (SEM), JEOL JSM-7001 equipped with an energy-dispersive X-ray spectrometer (EDS).

Transport properties measurements. The Hall coefficient (R_H) was measured by an

in-house-built apparatus using the van der Pauw technique (perpendicular to the hot-pressing direction) in vacuum under magnetic fields of up to ±1.5 T. The Hall carrier concentration, n, was obtained using n = 1/e R_H, where e is the elementary charge, and

n, R_H and σ are the carrier concentration, Hall coefficient and electrical conductivity, respectively. Disc-shaped pellets with densities ~94% of the theoretical density, 12 mm diameter and 2 mm thickness were used for this measurement. The electrical conductivity (σ) and Seebeck coefficient (S) were measured simultaneously under 0.1 atm helium from room temperature to 573 K using a Linseis LSR-3 instrument. The samples for measurement were cut from pressed pellets and polished into a parallelepiped shape; measurements were performed in the in-plane direction. The thermal diffusivity, D, was measured by the laser flash diffusivity method (Linseis LFA 1000) in the out-of-plane direction over the temperature range 300-573 K. The specific heat capacity (C_p) was calculated using the equation C_p (GeSe, (298.15-940) K) = (46.777+15.099 ×10-3_T-0.0316×10-6_T2_-1.231×105_T-2_)J.K-1_.mol-1_.48 _{The thermal} conductivity (κ) was calculated using κ = ρDC_p, where the density (ρ) of the pellets was calculated by measuring the mass and dimensions.

3.3

Results and discussion

Figure 3.2 shows the room temperature X-ray powder diffraction (XRD) patterns of the Ge_1-xNa_xSe compounds (x = 0.00, 0.01, 0.02 and 0.04). The main peaks of all samples could be indexed based on the orthorhombic α-GeSe structure with the unit cell parameters a = 10.8419(9) Å, b = 3.8389(6) Å and c = 4.3951(7) Å (space group, Pnma). Each primitive unit cell of α-GeSe phase consists of eight atoms, which form two zig-zag double layers. Each atom is coordinated to three nearest neighbors within its own layer and three more distant neighbors in adjacent layers;

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interactions within the layers.38,49,50_{.This phase is reported to transform to the high} symmetry cubic rocksalt structure (Fm3m, β-GeSe) at a temperature of 853 K (a = 5.73 Å).51-53 _{Table 3.1 lists the refined lattice parameters of the Ge}

1-xNaxSe (x = 0.00,

0.01, 0.02 and 0.04) compounds. There is no clear variation of lattice parameter with dopant concentration. X-ray diffraction analysis was performed on powders and pellets. For powder samples there is strong preferred orientation along the [100] direction (that is, the layer stacking direction in the crystallites tends to be perpendicular to the sample surface) which makes the [400] peak very strong. A similar degree of preferred orientation was observed in the x-ray diffraction patterns of the pellets, as shown in Figure 3.2b. This implies that the thermal conductivity was measured more along the a-direction, whereas the electrical resistivity and Seebeck coefficient measurements were performed largely in the bc-plane. Microstructural analysis of lightly and heavily doped GeSe samples was conducted by scanning electron microscopy (SEM). Figures 3.3a and b show representative back-scattered electron images (BSE) of Ge_0.99Na_0.01Se and Ge_0.96Na_0.04Se respectively. Precipitates are distributed in the GeSe matrix for both samples. The precipitates appear to vary in size and concentration with respect to the Na concentration. Precipitates of < 1 µm are most common in Ge_0.99Na_0.01Se, whereas those observed in Ge_0.96Na_0.04Se are typically 1-5 µm in size. The concentration of precipitates also appears to be increased for Ge_0.96Na_0.04Se.

Figure 3.2: (a) Room temperature XRD patterns of the powder Ge_1-xNa_xSe (x = 0.00, 0.01, 0.02 and 0.04) samples. The star indicates a graphite peak originating from the carbon-coated quartz tube and the circle at ~30 degrees indicates a peak from the sample holder. (b) Observed (black data points), fitted (red line) and difference (blue line) XRD profiles for the

x = 0.02 sample. The fit used the March-Dollase preferred orientation model incorporated

in the GSAS software. The green line represents the best fit obtained without any preferred orientation model. The inset shows a closer view of the fits; the symbols G and S indicate graphite and sample holder peaks, respectively.

Figure 3.3: BSE images of (a) Ge_0.99Na_0.01Se and (b) Ge_0.96Na_0.04Se. A secondary phase (darker grey) is observed in the GeSe matrix (lighter grey). (c) EDS characterization: BSE images of Ge_0.96Na_0.04Se showing a secondary phase within the GeSe matrix, with EDS elemental mapping for Ge, Se and Na. The secondary phase appears to be higher in Na and Se concentration and lower in Ge concentration than the surrounding GeSe matrix.

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Table. 3.1: Lattice parameters of Ge_1-xNa_xSe (x = 0, 0.01, 0.02, and 0.04) compounds Sample name Lattice parameter(Å)

a b c GeSe 10.8419(8) 3.8390(6) 4.3950(7) Ge_0.99Na_0.01Se 10.8437(4) 3.8389(7) 4.3978(8) Ge_0.98Na_0.02Se 10.8455(2) 3.8463(3) 4.3880(4) Ge_0.96Na_0.04Se 10.8398(2) 3.8376(8) 4.3966(7)

To probe the chemical composition of the secondary phase, energy dispersive X-ray spectroscopy (EDS) mapping was used. Figure 3.3c shows the EDS elemental map of precipitates within the GeSe matrix for the Ge_0.96Na_0.04Se sample. The precipitates are richer in Na and Se and poorer in Ge than the matrix, suggesting that sodium doping induces the formation of a ternary sodium germanium selenide as a secondary phase. The concentration of precipitates is too low to give rise to extra peaks in the XRD patterns, thus the phase could not be identified.

Figure 3.4a shows the total thermal conductivity, κ, of the Ge_1-xNa_xSe (x = 0.00, 0.01, 0.02 and 0.04) compounds as a function of temperature in the range of 300-573 K. The thermal conductivity for all samples decreases with temperature. The thermal conductivity of the undoped sample is 1.57 W m-1 _K-1 _{at 300 K which} is reduced to 0.76 W m-1 _K-1 _{at 573 K. This is significantly lower than the previously} measured values in polycrystalline samples of 2.2 W m-1 _K-1 _{and 1.3 W m}-1 _K-1 _{at 300} K and 573 K respectively in Ref. 43, but comparable to the values of 1.8 W m-1 _K-1_and 0.8 W m-1 _K-1 _{reported in Ref. 44 at the same temperatures. We note that the} Dulong-Petit approximation of the specific heat capacity was used for GeSe in Ref. 44; if used for our samples, the thermal conductivity plotted in Figure 3.4a would be ~10% lower at 573 K. Figure 3.4a also shows that the total thermal conductivity decreases with increasing dopant concentration and that samples with precipitates possess much lower thermal conductivity than lightly-doped samples. The lattice thermal conductivity, (Figure 3.4b), was obtained by subtracting the electronic contribution, κ_e,from the measured total thermal conductivity κ_L= κ_total-κ_e. The value of κ_e can be estimated via the Wiedemann-Franz law, κ_e = LσT, where σ is the electrical conductivity and L is the Lorenz number, which was calculated by using a single parabolic band model with the acoustic phonon scattering assumption.54 _{These estimated lattice}

thermal conductivities are compared with the previously predicted46 _{and measured}44 values in Figure 3.4b. The results indicate that the lattice thermal conductivity is the predominant part of the total thermal conductivity in agreement with the low carrier concentration of ~2×1016 _cm-3 _{obtained by Hall effect measurement for the pristine} sample at room temperature, and indicating that the electronic contribution to the total thermal conductivity is negligible (~10-6 _{– 10}-5 _{W m}-1 _K-1_{). However, the lattice} thermal conductivity of the undoped sample is higher than the extraordinarily low values of ~0.6 and 0.4 W m-1 _K-1 _{predicted for GeSe along the b axis}46 _{at 300 K and} 573 K respectively. The lattice thermal conductivity is reduced with Na content up to

x = 0.04, for which we measure κ_l = 0.44 W m-1 _K-1 _{at 573 K. This originates from the} scattering of phonons at an increased density of interfaces and defects due to the distribution of precipitates within the matrix;55,56 _{such a decrease in κ}

l has also been observed for Ag-doped GeSe44 _{although the possible presence of precipitates was} not investigated in that study.

In the calculations of thermal conductivity in Ref. 46, charge carrier concentrations of 4 ×1019 _{- 6.5 ×10}19 _cm-3 _{were used since this range is predicted to yield optimal} zT. The electronic component of the thermal conductivity for this range of carrier

concentration κ_e remains small, of the order of 0.2 W m-1 _K-1 _{at 600 K, thus the} calculations predict that the total thermal conductivity of GeSe should be even lower

Figure 3.4: (a) Measured total thermal conductivity, κ, of Ge_1-xNa_xSe (x = 0.00, 0.01, 0.02 and 0.04) in the temperature range 300-573 K. (b) Calculated lattice thermal conductivity, κ_L, of Ge_1-xNa_xSe (x = 0.00, 0.01, 0.02 and 0.04) compared with theoretical values46 _{calculated along}

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of 2.1 at 600 K.46 _{However, our results suggest that the predicted values for thermal} conductivity46 _{are underestimated unless the optimal carrier concentration can be} reached while also maintaining a distribution of precipitates.

Table 3.2 compares the room temperature transport properties of Na-doped polycrystalline GeSe in our study compared to another recent experimental report44 in which pellets with comparable preferred orientation to our samples were measured using the same geometry. The thermal conductivities of the low-doped samples are very similar, but our study yields lower thermal conductivity for heavily doped samples. The electrical resistivity of our samples is much lower than the reported values in Ref. 44 for samples with the same composition (Ge_0.98Na_0.02Se and Ge_0.96Na_0.04Se).

Table 3.2: Transport properties of GeSe doped with Na at 300 K

Composition S(μVK-1_{) ρ(mΩcm) κ( Wm}-1 _K-1₎ Ge_0.98Na_0.02Se44 _{627 6.81×10}5 _1.48 Ge_0.96Na_0.04Se44 _{631 2.99×10}7 _1.40 Ge_0.94Na_0.06Se44 _{501 3.39×10}7 _1.43 Ge_0.99Na_0.01Se (our work) 471 0.79×105 _1.47 Ge_0.98Na_0.02Se (our work) 508 1.71×105 _1.23 Ge_0.96Na_0.04Se (our work) 505 1.84×105 _1.06

The electrical resistivity of the Ge_1-xNa_xSe samples with x = 0.00, 0.01, 0.02 and 0.04 is shown as a function of temperature in the range 300-580 K in Figure 3.5a. The electrical resistivity decreases monotonically with temperature for all samples and remains roughly constant at temperatures above 450 K. At room temperature, sodium doping reduces the electrical resistivity of GeSe significantly from 1.0 × 106 _{mΩ cm for the undoped sample to 7.9 × 10}4 _{mΩ cm for x = 0.01, roughly by a} factor of 12. However, further doping beyond x = 0.01 has no beneficial effect; the electrical resistivity of the x = 0.02 and x = 0.04 samples is slightly higher, probably because the doping limit is soon reached and additional sodium is incorporated into the precipitate phase. The Seebeck coefficients (S) of all samples as a function of the temperature are shown in figure 3.5b. The positive values over the entire

temperature range indicate that all samples are p-type semiconductors. The Seebeck coefficients increase with temperature over the whole temperature range except for the undoped sample which exhibits a maximum value at ~450 K. The samples show no sign of a bipolar effect over the temperature range in which the measurements were performed (300-580 K). We note that a bipolar effect was observed at temperatures above 600 K (above the selected range of the current study), in previous work.44 This effect is commonly observed in narrow band gap materials. The contribution of minority carriers to the transport properties of such materials increases with temperature due to thermal excitation of minority carriers across the band gap.57 In the case of GeSe, since the band gap is wide (~1.1 eV35,36_{), at temperatures below} 600 K the probability of thermal excitation of the electrons to the conduction band is low, which results in suppression of the bipolar effect in this range of temperatures. Undoped GeSe shows the largest Seebeck coefficient (S = 990 μVK-1_{) at 450 K. The} Seebeck coefficient is smallest throughout the studied temperature range for the

x = 0.01 sample, whereas the x = 0.02 and 0.04 samples exhibit similar and slightly

larger values, which is consistent with the variation of the electrical resistivity since both the Seebeck coefficient and electrical resistivity are inversely proportional to the carrier concentration. This indicates that the carrier concentration increases with dopant concentration up to x = 0.02, beyond which it remains roughly constant. This

Figure 3.5: (a) Logarithmic temperature dependence of the electrical resistivity of Ge_1-xNa_xSe (x = 0.00, 0.01, 0.02 and 0.04) in the temperature range 300-580 K. (b) Temperature dependence of the Seebeck coefficient of Ge_1-xNa_xSe (x = 0.00, 0.01, 0.02 and 0.04) in the temperature range 300-580 K.

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is shown to increase with dopant concentration (Figure 3.3).

It was first proposed by Chasmar and Stratton58 _{that in order to achieve} a higher figure of merit in a thermoelectric semiconducting compound, a material parameter known as the thermoelectric quality factor, B, must be improved. The quality factor can be used to evaluate the performance of a thermoelectric material through the combination of several fundamental parameters:58-63

Here is the Boltzmann constant, is the reduced Planck constant, is the band degeneracy, is the density of states effective mass of a single band, is the mobility at the non-degenerate limit, T is the temperature, and is the lattice thermal conductivity. The potential of doped GeSe compounds as good thermoelectric materials can be evaluated by comparing the quality factor of undoped GeSe with that of SnSe, assuming similar band structures. Table 3.3 shows the quality factors estimated for polycrystalline GeSe and SnSe at 580 K and the parameters used (or ranges of parameters in cases where a quantity has been reported in more than one study). Here we assume that the measured values of mobility correspond to at the non-degenerate limit, which has been shown for SnSe to be a valid approximation.15 Taking into account the large uncertainty in these parameters, which are likely to be very sensitive to sample quality and small variations in stoichiometry, the two materials have similar quality factors. Therefore, it is likely that the thermoelectric performance of GeSe can be improved by choosing an effective dopant and by consequent band structure engineering.

Table 3.3: Parameters that determine quality factor B for SnSe and GeSe

Parameters T (K) κ_L ( Wm-1 _K-1_{) μ} 0 (cm2V-1s-1) B SnSe (n-type) 580 0.5-0.7514,15,64 ₂₀15_{* (28.54-42.81)×10}45_×m b*3/2 GeSe 580 0.76 34.75 48.94×1045_×m b*3/2 *value measured at 750 K; μ₀ = 45 cm2_V-1_s-1 _{at 300 K.}

3.4 Conclusions

In summary, we have investigated the effect of Na doping on the thermoelectric performance of GeSe. We have synthesized Ge_1-xNa_xSe (x = 0-0.04) compounds and measured their thermoelectric properties. Our experimental results show that the substitution of Na for Ge in GeSe gives rise to the formation of Na-rich precipitates within the GeSe matrix and thus that Na is an unsuitable dopant for GeSe. Although the power factor of these samples is low because the optimal carrier concentration cannot be reached, GeSe could nevertheless be a promising thermoelectric material if suitably doped because it shows intrinsically low lattice thermal conductivity. The presence of Na-rich precipitates decreases the lattice thermal conductivity by around 50% to ~0.5 W m-1 _K-1 _{at 500 K, thus a co-doping strategy may be a fruitful approach} to optimizing the thermoelectric performance of GeSe. Furthermore, the carrier mobility of GeSe is similar to that of the leading thermoelectric material SnSe, giving a similar thermoelectric quality factor. Therefore, identifying an effective dopant might lead to significant improvement in the thermoelectric figure of merit in GeSe-based materials.