Design of Advanced Thermoelectric Materials
Shaabani, Laaya
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Shaabani, L. (2018). Design of Advanced Thermoelectric Materials. Rijksuniversiteit Groningen.
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Chapter
1
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 missions7 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 = S2σT/κ =S2σT/ (κ
e + κl) (1.1)
where S is the Seebeck coefficient or thermopower (μVK-1), σ is the electrical
conductivity (Ω-1m-1), κ is the total thermal conductivity (Wm-1K-1), and T is the absolute
temperature (K).3,9,10 The electrical properties determine the power factor, defined
as S2σ or S2/ρ, where ρ is the electrical resistivity. The total thermal conductivity κ
has two contributions, one from the electrical carriers κe, and the other from lattice
vibrations κl.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, TH is the temperature of the hot end, TC is
the temperature of the cold end of the thermoelectric module, and Tm is the average
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
1
where kB is the Boltzmann constant, h is Planck’s constant, e is the charge of an 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 = κe + κl (1.5)
Here κe (electronic thermal conductivity) is the thermal conductivity from electrons
and holes transporting heat and κl (lattice thermal conductivity) originates from phonons travelling through the lattice. For many materials κe is directly related to the electrical conductivity through the Wiedemann–Franz law:
κe = LσT = neµLT (1.6)
where L, the Lorenz number, is given by π2k
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 Fj(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.
1
The relationship described by equation 1.10 is illustrated in figure 1.1 and was shown
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 = kBT/eg (eg is the band gap).36
In this model the band becomes more linear as eg decreases, until a Dirac cone is
obtained in the limit where eg = 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 1021 carriers
per cm3, which corresponds to heavily doped semiconductors. The lattice thermal
conductivity, κl, is the only parameter that is not correlated with the electronic structure of the material, thus manipulating this parameter is an important strategy
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
κl = 1/3 (Cv Vs λph) (1.11)
where Cv is the heat capacity Vs is the sound velocity and λph 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
1
1.3
Approaches for enhancing thermoelectric figure of merit
1.3.1 Reducing thermal conductivityThe 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 Pb0.99Ce0.01Se exhibits ferromagnetic behavior to well above room temperature.
1
Bibliography
1. L. E. Bell, Cooling, heating, generating power, and recovering waste heat with thermoelectric systems. Science 2008, 321, 1457.
2. E. Kh. Shokr, E. M. M. Ibrahim, A. M. Abdel Hakeem, and A. M. Adam, Structural, electrical, and thermoelectrical Properties of (Bi1-xSbx)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 Pb1−xYbxTe 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 Pb1−xMnxTe 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
1
25. S. Johnsen, J. Q. He, J. Androulakis, V. P. Dravid, I. Todorov, D. Y. Chung, and M. G. 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 PbTe0.7S0.3 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 Ba8Ga16−xGe30+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.
37. E. O. Kane, Band structure of indium antimonide. J. Phys. Chem. Solids 1957, 1, 249.
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 Zn1+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,
