**7. Band structure of AsF6 salt**

decreased with decreasing temperature. MS transition temperatures of PF6 and AsF6 salts

**Figure 10.** Simultaneous measurements of temperature dependence of thermoelectric power (•) and electrical resistivi-

Simultaneous measurements of temperature dependence of thermoelectric power and electrical resistivity of (EDOB-EDT-TTF)2SbF6 salt are shown in **Figure 11**. Thermoelectric power value of plate SbF6 salt was negative below 335 K and decreased with decreasing temperature. Negative value of thermoelectric power implies electron-like character of conduction charge carriers. Thermoelectric power exhibits *T*−1-temperature dependence,

**Figure 11.** Simultaneous measurements of temperature dependence of thermoelectric power (•) and resistivity (▪) of

observed in thermoelectric power decreased in order of 320 and 310 K.

40 Thermoelectrics for Power Generation - A Look at Trends in the Technology

ty (▪) of (EDOB-EDT-TTF)2AsF6 salt. Solid line extrapolates to zero at *T* = 0 K.

**6.3. Thermoelectric power of (EDOB-EDT-TTF)2SbF6**

which is a characteristic of semiconductor.

(EDOB-EDT-TTF)2SbF6 salt.

Band structures of PF6 and AsF6 salts were calculated on the basis of tight-binding approximation using intermolecular overlap integrals of HOMO, which were calculated by extended Hückel method [26]. Calculated intermolecular overlap integrals are listed in **Table 3**. Arrangements of donor centers and intermolecular overlaps in EDOB-EDT-TTF salts viewed onto *ab* plane are depicted in **Figure 12**. **Figure 13** shows energy band structures and Fermi surfaces of AsF6 salt at 293 and 350 K. Energy bands of these salts are three-quarters filled and metallic. Short S…S contacts are observed between stacks, not within the stacks. Such structural feature provides isotropic two-dimensional electronic structures in Fermi surfaces [27, 28].


Symbols *Sa*- *Sq2* represent the overlap integrals between donors shown in **Figure 12**

**Table 3.** Intermolecular overlap integrals (× 10−3) of EDOB-EDT-TTF salts.

**Figure 12.** Arrangement of donor centers ( , ) and intermolecular overlaps in PF6 salt at 298 K, AsF6 salts at 293 and 350 K viewed onto *ab* plane.

**Figure 13.** Calculated band structures and corresponding Fermi surfaces of (EDOB-EDT-TTF)2AsF6 salt at 293 K (a and b) and 350 K (c and d).

#### **8. Conclusion**

Synthesis of unsymmetrical EDOB-EDT-TTF donors was accomplished by two methods. New radical salts with octahedral PF6 − , AsF6 − and SbF6 − anions were prepared by electrochemical oxidation. Crystal structure of AsF6 salt was isostructural to PF6 salt, but crystal structure of plate SbF6 salt was not. According to conventional electrical conductivity measurements, both PF6 and AsF6 salts exhibited MS transitions at 340 and 315 K, respectively. Electrical resistivity and thermoelectric power of PF6, AsF6, and SbF6 salts were measured simultaneously on a single sample. Judging from the results of thermoelectric power measurements, MS transition temperatures of PF6 and AsF6 salts were around 320 and 310 K, respectively. From crystal structure analysis in AsF6 salt follows that intermolecular O…H distance along the stacking *b*-axis at 350, 330, 293, and 90 K decrease in that order by the dimerization. Formation of dimers results in semiconductor transition. Short S…S contacts were found only between the stacks and not within the stacks. They provided isotropic two-dimensional electronic structure in Fermi surfaces. Two-dimensional electronic structure derived from β-type arrangement is not so stable against packing modification [28]. MS transition is associated with some structural transition.

## **Acknowledgements**

The author wish to thank Drs. Maeda T and Yamashita K of Computer Automation Co. and Dr. Niwa N of System Approach Co. for programming the LabVIEW thermoelectric power measurement system and Emeritus Professor Matsumoto S of Aoyama Gakuin University for giving valuable comments.

## **Abbreviations**

TTF, tetrathiafulvalene; EDT, ethylenedithio; BEDT-TTF, bis(EDT)-TTF; DBTTF, dibenzo-TTF; EDO, ethylenedioxy; BEDO-DBTTF, bis(EDO)-DBTTF; EDOB-EDT-TTF, ethylenedioxybenzo-EDT-TTF; TCNQ, 7,7,8,8-tetracyanoquinodimethane; FTCNQ, 2-fluoro-TCNQ; F2TCNQ, 2,5 difluoro-TCNQ; Me2TCNQ, 2,5-dimethyl-TCNQ; TCE, 1,1,2-trichloroethane.

## **Author details**

Tomoko Inayoshi

Address all correspondence to: inayoshi@chem.aoyama.ac.jp

Department of Chemistry and Biological Science, College of Science and Engineering, Aoyama Gakuin University, Sagamihara, Kanagawa, Japan

## **References**

**Figure 13.** Calculated band structures and corresponding Fermi surfaces of (EDOB-EDT-TTF)2AsF6 salt at 293 K (a and

Synthesis of unsymmetrical EDOB-EDT-TTF donors was accomplished by two methods. New

oxidation. Crystal structure of AsF6 salt was isostructural to PF6 salt, but crystal structure of plate SbF6 salt was not. According to conventional electrical conductivity measurements, both PF6 and AsF6 salts exhibited MS transitions at 340 and 315 K, respectively. Electrical resistivity and thermoelectric power of PF6, AsF6, and SbF6 salts were measured simultaneously on a single sample. Judging from the results of thermoelectric power measurements, MS transition temperatures of PF6 and AsF6 salts were around 320 and 310 K, respectively. From crystal structure analysis in AsF6 salt follows that intermolecular O…H distance along the stacking *b*-axis at 350, 330, 293, and 90 K decrease in that order by the dimerization. Formation of dimers results in semiconductor transition. Short S…S contacts were found only between the stacks and not within the stacks. They provided isotropic two-dimensional electronic structure in Fermi surfaces. Two-dimensional electronic structure derived from β-type arrangement is not so stable against packing modification [28]. MS transition is associated with some structural

−

anions were prepared by electrochemical

and SbF6

− , AsF6 −

42 Thermoelectrics for Power Generation - A Look at Trends in the Technology

b) and 350 K (c and d).

**8. Conclusion**

transition.

radical salts with octahedral PF6


[20] Kobayashi H, Mori T, Kato R, Kobayashi A, Sasaki Y, Saito G, Inokuchi H. Transverse conduction and metalinsulator transition in β-(BEDT-TTF)2PF6. Chem. Lett. 1983; 12: 581–584. doi:10.1246/cl.1983.581

[6] Chaikin P M, Kwak J F. Apparatus for thermopower measurements on organic

[7] Mori T, Inokuchi H. Thermoelectric power of organic superconductors-calculation on the basis of the tight-binding theory. J. Phys. Soc. Jpn. 1988; 57: 3674–3677. doi:10.1143/

[8] Senga T, Kamoshida K, Kushch L A, Saito G, Inayoshi T, Ono I. Peculiarity of ethylenedioxy group in formation of conductive charge-transfer complexes of bis(ethylenedioxy)-dibenzotetrathiafulvalene (BEDO-DBTTF). Mol. Cryst. Liq. Cryst. 1997; 296: 97–

[9] Inayoshi T, Matsumoto S, Ono I. Physical properties of CT complexes of a new asymmetric donor: (EDOB)(EDT)TTF. Synth. Met. 2003; 133–134: 345–348. doi:10.1016/

[10] Inayoshi T, Matsumoto S. Synthesis, electronic properties, thermoelectric power, and crystal and band structures of unsymmetrical EDOB-EDT-TTF salts composed of PF6

[11] Mori T, Inokuchi H, Kini A M, Williams J M. Unsymmetrically substituted ethylenedioxytetrathiafulvalenes. Chem. Lett. 1990; 19: 1279–1282. doi:10.1246/cl.1990.1279

[12] Kim G T, Park J G, Lee J Y, Yu H Y, Choi E S, Suh D S, Ha Y S, Park Y W. Simple technique for the simultaneous measurements of the four-probe resistivity and the thermoelectric

[13] Park Y W. Structure and morphology: relation to thermopower properties of conductive polymers. Synth. Met. 1991; 45: 173–182. doi:10.1016/0379-6779(91)91801-G

[14] Barnard R D. Thermoelectricity in Metals and Alloys. London: Taylor & Francis; 1972.

[15] Chaikin P M, Kwak J F, Jones T E, Garito A F, Heeger A J. Thermoelectric power tetrathiofulvalinium tetracyanoquinodimethane. Phys. Rev. Lett. 1973; 31: 601–604. doi:

[16] Mori H. Materials viewpoint of organic superconductors. J. Phys. Soc. Jap. 2006; 75:

[17] Mori T, Kobayashi A, Sasaki Y, Kobayashi H, Saito G, Inokuchi H. Band structure of two types of (BEDT-TTF)2I3. Chem. Lett. 1984; 13: 957–960. doi:10.1246cl.1984.957

[18] Bondi A. Van der Waals volumes and radii. J. Phys. Chem. 1964; 68: 441–451. doi:

[19] Ishiguro T, Yamaji K, Saito G. Organic Superconductors. 2nd ed. Berlin: Springer; 1998.

power. Rev. Sci. Instrum. 1998; 69: 3705–3706. doi:10.1063/1.1149164

—at various temperatures. Mol. Cryst. Liq. Cryst. 2013; 582: 136–153. doi:

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44 Thermoelectrics for Power Generation - A Look at Trends in the Technology

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051003/1–14. doi:10.1143/JPST.75.051003

— SbF6


#### **Progress in Polymer Thermoelectrics Progress in Polymer Thermoelectrics**

Lukas Stepien, Aljoscha Roch, Roman Tkachov and Lukas Stepien, Aljoscha Roch, Roman

Tomasz Gedrange Tkachov and Tomasz Gedrange

Additional information is available at the end of the chapter Additional information is available at the end of the chapter

http://dx.doi.org/10.5772/66196

#### **Abstract**

This chapter addresses recent progress in the field of polymer thermoelectric materials. It covers a brief introduction to intrinsically conductive polymers and its motivation for thermoelectric utilization. A review about important and recent literature in the field of p-type and n-type polymers for thermoelectric applications is summarized here. For a better understanding of material development issues, doping mechanisms for intrinsically conducting polymers are discussed. Special emphasis is given to n-type polymers, since this group of polymers is often neglected due to unavailability or poor stability during processing. Different possibilities in terms of generator design and fabrication are presented. Recent challenges in this scientific field are discussed in respect to current material development, uncertainty during the measurement of thermoelectric properties as well as temperature stability for the most prominent p-type polymer used for thermoelectric, PEDOT:PSS.

**Keywords:** printing, coating, intrinsically conductive polymers, PEDOT:PSS, flexible, thermoelectric generator

## **1. Introduction**

Historically, the most famous intrinsically conducting polymer is polyacetylene, which was discovered in 1976 by Alan Heeger, Alan MacDiarmid, and Hideki Shirakawa, who were jointly awarded with Nobel Prize in the year 2000. After the discovery that doping (in the case of polyacetylene it is chemical oxidation with iodine) of polymer chains can increase electrical conductivity of the polymer dramatically, a lot of effort was put in investigating the doping process as well as polymer synthesis itself [1].

and reproduction in any medium, provided the original work is properly cited.

© 2016 The Author(s). Licensee InTech. This chapter is distributed under the terms of the Creative Commons © 2016 The Author(s). Licensee InTech. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution,

In contrast to known solid state semiconductors, polymers can be doped by different approaches following the concept of MacDiarmid on primary and secondary doping. Primary doping includes chemical doping mechanism, which can be oxidizing/reducing or protonating/deprotonating. Secondary doping addresses the change in the polymer morphology like chain alignment, chain orientation, crystallinity, and so on.

However, for a reasonable utilization of these electrical conducting polymers, good processability and stability are the major requirements. This leads to considerable amount of different intrinsically conducting polymers, e.g., polyaniline, polycarbazole, and polythiopene.

In recent years, significant progress in the development of new types of conductive polymers has been achieved. Plenty of scientific publications can be found in scientific journals for polymer synthesis, polymer modification, or characterization.

For thermoelectric applications, both types of conducting polymers were investigated, on the one hand, pure organic polymers such as PANI [2], PPV [3], PPy:Tos [4], PEDOT:PSS [5], or PEDOT: PEDOT:TOS [6, 7], but on the other hand, metal organic complexes [8] as well as composites with nanostructures. The pure organic polymers are generally semiconductors and need to be primary doped in order to become electrically conductive. The oxidation leads to p-type conductivity. The degree of oxidation determines charge carriers' concentration and, therefore, affects the electrical conductivity directly. Electrical conductivity of p-type polymer like PEDOT:PSS with high degree of oxidation can reach up to 2000 S/cm [9] and even 3300 S/cm [10]. It was reported recently [11] about reaching electrical conductivity up to 4600 S/cm by active control of the deposition procedure of polymer PEDOT:PSS. It was possible to achieve conductivity up to 5400 S/cm by changing the counter ions of PEDOT [12]. Vapor-phase-grown single crystal PEDOT nanowires showed electrical conductivity of 8797 S/cm [13], which is the highest value known for this group of polymers. In spite of this outstanding electrical conductivity, Seebeck coefficient is usually relatively small for polymers.

Among p-type polymers, PEDOT, modified in PEDOT:TOS and PEDOT:PSS, respectively, is the most investigated polymer for thermoelectric utilization. Reported ZT values are in the range 0.2–1.02 for PEDOT:TOS [5–7]. Unfortunately, the reported performances often lack of reproducibility by other working groups.

The synthesis of n-type polymers involves other challenges compared to the development of p-type polymers. Stability of n-type polymer under ambient conditions is often critical, and electrical conductivity is in general not as high as for p-type polymers. However, a synthesis approach with metal organic polymers is promising and it was shown, that ZT value of this material can reach 0.2 [8].

**Figure 1** shows overview about last years' progress in ZT values of conductive polymers.

## **2. Intrinsically conductive polymers for thermoelectric application**

This section gives an overview of the recent advances made in polymer thermoelectric materials, which covers different material classes. First, considerations regarding the benefits of polymers for thermoelectric applications are discussed. Second, short introduction to doping of intrinsically conductive polymers is given. Subsequently, overview of p-type and n-type polymers is presented.

In contrast to known solid state semiconductors, polymers can be doped by different approaches following the concept of MacDiarmid on primary and secondary doping. Primary doping includes chemical doping mechanism, which can be oxidizing/reducing or protonating/deprotonating. Secondary doping addresses the change in the polymer morphology like

However, for a reasonable utilization of these electrical conducting polymers, good processability and stability are the major requirements. This leads to considerable amount of different

In recent years, significant progress in the development of new types of conductive polymers has been achieved. Plenty of scientific publications can be found in scientific journals for poly-

For thermoelectric applications, both types of conducting polymers were investigated, on the one hand, pure organic polymers such as PANI [2], PPV [3], PPy:Tos [4], PEDOT:PSS [5], or PEDOT: PEDOT:TOS [6, 7], but on the other hand, metal organic complexes [8] as well as composites with nanostructures. The pure organic polymers are generally semiconductors and need to be primary doped in order to become electrically conductive. The oxidation leads to p-type conductivity. The degree of oxidation determines charge carriers' concentration and, therefore, affects the electrical conductivity directly. Electrical conductivity of p-type polymer like PEDOT:PSS with high degree of oxidation can reach up to 2000 S/cm [9] and even 3300 S/cm [10]. It was reported recently [11] about reaching electrical conductivity up to 4600 S/cm by active control of the deposition procedure of polymer PEDOT:PSS. It was possible to achieve conductivity up to 5400 S/cm by changing the counter ions of PEDOT [12]. Vapor-phase-grown single crystal PEDOT nanowires showed electrical conductivity of 8797 S/cm [13], which is the highest value known for this group of polymers. In spite of this outstanding electrical conductivity, Seebeck coefficient is usually relatively small for polymers. Among p-type polymers, PEDOT, modified in PEDOT:TOS and PEDOT:PSS, respectively, is the most investigated polymer for thermoelectric utilization. Reported ZT values are in the range 0.2–1.02 for PEDOT:TOS [5–7]. Unfortunately, the reported performances often lack of

The synthesis of n-type polymers involves other challenges compared to the development of p-type polymers. Stability of n-type polymer under ambient conditions is often critical, and electrical conductivity is in general not as high as for p-type polymers. However, a synthesis approach with metal organic polymers is promising and it was shown, that ZT value of this

**Figure 1** shows overview about last years' progress in ZT values of conductive polymers.

This section gives an overview of the recent advances made in polymer thermoelectric materials, which covers different material classes. First, considerations regarding the benefits of polymers for thermoelectric applications are discussed. Second, short introduction to doping

**2. Intrinsically conductive polymers for thermoelectric application**

intrinsically conducting polymers, e.g., polyaniline, polycarbazole, and polythiopene.

chain alignment, chain orientation, crystallinity, and so on.

48 Thermoelectrics for Power Generation - A Look at Trends in the Technology

mer synthesis, polymer modification, or characterization.

reproducibility by other working groups.

material can reach 0.2 [8].

**Figure 1.** Overview of ZT values of conductive polymers, which were published recently [2, 3, 5–8, 14–16].

The main requirement for a polymer to be electrically conductive is the formation of a conjugated pi-electron system. With the increase of the delocalized pi-electron system, the polymer changes its nature from an isolator to a semiconductor [17]. The band gap of intrinsically conductive polymers can vary from 1.36 eV (for polyacetylene) to 5.96 eV (for polypyrrole) [18]. In order to increase electrical conductivity of these semiconductive polymers, one has to increase the free charge carriers concentration (analogy to silicon-based semiconductors). This doping leads to the formation of additional energy levels (allowed energy levels) within the band gap. Due to these new energy levels, free charge carriers can arise, which can be dislocated along the polymer chain or hop/tunnel between individual polymer chains. A brief introduction can be found in reference [19].

In the beginning, conductive polymers were investigated for thermoelectric applications, especially because of their alleged low thermal conductivity and high electrical conductivity. Low thermal conductivity would make them attractive for producing advanced thermoelectric materials. For technical polymers like PVC or PMMA, thermal conductivity is in the range 0.13–0.3 W/(m K) [20]. In the case of intrinsically conductive polymers, thermal conductivity is higher due to the contribution to heat transport by charge carriers. In the case of drop casted films of PEDOT:PSS, thermal conductivity can vary from 0.29 to 1 W/(m K) for cross-plane and in-plane measurements, respectively. It was also shown, that in-plane thermal conductivity of these films increases with electrical conductivity [21]. For comparison, spark plasma sintered BiTe compounds also show a relatively low thermal conductivity of 0.8 W/(m K) for cross-plane and 1.2 W/(m K) for in-plane measurements [22]. For nanostructured thermoelectric materials, thermal conductivity can be even lower [23]. This example shows also, the importance of distinguishing between in-plane and cross-plane measurements. This should also be applied to electrical properties measurements.

True arguments regarding advantages, comparing to other (brittle) thermoelectric materials, are possible flexibility and mostly nontoxic properties. Abundance, independence on volatile raw material costs, feasible scale-up for material production, as well as, efficient processability of polymer material can be considered as advantages for polymer thermoelectric materials. Polymers are processable by different (industrial) established and sophisticated technologies and the final building up of thermoelectric modules based on polymers is possible with printing techniques. This offers cost-effective production of thermoelectric generators (TEG) at industrial scale.

To facilitate the usage of intrinsically conductive polymers for thermoelectric applications, one has to consider several requirements besides, undoubtedly important, thermoelectric properties. These requirements imply costs, abundance, recyclability, environmental stability, thermal stability, processability, and more.

Basic factors that determine thermoelectric properties of polymers are as follows:


Of course, other factors like charge carriers density and morphology play an important role in terms of thermoelectric properties and will be discussed below.

#### **2.1. Doping mechanism for intrinsically conductive polymers**

Thermoelectric properties of polymers are predominantly governed by doping. While undoped polymers are considered to be bad conductive semiconductors, doping can change this state and transfer into metallic-like behavior. Following doping concept of MacDiarmid [24], doping of polymers can be subdivided into primary and secondary doping.

In general, **primary doping** affects charge carriers density in the polymer material, which influences Seebeck coefficient and electrical conductivity directly. The extent of this effect is related to the used doping agent, which chemically affects polymer backbone, hence creating/ reducing number of free charge carriers.

Changes in thermoelectric properties from **secondary doping** are related to morphological modification of polymer chains (atomic scale) or grains/crystals (nano-to-microscale). Since this modification does not change the chemical environment of the polymer, thus not changing of charge carriers density, no influence on Seebeck coefficient is expected.

Mobile charge carriers can be dislocated over the polymer backbone. However, not only movement of charge carriers along polymer chain, but also from chain to chain can occur. Charge transfer between chains is considered in many models (e.g., variable-range-hopping, Sheng's model). Notably, charge carriers' mobility along the chain and interchain is different. Typically, charge carriers' mobility along chain is higher than for hopping events. From this follows that better chain alignment, or crystallinity, will directly affect macroscopic electrical conductivity. Yet, increased orientation will also increase anisotropy of the material.

For instance, electrical conductivity of iodine doped polyacetylene could be increased by one order of magnitude after stretching [25].

## **2.2. P-type conductive polymers**

True arguments regarding advantages, comparing to other (brittle) thermoelectric materials, are possible flexibility and mostly nontoxic properties. Abundance, independence on volatile raw material costs, feasible scale-up for material production, as well as, efficient processability of polymer material can be considered as advantages for polymer thermoelectric materials. Polymers are processable by different (industrial) established and sophisticated technologies and the final building up of thermoelectric modules based on polymers is possible with printing techniques. This offers cost-effective production of thermoelectric generators (TEG) at

To facilitate the usage of intrinsically conductive polymers for thermoelectric applications, one has to consider several requirements besides, undoubtedly important, thermoelectric properties. These requirements imply costs, abundance, recyclability, environmental stabil-

Of course, other factors like charge carriers density and morphology play an important role in

Thermoelectric properties of polymers are predominantly governed by doping. While undoped polymers are considered to be bad conductive semiconductors, doping can change this state and transfer into metallic-like behavior. Following doping concept of MacDiarmid

In general, **primary doping** affects charge carriers density in the polymer material, which influences Seebeck coefficient and electrical conductivity directly. The extent of this effect is related to the used doping agent, which chemically affects polymer backbone, hence creating/

Changes in thermoelectric properties from **secondary doping** are related to morphological modification of polymer chains (atomic scale) or grains/crystals (nano-to-microscale). Since this modification does not change the chemical environment of the polymer, thus not chang-

Mobile charge carriers can be dislocated over the polymer backbone. However, not only movement of charge carriers along polymer chain, but also from chain to chain can occur. Charge transfer between chains is considered in many models (e.g., variable-range-hopping, Sheng's model). Notably, charge carriers' mobility along the chain and interchain is different. Typically, charge carriers' mobility along chain is higher than for hopping events. From this follows that better chain alignment, or crystallinity, will directly affect

[24], doping of polymers can be subdivided into primary and secondary doping.

ing of charge carriers density, no influence on Seebeck coefficient is expected.

Basic factors that determine thermoelectric properties of polymers are as follows:

industrial scale.

ity, thermal stability, processability, and more.

50 Thermoelectrics for Power Generation - A Look at Trends in the Technology

– polymer chain length, structural order; and

reducing number of free charge carriers.

– environmental factors like temperature and humidity.

terms of thermoelectric properties and will be discussed below.

**2.1. Doping mechanism for intrinsically conductive polymers**

– nature of polymer structure itself;

– kind of counterions;

In spite of high electrical conductivity and power factor, polyacetylene plays no role in thermoelectric usage due to poor processability, unstable doping (with iodine), and high reactivity of solitons (charge carriers), leading to decrease in electrical conductivity over time.

The most prominent representatives of p-type polymers are aromatic polymers with polaron conduction mechanism. This can be found in the family of polythiopenes and others. The most promising polymer is currently PEDOT. Other polymers like P3HT or PANI also showed good improvement, however, they cannot reach the outstanding performance of PEDOT yet.

Review of recently reported material properties are given in **Table 1**. Further data can be found in references [26–32].


**Table 1.** Thermoelectric properties of selected p-type polymer semiconductors.

#### **2.3. N-type conductive polymers**

To make complete thermoelectric (TE) module, an n-type TE material is also required. However, the number of n-type organic materials with good thermoelectric properties is much smaller in comparison to that of p-type materials.

The main reasons are difficulties in n-type doping, because, typically, dopants providing one-electron transfer must have low ionization energies, which leads to instability in air. The next reason is the absence of a large variety of intrinsically conductive polymers. But, in the past 5 years, the number of reports, devoted to n-type organic materials, is steadily growing. It was found that promising materials are n-type fullerenes K*<sup>x</sup>* C70 [44], fullerenes C60 doped with Cr2 (hpp)<sup>4</sup> (hpp = 1,3,4,6,7,8-hexahydro-2 H-pyrimido[1, 2-a]pyrimidine) [45], poly[K*<sup>x</sup>* (Ni-ett)] (ett = 1,1,2,2-ethenetetrathiolate) [8], poly{N,N′-bis(2-octyl-dodecyl)- 1,4,5,8-napthalene dicarboximide-2,6-diyl]-alt-5,5′-(2,2′-bithiophene)} P(NDIOD-T2) doped by dihydro-1H-benzimidazole-2-yl (N-DBI) derivatives [46], self-doped perylene diimides (PDI) [47], polyethylenimine (PEI)/diethylenetriamine (DETA)-doped CNT, that were further reduced by NaBH4 [48], poly(p-phenylene vinylene) derivatives (FBDPPV) doped with (4-(1,3-dimethyl-2,3-dihydro-1H-benzoimidazol-2-yl)phenyl)dimethylamine (N-DMBI) [49], CoCp2@SWNTs [50], three-dimensional copper 7,7,8,8-tetracyanoquinodimethane (CuTCNQ) [51], isoindigo-based conjugated polymers (IIDT) [52], nanostructured tetrathiotetracene (TCNQ)2 (TTT(TCNQ)2) [53], and polyaniline doped with aprotic ionic liquid [54] (**Table 2**).


**Table 2.** Thermoelectric properties of selected n-type organic semiconductors.

Taking into account the very recent research of poly[K*<sup>x</sup>* (Ni-ett)] [55], it is one of the most promising n-type materials due to its excellent thermoelectric properties. Despite the very simple synthesis (**Figure 2**), chemical structure of this polymer is still not exhaustively clear, and is currently the research object. However, prototypes of generators based on this polymer have already shown very promising results. So, provided achieving good processability of this polymer, it can become one of main n-type materials for manufacture of TEGs. Below, we describe in a little more detailed manner, the present state-of-the-art in this topic.

**Figure 2.** Synthesis of poly[K*<sup>x</sup>* (Ni-ett)].

**2.3. N-type conductive polymers**

C60 doped with Cr2

[45], poly[K*<sup>x</sup>*

K*x*

C6

poly[K*<sup>x</sup>*

poly[K*<sup>x</sup>*

method [55]

0 doped with Cr2

(hpp)<sup>4</sup>

much smaller in comparison to that of p-type materials.

52 Thermoelectrics for Power Generation - A Look at Trends in the Technology

(hpp)<sup>4</sup>

growing. It was found that promising materials are n-type fullerenes K*<sup>x</sup>*

**Material, reference Conduc-tivity, S/cm Seebeck coefficient,** 

IIDT [52] 7 × 10−8 −898

**Table 2.** Thermoelectric properties of selected n-type organic semiconductors.

(Ni-ett)], prepared by an electrochemical

nanostructured TTT(TCNQ)2 [53] 12000 (asses.) −150 (asses.)

C70 [44] 550 −22.5 28

(Ni-ett)] [8] 40 −122 60 P(NDIOD-T2)) doped with N-DBI [46] 0.008 −850 0.6 PDI [47] 0.5 −168 1.4 PEI/DETA-doped CNT [48] 52 −86 38 FBDPPV doped with N-DMBI [49] 14 −141 28 CoCp2@SWNTs [50] 432 −41.8 75.4 CuTCNQ [51] 0.037 −632 1.5

polyaniline doped with aprotic ionic liquid [54] 0.0023 −138.8 4.43 × 10−3

[45] 4 *−*175 12

To make complete thermoelectric (TE) module, an n-type TE material is also required. However, the number of n-type organic materials with good thermoelectric properties is

The main reasons are difficulties in n-type doping, because, typically, dopants providing one-electron transfer must have low ionization energies, which leads to instability in air. The next reason is the absence of a large variety of intrinsically conductive polymers. But, in the past 5 years, the number of reports, devoted to n-type organic materials, is steadily

1,4,5,8-napthalene dicarboximide-2,6-diyl]-alt-5,5′-(2,2′-bithiophene)} P(NDIOD-T2) doped by dihydro-1H-benzimidazole-2-yl (N-DBI) derivatives [46], self-doped perylene diimides (PDI) [47], polyethylenimine (PEI)/diethylenetriamine (DETA)-doped CNT, that were further reduced by NaBH4 [48], poly(p-phenylene vinylene) derivatives (FBDPPV) doped with (4-(1,3-dimethyl-2,3-dihydro-1H-benzoimidazol-2-yl)phenyl)dimethylamine (N-DMBI) [49], CoCp2@SWNTs [50], three-dimensional copper 7,7,8,8-tetracyanoquinodimethane (CuTCNQ) [51], isoindigo-based conjugated polymers (IIDT) [52], nanostructured tetrathiotetracene (TCNQ)2 (TTT(TCNQ)2) [53], and polyaniline doped with aprotic ionic liquid [54] (**Table 2**).

(hpp = 1,3,4,6,7,8-hexahydro-2 H-pyrimido[1, 2-a]pyrimidine)

**µV/K**

200 to 400 −90 to −140 453

(Ni-ett)] (ett = 1,1,2,2-ethenetetrathiolate) [8], poly{N,N′-bis(2-octyl-dodecyl)-

C70 [44], fullerenes

**Power Factor, µW/mK<sup>2</sup>**

Poly(nickel1,1,2,2-ethenetetrathiolate), poly[Kx (Ni-ett)] (K is an alkali metal) (**Figure 2**) as an n-type organic polymer has been already known for a long time [56–64], its thermoelectric properties were carefully evaluated by Zhu's group [8] and an "all-organic" TEG device was fabricated.

Thanks to ambient stability and exciting thermoelectric characteristics, ZT value was equal to 0.2 at 400 K. This inspired other groups to work with this polymer for thermoelectrical applications [65] or to develop its composites with carbon nanotubes [66–68]. One major drawback of poly[K*<sup>x</sup>* (Ni-ett)] is its poor processability due to its completely insoluble nature leading to suspensions with broad particle size distributions.

Since this polymer is totally insoluble, commonly used structure characterization methods cannot be applied for this polymer, so these compounds have no clearly established structure. Its thermoelectric properties are not completely reproducible, even by the same personnel in the same laboratory. Due to the same reason, it is not possible to control polymerization reaction, for example, to control the degree of polymerization and have an influence on polydispersity of the resulting product. The exact structures of the terminal groups are also not known. Also, because of insolubility, it is not possible to improve properties of polymer after its production—methods like Soxhlet extraction, reprecipitation, or separation of products with the help of column chromatography cannot be applied. The most significant disadvantage of such insolubility and, as a result, bad processability is difficulty for utilization in devices like thermoelectric generators.

To solve the above-mentioned problem, many researchers tried to obtain different composite materials on the basis of these polymers and another compound—poly(vinylidene fluoride) (PVDF) solution [69], 1-butyl(or decyl)-3-methylimidazolium tetrafluoroborate [70], and dodecyltrimethylammonium bromide [71]. It results in great improvement of its processability, but TE properties of such material decrease dramatically, especially the electrical conductivity.

But, there is also another approach for making paste suitable for printing, which allows avoiding the degradation in thermoelectric performance. It is possible not to modify the polymer itself, but to change the procedure of its preparation (temperature of reaction mixture, speed of rotation, different system of solvents, and the ratio of the solvents, access of oxygen, and so on). Usually, such procedure consists of two sequential stages. First one (preparation of the monomer in fact) is reaction of 1,3,4,6-tetrathiapentalene-2,5-dione (TPD) with potassium methoxide. The second stage (namely, polymerization) is the addition of a metal salt to the solution. Usually [8, 56], both steps are carried out in methanol, and both with reflux. After that, the final product is modified to obtain flexible composites [69–71]. But carrying out the polymerization reaction in N-methylformamide (NMF)-methanol medium under certain temperature conditions allows obtaining of the product as a paste with controllable viscosity. Further evaporation of solvent and washing sequentially with water and methanol provide the thermoelectric material with characteristics similar to the powder.

The product of polymerization reaction poly[K*<sup>x</sup>* (Ni-ett)] (**Figure 2**) is an alternating copolymer with organic and inorganic monomeric units. The important feature of this reaction is that it occurs without a catalyst. Also, at the moment, it is not possible for the quantitative description of the role of atmospheric oxygen as an oxidizing agent in the polymerization process. Therefore, it is not suitable to describe the rate of reaction with patterns of chain growth or step growth mechanism.

By creating the proper conditions of this synthesis, the produced gel has no fluidity and is stable indefinitely under inert conditions. Even 1 month after the formation and storage under an inert atmosphere, it shows no signs of aging. However, when the gel is placed in the ambient atmosphere, it starts to slowly delaminate, by forming two phases—liquid and precipitate. Obviously, the reason of delamination is oxidation of paste components, leading to further polymerization and formation of insoluble product. It is possible to see very clearly the formation of a gel-like phase and its further separation, accompanied by reduction in viscosity which can be shown by rheological experiments. The diagram (**Figure 3**) reflects the dependence of the shear viscosity over time in a methanol-N-methylformamide system. During gel formation, a sharp increase in shear viscosity can be noticed and a subsequent reduction of shear viscosity related obviously to delamination of gel during the oxidation process.

**Figure 3.** Measurement of shear-viscosity in the ambient atmosphere.

The film, produced by airbrush-gun, is inhomogeneous and thin (~763 nm). But it still has a relatively good conductivity (0,13 S/cm (make units used equal)). More homogeneous films are formed by using dispenser printer. Prepared films on Kapton substrate have shown poor adhesion and could be easily removed in water. However, gentle immersion in water kept the film intact and improved its performance (*S* = −53.6 µV/K, ϭ = 1.60 S/cm). Interestingly, it has almost the same thermoelectric characteristics like the powder produced by drying of solvent from paste (see **Table 3**). Bending test shows, that any appreciable change in conductivity of this film occurs only when winding the tube diameter of less than 4 mm. It is important to note, that in an inert atmosphere thermoelectric properties of polymer are stable.


**Table 3.** Thermoelectric properties of selected poly[K*<sup>x</sup>* (Ni-ett)].

But, there is also another approach for making paste suitable for printing, which allows avoiding the degradation in thermoelectric performance. It is possible not to modify the polymer itself, but to change the procedure of its preparation (temperature of reaction mixture, speed of rotation, different system of solvents, and the ratio of the solvents, access of oxygen, and so on). Usually, such procedure consists of two sequential stages. First one (preparation of the monomer in fact) is reaction of 1,3,4,6-tetrathiapentalene-2,5-dione (TPD) with potassium methoxide. The second stage (namely, polymerization) is the addition of a metal salt to the solution. Usually [8, 56], both steps are carried out in methanol, and both with reflux. After that, the final product is modified to obtain flexible composites [69–71]. But carrying out the polymerization reaction in N-methylformamide (NMF)-methanol medium under certain temperature conditions allows obtaining of the product as a paste with controllable viscosity. Further evaporation of solvent and washing sequentially with water and methanol provide

with organic and inorganic monomeric units. The important feature of this reaction is that it occurs without a catalyst. Also, at the moment, it is not possible for the quantitative description of the role of atmospheric oxygen as an oxidizing agent in the polymerization process. Therefore, it is not suitable to describe the rate of reaction with patterns of chain growth or step growth mechanism. By creating the proper conditions of this synthesis, the produced gel has no fluidity and is stable indefinitely under inert conditions. Even 1 month after the formation and storage under an inert atmosphere, it shows no signs of aging. However, when the gel is placed in the ambient atmosphere, it starts to slowly delaminate, by forming two phases—liquid and precipitate. Obviously, the reason of delamination is oxidation of paste components, leading to further polymerization and formation of insoluble product. It is possible to see very clearly the formation of a gel-like phase and its further separation, accompanied by reduction in viscosity which can be shown by rheological experiments. The diagram (**Figure 3**) reflects the dependence of the shear viscosity over time in a methanol-N-methylformamide system. During gel formation, a sharp increase in shear viscosity can be noticed and a subsequent reduction of

shear viscosity related obviously to delamination of gel during the oxidation process.

(Ni-ett)] (**Figure 2**) is an alternating copolymer

the thermoelectric material with characteristics similar to the powder.

The product of polymerization reaction poly[K*<sup>x</sup>*

54 Thermoelectrics for Power Generation - A Look at Trends in the Technology

**Figure 3.** Measurement of shear-viscosity in the ambient atmosphere.

During first day of exposure in the ambient atmosphere, electrical conductivity of the film, as well as, the pure powder tends to deteriorate. After the fifth day, the thermoelectric properties remained stable for several months (shown in **Figure 4**).

**Figure 4.** Evolution of thermoelectric properties of Poly [K*<sup>x</sup>* (Ni-ett)] under ambient atmosphere.

To conclude, a simple procedure has been proposed to obtain printable paste based on insoluble conductive polymer poly[K*<sup>x</sup>* (Ni-ett)]. This method opens a way for various applications, such as aerosol and dispenser printing.

## **3. Thermoelectric modules**

The performance of polymer TEG is in general lower in comparison to TEGs made by inorganic materials like BiTe. The main reason for this is, of course, the higher thermoelectric performance of BiTe. The ZT value of BiTe is around 1 [22]. ZT values of p-type and n-type polymers are generally clearly below 1 or even below 0.1.

However, polymers offer other advantages like flexibility or easy processing and fabrication techniques. Most polymers can be printed without losing dramatically electrical and thermoelectric performance. For other materials like BiTe that performance is generally dependent on hot pressing or spark plasma sintering (SPS) techniques followed by cutting which may include manual work or other different processing steps. This advantage of polymers opens opportunities for industrial and economical production of thermoelectric devices.

A well-known technique for printing polymer TEG is the dispense technique. With dispenser, both types of TEGs, mono-leg-TEG (only one polymer), as well as, TEG with p- and n- type polymers can be easily printed, as shown in different publications. **Figure 5** shows mono-leg TEG designs.

**Figure 5.** Typical design for printed polymer TEG as mono-leg with one polymer (lateral design). The printing sequence is shown (a). A top view and cross section is displayed (b). In (c), a mono-leg TEG printed with PEDOT:PSS and Ag-paste is shown. TEG is wrapped around holder. (d) Scheme of a stacked mono-leg TEG design. (e) Printed sheets of a mono-leg TEG before assembly.

The same concept is also used for polymer TEG with both p-type and n-type materials. In this case, conductive paste (e.g., silver paste) is replaced by second polymer (see **Figure 6**). The design concepts shown in **Figures 5** and **6** have a disadvantage consisting in the fact that heat flow is parallel to the substrate and, therefore, parasitic heat flows exist through the substrate.

Furthermore, thermal connection to a heat source and a heat sink is relatively complex and difficult. **Figure 7** shows another mono-leg TEG concept orientated on classical TEG design.

To conclude, a simple procedure has been proposed to obtain printable paste based on insol-

The performance of polymer TEG is in general lower in comparison to TEGs made by inorganic materials like BiTe. The main reason for this is, of course, the higher thermoelectric performance of BiTe. The ZT value of BiTe is around 1 [22]. ZT values of p-type and n-type

However, polymers offer other advantages like flexibility or easy processing and fabrication techniques. Most polymers can be printed without losing dramatically electrical and thermoelectric performance. For other materials like BiTe that performance is generally dependent on hot pressing or spark plasma sintering (SPS) techniques followed by cutting which may include manual work or other different processing steps. This advantage of polymers opens

A well-known technique for printing polymer TEG is the dispense technique. With dispenser, both types of TEGs, mono-leg-TEG (only one polymer), as well as, TEG with p- and n- type polymers can be easily printed, as shown in different publications. **Figure 5** shows mono-leg TEG designs.

The same concept is also used for polymer TEG with both p-type and n-type materials. In this case, conductive paste (e.g., silver paste) is replaced by second polymer (see **Figure 6**). The design concepts shown in **Figures 5** and **6** have a disadvantage consisting in the fact that heat flow is parallel to the substrate and, therefore, parasitic heat flows exist through

**Figure 5.** Typical design for printed polymer TEG as mono-leg with one polymer (lateral design). The printing sequence is shown (a). A top view and cross section is displayed (b). In (c), a mono-leg TEG printed with PEDOT:PSS and Ag-paste is shown. TEG is wrapped around holder. (d) Scheme of a stacked mono-leg TEG design. (e) Printed sheets of a mono-leg

Furthermore, thermal connection to a heat source and a heat sink is relatively complex and difficult. **Figure 7** shows another mono-leg TEG concept orientated on classical TEG design.

opportunities for industrial and economical production of thermoelectric devices.

(Ni-ett)]. This method opens a way for various applications,

uble conductive polymer poly[K*<sup>x</sup>*

**3. Thermoelectric modules**

the substrate.

TEG before assembly.

such as aerosol and dispenser printing.

polymers are generally clearly below 1 or even below 0.1.

56 Thermoelectrics for Power Generation - A Look at Trends in the Technology

**Figure 6.** (a) Scheme of a TEG design with p-type (red) and n-type (blue) polymers and the actually printed polymer TEG with PEDOT:PSS and Poly[K*<sup>x</sup>* (Ni-ett)] on Polyimide (PI) substrate. (b) TEG wrapped around a holder for measuring power output by applying defined temperature difference. The heat flow is parallel to the substrate.

**Figure 7.** (a) Printing sequence and scheme of a vertical TEG design. (b) Vertical polymer TEG printed with dispenser, substrate is PI, polymer is PEDOT:PSS with 5 % DMSO. (c) Schematic cross section and dimensions of printed vertical TEG.

This design has the advantage consisting in the fact that heat flow goes only thorough the active polymer, preventing parasitic heat flows. Furthermore, fill factor and contact resistances can be reduced by larger contact areas in comparison to the other design. The challenge in printing polymer TEG is, however, that the pastes/ink which are used for printing TEGs have very high amount of solvents, which makes it difficult to quickly build up thick layers. PEDOT:PSS paste used for printing TEG in **Figure 7** contained ~ 2 wt.% PEDOT:PSS. This ratio of solvent and solid component is necessary for avoiding agglomeration and, thus, for providing stable printable polymer paste. Therefore, printing of thick layers is time consuming, because after deposition of each layer it is necessary to heat up polymer to evaporate solvent. Typical thickness of one layer after removing the solvent is in the range of 10–20 µm. Therefore, printing time of TEG shown in **Figure 7** was relatively long about 5 hours (in a lab environment).

Thus, polymer TEGs designs and configurations are still not satisfying and need to be improved. Simulations by Oshima et al. [71] based on the work of Aranguren et al. [72] have shown theoretically the possibility to reach power output in the range of MWh/year by polymer TEGs with a new optimized design based on porous substrate. In this publication, relatively high temperatures of >100°C were assumed. However, experimental realization is still missing.

But, potential application of polymer TEG is strongly limited by physical and chemical properties of polymers. Thermal stability of polymers is very critical for applications, as was shown recently by Stepien et al. It was shown for PEDOT:PSS, that electrical conductivity drops irreversibly down for temperatures >55°C (further details are given in Subsection 4.2.). It was assumed, that the reason might be degradation of the polymer. This behavior was observed under ambient conditions as well as in glove box under an inert atmosphere. That means, degradation of polymer properties starts at temperatures around 50°C and limits possible application dramatically. Thus, investigation by Stepien et al. has shown that the challenge for polymers is, on the one hand, to increase ZT values, but, on the other hand, to increase thermal stability also.

Power output and efficiency of polymer TEG are dependent on both the ZT value and maximum possible temperature difference.

Theoretical expression of the maximum efficiency of TEG is:

$$\eta\_{\text{max}} = \frac{T\_H - T\_C}{T\_H} \frac{\sqrt{1 + ZT} - 1}{\sqrt{1 + ZT} + \frac{T\_c}{T\_H}} \tag{1}$$

with *ZT* value for TE module according to Eq. (2):

\*\*With 2.1\*\* value to 12:moume according to Eq. (2). 
$$ZT = \frac{\left(\mathbf{S}\_r - \mathbf{S}\_r\right)^2 T}{\left[\left(\boldsymbol{\rho}\_r \,\mathbf{x}\_r\right)^{\text{\text{\textquotedbl{}}}} + \left(\boldsymbol{\rho}\_r \,\mathbf{x}\_r\right)^{\text{\textquotedbl{}}}\right]^{\text{\textquotedbl{}}} \tag{2}$$

where *TC*, *TH*, and *T*¯ are the temperature at the cold side, hot side, and average ambient absolute temperature, respectively; *Sn, Sp, ρn, ρp, κn,* and *κ<sup>p</sup>* are Seebeck coefficient, electrical resistivity, and thermal conductivity of n- and p-type polymers, respectively.

The temperature dependence of TEG efficiency calculated according to Eq. (1) is shown in **Figure 8**. Calculations performed with ZT values equals 1 [7] and 0.2 [8] for p-type and n-type polymers, respectively, efficiency below 0.25% can be reached by applying maximum temperature difference of 60 K (333–273 K).

**Figure 8.** Theoretical temperature dependence of maximum efficiency for polymer TEG with p- and n-type polymers from references [7, 8]. Cold side temperature equals to 273 K. Internal contact resistance was assumed as ideal.

Polymer TEGs based on metal organic materials with 35 thermocouples (p- and n-type legs) have delivered around 1 µW/cm2 at temperature difference of 25 K [8]. Another TEG made of PEDOT:TOS in a different design delivered 0.27 µW/cm2 at a temperature difference of 30 K.

If ZT value or working temperature difference between hot and cold sides of polymer TEG cannot be increased, then polymer TEG can be used for low power application only. Therefore, there is a big challenge to avoid degradation of polymers at higher temperatures.

Another reason for relatively low power output is high contact resistance between polymer and metal contacts. The measurement of contact resistance between PEDOT:PSS and Silver paste reached 5 x 10−2 Ohm x cm2 . This leads to relatively high internal resistance values for printed polymer TEG. Measured internal resistance of printed TEGs was equal to a few kOhm. Internal resistance of commercial TEG with areas of, for example, 4 cm × 4 cm is <10 Ohm and efficiency for energy conversion is indicated around 5% by TEG suppliers. Conventional thermoelectric modules and materials were developed, of course, over decades. Design of commercial TEG was developed and simulated carefully. Leg-length and leg-cross sections were studied in order to get high fill factor, low internal resistances, and optimized power output. Such optimization processes are still missing for polymer TEG.

Estimated costs per Watt (\$/W) of conventional TEG are in the range of 4 \$/W. More than 50% of the costs are for system itself and manufacturing and just small part for thermoelectric material itself [73].

On the one hand, printing technology is, of course, advantageous for polymer thermoelectrics, because it has the potential for reducing system costs in general. However, on the other hand, if we compare polymer material costs to, for example, today costs of BiTe-based material, we find a large discrepancy. Assuming that costs for producing 1 kg BiTe-based material equals to 1000 €, we have costs for 500 ml of PEDOT:PSS dispersion of ~400 € today. Thus, cost for 500 ml PEDOT:PSS or more precisely 1 kg pure PEDOT:PSS is much higher than that of the BiTe-based material, considering the fact that PEDOT:PSS dispersion is purchased with a solid content of only around 2 wt%. Using cost-saving manufacturing technique like printing is an advantage for polymer thermoelectrics of course; however, this advantage is not the key for economical applications without much lower polymer material costs.

The applications of polymer thermoelectrics seem to be for the medium–long term in the lowpower area. The amortization of TEG costs by energy harvesting with polymer TEG is today still difficult and ambitiously.

First applications for polymer TEGs are imaginable if the flexibility and the low weight of the polymer devices are the criteria for choosing the polymer material for thermoelectrics.

## **4. Challenges**

down for temperatures >55°C (further details are given in Subsection 4.2.). It was assumed, that the reason might be degradation of the polymer. This behavior was observed under ambient conditions as well as in glove box under an inert atmosphere. That means, degradation of polymer properties starts at temperatures around 50°C and limits possible application dramatically. Thus, investigation by Stepien et al. has shown that the challenge for polymers is, on the one

Power output and efficiency of polymer TEG are dependent on both the ZT value and maxi-

\_\_\_\_\_ 1 + *ZT*¯ \_\_\_\_\_\_\_\_ − 1

2 *T*¯ \_\_\_\_\_\_\_\_\_\_\_\_\_\_

(1)

, (2)

*TH* <sup>√</sup>

[(*ρ<sup>n</sup> κn*) 1⁄2 + (*ρ<sup>p</sup> κp*) 1⁄2 ] 2

tivity, and thermal conductivity of n- and p-type polymers, respectively.

where *TC*, *TH*, and *T*¯ are the temperature at the cold side, hot side, and average ambient absolute temperature, respectively; *Sn, Sp, ρn, ρp, κn,* and *κ<sup>p</sup>* are Seebeck coefficient, electrical resis-

The temperature dependence of TEG efficiency calculated according to Eq. (1) is shown in **Figure 8**. Calculations performed with ZT values equals 1 [7] and 0.2 [8] for p-type and n-type polymers, respectively, efficiency below 0.25% can be reached by applying maximum tem-

**Figure 8.** Theoretical temperature dependence of maximum efficiency for polymer TEG with p- and n-type polymers from references [7, 8]. Cold side temperature equals to 273 K. Internal contact resistance was assumed as ideal.

√ \_\_\_\_\_ 1 + *ZT*¯ + *T*\_\_\_*c TH* 

hand, to increase ZT values, but, on the other hand, to increase thermal stability also.

mum possible temperature difference.

perature difference of 60 K (333–273 K).

*<sup>η</sup>*max = *TH* <sup>−</sup> *<sup>T</sup>* \_\_\_\_\_\_*<sup>C</sup>*

with *ZT* value for TE module according to Eq. (2):

*ZT*¯ <sup>=</sup> (*Sp* <sup>−</sup> *Sn*)

Theoretical expression of the maximum efficiency of TEG is:

58 Thermoelectrics for Power Generation - A Look at Trends in the Technology

#### **4.1. Material optimization**

Concerning optimization of thermoelectric material, one advantage over nonpolymer materials is the possibility to decouple partially chemistry from morphology. Indeed, changes in chemistry also have effect on the conformation of polymer chains, thus the morphology is affected; however, it can be stated that Seebeck coefficient is mainly governed by chemical factors, for example, the kind of counterions used or degree of oxidation, while electrical conductivity is additionally influenced by morphological aspects like crystal orientation, crystal size, or namely charge carrier mobility. Therefore, it is favorable to optimize these two aspects separately. Therefore, parameters of polymer thermoelectric materials can be improved according to the following concept, which can be applied to almost all thermoelectric polymer materials; here special emphasis is given to PEDOT.

#### *4.1.1. Maximizing electrical conductivity*

Morphology should be optimized by using a proper deposition technique and/or using cosolvents or other additives. The aim of this step is to maximize electrical conductivity. The solution-sheared deposition technique seems to be a promising approach. In this case, Seebeck coefficient should not be influenced significantly.

#### *4.1.2. Optimization of Seebeck coefficient*

Continuing theme of high electrically conductive material, increase in Seebeck coefficient with proper reduction/oxidation (deprotonating/protonating) methods will be required to obtain good thermoelectric material.

Reduction can be done by electrochemical methods due to its good control of the degree of oxidation. Reduction can also be done by other methods like dipping or immersion in corresponding agents. The aim here is to find the optimum between electrical conductivity and Seebeck coefficient, because change in charge carrier density will affect Seebeck coefficient and electrical conductivity to the contrary.

It should be emphasized, that possible formation of crystals, because of the reducing agents used, should be avoided in order to maintain the crystal structure prepared in step one. This is also true for the use of composite materials. Composites with beneficial thermoelectric properties contain often high quantity of nanoparticles like nanowires, graphene sheets, or others (often over 50 wt%), which as a result is nanoparticle-matrix filled with polymers. For these improvements, it is crucial to have absolutely robust processing techniques, as well as, characterization routines.

If these factors cannot be controlled properly, then poor reproducibility of material parameters will be the result. Since thermoelectric properties of polymers are highly dependent on morphological aspects, it is necessary to have ultimate control of film formation and conformation of polymer chains during this processing step.

Reported results often lack comparability because of different characterization methods. For instance, Seebeck coefficient can vary significantly, when electrodes with different geometries are used during the measurement. It was shown, that variation in electrode geometry can influence Seebeck coefficient by a factor of 3 or more [74]. Regarding electrical conductivity, it is known that different methods, for example, van der Pauw or linear 4-point-probe, can result in different sheet resistances because of possible anisotropies in the samples. The same applies for measuring film thickness. Regarding the method used, variations of more than 30% for films in nanometer range can occur. These systematic uncertainties, as well as, nonsystematic ones, will have significant impact on power factor and, hence, the figure of merit. **Figure 9** shows the range of uncertainty for power factor over electrical conductivity.

**Figure 9.** Range of uncertainty for power factor over electrical conductivity. Total uncertainties for Seebeck coefficient and electrical conductivity are 10% and 5%, respectively.

It can be seen, that overestimated Seebeck coefficient (maybe due to not proper electrode contacts) can lead to dramatic differences. This is especially true for high conducting materials.

Note that more efforts focus recently on measurements of thermal conductivities, as well as, anisotropy of the overall material properties and should be further encouraged.

#### **4.2. Thermal stability**

chemistry also have effect on the conformation of polymer chains, thus the morphology is affected; however, it can be stated that Seebeck coefficient is mainly governed by chemical factors, for example, the kind of counterions used or degree of oxidation, while electrical conductivity is additionally influenced by morphological aspects like crystal orientation, crystal size, or namely charge carrier mobility. Therefore, it is favorable to optimize these two aspects separately. Therefore, parameters of polymer thermoelectric materials can be improved according to the following concept, which can be applied to almost all thermoelectric polymer

Morphology should be optimized by using a proper deposition technique and/or using cosolvents or other additives. The aim of this step is to maximize electrical conductivity. The solution-sheared deposition technique seems to be a promising approach. In this case, Seebeck

Continuing theme of high electrically conductive material, increase in Seebeck coefficient with proper reduction/oxidation (deprotonating/protonating) methods will be required to

Reduction can be done by electrochemical methods due to its good control of the degree of oxidation. Reduction can also be done by other methods like dipping or immersion in corresponding agents. The aim here is to find the optimum between electrical conductivity and Seebeck coefficient, because change in charge carrier density will affect Seebeck coefficient

It should be emphasized, that possible formation of crystals, because of the reducing agents used, should be avoided in order to maintain the crystal structure prepared in step one. This is also true for the use of composite materials. Composites with beneficial thermoelectric properties contain often high quantity of nanoparticles like nanowires, graphene sheets, or others (often over 50 wt%), which as a result is nanoparticle-matrix filled with polymers. For these improvements, it is crucial to have absolutely robust processing techniques, as well as,

If these factors cannot be controlled properly, then poor reproducibility of material parameters will be the result. Since thermoelectric properties of polymers are highly dependent on morphological aspects, it is necessary to have ultimate control of film formation and confor-

Reported results often lack comparability because of different characterization methods. For instance, Seebeck coefficient can vary significantly, when electrodes with different geometries are used during the measurement. It was shown, that variation in electrode geometry can influence Seebeck coefficient by a factor of 3 or more [74]. Regarding electrical conductivity, it is known that different methods, for example, van der Pauw or linear 4-point-probe, can result in different sheet resistances because of possible anisotropies in the samples. The same

materials; here special emphasis is given to PEDOT.

60 Thermoelectrics for Power Generation - A Look at Trends in the Technology

coefficient should not be influenced significantly.

*4.1.1. Maximizing electrical conductivity*

*4.1.2. Optimization of Seebeck coefficient*

obtain good thermoelectric material.

and electrical conductivity to the contrary.

mation of polymer chains during this processing step.

characterization routines.

Thermoelectric energy conversion is considered to be a robust and sustainable process. This claim can only be fulfilled if material degradation can be avoided. One drawback, compared to other low temperature materials like BiTe, is besides thermoelectric performance, low thermal stability. Usually, glass transition and crystal melting for polymers occurs at much lower temperatures as for BiTe. This can lead to unfavorable change in nano- and microstructure of the polymer material.

In the case of DMSO doped PEDOT:PSS films, it was shown, that during 50 hours of thermal stress at 75°C ambient temperature, electrical conductivity decreased irreversibly by 17% (**Figure 10**). For higher temperatures, decrease in electrical conductivity was even more pronounced. Significant chemical degradation is found to start between 140 and 160°C, which is highly undesirable for real long-term applications. This leads to the conclusion that thermoelectric generators made of currently most promising p-type polymer PEDOT:PSS should be deployed only for moderate temperatures, which limits possible applications.

**Figure 10.** Decrease of normalized electrical conductivity of PEDOT:PSS (+DMSO) films at thermal stress for over 50 hours. Stepien et al. not accepted yet.

Comparing intrinsically conductive polymers with BiTe in terms of thermoelectric performance and thermal stability still a lot of effort has to be put in polymer materials in order to compete with BiTe.

## **Acknowledgement**

This work has received partial funding from the European Unions' Seventh Framework Programme for research, technological development, and demonstration under the grant agreement No 604647.

## **Author details**

Lukas Stepien1,\*, Aljoscha Roch<sup>1</sup> , Roman Tkachov<sup>1</sup> and Tomasz Gedrange2

\*Address all correspondence to: lukas.stepien@iws.fraunhofer.de

1 Fraunhofer Institute for Material and Beam Technology IWS, Dresden, Germany

2 University Hospital Carl Gustav Carus at the TU Dresden, Dresden, Germany

## **References**

highly undesirable for real long-term applications. This leads to the conclusion that thermoelectric generators made of currently most promising p-type polymer PEDOT:PSS should be

Comparing intrinsically conductive polymers with BiTe in terms of thermoelectric performance and thermal stability still a lot of effort has to be put in polymer materials in order to

**Figure 10.** Decrease of normalized electrical conductivity of PEDOT:PSS (+DMSO) films at thermal stress for over 50

This work has received partial funding from the European Unions' Seventh Framework Programme for research, technological development, and demonstration under the grant

and Tomasz Gedrange2

, Roman Tkachov<sup>1</sup>

1 Fraunhofer Institute for Material and Beam Technology IWS, Dresden, Germany

2 University Hospital Carl Gustav Carus at the TU Dresden, Dresden, Germany

\*Address all correspondence to: lukas.stepien@iws.fraunhofer.de

compete with BiTe.

**Acknowledgement**

hours. Stepien et al. not accepted yet.

agreement No 604647.

Lukas Stepien1,\*, Aljoscha Roch<sup>1</sup>

**Author details**

deployed only for moderate temperatures, which limits possible applications.

62 Thermoelectrics for Power Generation - A Look at Trends in the Technology


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**Chapter 4 Provisional chapter**

## **Tetrahedrites: Prospective Novel Thermoelectric Materials Tetrahedrites: Prospective Novel Thermoelectric Materials**

Christophe Candolfi, Yohan Bouyrie, Selma Sassi, Anne Dauscher and Bertrand Lenoir Christophe Candolfi, Yohan Bouyrie, Selma Sassi, Anne Dauscher and Bertrand Lenoir

Additional information is available at the end of the chapter Additional information is available at the end of the chapter

http://dx.doi.org/10.5772/65638

#### **Abstract**

Since their discovery in 1845, tetrahedrites, a class of minerals composed of relatively earth‐abundant and nontoxic elements, have been extensively studied in mineralogy and geology. Despite a large body of publications on this subject, their transport properties had not been explored in detail. The discovery of their interesting high‐temperature ther‐ moelectric properties and peculiar thermal transport has led to numerous experimental and theoretical studies over the last 4 years with the aim of better understanding the rela‐ tionships between the crystal, electronic, and thermal properties. Tetrahedrites provide a remarkable example of anharmonic system giving rise to a temperature dependence of the lattice thermal conductivity that mirrors that of amorphous compounds. Here, we review the progress of research on the transport properties of tetrahedrites, highlight‐ ing the main experimental and theoretical results that have been obtained so far and the important issues and questions that remain to be investigated.

**Keywords:** tetrahedrites, thermoelectric, thermal conductivity, exsolution, composite

## **1. Introduction**

Thermoelectric effects provide a reliable way for converting waste heat into useful electricity and vice versa [1, 2]. This solid‐state conversion process is realized without hazardous gas emissions and moving parts, ranking this technology among clean and sustainable energy sources. Thermoelectric generators have been successfully used to reliably power deep‐ space probes and rovers over several decades, and have been used as solid‐state coolers for electronic devices [1, 2]. Yet, a widespread use of this versatile technology is hampered by the rather low conversion efficiency achieved. The thermoelectric efficiency, with which a

and reproduction in any medium, provided the original work is properly cited.

© 2016 The Author(s). Licensee InTech. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, © 2016 The Author(s). Licensee InTech. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

thermoelectric device converts heat into electricity and vice versa is directly dependent of the dimensionless figure of merit *ZT* of the active thermoelectric legs [1, 2]. This parame‐ ter is defined at an absolute temperature *T* as <sup>2</sup> L e *ZT T* = + α ρκ κ /( ) , where *α* is the thermo‐ power (or Seebeck coefficient), *ρ* is the electrical resistivity, and L κ and e κ are the lattice and electronic thermal conductivities, respectively. Thus, a good thermoelectric material should possess a combination of high thermopower to produce a sizeable thermoelectric effect, low electrical resistivity to avoid Joule effect, and low thermal conductivity to maintain a large thermal gradient across the device [3, 4].

While quite simple at first sight, this expression however underlies a formidable material challenge since the ideal thermoelectric material should be concomitantly a thermal insulator and an electrical conductor. The question is therefore how far these two seemingly conflicting aspects can be reconciled within the same material. The quest for this long‐sought ideal mate‐ rial has led to thousands of experimental and theoretical investigations on a large number of material's families and on the possibilities to optimize their thermoelectric performances through various strategies such as the optimization of the carrier concentration by doping or the reduction of the lattice thermal conductivity via substitutions or nanostructuring [1–4]. These studies have increased the number of known crystalline compounds that show the remarkable ability to conduct heat akin to glassy systems [5–14]. In addition to being ideal systems for improving our understanding of the physical mechanisms leading to this behav‐ ior, these materials provide interesting playgrounds to achieve high thermoelectric perfor‐ mances. When the lattice thermal conductivity is intrinsically lowered to a value close to the theoretical minimum value, the electrical resistivity and thermopower remain the only key properties to be optimized to reach high *ZT* values.

This approach has led to the identification of several new families of thermoelectric materials, some of which exhibiting thermoelectric performances that surpass those of the state‐of‐the‐ art thermoelectric materials such as PbTe or Si1‐*<sup>x</sup>* Ge*<sup>x</sup>* alloys at moderate and high temperatures, respectively [2, 5–14]. Among these new families, tetrahedrites have recently draw attention due to the relatively nontoxic, earth‐abundant elements that enter their chemical composi‐ tion [15]. These compounds are a class of copper antimony sulfosalt minerals geologically formed in hydrothermal veins at low‐to‐moderate temperatures making them abundant in the Earth's crust. Tetrahedrites are minor ores of copper that were first discovered in 1845 in Germany. While they were the subject of a large number of experimental and theoretical stud‐ ies in geology and mineralogy, it is not until recently, however, that their transport properties have been investigated in detail [15, 16]. Both natural and synthetic tetrahedrites, i.e., synthe‐ sized in laboratory environment, have been recently studied indicating that these compounds are interesting candidates for thermoelectric applications in power generation.

This chapter provides an updated review on the experimental and theoretical results obtained and an overview of the status of the research activities on the thermoelectric properties of these materials. Our goal is to highlight the important structural and chemical aspects that influence their transport properties and thus play a role in their thermoelectric performances. This review will also cover the first experimental attempts at scaling‐up the synthesis process via chemical or metallurgical approaches.

## **2. Crystal structure and chemical composition**

thermoelectric device converts heat into electricity and vice versa is directly dependent of the dimensionless figure of merit *ZT* of the active thermoelectric legs [1, 2]. This parame‐

electronic thermal conductivities, respectively. Thus, a good thermoelectric material should possess a combination of high thermopower to produce a sizeable thermoelectric effect, low electrical resistivity to avoid Joule effect, and low thermal conductivity to maintain a large

While quite simple at first sight, this expression however underlies a formidable material challenge since the ideal thermoelectric material should be concomitantly a thermal insulator and an electrical conductor. The question is therefore how far these two seemingly conflicting aspects can be reconciled within the same material. The quest for this long‐sought ideal mate‐ rial has led to thousands of experimental and theoretical investigations on a large number of material's families and on the possibilities to optimize their thermoelectric performances through various strategies such as the optimization of the carrier concentration by doping or the reduction of the lattice thermal conductivity via substitutions or nanostructuring [1–4]. These studies have increased the number of known crystalline compounds that show the remarkable ability to conduct heat akin to glassy systems [5–14]. In addition to being ideal systems for improving our understanding of the physical mechanisms leading to this behav‐ ior, these materials provide interesting playgrounds to achieve high thermoelectric perfor‐ mances. When the lattice thermal conductivity is intrinsically lowered to a value close to the theoretical minimum value, the electrical resistivity and thermopower remain the only key

This approach has led to the identification of several new families of thermoelectric materials, some of which exhibiting thermoelectric performances that surpass those of the state‐of‐the‐

respectively [2, 5–14]. Among these new families, tetrahedrites have recently draw attention due to the relatively nontoxic, earth‐abundant elements that enter their chemical composi‐ tion [15]. These compounds are a class of copper antimony sulfosalt minerals geologically formed in hydrothermal veins at low‐to‐moderate temperatures making them abundant in the Earth's crust. Tetrahedrites are minor ores of copper that were first discovered in 1845 in Germany. While they were the subject of a large number of experimental and theoretical stud‐ ies in geology and mineralogy, it is not until recently, however, that their transport properties have been investigated in detail [15, 16]. Both natural and synthetic tetrahedrites, i.e., synthe‐ sized in laboratory environment, have been recently studied indicating that these compounds

This chapter provides an updated review on the experimental and theoretical results obtained and an overview of the status of the research activities on the thermoelectric properties of these materials. Our goal is to highlight the important structural and chemical aspects that influence their transport properties and thus play a role in their thermoelectric performances. This review will also cover the first experimental attempts at scaling‐up the synthesis process

are interesting candidates for thermoelectric applications in power generation.

Ge*<sup>x</sup>*

L e *ZT T* = + α

 ρκ  κ

κ

/( ) , where *α* is the thermo‐

are the lattice and

 and e κ

alloys at moderate and high temperatures,

ter is defined at an absolute temperature *T* as <sup>2</sup>

72 Thermoelectrics for Power Generation - A Look at Trends in the Technology

properties to be optimized to reach high *ZT* values.

art thermoelectric materials such as PbTe or Si1‐*<sup>x</sup>*

via chemical or metallurgical approaches.

thermal gradient across the device [3, 4].

power (or Seebeck coefficient), *ρ* is the electrical resistivity, and L

The general chemical formula of tetrahedrites can be written as *A*12*X*<sup>4</sup> *Y*13, where *A* is mainly Cu that can be partially substituted by transition metals (Ag, Zn, Fe, Ni, Co, Mn, and Hg), *X* is a pnictide (Sb or As with possible partial substitution by Te or Bi), and *Y* is sulfur (S can be substituted in small quantities by Se). All these elements can be found in the chemical composition of natural tetrahedrites and numerous experimental and theoretical studies in geology and mineralogy focused on the link between their composition and the geological place where they were discovered.

With no exceptions, all tetrahedrites, should they be natural or synthetic, crystallize within a cubic crystal structure described in the *I m* 43 space group with 58 atoms per unit cell (**Figure 1**)

[17, 18]. The different *A*, *X,* and *Y* elements are distributed over five distinct crystallographic sites. Taking the ternary compound Cu12Sb4 S13 as an example, the copper atoms possess two different chemical environments. The Cu1 atoms show a tetrahedral coordination with three S and one surrounding Sb atoms. The Cu2 atoms lie within a triangular environment formed by three sulfur atoms in a nearly coplanar coordination. Twelve of the 13 S atoms exhibit a tetrahe‐ dral environment while the remaining S atom is surrounded by six Cu atoms forming an octa‐ hedron. The main peculiarity of this crystal structure is related to the Cu2 atoms that show large and anisotropic atomic thermal displacement parameters (ADPs), i.e., a strong ability to vibrate about their equilibrium position (see **Figure 1**) [19]. In addition, the tetrahedral environment of the Sb atoms lacks one sulfur atom to be complete. The presence of only three S atoms thus gives rise to 5s lone pair electrons on the Sb atoms. These "free" electrons can be oriented along the missing vertex of the tetrahedron according to the valence shell electron pair repulsion theory. Several studies have pointed out the decisive influence of lone pair electrons on the thermal conductivity, the delocalization of the lone pair away from the Sb nucleus yielding anharmonic forces in the lattice [20–22]. As we shall see below, a similar situation is probably at play in tetrahedrites, explaining their extremely low lattice thermal conductivity values.

While the crystal structure of tetrahedrites is simple to describe, their chemical composition displays some subtleties that make these compounds particularly interesting. Specifically, synthetic tetrahedrites often show deviations from stoichiometry, a characteristic usually absent in natural specimens that possess the exact 12–4–13 composition to within the detec‐ tion limits of the instruments used [23–26]. The most prominent example of such behavior is provided by the ternary compound Cu12Sb4 S13, which has been the subject of thorough experimental studies in the 1970s [23–26]. These investigations have shown that the chemical composition of this compound is best described by the general chemical formula Cu12+*<sup>x</sup>* Sb4+*<sup>y</sup>* S13 with 0.08 ≤ *x* ≤ 1.72 and 0.06 ≤ *y* ≤ 0.30 [23, 24]. This formula indicates that an excess of Cu is systematically observed together with a possible excess on the Sb sites, both of which depend on the synthesis conditions. These deviations are clearly correlated to the lattice parameter: an increase in either the Cu or Sb content always expands the unit cell from 10.327 Å for (*x*, *y*) = (0.08, 0.06) up to 10.448 Å for (*x*, *y*) = (1.72, 0.09). In addition to these deviations from the ideal stoichiometry, the ternary compositions undergo an exsolution process, i.e., a separation of the main tetrahedrite phase into two tetrahedrite phases of close compositions below the so‐called exsolution temperature [23, 24]. Such phase separation has been widely observed in minerals and often results in lamellar microstructures. In Cu12+*<sup>x</sup>* Sb4+*<sup>y</sup>* S13, this process occurs below about 120°C, the exact value slightly varying with the chemical composition [23, 24]. Below this temperature, Cu‐rich and Cu‐poor phases coexist, the lattice parameters of both phases differing significantly from each other. This mechanism is reversible and disappears upon heating above 120°C to show up again upon cooling back below this temperature.

**Figure 1.** Perspective view of the crystal structure of Cu12Sb4 S13 in the ellipsoidal representation (drawn at the 95% probability level). The Cu1 and Cu2 atoms are in blue and green, respectively. Sb atoms are shown in brown while S1 and S2 atoms are in yellow and red, respectively.

#### **3. Electronic properties**

While the chemical and structural trends in natural and synthetic tetrahedrites are rather well understood, their transport properties have been investigated in detail only very recently [15, 16]. In order to better understand why these materials may be interesting for thermoelectric applica‐ tions, it is helpful to assume that the atomic bonds are purely ionic. Within this assumption, the general chemical formula may be rewritten as (Cu<sup>+</sup> ) <sup>10</sup>(Cu2+) 2 (Sb3+) 4 (S2 ⁻)13 which corresponds to 204 valence electrons per chemical formula [27]. From an electronic point of view, these valence electrons do not entirely fill the valence bands leaving two holes per formula unit. The ternary compound is thus predicted to behave as a *p*‐type metal. This metallic state can nevertheless be driven toward a semiconducting state when two electrons per chemical formula are added (resulting in a total of 208 valence electrons per chemical formula) [27]. This progressive filling thus leads to highly doped semiconducting states more favorable to achieve high thermoelectric performances. Further, based on this simple electronic structure model, it was argued that natu‐ ral tetrahedrites crystallize preferentially with a composition that corresponds to 208 valence electrons in agreement with the results based on a large survey of the literature data [27]. In particular, this model predicts that metallic compositions are energetically less favorable which might explain why Cu12Sb4 S13 tends to exsolve into Cu‐poor and Cu‐rich phases.

The first experimental results on the transport properties of the ternary tetrahedrite Cu12Sb4 S13 have been reported by Suekuni et al. [15] who measured the temperature dependence of the magnetic susceptibility, electrical resistivity, thermopower, and thermal conductivity between 5 and 350 K (**Figure 2**). The results have shown that this compound exhibits several interesting features. A first one is a metal‐insulator transition that sets in near 85 K and leaves clear signatures on the transport and magnetic properties. Below this temperature, the electri‐ cal resistivity significantly increases by approximately two orders of magnitude upon cooling from 85 to 5 K. A concomitant strong increase in the thermopower values from 25 μV K⁻<sup>1</sup> at 85 K to 100 μV K⁻<sup>1</sup> at 60 K further corroborates a semiconducting‐like state of the low‐tem‐ perature phase. The thermal conductivity drops below the transition temperature due to both a reduced electronic contribution as a result of the increase in *ρ* and to the influence of this transition on the lattice thermal conductivity. The magnetic susceptibility, indicative of para‐ magnetic behavior across the entire temperature range, suddenly drops below about 100 K.

so‐called exsolution temperature [23, 24]. Such phase separation has been widely observed

below about 120°C, the exact value slightly varying with the chemical composition [23, 24]. Below this temperature, Cu‐rich and Cu‐poor phases coexist, the lattice parameters of both phases differing significantly from each other. This mechanism is reversible and disappears upon heating above 120°C to show up again upon cooling back below this temperature.

While the chemical and structural trends in natural and synthetic tetrahedrites are rather well understood, their transport properties have been investigated in detail only very recently [15, 16]. In order to better understand why these materials may be interesting for thermoelectric applica‐ tions, it is helpful to assume that the atomic bonds are purely ionic. Within this assumption, the

probability level). The Cu1 and Cu2 atoms are in blue and green, respectively. Sb atoms are shown in brown while S1

204 valence electrons per chemical formula [27]. From an electronic point of view, these valence electrons do not entirely fill the valence bands leaving two holes per formula unit. The ternary compound is thus predicted to behave as a *p*‐type metal. This metallic state can nevertheless be driven toward a semiconducting state when two electrons per chemical formula are added (resulting in a total of 208 valence electrons per chemical formula) [27]. This progressive filling thus leads to highly doped semiconducting states more favorable to achieve high thermoelectric performances. Further, based on this simple electronic structure model, it was argued that natu‐ ral tetrahedrites crystallize preferentially with a composition that corresponds to 208 valence electrons in agreement with the results based on a large survey of the literature data [27]. In particular, this model predicts that metallic compositions are energetically less favorable which

) <sup>10</sup>(Cu2+) 2 (Sb3+) 4 (S2

S13 tends to exsolve into Cu‐poor and Cu‐rich phases.

Sb4+*<sup>y</sup>*

S13 in the ellipsoidal representation (drawn at the 95%

S13, this process occurs

⁻)13 which corresponds to

in minerals and often results in lamellar microstructures. In Cu12+*<sup>x</sup>*

74 Thermoelectrics for Power Generation - A Look at Trends in the Technology

**3. Electronic properties**

might explain why Cu12Sb4

general chemical formula may be rewritten as (Cu<sup>+</sup>

**Figure 1.** Perspective view of the crystal structure of Cu12Sb4

and S2 atoms are in yellow and red, respectively.

**Figure 2.** Temperature dependence of the electrical resistivity, thermopower, and total thermal conductivity of the tetrahedrite Cu10*Tr*<sup>2</sup> Sb4 S13 (*Tr* = Cu, Fe, Co, Ni, Zn, and Mn). Copyright 2012 by the Japan Society of Applied Physics.

Using low‐temperature powder X‐ray diffraction measurements, May et al. [28] demonstrated that this transition is accompanied by a cubic‐to‐tetragonal lattice distortion characterized by an in‐plane ordering that doubles the unit cell volume (**Figure 3**). The low‐temperature crystal structure has been described in the *P*4 space group using a supercell model 2 2 *a ac* × × . Owing to the high number of atomic position parameters to be refined (83), the crystal struc‐ ture could not be entirely solved and remains to be determined in future studies.

**Figure 3.** (Panel a) Powder X‐ray diffraction pattern collected upon cooling across the 85 K phase transition in Cu12Sb4 S13. The appearance of additional Bragg reflections (Panel b) is indicative of the cubic‐to‐tetragonal structural transition that accompanies the metal‐insulator transition. Reproduced **Figure 1** with permission from May et al. [28]. Copyright 2016 by the American Physical Society. DOI: 10.1103/PhysRevB.93.064104.

Kitagawa et al. [29] further investigated the metal‐to‐insulator transition through measure‐ ments of the electrical resistivity and magnetic susceptibility at high pressures (up to 4.06 GPa) and of the 63Cu‐NMR spectra. The results evidence a transition from a paramagnetic bad metal to a nonmagnetic insulating state below 85 K at ambient pressure. The nonmagnetic ground state evolves toward a metallic state under pressure. Tanaka et al. [30] further investi‐ gated the pressure dependence of this transition as well as its evolution upon substituting As for Sb (Cu12Sb4₋*<sup>x</sup>* As*<sup>x</sup>* S13). In agreement with the study of Kitagawa et al., the transition is sup‐ pressed under pressure. The substitution of As for Sb that decreases the unit cell volume acts similarly and supresses the transition for relatively low substitution levels (*x* ≤ 0.5).

In their initial study on Cu12Sb4 S13, Suekuni et al. [15] have also reported the transport prop‐ erties of several tetrahedrites Cu10*Tr*<sup>2</sup> Sb4 S13 with Cu substituted by various transition metals (*Tr* = Ni, Zn, Co, Fe, or Mn) (see **Figure 2**). In agreement with the aforementioned simple ionic model, all these quaternary tetrahedrites exhibit semiconducting‐like properties characterized by an activated‐like temperature dependence of the electrical resistivity and high thermopower values. Further, all samples display extremely low thermal conductivity values of the order of 0.4 W m−1 K−1 at 300 K regardless of the nature of the transition metal. However, although this study has demonstrated that a semiconducting state can be achieved thanks to substitution on the Cu site, the too high electrical resistivity values measured preclude achieving high *ZT* values. In order to optimize the thermoelectric properties, it thus appears necessary to adjust the concentration of the transition metal to optimize the hole concentration and hence, the power factor. This strategy was at the core of the study reported by Lu et al. [16] who reported high‐temperature transport properties measurements on the tetrahedrites Cu12₋*<sup>x</sup>* Fe*<sup>x</sup>* Sb4 S13 and Cu12₋*<sup>x</sup>* Zn<sup>x</sup> Sb4 S13. This investigation has demonstrated for the first time that high thermoelectric performances could be achieved around 700 K with maximum *ZT* values of 0.8 for the composi‐ tion Cu11.5Fe0.5Sb4 S13.

structure has been described in the *P*4 space group using a supercell model 2 2 *a ac* × × . Owing to the high number of atomic position parameters to be refined (83), the crystal struc‐

Kitagawa et al. [29] further investigated the metal‐to‐insulator transition through measure‐ ments of the electrical resistivity and magnetic susceptibility at high pressures (up to 4.06 GPa) and of the 63Cu‐NMR spectra. The results evidence a transition from a paramagnetic bad metal to a nonmagnetic insulating state below 85 K at ambient pressure. The nonmagnetic ground state evolves toward a metallic state under pressure. Tanaka et al. [30] further investi‐ gated the pressure dependence of this transition as well as its evolution upon substituting As

**Figure 3.** (Panel a) Powder X‐ray diffraction pattern collected upon cooling across the 85 K phase transition in Cu12Sb4

The appearance of additional Bragg reflections (Panel b) is indicative of the cubic‐to‐tetragonal structural transition that accompanies the metal‐insulator transition. Reproduced **Figure 1** with permission from May et al. [28]. Copyright 2016

pressed under pressure. The substitution of As for Sb that decreases the unit cell volume acts

similarly and supresses the transition for relatively low substitution levels (*x* ≤ 0.5).

Sb4

S13). In agreement with the study of Kitagawa et al., the transition is sup‐

S13, Suekuni et al. [15] have also reported the transport prop‐

S13 with Cu substituted by various transition metals

S13.

for Sb (Cu12Sb4₋*<sup>x</sup>*

As*<sup>x</sup>*

by the American Physical Society. DOI: 10.1103/PhysRevB.93.064104.

In their initial study on Cu12Sb4

erties of several tetrahedrites Cu10*Tr*<sup>2</sup>

ture could not be entirely solved and remains to be determined in future studies.

76 Thermoelectrics for Power Generation - A Look at Trends in the Technology

These encouraging results led other groups to investigate in detail the influence of several tran‐ sition metals on the crystal structure and the high‐temperature thermoelectric properties [31– 41]. All these studies have confirmed the main traits of these compounds, i.e., a favorable combination of intrinsically extremely low thermal conductivity values and semiconducting‐ like electrical properties that can be tuned by varying the concentration of the substituting element. Peak *ZT* values ranging between 0.7 and 0.9 around 700 K were achieved in Ni‐, Co‐, or Mn‐substituted tetrahedrites. The highest *ZT* value of 1.1 at 575 K has been reported by Heo et al. [33] in Mn‐substituted tetrahedrites. This value, not reproduced independently so far to the best of our knowledge, mainly originates from thermal conductivity values twice lower than usually measured in these materials. Further investigations seem necessary before drawing a definitive conclusion on the validity of this high value.

Lu et al. [39] explored the possibility to substitute Te for Sb and showed that Te also pro‐ vides additional electrons that enable optimizing the power factor. As a result, a maximum *ZT* value of 0.92 at 723 K has been achieved for the composition Cu12Sb3 TeS13. Bouyrie et al. [38] further extended these investigations and synthesized Te‐containing tetrahedrites by considering two different synthetic routes: using precursor compounds (CuS, Sb<sup>2</sup> S3 , and Te) and from direct reaction of pure elemental powders, both syntheses being performed in evacuated and sealed silica tubes. Surprisingly, the results have evidenced that both routes are not strictly equivalent indicating that the final chemical compositions could be sensitive to the synthesis conditions used. The differences between the two series of samples was revealed by significantly higher lattice parameters for Te‐concentrations below *x* = 1.5 in the series of samples prepared from precursors (**Figure 4**).

In the series of samples synthesized from direct reaction of the elements, the lattice param‐ eter monotonically increases in a linear manner with increasing the Te‐content. While this difference does not seem to affect the thermoelectric performances at high temperatures, the measurements of the low‐temperature transport properties showed that these quaternary tetrahedrites undergo an exsolution process at 250 K [42]. This phenomenon has a drastic influence on the transport properties and more particularly on the thermal transport. Below the exsolution temperature, the lattice thermal conductivity drops significantly by 40% reach‐ ing values as low as 0.25 W m−1 K−1 around 200 K (**Figure 5**). This behavior, which seems to be tied to the large lattice parameters of these samples, is not present in the series of samples prepared by direct reaction of the elements. The exact origin of these differences is not yet set‐ tled and requires further investigations. In addition, low‐temperature transmission electron microscopy experiments on the Te‐containing tetrahedrites would be helpful in determining the microstructure and perhaps the chemical composition of the two exsolved phases.

**Figure 4.** Lattice parameter *a* as a function of the actual Te content *x* for the series of samples prepared from precursors (a) and directly from reaction of elemental powders (b). As a reference, the lattice parameter of the ternary compound Cu12Sb4 S13 (filled blue square) has been added. Reproduced from Ref. [38] with permission from The Royal Society of Chemistry.

**Figure 5.** Temperature dependence of the total thermal conductivity for the samples prepared from precursors (a) and from reaction of elemental powders (b). For the first series, the exsolution process results in a significant drop in the thermal conductivity values near 250 K (panel a). Reprinted (adapted) with permission from Bouyrie et al. [42]. Copyright 2015 by the American Chemical Society.

The possibility to substitute on the S site has only been recently considered by Lu et al. [43] who reported a detailed study on the Cu12Sb4 S13₋*<sup>x</sup>* Se*<sup>x</sup>* tetrahedrites. Although a maximum *ZT* value of 0.9 was achieved for *x* = 1, these authors have shown that the presence of selenium tends to result in phase separation yielding samples with rather poor chemical homogeneity.

While all these studies focused on the influence of a single isovalent or aliovalent substitution on the thermoelectric properties, only few works have been devoted so far to double substitu‐ tions. Lu et al. [40] have extended their investigations to double‐substituted tetrahedrites with Ni and Zn substituting for Cu. These authors have shown that this combination of elements results in higher thermoelectric performances with a peak *ZT* value of 1 at 700 K. Of note, this increase was mainly due to increased thermopower values while maintaining the electrical resistivity to relatively low values. These results suggest that judicious combinations of ele‐ ments substituting for Cu can lead to improved thermoelectric properties. Following these ideas, Bouyrie et al. [41, 44] have investigated double substitutions on both the Cu and Sb sites with Co and Te, respectively. The presence of Co and Te did not result in enhanced thermo‐ electric performances with respect to the single‐substituted compounds with a maximum *ZT* value of 0.8 at 673 K achieved in Cu11.47Co0.82Sb3.78Te0.41S13.

## **4. Thermal properties**

the exsolution temperature, the lattice thermal conductivity drops significantly by 40% reach‐ ing values as low as 0.25 W m−1 K−1 around 200 K (**Figure 5**). This behavior, which seems to be tied to the large lattice parameters of these samples, is not present in the series of samples prepared by direct reaction of the elements. The exact origin of these differences is not yet set‐ tled and requires further investigations. In addition, low‐temperature transmission electron microscopy experiments on the Te‐containing tetrahedrites would be helpful in determining the microstructure and perhaps the chemical composition of the two exsolved phases.

78 Thermoelectrics for Power Generation - A Look at Trends in the Technology

**Figure 4.** Lattice parameter *a* as a function of the actual Te content *x* for the series of samples prepared from precursors (a) and directly from reaction of elemental powders (b). As a reference, the lattice parameter of the ternary compound Cu12Sb4

**Figure 5.** Temperature dependence of the total thermal conductivity for the samples prepared from precursors (a) and from reaction of elemental powders (b). For the first series, the exsolution process results in a significant drop in the thermal conductivity values near 250 K (panel a). Reprinted (adapted) with permission from Bouyrie et al. [42].

Copyright 2015 by the American Chemical Society.

(filled blue square) has been added. Reproduced from Ref. [38] with permission from The Royal Society of Chemistry.

S13

In addition to being one of the key ingredients that leads to high *ZT* values, the extremely low lattice thermal conductivity of tetrahedrites is a remarkable property on its own. Both the values measured and the temperature dependence of the lattice thermal conductivity are reminiscent to those observed in amorphous systems (**Figure 6**) [45].

**Figure 6.** Temperature dependence of the total thermal conductivity of the tetrahedrite Cu10Zn<sup>2</sup> Sb4 S13 and of the colusite Cu23Zn<sup>3</sup> V2 Sn6 S32. The temperature dependence observed in the tetrahedrite below 1 K is similar to that observed in glassy SiO2 . Copyright 2015 by the Physical Society of Japan (Suekuni et al. [45]).

The large and anisotropic thermal displacement parameters of the Cu2 atoms had been thought to play a major role in disrupting efficiently the heat‐carrying acoustic waves. A detailed study of the lattice dynamics of tetrahedrites has been undertaken recently using a combination of inelastic neutron scattering on poly‐ and single‐crystalline tetrahedrites [46]. The conventional temperature dependence of the lattice thermal conductivity in the Cu‐deficient tetrahedrite Cu10Te4 S13 offered an interesting experimental platform to unveil the microscopic mechanisms responsible for the low, glass‐like thermal conductivity of tetrahedrites (**Figure 7**).

**Figure 7.** Temperature dependence of the total thermal conductivity of the tetrahedrites Cu12Sb2 Te2 S13 (red filled circles) and Cu10Te4 S13 (blue filled squares). Adapted from Ref. [46] with permission from the PCCP Owner Societies.

Bouyrie et al. [46] carried out a comparison study between this compound and the tetrahe‐ drite Cu12Sb2 Te2 S13 that behaves as a glassy system. Despite adopting the same crystal struc‐ ture, the contrast between the thermal transports in these compounds suggests that distinct microscopic mechanisms are at play.

A first important difference between these two compounds was found in the temperature dependence of the ADPs of the Cu2 atoms investigated by laboratory X‐ray diffraction on single crystals. The ADPs inferred in Cu10Te4 S13 were nearly three times smaller than those observed in Cu12Sb2 Te2 S13 providing a first experimental hint of the direct link between the thermal vibrations of the Cu2 atoms and the lattice thermal conductivity. Further decisive evidences were delivered by inelastic neutron scattering and Raman spectroscopy performed on polycrystalline samples of Cu10Te4 S13 and Cu12Sb2 Te2 S13 between 2 and 500 K. The results showed the presence of an excess of vibrational density of states at low energies in Cu12Sb2 Te2 S13, which is clearly absent in the isostructural compound Cu10Te4 S13 (**Figure 8**). This finding is con‐ sistent with recent INS measurements performed by May et al. [28] on the ternary compound Cu12Sb4 S13. The temperature dependence of this low‐energy excess of vibrational states further indicates that this excess can be unambiguously attributed to the thermal vibrations of the Cu2 atoms. Upon cooling, this excess experiences a strong renormalization of its characteristic energy, which shifts significantly toward lower energies. This dependence, at odds with a con‐ ventional quasi‐harmonic behavior, indicates a strongly anharmonic character of this excess.

The large and anisotropic thermal displacement parameters of the Cu2 atoms had been thought to play a major role in disrupting efficiently the heat‐carrying acoustic waves. A detailed study of the lattice dynamics of tetrahedrites has been undertaken recently using a combination of inelastic neutron scattering on poly‐ and single‐crystalline tetrahedrites [46]. The conventional temperature dependence of the lattice thermal conductivity in the Cu‐deficient tetrahedrite

Bouyrie et al. [46] carried out a comparison study between this compound and the tetrahe‐

S13 (blue filled squares). Adapted from Ref. [46] with permission from the PCCP Owner Societies.

**Figure 7.** Temperature dependence of the total thermal conductivity of the tetrahedrites Cu12Sb2

ture, the contrast between the thermal transports in these compounds suggests that distinct

A first important difference between these two compounds was found in the temperature dependence of the ADPs of the Cu2 atoms investigated by laboratory X‐ray diffraction on

thermal vibrations of the Cu2 atoms and the lattice thermal conductivity. Further decisive evidences were delivered by inelastic neutron scattering and Raman spectroscopy performed

sistent with recent INS measurements performed by May et al. [28] on the ternary compound

S13. The temperature dependence of this low‐energy excess of vibrational states further indicates that this excess can be unambiguously attributed to the thermal vibrations of the

S13 and Cu12Sb2

showed the presence of an excess of vibrational density of states at low energies in Cu12Sb2

S13 that behaves as a glassy system. Despite adopting the same crystal struc‐

S13 providing a first experimental hint of the direct link between the

Te2

S13 were nearly three times smaller than those

S13 between 2 and 500 K. The results

Te2

S13 (red filled circles)

S13 (**Figure 8**). This finding is con‐

Te2 S13,

responsible for the low, glass‐like thermal conductivity of tetrahedrites (**Figure 7**).

80 Thermoelectrics for Power Generation - A Look at Trends in the Technology

S13 offered an interesting experimental platform to unveil the microscopic mechanisms

Cu10Te4

drite Cu12Sb2

and Cu10Te4

observed in Cu12Sb2

Cu12Sb4

Te2

microscopic mechanisms are at play.

single crystals. The ADPs inferred in Cu10Te4

which is clearly absent in the isostructural compound Cu10Te4

Te2

on polycrystalline samples of Cu10Te4

**Figure 8.** (a) Generalized phonon density of states measured at room temperature on the tetrahedrites Cu12Sb2 Te2 S13 (red filled circles) and Cu10Te4 S13 (blue filled squares). A clear excess at low energies is present in Cu12Sb2 Te2 S13. (b) Raman spectra of Cu12Sb2 Te2 S13 (red) and Cu10Te4 S13 (blue) measured at the Stokes and anti‐Stokes line. Reproduced from Ref. [46] with permission from the PCCP Owner Societies.

INS measurements performed on natural, single‐crystalline specimen further shed light on the role played by this excess on the lattice thermal conductivity [46]. These experiments enable to directly probe the dispersion of transverse acoustic phonons and the optical branch associated with the thermal vibrations of the Cu2 atoms. The low‐energy optical branch strongly limits the phase space over which the acoustic phonon branch disperses (**Figure 9**). This strong limitation is accompanied by a drastic suppression of their intensity. The presence of this low‐energy optical mode has two main consequences: (i) the suppression of the acoustic pho‐ non states that are the main heat carriers and (ii) the presence of a novel channel of Umklapp processes that remain active even at low temperatures. The first of these two consequences naturally explains the very low lattice thermal conductivity values measured in tetrahedrites, while the second consequence explains the absence of an Umklapp peak at low temperatures in Cu12Sb2 Te2 S13 suppressed by active Umklapp processes. The lack of this excess in Cu10Te4 S13 is thus at the origin of its higher lattice thermal conductivity values and the presence of the Umklapp peak centered at 25 K.

**Figure 9.** (a) Mapping of the transverse acoustic phonon propagating along the (011) direction and polarized along the (100) direction measured in a natural specimen. (b) Raw data of constant energy scan performed at the constant wave vector *q*<sup>1</sup> = 0.91 Å‐1. The black solid line corresponds to the fit of the measured scattering profile using damped harmonic oscillator for acoustic phonons (ac) and Gaussian functions for the low‐lying optical excitations. Reproduced from Ref. [46] with permission from the PCCP Owner Societies.

The origin of the strong anharmonicity has been attributed to the active 5*s* lone pair electrons of the Sb atoms located at either side of the Cu2 atoms. Electronic band structure calculations have suggested that the lone pair electrons are inactive in Cu10Te4 S13. A study of Wei et al. [47] based on a combination of theoretical calculations with synchrotron X‐ray diffraction has fur‐ ther corroborated that the strong anharmonic potential felt by the Cu2 is linked to the lone pair electrons of the Sb atoms.

## **5. Scaling up tetrahedrite synthesis**

low‐energy optical mode has two main consequences: (i) the suppression of the acoustic pho‐ non states that are the main heat carriers and (ii) the presence of a novel channel of Umklapp processes that remain active even at low temperatures. The first of these two consequences naturally explains the very low lattice thermal conductivity values measured in tetrahedrites, while the second consequence explains the absence of an Umklapp peak at low temperatures

is thus at the origin of its higher lattice thermal conductivity values and the presence of the

**Figure 9.** (a) Mapping of the transverse acoustic phonon propagating along the (011) direction and polarized along the (100) direction measured in a natural specimen. (b) Raw data of constant energy scan performed at the constant

harmonic oscillator for acoustic phonons (ac) and Gaussian functions for the low‐lying optical excitations. Reproduced

= 0.91 Å‐1. The black solid line corresponds to the fit of the measured scattering profile using damped

S13 suppressed by active Umklapp processes. The lack of this excess in Cu10Te4

S13

in Cu12Sb2

wave vector *q*<sup>1</sup>

from Ref. [46] with permission from the PCCP Owner Societies.

Te2

Umklapp peak centered at 25 K.

82 Thermoelectrics for Power Generation - A Look at Trends in the Technology

Owing to their interesting thermoelectric properties, tetrahedrites hold promise to be used as *p*‐type legs in thermoelectric generators. Yet, any widespread thermoelectric application would require fast, easily scalable, and cost‐efficient synthetic methods to produce these materials in high yield. Several studies have dealt with these issues and focused either on the direct use of natural ore to decrease the cost and the time of preparation or on different synthetic routes faster than conventional powder metallurgy techniques. In this regard, James et al. [48] have recently developed a solvothermal route to produce synthetic tetrahedrites without using long‐chain ligands that usually leads to a strong increase in the electrical resis‐ tivity due to difficulties in separating them from the targeted compound. Upon optimizing their process, these authors successfully synthesized phase‐pure tetrahedrites within only one day at moderate temperatures (around 150°C). Of note, this fast synthesis process was not at the expense of the thermoelectric performances since the tetrahedrites prepared by solvothermal and solid‐state synthesis methods showed similar *ZT* values.

Barbier et al. [49] have investigated another processing technique based on a combination of high‐energy ball milling of stoichiometric mixtures of elemental powders and spark plasma sintering. This study, performed on the composition Cu10.4Ni1.6Sb4 S13, has demonstrated that pure, highly dense samples of this tetrahedrite can be synthesized over a reduced period of time (estimated to eight times shorter by the authors) with respect to conventional solid‐state synthesis. Similarly to the study of James et al. [48], the thermoelectric performances were not adversely affected and were comparable to those prepared by conventional methods in prior studies with a peak *ZT* value of 0.8 at 700 K.

Besides these two direct processes, Gonçalves et al. [50] used a different approach to synthe‐ size within less than one day a tetrahedrite phase. This approach relies on the preparation of a glass of composition Cu12Sb3.6Bi0.4S10Se3 by melt‐spinning, i.e., fast quenching of the melt on a fast‐rotating copper wheel, and subjected to controlled heat treatments to crystallize the targeted tetrahedrite phase. Within this strategy, both Se and Bi were introduced as vitrify‐ ing and nucleation agents to produce a homogeneous glassy sample. The authors further showed that annealing treatments at temperatures close to the crystallization peaks (around 200°C) leads to the crystallization of a tetrahedrite phase. Analysis of the chemical composi‐ tion revealed the presence of Se partially substituting S, while Bi could not be detected within the experimental uncertainty of the instruments used. Thermopower and electrical resistivity measurements resulted in room‐temperature power factors that are close to those measured in the ternary Cu12Sb4 S13 tetrahedrite (~400 μW m−1 K−2). Further investigations on the thermal conductivity of these samples will be essential in determining whether high thermoelectric performances can be equally achieved by this technique.

Finally, a radically different approach has been used by Lu et al. [31] who synthesized "com‐ posite" tetrahedrites from a mixture of synthetic and natural samples. Achieving high *ZT* values in such composite system would significantly reduce the time and cost required to synthesize synthetic specimens. While tetrahedrite minerals exhibit too high electrical resis‐ tivity to be viable thermoelectric materials, mixing ore with a fraction of synthetic tetrahedrite exhibiting metallic‐like properties were shown to result in maximum *ZT* values of 1.0 at 700 K. The authors used two ores of composition Cu10.5Fe1.5As3.6Sb0.4S13 and Cu9.7Zn1.9Fe0.4As<sup>4</sup> S13, i.e., two As‐rich tetrahedrites which are then named tennantites. These ores were mixed with the ternary tetrahedrite Cu12Sb4 S13 that behaves as a metal by ball milling. Remarkably, the powder X‐ray diffraction pattern collected after ball‐milling showed only one single tetrahe‐ drite phase. This process thus provides an interesting and time‐efficient way of producing single‐phased tetrahedrite displaying high thermoelectric performances. Further investiga‐ tions aiming at determining the influence on the chemical composition of the mineral on the thermoelectric properties will be interesting to undertake. In this regard, a preliminary study carried out on minerals from various geographical origins has shown that all of them show semiconducting‐like properties despite differences in their chemical composition [51].

## **6. Conclusion**

Progress in synthesizing tetrahedrites in laboratory environment and in understanding their transport properties have significantly advanced over the last 4 years, thanks to both experi‐ mental and theoretical efforts. Tetrahedrites possess transport properties not only interest‐ ing for thermoelectric applications but also for fundamental reasons. Subtle differences in their chemical compositions have a sizeable influence on their transport properties thereby adding another degree of freedom to study the interplay between their crystallographic, chemical, and transport properties. This is one of the main reasons why these materials have attracted attention in thermoelectricity yielding several *p*‐type materials with *ZT* values rang‐ ing between 0.7 and 1.0 at 700 K. These high values originate from a favorable combination of semiconducting‐like electronic properties and extremely low lattice thermal conductiv‐ ity. The electronic properties can be tuned by substituting on the three possible sites, all of them resulting in either a control of the hole concentration or a favorable modification of the electronic band structure. Spectroscopic tools used to investigate the lattice dynamics of these materials have unveiled the presence of strong anharmonicity whose exact origin seems to be tied to the lone pair electrons revolving around the Sb atoms.

On the application side, several studies have successfully speed up the synthetic procedures used to obtain phase‐pure tetrahedrites. Combined with the possibility to mix synthetic tetra‐ hedrites with natural ores, these techniques may lead to the production in high yield of low‐ cost efficient tetrahedrites for thermoelectric applications. Despite proved to be feasible, these "composite" tetrahedrites have so far received little attention and future research will lead to an improved knowledge of their transport properties and of the influence on the chemical composition of the ore on the thermoelectric properties of the composite.

## **Author details**

conductivity of these samples will be essential in determining whether high thermoelectric

Finally, a radically different approach has been used by Lu et al. [31] who synthesized "com‐ posite" tetrahedrites from a mixture of synthetic and natural samples. Achieving high *ZT* values in such composite system would significantly reduce the time and cost required to synthesize synthetic specimens. While tetrahedrite minerals exhibit too high electrical resis‐ tivity to be viable thermoelectric materials, mixing ore with a fraction of synthetic tetrahedrite exhibiting metallic‐like properties were shown to result in maximum *ZT* values of 1.0 at 700 K. The authors used two ores of composition Cu10.5Fe1.5As3.6Sb0.4S13 and Cu9.7Zn1.9Fe0.4As<sup>4</sup>

i.e., two As‐rich tetrahedrites which are then named tennantites. These ores were mixed with

powder X‐ray diffraction pattern collected after ball‐milling showed only one single tetrahe‐ drite phase. This process thus provides an interesting and time‐efficient way of producing single‐phased tetrahedrite displaying high thermoelectric performances. Further investiga‐ tions aiming at determining the influence on the chemical composition of the mineral on the thermoelectric properties will be interesting to undertake. In this regard, a preliminary study carried out on minerals from various geographical origins has shown that all of them show

semiconducting‐like properties despite differences in their chemical composition [51].

tied to the lone pair electrons revolving around the Sb atoms.

composition of the ore on the thermoelectric properties of the composite.

Progress in synthesizing tetrahedrites in laboratory environment and in understanding their transport properties have significantly advanced over the last 4 years, thanks to both experi‐ mental and theoretical efforts. Tetrahedrites possess transport properties not only interest‐ ing for thermoelectric applications but also for fundamental reasons. Subtle differences in their chemical compositions have a sizeable influence on their transport properties thereby adding another degree of freedom to study the interplay between their crystallographic, chemical, and transport properties. This is one of the main reasons why these materials have attracted attention in thermoelectricity yielding several *p*‐type materials with *ZT* values rang‐ ing between 0.7 and 1.0 at 700 K. These high values originate from a favorable combination of semiconducting‐like electronic properties and extremely low lattice thermal conductiv‐ ity. The electronic properties can be tuned by substituting on the three possible sites, all of them resulting in either a control of the hole concentration or a favorable modification of the electronic band structure. Spectroscopic tools used to investigate the lattice dynamics of these materials have unveiled the presence of strong anharmonicity whose exact origin seems to be

On the application side, several studies have successfully speed up the synthetic procedures used to obtain phase‐pure tetrahedrites. Combined with the possibility to mix synthetic tetra‐ hedrites with natural ores, these techniques may lead to the production in high yield of low‐ cost efficient tetrahedrites for thermoelectric applications. Despite proved to be feasible, these "composite" tetrahedrites have so far received little attention and future research will lead to an improved knowledge of their transport properties and of the influence on the chemical

S13 that behaves as a metal by ball milling. Remarkably, the

performances can be equally achieved by this technique.

84 Thermoelectrics for Power Generation - A Look at Trends in the Technology

the ternary tetrahedrite Cu12Sb4

**6. Conclusion**

Christophe Candolfi, Yohan Bouyrie, Selma Sassi, Anne Dauscher and Bertrand Lenoir\*

\*Address all correspondence to: bertrand.lenoir@univ‐lorraine.fr

Institut Jean Lamour, University of Lorraine, Nancy, France

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88 Thermoelectrics for Power Generation - A Look at Trends in the Technology


#### **Thermoelectric Effect and Application of Organic Semiconductors** Thermoelectric Effect and Application of Organic Semiconductors

Nianduan Lu, Ling Li and Ming Liu Nianduan Lu, Ling Li and Ming Liu

Additional information is available at the end of the chapter Additional information is available at the end of the chapter

http://dx.doi.org/10.5772/65872

#### Abstract

Human development and society progress require solving many pressing issues, including sustainable energy production and environmental conservation. Thermoelectric power generation looks like promising opportunity converting huge heat from the sun and waste heat from industrial sector, housing appliances and infrastructure and automobile and other fuel combustion exhaust directly to electrical energy. Thermoelectric power generation will be of high demand, when technology will be affordable, providing low price, high conversion efficiency, reliability, easy applicability and advanced ecological properties of end products. In this context, organic thermoelectric materials attract great interest caused by non-scarcity of raw materials, non-toxicity, potentially low costs in high-scale production, low thermal conductivity and wide capabilities to control thermoelectric properties. In this chapter, we focus mainly on thermoelectric effect in several organic semiconductors, both crystalline and disordered. We present theory of some transport phenomena determining thermoelectric properties of organic semiconductors, including general expression of thermoelectric effect, percolation theory of Seebeck coefficient, hybrid model of Seebeck coefficient, Monte Carlo simulation and first-principle theory. Finally, a future outlook of this field is briefly discussed.

Keywords: organic semiconductor, thermoelectric effect, theoretical model

### 1. Introduction

#### 1.1. Organic semiconductors

#### 1.1.1. History

Organic semiconductors have revealed promising performance and received considerable attentions due to large area, low-end, lightweight and flexible electronics applications [1]. Currently, organic semiconductors have appealed for a broad range of devices including sensors, solar cells, light-emitting devices and thermoelectric application [2, 3]. Historically, organic materials were

© The Author(s). Licensee InTech. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, © 2016 The Author(s). Licensee InTech. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

distribution, and eproduction in any medium, provided the original work is properly cited.

viewed as insulators with applications commonly seen in inactive packaging, coating, containers, moldings and so on. The earliest research on electrical behavior of organic materials dates back to the 1960s [4]. In the 1970s, photoconductive organic materials were recognized and were used in solar cells and xerographic sensors, etc. [5]. In about the same age, organic thermoelectric materials, such as conducting polymers, had been investigated [6], although First European Conference on Thermoelectric in 1988 had no mention of organic materials in their proceeding. Since proof of concept for organic semiconductors occurred in the 1980s, remarkable development of organic semiconductors has promoted improvement of performance that maybe competitive with amorphous silicon (a-Si), increasing their suitability for commercial applications [7]. Appearance of conductive polymers in the late 1970s, and of conjugated semiconductors and photoemission polymers in the 1980s, greatly accelerated development in the field of organic electronics [8]. Polyacetylene was one of the earliest polymer materials known to be potential as conducting electricity [9], and one could find that oxidative dopant with iodine could greatly increase conductivity by 12 orders of magnitude [10]. This discovery and development of highly conductive organic materials were attributed to three scientists: Alan J. Heeger, Alan G. MacDiarmid and Hideki Shirakawa, who were jointly awarded the Nobel Prize in Chemistry in 2000 for their discovery in 1977 and development of oxidized, iodine-doped polyacetylene. After that, plenty of organic semiconductor materials were synthesized, and research field of organic electronics matured over the years from proof-of-principle phase into major interdisciplinary research area, involving physics, chemistry and other disciplines. As important branch of organic semiconductors, in the past decade, organic thermoelectric effect has received much attention. Figure 1 shows Thomson Reuters Web of Science publication report for the topic "organic thermoelectric Seebeck effect" for the last 16 years [3]. Research interest in organic thermoeletrics Seebeck effect has been growing remarkably over the last 5 years.

Figure 1. Thomson Reuters web of science publication report for the topic "organic thermoelectric Seebeck effect" from 2000 to 2015.

#### 1.1.2. Structure

Organic semiconductors can be usually classified as two types: crystalline and amorphous materials, in terms of crystalline fraction (also static disorder) [3, 11].

All organic semiconductor materials are generally characterized by weak van der Waals bonding, which leads to weak intermolecular interactions. This weak coupling of molecules would induce weak interaction energy to give narrow electronic bandwidths. Otherwise, existing narrow electronic bands will be eliminated by statistical variation of width in energy level distribution of molecules, which, hence, creates Anderson charge localization. For crystalline organic semiconductor materials, localization of charge carriers is attributed to intermolecular thermal fluctuations (dynamic disorder), at which size of localized wave function is expected to be on the order of molecular spacing and charge carrier transport in this weakly localized field is treated as "intermediate hopping transport regime" [12]. Because of high density of crystal imperfections in disordered organic semiconductors, such as impurities, grain boundaries, dangling bonds and periodicity loss of crystal, localization of charge carriers is attributed to spatial and energetic disorder due to weak intermolecular interactions [13]. Disorder in organic semiconductors results in basic charge transport mechanism, common for very rich variety of such materials [14], incoherent tunneling (hopping) of charge carriers between localized states [15].

#### 1.2. Charge transport mechanism in organic semiconductors

#### 1.2.1. Dispersive transport

viewed as insulators with applications commonly seen in inactive packaging, coating, containers, moldings and so on. The earliest research on electrical behavior of organic materials dates back to the 1960s [4]. In the 1970s, photoconductive organic materials were recognized and were used in solar cells and xerographic sensors, etc. [5]. In about the same age, organic thermoelectric materials, such as conducting polymers, had been investigated [6], although First European Conference on Thermoelectric in 1988 had no mention of organic materials in their proceeding. Since proof of concept for organic semiconductors occurred in the 1980s, remarkable development of organic semiconductors has promoted improvement of performance that maybe competitive with amorphous silicon (a-Si), increasing their suitability for commercial applications [7]. Appearance of conductive polymers in the late 1970s, and of conjugated semiconductors and photoemission polymers in the 1980s, greatly accelerated development in the field of organic electronics [8]. Polyacetylene was one of the earliest polymer materials known to be potential as conducting electricity [9], and one could find that oxidative dopant with iodine could greatly increase conductivity by 12 orders of magnitude [10]. This discovery and development of highly conductive organic materials were attributed to three scientists: Alan J. Heeger, Alan G. MacDiarmid and Hideki Shirakawa, who were jointly awarded the Nobel Prize in Chemistry in 2000 for their discovery in 1977 and development of oxidized, iodine-doped polyacetylene. After that, plenty of organic semiconductor materials were synthesized, and research field of organic electronics matured over the years from proof-of-principle phase into major interdisciplinary research area, involving physics, chemistry and other disciplines. As important branch of organic semiconductors, in the past decade, organic thermoelectric effect has received much attention. Figure 1 shows Thomson Reuters Web of Science publication report for the topic "organic thermoelectric Seebeck effect" for the last 16 years [3]. Research interest in organic thermoeletrics Seebeck effect has been

92 Thermoelectrics for Power Generation - A Look at Trends in the Technology

Organic semiconductors can be usually classified as two types: crystalline and amorphous

Figure 1. Thomson Reuters web of science publication report for the topic "organic thermoelectric Seebeck effect" from

materials, in terms of crystalline fraction (also static disorder) [3, 11].

growing remarkably over the last 5 years.

1.1.2. Structure

2000 to 2015.

Charge carriers are always slowing down during conduction processes in dispersive transport regime. It happens only when charge carriers' distribution is thermally nonequilibrium. In dispersive transport regime, energy fluctuations allow release (emission) of charge carrier captured by localized state (trap), when state (trap) becomes temporarily shallow during fluctuations [16]. Otherwise, charge carrier release time is strongly dependent on both temperature and energy. Charge carriers localized on shallow states are usually released before the states can change their energies noticeably. In contrast, charge carriers, always being trapped in energetically deeper and deeper states, have to perform longer and longer tunneling transitions to hop to the next destination site. As a result, temperature-dependent distribution of effective activation energies just follows the density of states (DOS) function within domain of shallow states, while these distributions appear to be very different for deep traps.

#### 1.2.2. Nearest-neighbor hopping

Transport in disordered organic semiconductors is generally characterized by charge carrier's localization and hopping transport mechanism [17]. Localized states, randomly distributed in energy and space, form discrete array of sites in hopping space. The most probable hop for charge carrier on site with particular energy is to the closest empty site, that is, to its nearest-neighbor site in hopping space. In conjunction with hopping probability rate, it gives mobility for carriers at this energy. In a word, nearest-neighbor hopping describes hopping regime, in which tunneling part of hopping rates in Eq. (1) referred as hopping rates of Miller-Abrahams is so much slower than energy contribution, that only the nearest neighbors are addressed in hops [18]:

$$\gamma\_{\vec{\eta}} = \nu\_0 \times \exp\left(-\mathsf{R}\right) = \nu\_0 \times \begin{cases} \exp\left(-2 \times \alpha \times \mathrm{R}\_{\vec{\eta}} - \frac{\mathsf{E}\_{\vec{\eta}} - \mathsf{E}\_i}{\mathsf{k} \cdot \mathsf{T}}\right) \\\ \exp\left(-2 \times \alpha \times \mathrm{R}\_{\vec{\eta}}\right), \quad \mathsf{E}\_{\vec{\eta}} - \mathsf{E}\_i < 0 \end{cases} , \qquad \mathsf{T}\_{\vec{\eta}} - \mathsf{E}\_i > 0, \tag{1}$$

where ν<sup>0</sup> is attempt-to-jump frequency, R is hopping range, α is inverse localized length describing extension of wave function of localized state, Rij is distance between site i and site j, Ei and Ej are energies of sites i and j, respectively. As long as charge carrier can find shallow and empty sites with energies below its current state, it will perform nearest-neighbor hopping to energetically lower sites, since in this case rates are limited by spatial tunneling distances only.

#### 1.2.3. Variable-range hopping

Variable-range hopping (VRH) theory was first proposed by Neville Mott in 1971 [19] and hence was called Mott VRH, which is model describing low temperature conduction in strongly disordered systems with localized states. VRH transport has characteristic temperature dependence of 3D electrical conductance:

$$
\sigma = \sigma\_0 \times \exp\left[-\left(\frac{T\_0}{T}\right)^{1/4}\right],\tag{2}
$$

here kBT<sup>0</sup> <sup>¼</sup> <sup>β</sup> <sup>g</sup>ðEf <sup>Þ</sup> · <sup>α</sup>3, <sup>σ</sup><sup>0</sup> is prefactor, <sup>α</sup><sup>−</sup><sup>1</sup> is localization length, kB is Boltzmann constant, <sup>g</sup>ðEf<sup>Þ</sup> is DOS function at Fermi energy Ef, and β is constant coefficient with value in interval 10.0–37.2 according to different theories.

For 3D electrical conductance, and in general for d-dimensions, VRH transport is expressed as:

$$
\sigma = \sigma\_0 \times \exp\left[-\left(\frac{T\_0}{T}\right)^{1/(d+1)}\right],\tag{3}
$$

here d is dimensionality.

#### 1.2.4. Multiple trapping and release theory

Multiple trapping and release theory assume that charge carrier transport occurs in extended states, and that most of charge carriers are trapped in localized states. Energy of localized state is separated from mobility edge energy. When localized state energy is slightly lower mobility edge, then localized state acts as shallow trap, from which charge carrier can be released (emitted) by thermal excitations. But, if that energy is far below mobility edge energy, then charge carrier cannot be thermally excited (emitted). In multiple trapping and release theory, total charge carriers' concentration ntotal is equal to sum of concentrations ne in extended states and in localized states as in Ref. [20]:

$$n\_{\text{total}} = n\_\epsilon + \int\_{-\infty}^{0} g(E)f(E)dE,\tag{4}$$

where fðEÞ is Fermi-Dirac distribution function.

## 2. Organic thermoelectric materials

where ν<sup>0</sup> is attempt-to-jump frequency, R is hopping range, α is inverse localized length describing extension of wave function of localized state, Rij is distance between site i and site j, Ei and Ej are energies of sites i and j, respectively. As long as charge carrier can find shallow and empty sites with energies below its current state, it will perform nearest-neighbor hopping to energetically lower sites, since in this case rates are limited by spatial tunneling distances

Variable-range hopping (VRH) theory was first proposed by Neville Mott in 1971 [19] and hence was called Mott VRH, which is model describing low temperature conduction in strongly disordered systems with localized states. VRH transport has characteristic tempera-

DOS function at Fermi energy Ef, and β is constant coefficient with value in interval 10.0–37.2

For 3D electrical conductance, and in general for d-dimensions, VRH transport is expressed

Multiple trapping and release theory assume that charge carrier transport occurs in extended states, and that most of charge carriers are trapped in localized states. Energy of localized state is separated from mobility edge energy. When localized state energy is slightly lower mobility edge, then localized state acts as shallow trap, from which charge carrier can be released (emitted) by thermal excitations. But, if that energy is far below mobility edge energy, then charge carrier cannot be thermally excited (emitted). In multiple trapping and release theory, total charge carriers' concentration ntotal is equal to sum of concentrations ne in extended states

> ð 0

−∞

T � �<sup>1</sup>=ðdþ1<sup>Þ</sup> " #

<sup>σ</sup> <sup>¼</sup> <sup>σ</sup><sup>0</sup> · exp <sup>−</sup> <sup>T</sup><sup>0</sup>

ntotal ¼ ne þ

T � �<sup>1</sup>=<sup>4</sup> " #

<sup>g</sup>ðEf <sup>Þ</sup> · <sup>α</sup>3, <sup>σ</sup><sup>0</sup> is prefactor, <sup>α</sup><sup>−</sup><sup>1</sup> is localization length, kB is Boltzmann constant, <sup>g</sup>ðEf<sup>Þ</sup> is

, (2)

, (3)

gðEÞfðEÞdE, (4)

<sup>σ</sup> <sup>¼</sup> <sup>σ</sup><sup>0</sup> · exp <sup>−</sup> <sup>T</sup><sup>0</sup>

only.

1.2.3. Variable-range hopping

here kBT<sup>0</sup> <sup>¼</sup> <sup>β</sup>

as:

according to different theories.

here d is dimensionality.

1.2.4. Multiple trapping and release theory

and in localized states as in Ref. [20]:

where fðEÞ is Fermi-Dirac distribution function.

ture dependence of 3D electrical conductance:

94 Thermoelectrics for Power Generation - A Look at Trends in the Technology

#### 2.1. Polymer-based thermoelectric materials

Polymers as thermoelectric materials recently have attracted much attention due to easy fabrication processes and low material cost [21, 22], as well as, low thermal conductivity, which is highly desirable for thermoelectric applications. Different types of polymers have been used in thermoelectric devices [23–25], such as polyaniline (PANI), poly(p-phenylenevinylene) (PPV), poly(3,4-ethylenedioxythiophene) (PEDOT), tosylate(tos), poly(styrenesulfonate) (PSS), and poly(2,5-dimethoxy phenylenevinylene) (PMeOPV), poly[2-methoxy-5-(2-ethylhexyloxy)- 1,4-phenylenevinylene] (MEHPPV) and poly(3-hexylthiophene-2,5-diyl) (P3HT). Figure 2 shows chemical structure of some polymers. These polymers are chosen as thermoelectric materials for their conductive nature. Takao Ishida's group has reported high power factor (PF) values of over 100 μW/(m K<sup>2</sup> ) on PEDOT films through chemical reduction with different chemicals in their review [25], as shown in Table 1.

Thermoelectric properties of 1,1,2,2-ethenetetrathiolate(ett)–metal coordination polymers poly [Ax(M–ett)] (A = Na, K; M = Ni, Cu) also have been studied, as shown in Figure 3a [26]. P-type poly[Cux(Cu–ett)] exhibited best ZT of 0.014 at 380 K with electrical conductivity of ~15 S/cm, Seebeck coefficient of 80 μV/K and thermal conductivity of 0.45 W/(m K); n-type poly[Kx(Ni– ett)] showed best ZT of 0.2 at 440 K with electrical conductivity of ~60 S/cm, Seebeck coefficient of 150 μV/K and thermal conductivity of 0.25 W/(m K). Otherwise, thermoelectric module based on p-type poly[Cux(Cu–ett)] and n-type poly[Nax(Ni–ett)] (i.e., ZT of 0.1 at 440 K) was built (Figure 3b and c ). More recently, Pipe et al. reported thermoelectric measurements of PEDOT: PSS with 5% of dimethylsulfoxide (DMSO) and ethylene glycol (EG) after submerging films in EG several times (from 0 to 450 min) [27]. Insulating polymer (PSS) is removed, and consequently, electrical conductivity and Seebeck coefficient increase simultaneously. ZT value of 0.42 reported in Pipe et al.'s work is the highest ever obtained for polymer until date.

Figure 2. Molecular structures of some typical polymers [23].


Table 1. Thermoelectric properties of polymer-based materials (tos: tosylate, and PSS: poly(stryrenesulfonate) [25].

Figure 3. (a) Synthetic route of poly[Ax(M-ett)]s, (b) module structure and (c) photograph of module and measurement system with a hot plane and cooling fan.

Although thermoelectric performance of organic semiconductors has been increased by using different fabricated methods or dopant, as compared with inorganic thermoelectric materials, organic thermoelectric materials still exhibit lower ZT so far. Nevertheless, researchers are making their great efforts in organic semiconductors instead of inorganic materials, due to several more advantages in organic thermoelectric materials, for example, the non-scarcity of raw materials, non-toxicity and large area applications.

#### 2.2. Small molecule-based thermoelectric materials

Currently, investigation of small molecule-based organic thermoelectric materials is lagging behind that of polymers-based organic materials. However, small molecule-based organic thermoelectric materials exhibit plenty of attractions. For example, small molecules are easier to be purified and crystallized and may be more feasible to achieve n-type conduction. Figure 4 shows chemical structures of some small molecules studied as organic thermoelectric materials [24].

As the benchmark of p-type organic semiconductors, pentacene is the best-known small molecule studied for organic thermoelectric applications. A remarkable attraction for pentacene is attributed to its high mobility up to 3 cm2 /V s in thin film transistors (TFT). Due to low charge carriers' concentration of pentacene in neutral state, appropriate doping treatment is critical to optimization of its thermoelectric properties. So far, F4TCNQ and iodine are efficient dopant for pentacene [24]. F4TCNQ is strong electron acceptor that is frequently used as p-type dopant in organic electronics [28]. Harada et al. have achieved maximum electrical conductivity of 4.1 +10−<sup>2</sup> S/cm and maximum PF of 0.16 μW/(m K2 ) by using dopant of 2.0 mol.%, as shown in Figure 5a. Furthermore, when thickness of pentacene layer was varied, electrical conductivity could be optimized, while Seebeck coefficient was unaffected (around 200 μV/K). Finally, maximum PF of 2.0 μW/(m K<sup>2</sup> ) was obtained in 6-nm-thick pentacene sample, as shown in Figure 5b. For using iodine dopant, Minakata et al. have achieved highest electrical conductivity of 60 S/cm with Seebeck coefficient in the range of 40–60 μV/K [29]. As a result, the highest PF is 13 μW/(m K<sup>2</sup> ), which is more than six times that of pentacene/F4TCNQ bilayer sample. In a word, as compared with polymer-based thermoelectric materials, small molecule-based materials are relatively less explored and need to put in more effort in the future.

Figure 4. Chemical structures of some small molecules studied as organic thermoelectric materials.

Although thermoelectric performance of organic semiconductors has been increased by using different fabricated methods or dopant, as compared with inorganic thermoelectric materials, organic thermoelectric materials still exhibit lower ZT so far. Nevertheless, researchers are making their great efforts in organic semiconductors instead of inorganic materials, due to several more advantages in organic thermoelectric materials, for example, the non-scarcity of

Figure 3. (a) Synthetic route of poly[Ax(M-ett)]s, (b) module structure and (c) photograph of module and measurement

Materials S (μV/K) PF (μW/m K2

96 Thermoelectrics for Power Generation - A Look at Trends in the Technology

PEDOT:PSS 22 47 0.1 PEDOT:tos (dedoped) 200 324 0.25 PEDOT:PSS 73 469 0.42 PEDOT:tos ~85 12,900 – PEDOT:tos 55 453 – PEDOT:BTFMS ~40 147 0.22 PEDOT:PSS (dedoped) ~50 112 0.093 PEDOT:PSS (dedoped) 43 116 0.2 PEDOT:PSS 65 355 ~0.3

Table 1. Thermoelectric properties of polymer-based materials (tos: tosylate, and PSS: poly(stryrenesulfonate) [25].

) ZT

raw materials, non-toxicity and large area applications.

system with a hot plane and cooling fan.

Figure 5. Thermoelectric properties of pentacene samples doped by (a) co-evaporation with F4TCNQ and (b) forming pentacene/F4TCNQ bilayer structures.

#### 3. Thermoelectric transport theory of organic semiconductors

#### 3.1. General expression of thermoelectric effect

Since organic semiconductors consist of amorphous and crystal structure, theoretical model of charge carrier thermoelectric transport should be more general. Derivation of present expression of thermoelectric effect was inspired by work of Cutler and Mott [30]. Basic expression was in terms of electrical conductivity σ. Based on definition of Cutler and Mott, for hopping system in disordered lattice at zero and finite temperature, σ was expressed as:

$$
\sigma = -\int \left[ \sigma\_E \frac{\partial f}{\partial E} \right] dE. \tag{5}
$$

Otherwise, one can start out by writing electrical conductivity as integral over single states neglecting electron correlation effects [31]:

$$
\sigma = e \int g(E) \mu(E) f(E) [1 - f(E)] dE. \tag{6}
$$

Then, energy dependence of electrical conductivity is written as:

$$
\sigma(E) = \text{eg}(E)\mu(E)f(E)[1-f(E)],\tag{7}
$$

here gðEÞ is density of states, μðEÞ is mobility, and fðEÞ is Fermi-Dirac distribution function. Seebeck coefficient S is related to Peltier coefficient Π as follows:

$$S = \frac{\Pi}{T}.\tag{8}$$

Peltier coefficient Π is energy carried by electrons per unit charge. Carried energy is characterized connected with Fermi energy Ef. Contribution to Π of each electron is in proportion to its correlative contribution to total conduction. Weighting factor for electrons in interval dE at energy E is thus <sup>σ</sup>ðE<sup>Þ</sup> <sup>σ</sup> dE, with energy dependence of conductivity σðEÞ as Eq. (7). Therefore, one can obtain general expression of Seebeck coefficient as [32]:

$$S = \frac{-k\_B}{e} \int \left(\frac{E - E\_f}{k\_B T}\right) \frac{\sigma(E)}{\sigma} dE. \tag{9}$$

To distinguish crystalline solids, general Seebeck coefficient also can be defined as shape of transport energy with mean energy of conducting charge carriers as in Ref. [33]:

$$S = -\frac{1}{\varepsilon T} \times (E\_{trans} - E\_f),\tag{10}$$

where transport energy Etrans is defined as averaged energy weighted by electrical conductivity distribution:

$$E\_{\text{trans}} = \int E \frac{\sigma(E)}{\sigma} dE. \tag{11}$$

Usual expression of Seebeck coefficient was used early in doped organic materials by Roland Schmechel in 2003 [33]. In Schmechel's article, a detailed method to complex hopping transport in doped system (p-doped zinc-phthalocyanine) was proposed and used to discuss experimental data on effect of doping on conductivity, mobility and Seebeck coefficient.

#### 3.2. Percolation theory of Seebeck coefficient

3. Thermoelectric transport theory of organic semiconductors

system in disordered lattice at zero and finite temperature, σ was expressed as:

σ ¼ e ð

Then, energy dependence of electrical conductivity is written as:

Seebeck coefficient S is related to Peltier coefficient Π as follows:

σ ¼ − ð σE ∂f ∂E � �

Since organic semiconductors consist of amorphous and crystal structure, theoretical model of charge carrier thermoelectric transport should be more general. Derivation of present expression of thermoelectric effect was inspired by work of Cutler and Mott [30]. Basic expression was in terms of electrical conductivity σ. Based on definition of Cutler and Mott, for hopping

Figure 5. Thermoelectric properties of pentacene samples doped by (a) co-evaporation with F4TCNQ and (b) forming

Otherwise, one can start out by writing electrical conductivity as integral over single states

here gðEÞ is density of states, μðEÞ is mobility, and fðEÞ is Fermi-Dirac distribution function.

<sup>S</sup> <sup>¼</sup> <sup>Π</sup>

Peltier coefficient Π is energy carried by electrons per unit charge. Carried energy is characterized connected with Fermi energy Ef. Contribution to Π of each electron is in proportion to its

dE: (5)

gðEÞμðEÞfðEÞ½1−fðEÞ�dE: (6)

<sup>T</sup> : (8)

σðEÞ ¼ egðEÞμðEÞfðEÞ½1−fðEÞ�, (7)

3.1. General expression of thermoelectric effect

98 Thermoelectrics for Power Generation - A Look at Trends in the Technology

pentacene/F4TCNQ bilayer structures.

neglecting electron correlation effects [31]:

Percolation theory is considered as the best way known to analytically investigate charge carriers hopping transport characteristics. Percolation problem for charge carriers transport properties in disordered semiconductors has been argued early by Ziman and a number of researchers [34, 35], at which charge transport should be in proportion to percolation probability PðpÞ. A simple definition is that approximates firstly electrical conductivity as [36]:

$$
\sigma(E) = \sigma\_0 \times P(p(E)),
\tag{12}
$$

where PðpÞ percolation probability is fraction of the volume allowed, but not isolated, and σ<sup>0</sup> denotes a large allowed value of the material. PðpÞ is known to vanish for p less than critical value Bc, but drops sharply to zero as p ! Bc. To make percolation question simple, researchers have put forward two kinds of standpoints for critical Bc, that is, Bc ¼ 1, and Bc ¼ 2:8 or Bc ¼ 2:7. Although researchers have not achieved unified agreement, percolation theory in hopping system was generally established to explain charge carrier transport characteristics.

Generally speaking, charge carrier transport is described by a four-dimensional (4D) hopping space, including three spatial coordinates and one energy coordinate, at which probability of charge carrier hopping between localized sites associated with these four coordinates. Therefore, charge carrier transport would be more complex based on percolation approach addressing, if all of positions, that is, spatial positions of sites and their energies and occupation of sites, must be included. In Eq. (12), to simulate electrical conductivity σðEÞ, the key is to seek out percolation path in hopping space. Thus, a random resistor network linking all of molecular sites under percolation model is essential. Figure 6 shows schematic diagram of charge carrier transport in hopping system and corresponding percolation current through polymer matrix for charge carrier to travel through [37].

Figure 6. (a) Schematic diagram of charge carrier transport in hopping space with density of states and (b) corresponding percolation current in disordered organic semiconductor.

Based on the following general definition through Kelvin-Onsager relation to Peltier coefficient Π, percolation theory to calculate Seebeck coefficient S in hopping transport is expressed as in Eq. (8), where Π is generally identified with average site energy on percolation cluster and can be written as:

$$
\Pi = \int E\_i P(E\_i) dE\_i,\tag{13}
$$

where PðEiÞ is probability that site of energy Ei is on current-carrying percolation cluster and was further given by:

$$P(E\_i) = \frac{g(E\_i)P\_1(Z\_m|E\_i)}{\int\_{-\mathcal{E}\_m}},\tag{14}$$

$$\int\_{-\mathcal{E}\_m} g(E\_i)P\_1(Z\_m|E\_i)dE$$

where gðEiÞ is density of states per unit volume, Em is maximum site energy, and P1ðZmjEiÞ is probability that second smallest resistance emanating from site with energy Ei is not larger than maximum resistance on percolation cluster Zm. Expression of probability P1ðZmjEiÞ is written as:

$$P\_1(Z\_{\mathfrak{m}}|E\_i) = 1 - \exp\left[-P(Z\_{\mathfrak{m}}|E\_i)\right] \times \left[1 + P(Z\_{\mathfrak{m}}|E\_i)\right],\tag{15}$$

where PðZmjEiÞ is bonds' density, which means average number of resistance of Zm or less connected to site energy Ei . To calculate Peltier coefficient (or Seebeck coefficient), an expression for PðZmjEiÞ is necessary.

Based on percolation theory, disordered organic material is regarded as a random resistor network (see Figure 6b). To address total electrical conductivity in disordered system, the initial is to obtain reference conductance Z and eliminate all conductive pathways between sites i and j with Zij < Z. Conductance between sites i and j is given by Zij∝exp ð−SijÞ with [38]:

$$\mathcal{S}\_{\vec{\eta}} = 2\alpha \mathcal{R}\_{\vec{\eta}} + \frac{|E\_{\vec{\imath}} - E\_f| + |E\_{\vec{\jmath}} - E\_f| + |E\_{\vec{\imath}} - E\_{\vec{\jmath}}|}{2k\_B T}. \tag{16}$$

The density of bonds PðZmjEiÞ then can be written as:

occupation of sites, must be included. In Eq. (12), to simulate electrical conductivity σðEÞ, the key is to seek out percolation path in hopping space. Thus, a random resistor network linking all of molecular sites under percolation model is essential. Figure 6 shows schematic diagram of charge carrier transport in hopping system and corresponding percolation current through

Based on the following general definition through Kelvin-Onsager relation to Peltier coefficient Π, percolation theory to calculate Seebeck coefficient S in hopping transport is expressed as in Eq. (8), where Π is generally identified with average site energy on percolation cluster and can

Figure 6. (a) Schematic diagram of charge carrier transport in hopping space with density of states and (b) corresponding

where PðEiÞ is probability that site of energy Ei is on current-carrying percolation cluster and

where gðEiÞ is density of states per unit volume, Em is maximum site energy, and P1ðZmjEiÞ is probability that second smallest resistance emanating from site with energy Ei is not larger than maximum resistance on percolation cluster Zm. Expression of probability P1ðZmjEiÞ is written as:

gðEiÞP1ðZmjEiÞdE

P1ðZmjEiÞ ¼ 1− exp ½−PðZmjEiÞ� · ½1 þ PðZmjEiÞ�, (15)

<sup>P</sup>ðEiÞ ¼ <sup>g</sup>ðEiÞP1ðZmjEi<sup>Þ</sup> E ðm

−Em

EiPðEiÞdEi, (13)

, (14)

Π ¼ ð

polymer matrix for charge carrier to travel through [37].

100 Thermoelectrics for Power Generation - A Look at Trends in the Technology

percolation current in disordered organic semiconductor.

be written as:

was further given by:

$$P(Z\_m|E\_i) = \int 4\pi R \int\_{i\dagger}^2 \mathbf{g}(E\_i)\mathbf{g}(E\_j)d\mathbf{R}\_{i\dagger}dE\_i dE\_j \Theta(\mathbf{S}\_c - \mathbf{S}\_{i\dagger}).\tag{17}$$

If the density of participating sites is Ps, then critical parameter Sc is found by solving equation:

$$P(Z\_m|E\_i) = B\_c P\_s = B\_c \int g(E) dE \theta(S\_c k\_B T - |E - E\_f|). \tag{18}$$

Based on numerical studies for three-dimensional amorphous system, the formation of infinite cluster corresponds to Bc ¼ 2:7 [38]. By connecting Eqs. (16)–(18), bonds' density can be formulated as:

<sup>P</sup>ðZmjEiÞ ¼ <sup>4</sup>πR<sup>3</sup> 3ð2αÞ 3 · ð ∈i ∈f ðSc−∈<sup>j</sup> þ ∈fÞ 3 gð∈jÞd∈<sup>j</sup> þ ð Scþ∈<sup>f</sup> ∈i ðSc−∈<sup>j</sup> þ ∈fÞ 3 gð∈jÞd∈<sup>j</sup> þ ð ∈f ∈i−Sc ðSc−∈<sup>i</sup> þ ∈jÞ 3 gð∈jÞd∈<sup>j</sup> ð ∈f ∈i ðSc þ ∈i−∈fÞ 3 gð∈jÞd∈<sup>j</sup> þ ð ∈i ∈<sup>f</sup> −Sc ðSc þ ∈i−∈fÞ 3 gð∈jÞdEj þ <sup>ð</sup> <sup>∈</sup>iþSc ∈f ðSc−∈<sup>j</sup> þ ∈iÞ 3 gð∈jÞd∈<sup>j</sup> ∈<sup>i</sup> > ∈<sup>f</sup> ∈<sup>i</sup> < ∈<sup>f</sup> � 8 >>>>>>>>< >>>>>>>>: (19)

here <sup>∈</sup> is normalized energy as <sup>∈</sup> <sup>¼</sup> <sup>E</sup> kBT. This expression has been split into two regimes of ∈<sup>i</sup> > ∈<sup>f</sup> and ∈<sup>i</sup> < ∈<sup>f</sup> , which are corresponding to contributions of ∈<sup>i</sup> above or below Fermi energy to PðZmjEiÞ and, therefore, Seebeck coefficient S, respectively. Above Fermi energy, charge carriers in shallow states will move by hopping to other shallow states. While below Fermi energy, charge carriers in deep states will move by thermal excitation to shallower states. By substituting Eqs. (13)–(15) and Eq. (19) into Eq. (8), one can obtain the final result of Seebeck coefficient.

Figure 7 shows simulated and experimental dependences of Seebeck coefficient on charge carriers' density; simulation is based on percolation theory, experimental data measured by using field-effect transistor (FET) from three kinds of conjugated polymers, that is, IDTBT, PBTTT and PSeDPPBT [39]. Model of percolation theory can reasonably reproduce experimental data under the whole range of charge carriers' density for different conjugated polymers.

Figure 7. Charge carrier's density dependence of Seebeck coefficient for different materials at room temperature [37]. Symbols and solid lines are experimental and simulated results, respectively.

#### 3.3. Hybrid model of Seebeck coefficient

Usual behavior of Seebeck coefficient is to decrease with increasing charge carriers' density. However, Germs et al. have observed unusual thermoelectric behavior for pentacene in TFT [40], indeed, at room temperature, increasing charge carriers' density results in expected decrease in S, while with decreasing temperature to values below room temperature, S demonstrates growth with increasing charge carriers' density at T = 250 K and even more pronounced at T = 200 K, as shown in Figure 8.

To explain this unusual thermoelectric behavior, Germs et al. developed simplified hybrid model that incorporates both variable-range hopping (VRH) and mobility edge (ME) transport [40]. Charge carrier and energy transport can be described independently by two processes: VRH-type process that occurs within exponential tail of localized states and band-like type transport that occurs within band-like states above mobility edge. Then, Seebeck coefficient of hybrid model is expressed as conductivity-weighted average of two contributing transport channels:

Thermoelectric Effect and Application of Organic Semiconductors http://dx.doi.org/10.5772/65872 103

$$S = \frac{S\_{ME}\sigma\_{ME} + S\_{VRH}\sigma\_{VRH}}{\sigma\_{ME} + \sigma\_{VRH}},\tag{20}$$

where SME and σME are Seebeck coefficient and electrical conductivity in ME part, and SVRH and σVRH are Seebeck coefficient and electrical conductivity in VRH part, respectively.

Then, general expression of Seebeck coefficient in Eq. (9) reduces:

$$\mathcal{S}\_{ME} = \frac{(E\_c - E\_f)}{eT} + A,\tag{21}$$

with

Figure 7 shows simulated and experimental dependences of Seebeck coefficient on charge carriers' density; simulation is based on percolation theory, experimental data measured by using field-effect transistor (FET) from three kinds of conjugated polymers, that is, IDTBT, PBTTT and PSeDPPBT [39]. Model of percolation theory can reasonably reproduce experimental data under the whole range of charge carriers' density for different conjugated

Usual behavior of Seebeck coefficient is to decrease with increasing charge carriers' density. However, Germs et al. have observed unusual thermoelectric behavior for pentacene in TFT [40], indeed, at room temperature, increasing charge carriers' density results in expected decrease in S, while with decreasing temperature to values below room temperature, S demonstrates growth with increasing charge carriers' density at T = 250 K and even more pro-

Figure 7. Charge carrier's density dependence of Seebeck coefficient for different materials at room temperature [37].

To explain this unusual thermoelectric behavior, Germs et al. developed simplified hybrid model that incorporates both variable-range hopping (VRH) and mobility edge (ME) transport [40]. Charge carrier and energy transport can be described independently by two processes: VRH-type process that occurs within exponential tail of localized states and band-like type transport that occurs within band-like states above mobility edge. Then, Seebeck coefficient of hybrid model is expressed as conductivity-weighted average of two contributing

polymers.

3.3. Hybrid model of Seebeck coefficient

Symbols and solid lines are experimental and simulated results, respectively.

102 Thermoelectrics for Power Generation - A Look at Trends in the Technology

nounced at T = 200 K, as shown in Figure 8.

transport channels:

$$A = \frac{\int\_{\varepsilon}^{\varepsilon} \varepsilon \sigma(\varepsilon) d\varepsilon}{\int\_{\varepsilon}^{0}},\tag{22}$$
 
$$\int\_{0}^{\varepsilon} \sigma(\varepsilon) d\varepsilon$$

where ε ¼ E−Ec, Ec is energy value at mobility edge.

Figure 8. Measurements (symbols) and calculation (lines) of Seebeck coefficient as function of gate bias in pentacene TFT. Gate voltage Vg is corrected for threshold voltage Vth of TFT.

In Eq. (21), A accounts for excitations beyond the band edge with 1–20% of SME. Similarly, within VRH model, it is assumed that transport is determined by hopping event from equilibrium energy state to relatively narrow transport energy E<sup>∗</sup> [41], and Eq. (9) becomes:

$$\mathcal{S}\_{VRH} = \frac{(E^\*-E\_f)}{eT},\tag{23}$$

Electrical conductivity in ME part is calculated as:

$$
\sigma\_{\rm ME} = \varepsilon n\_{\rm free} \mu\_{\rm free}(T), \tag{24}
$$

with power law dependence on temperature, <sup>μ</sup>f reeðTÞ ¼ <sup>μ</sup>0T<sup>−</sup><sup>m</sup>.

VRH part is described by Mott-Martens model that assumes transport to be dominated by hops from Fermi energy to transport level E<sup>∗</sup> . Electrical conductivity in VRH part is subsequently calculated by optimizing Miller-Abrahams expression as:

$$
\sigma\_{VRH} = \sigma\_0 \exp\left[-2\alpha \mathcal{R}^\* - \frac{(E^\* - E\_f)}{k\_B T}\right],\tag{25}
$$

where position of transport level E<sup>∗</sup> and typical hopping distance R<sup>∗</sup> is connected via percolation argument:

$$B\_c = \frac{4}{3}\pi (R^\*)^3 \int\_{E\_f}^{E^\*} g(E) dE,\tag{26}$$

where Bc ¼ 2:8 is critical number of bonds, gðEÞ represents DOS, which here is simplified to single exponential trap tail below mobility edge and constant density of extended states above Ec:

$$g(E) = \begin{cases} \frac{n\_{\rm trap}}{k\_B T\_0} \exp\left(-\frac{E}{k\_B T\_0}\right) & \text{for } E < E\_c\\ & \frac{n\_0}{k\_B T\_0} \quad \text{for } E \ge E\_c \end{cases} \quad (E\_c = 0), \tag{27}$$

where n<sup>0</sup> is divided by kBT<sup>0</sup> for dimensional reasons. The number of charge carriers above Ec, nf ree follows from Fermi-Dirac distribution.

Figure 9 shows measured and calculated dependences of Seebeck coefficient on difference between gate voltage Vg and threshold voltage Vth on TFT at T = 200 K. One can see that at 200 K heat transported at mobility edge <sup>ð</sup>Ec−Ef<sup>Þ</sup> and heat transported at transport level <sup>ð</sup>E<sup>∗</sup> −EfÞ both decrease with increasing charge carriers'density, accounting for downward trends in SME and SVRH. Consequently, weight-averaged Seebeck coefficient SHyb shifts from SVRH values at small gate bias up toward SME for large gate bias. Relatively large value of SME at lower temperatures follows from Eq. (21) and temperature independence of EC.

#### 3.4. Monte Carlo simulation

As compared with numeric model, analytical thermoelectric transport models exhibit more context and physical property, but they also have inevitable shortcoming due to the use of plenty of free parameters during simulation and calculation. In order to eliminate these hindrances, universal method has been used based on Monte Carlo (MC) simulation for describing hopping transport and insuring validity and accuracy of thermoelectric transport.

Figure 9. Measured (symbols) and calculated (lines) dependences of Seebeck coefficient on gate bias at T = 200 K [40]. SHyb is conductivity-weighted average of SVRH and SME.

Kinetic Monte Carlo simulation generally includes six steps as follows [42]:

σME ¼ enf reeμf reeðTÞ, (24)

. Electrical conductivity in VRH part is subse-

gðEÞdE, (26)

ðEc ¼ 0Þ,

, (25)

(27)

−EfÞ

with power law dependence on temperature, <sup>μ</sup>f reeðTÞ ¼ <sup>μ</sup>0T<sup>−</sup><sup>m</sup>.

104 Thermoelectrics for Power Generation - A Look at Trends in the Technology

quently calculated by optimizing Miller-Abrahams expression as:

hops from Fermi energy to transport level E<sup>∗</sup>

gðEÞ ¼

nf ree follows from Fermi-Dirac distribution.

3.4. Monte Carlo simulation

ntrap kBT<sup>0</sup>

8 ><

>:

tion argument:

Ec:

VRH part is described by Mott-Martens model that assumes transport to be dominated by

where position of transport level E<sup>∗</sup> and typical hopping distance R<sup>∗</sup> is connected via percola-

Ef

where Bc ¼ 2:8 is critical number of bonds, gðEÞ represents DOS, which here is simplified to single exponential trap tail below mobility edge and constant density of extended states above

ðE∗ −EfÞ kBT

f or E < Ec

� �

<sup>σ</sup>VRH <sup>¼</sup> <sup>σ</sup><sup>0</sup> exp <sup>−</sup>2αR<sup>∗</sup><sup>−</sup>

Bc <sup>¼</sup> <sup>4</sup> 3 <sup>π</sup>ðR<sup>∗</sup><sup>Þ</sup> 3 E ð ∗

exp <sup>−</sup> <sup>E</sup>

n0 kBT<sup>0</sup>

temperatures follows from Eq. (21) and temperature independence of EC.

kBT<sup>0</sup> � �

where n<sup>0</sup> is divided by kBT<sup>0</sup> for dimensional reasons. The number of charge carriers above Ec,

Figure 9 shows measured and calculated dependences of Seebeck coefficient on difference between gate voltage Vg and threshold voltage Vth on TFT at T = 200 K. One can see that at 200 K heat transported at mobility edge <sup>ð</sup>Ec−Ef<sup>Þ</sup> and heat transported at transport level <sup>ð</sup>E<sup>∗</sup>

both decrease with increasing charge carriers'density, accounting for downward trends in SME and SVRH. Consequently, weight-averaged Seebeck coefficient SHyb shifts from SVRH values at small gate bias up toward SME for large gate bias. Relatively large value of SME at lower

As compared with numeric model, analytical thermoelectric transport models exhibit more context and physical property, but they also have inevitable shortcoming due to the use of plenty of free parameters during simulation and calculation. In order to eliminate these hindrances, universal method has been used based on Monte Carlo (MC) simulation for describ-

ing hopping transport and insuring validity and accuracy of thermoelectric transport.

f or E≥Ec


Otherwise, renormalizing hopping rates <sup>Γ</sup>ij as pij <sup>¼</sup> <sup>Γ</sup>ij ∑ i ′ , j ′ Γi ′ j ′ . Sum of rates includes only

jumps from occupied to unoccupied sites, that is, Γij ¼ 0 for occupied site j or unoccupied site i. For every pair ij, index k (i.e., ij ! k and pij ¼ pk), where k∈f1, :::, kmaxg with kmax being total number of all possible hopping events. Then, partial sum Sk is defined for every index k:

$$\mathcal{S}\_k = \sum\_{\vec{k'}=1}^k p\_{\vec{k'}}.\tag{28}$$

Apparently, for every <sup>k</sup>, extent from interval <sup>½</sup>Sk<sup>−</sup>1, Sk� equals to probability pk for kth jump, and total extent of all intervals equals to 1, for example Skmax ¼ 1. Then, determining a random real number r from interval [0, 1] and finding index k, here Sk<sup>−</sup><sup>1</sup> << r << Sk, and one can find hopping event. After determining hoping event, one would move charge carrier between corresponding sites i and j.

	- i. It is, therefore, written as:

$$
\pi = \frac{-1}{\nu\_i} \ln(x),
\tag{29}
$$

where random number x is drawn from interval [0, 1].

v. Calculating current density. Every time, when predefined numbers of jumps have occurred, current density JðtÞ can be expressed as:

$$J(t) = \frac{e(N^+ - N^-)}{tN\_yN\_za^2},\tag{30}$$

where N<sup>þ</sup> and N<sup>−</sup> are the total number of jumps in and opposite direction of electric field for cross-sectional slice in yz plane, and a is lattice constant.

vi. Calculating Seebeck coefficient. Seebeck coefficient is given by expression as in Eq. (10), where transport energy is defined as averaged energy weighted by electrical conductivity distribution:

$$E\_{trans} = \frac{\int E\sigma(E, T) \left(-\frac{\partial f}{\partial E}\right) dE}{\sigma(T)},\tag{31}$$

$$\text{with } \sigma(T) = \int \sigma(E, T) \left( -\frac{\partial f}{\partial E} \right) dE.$$

Although kinetic MC technique gives a direct simulation of thermoelectric transport in organic semiconductor materials and, therefore, it is accurate for the most description of electronic conductivity, its negative factor is to require extensive computational resources, which leads to difficultly analyze and fit experimental data. Figure 10 shows comparison of analytical model with MC simulation for Seebeck coefficient [42]. It is seen in Figure 10, that results exhibit qualitative agreement for all values of parameter α. For large α in Figure 10a, Ssa and SMC show not only qualitative, but even relatively good quantitative agreement in energy interval E < 0 (corresponding to relative charge carriers' concentration n=N<sup>0</sup> < 0:5). For higher energies (and thus for higher concentrations), difference between Ssa and SMC increases. As parameter α decreases, functional dependencies Ssa and SMC remain very close to each other, but Ssa gets shifted with respect to SMC (Figure 10b).

Figure 10. Monte Carlo and semi-analytical calculations of Seebeck coefficient for different values of localization length (a) <sup>α</sup><sup>−</sup><sup>1</sup> = 1 nm and (b) <sup>α</sup><sup>−</sup><sup>1</sup> = 0.2 nm. Ef is in units of <sup>Δ</sup>, <sup>Δ</sup> <sup>¼</sup> <sup>4</sup>kBT and T = 300 K.

#### 3.5. First-principle calculation theory

random real number r from interval [0, 1] and finding index k, here Sk<sup>−</sup><sup>1</sup> << r << Sk, and one can find hopping event. After determining hoping event, one would move charge

νij being the total rate for charge carrier hopping from site

lnðxÞ, (29)

tNyNza<sup>2</sup> , (30)

<sup>σ</sup>ðT<sup>Þ</sup> , (31)

iv. Calculation of waiting time. After finding each hopping transport, total simulation time t and waiting time τ would be added that has passed until the event took place. This time is determined by describing a random number from exponential waiting time distribution

> <sup>τ</sup> <sup>¼</sup> <sup>−</sup><sup>1</sup> νi

v. Calculating current density. Every time, when predefined numbers of jumps have

<sup>J</sup>ðtÞ ¼ <sup>e</sup>ðNþ−N<sup>−</sup>

where N<sup>þ</sup> and N<sup>−</sup> are the total number of jumps in and opposite direction of electric field

vi. Calculating Seebeck coefficient. Seebeck coefficient is given by expression as in Eq. (10), where transport energy is defined as averaged energy weighted by electrical conductivity

<sup>E</sup>σðE, <sup>T</sup><sup>Þ</sup> <sup>−</sup> <sup>∂</sup><sup>f</sup>

Although kinetic MC technique gives a direct simulation of thermoelectric transport in organic semiconductor materials and, therefore, it is accurate for the most description of electronic conductivity, its negative factor is to require extensive computational resources, which leads to difficultly analyze and fit experimental data. Figure 10 shows comparison of analytical model with MC simulation for Seebeck coefficient [42]. It is seen in Figure 10, that results exhibit qualitative agreement for all values of parameter α. For large α in Figure 10a, Ssa and SMC show not only qualitative, but even relatively good quantitative agreement in energy interval E < 0 (corresponding to relative charge carriers' concentration n=N<sup>0</sup> < 0:5). For higher energies (and thus for higher concentrations), difference between Ssa and SMC increases. As parameter α decreases, functional dependencies Ssa and SMC remain very close to each other, but Ssa gets

∂E � �

dE

Þ

carrier between corresponding sites i and j.

106 Thermoelectrics for Power Generation - A Look at Trends in the Technology

j

where random number x is drawn from interval [0, 1].

for cross-sectional slice in yz plane, and a is lattice constant.

Etrans ¼

dE.

ð

occurred, current density JðtÞ can be expressed as:

PðτÞ ¼ ν<sup>i</sup> exp ð−νiτÞ with ν<sup>i</sup> ¼ ∑

i. It is, therefore, written as:

distribution:

with σðTÞ ¼

ð

shifted with respect to SMC (Figure 10b).

<sup>σ</sup>ðE, <sup>T</sup><sup>Þ</sup> <sup>−</sup> <sup>∂</sup><sup>f</sup>

∂E � � First-principle (ab initio) theory would be deemed to the best type of theory for hopping charge transport in organic semiconductors, since it starts from particular chemical and geometrical structure of the system, and it starts directly at the level of established science and does not make assumptions, such as empirical model and fitting parameters. So far, a few researches on charge carriers transport properties based on first-principle theory are hardly beyond the scope of crystalline. Otherwise, direct calculation of Seebeck coefficient is hardly realistic. Current method combines generally first-principle calculations with transport theory. For example, Gao et al. have investigated theoretically Seebeck coefficient of narrow bandgap crystalline polymers, including crystalline solids β-Zn4Sb3 and AuIn2 and these polymers, based on muffin-tin orbital and full-potential linearized augmented plane-wave (FLAPW) electronic structure code [43]. In essence, Gao et al.'s method for calculation of transport properties of crystalline solid is firstly based on semiclassical Boltzmann theory, following as:

$$
\sigma\_0(T) = \frac{e^2}{3} \int \tau(E, T) N(E) \nu^2(E) \left( -\frac{\partial f(E)}{\partial E} \right) dE,\tag{32}
$$

where e, τ, f and ν represent free electron charge, electronic relaxation time, Fermi-Dirac distribution function and Fermi velocity, respectively. If relaxation time for electron scattering processes is assumed to be constant, that is, τðE, TÞ ¼ const, which may yield reasonable simulated results in a wide range of materials, then temperature dependence of σ0ðTÞ can be simulated based on constant relaxation time τ:

$$\frac{\sigma\_0(T)}{\tau} = \frac{e^2}{3} \int N(E) \nu^2(E) \left( -\frac{\partial f(E)}{\partial E} \right) dE. \tag{33}$$

Then, Seebeck coefficient is calculated from ratio of the zeroth and first moments of electrical conductivity with respect to energy:

$$S(T) = \frac{1}{eT} \times \frac{I^1}{I^0},\tag{34}$$

where

$$I^x(T) = \int \pi(E, T) N(E) \nu^2(E) (E - E\_f)^x \left(-\frac{\partial f(E)}{\partial E}\right) dE. \tag{35}$$

Product of the density of states NðEÞ and arbitrary quantity g, which is relative to energy and kvector as in Eqs. (33) and (35), can be calculated by using integration on constant energy surface S in k space. Electronic band structure can be calculated by using WIEN97 and WIEN2K FLAPW [44] or pseudopotential plane-wave code in Vienna ab initio simulation package (VASP) [45].

Figure 11a and b shows simulated energy band structure of polythiophene polymer. Here, internal structural parameters of the polymer are fully optimized, and electronic band structure is calculated by pseudopotential plane-wave calculations employing ultrasoft Vanderbilt pseudopotential and generalized gradient scheme. Simulated results display that band structure of polythiophene is very simple, which exhibits semiconductor performance with band gap of 0.9 eV. Neutral polythiophene is electrical insulator. Otherwise, by inspecting band structure, one can find that, except very close to zone center, where the density of states is high, band dispersions are considerable. The special band structure, thus, induces very low value of Seebeck coefficient (~20 μV/K), as shown in Figure 11.

Figure 11. Calculated energy band structure (a), (b), and Seebeck coefficient (c), (d), for polythiophene (left) and polyaminosquarine (right), respectively [43]. Isolated planar polymer chains were used for this calculation.

Similar to calculated method from Gao et al., Shuai et al. have combined first-principles band structure calculations and Boltzmann transport theory to study thermoelectric in pentacene and rubrene crystals [46]. Electronic contribution to Seebeck coefficient is obtained in approximations of constant relaxation time and rigid band, as shown in Figure 12. Calculation results exhibited also the similar trend compared with experimental Seebeck coefficient.

<sup>S</sup>ðTÞ ¼ <sup>1</sup> eT · I 1 I

<sup>τ</sup>ðE, <sup>T</sup>ÞNðEÞν<sup>2</sup>ðEÞðE−Ef<sup>Þ</sup>

Product of the density of states NðEÞ and arbitrary quantity g, which is relative to energy and kvector as in Eqs. (33) and (35), can be calculated by using integration on constant energy surface S in k space. Electronic band structure can be calculated by using WIEN97 and WIEN2K FLAPW [44] or pseudopotential plane-wave code in Vienna ab initio simulation

Figure 11a and b shows simulated energy band structure of polythiophene polymer. Here, internal structural parameters of the polymer are fully optimized, and electronic band structure is calculated by pseudopotential plane-wave calculations employing ultrasoft Vanderbilt pseudopotential and generalized gradient scheme. Simulated results display that band structure of polythiophene is very simple, which exhibits semiconductor performance with band gap of 0.9 eV. Neutral polythiophene is electrical insulator. Otherwise, by inspecting band structure, one can find that, except very close to zone center, where the density of states is high, band dispersions are considerable. The special band structure, thus, induces very low

Figure 11. Calculated energy band structure (a), (b), and Seebeck coefficient (c), (d), for polythiophene (left) and

polyaminosquarine (right), respectively [43]. Isolated planar polymer chains were used for this calculation.

<sup>x</sup> −

∂fðEÞ ∂E � �

where

package (VASP) [45].

I x ðTÞ ¼ ð

108 Thermoelectrics for Power Generation - A Look at Trends in the Technology

value of Seebeck coefficient (~20 μV/K), as shown in Figure 11.

<sup>0</sup> , (34)

dE: (35)

Figure 12. Seebeck coefficient calculated as function of charge carrier's concentration (a) for pentacene and rubrene at room temperature and compared to FET measurements. Calculated Seebeck coefficients have been averaged over three crystal directions (b) for rubrene at temperature in the range between 200 and 300 K [46].

Afterward, Shuai et al. applied also combining method to calculate thermoelectric properties of organic materials, which is used to calculating α-form phthalocyanine crystals H2Pc, CuPc, NiPc and TiOPc [47]. This combining method includes first-principles band structure calculations, Boltzmann transport theory and deformation potential theory. They used first-principles calculations in VASP to calculate Seebeck coefficient. After obtaining band structure, Boltzmann transport theory was performed to calculate properties related to charge carrier transport, as in Eqs. (32) and (33).

Being different from Gao et al.'s and Shuai et al.'s previous works, it is assumed that relaxation time is a constant, which can be estimated by deformation potential theory for treating electron-phonon scattering. In terms of corresponding articles [46, 48], acoustic phonon scattering in both pristine and doped system was simulated by this theory including scattering matrix element for electrons from k state to k′ state expressing as:

$$\left|M(\mathbf{k}, \mathbf{k}')\right|^2 = \frac{E\_1^2}{\mathbf{C}\_{ii}} k\_{\mathcal{B}} T,\tag{36}$$

where E<sup>1</sup> is deformation potential constant that represents energy band shift caused by crystal lattice deformation, and Cii is elastic constant in the direction of lattice wave's propagation. Then, relaxation time can be expressed by scattering probability:

$$\frac{1}{\tau(i,k)} = \sum\_{k' \in \mathcal{BZ}} \left\{ \frac{2\pi}{\hbar} |M(\mathbf{k}, \mathbf{k'})|^2 \delta[\varepsilon(i,k) - \varepsilon(i,k')] (1 - \cos \theta) \right\},\tag{37}$$

where δ½εði, kÞ−εði, k ′ Þ� is Dirac delta function, and <sup>θ</sup> is angle between <sup>k</sup> and <sup>k</sup>′ . In Bardeen and Shockley's method, scattering is assumed to be isotropic, and matrix element of interactions <sup>M</sup>ðk, <sup>k</sup>′ <sup>Þ</sup> is not relative with <sup>k</sup> and <sup>k</sup>′ .

Calculated dependences of Seebeck coefficient on charge carriers' concentration are shown in Figure 13. Calculated dependences of Seebeck coefficient display different properties such as positive S values for holes and negative S values for electrons. Seebeck coefficient value is isotropic at first glance, and it decreases rapidly as charge carriers' concentration increases.

Figure 13. Seebeck coefficient for (a) H2Pc, (b) CuPc, (c) NiPc, (d) TiOPc calculated as a function of the charge carriers concentration at 298 K [47]. a, b and c denote a, b and c crystal axes, respectively.

#### 4. Conclusion and outlook

In the past decades, the research on organic thermoelectric materials has made great progress. Rich variety of novel organic materials has been synthesized and applied in thermoelectric devices, and thermoelectric performances of organic semiconductors have been promoted greatly. However, as compared to inorganic thermoelectric materials, organic thermoelectric materials still exhibit lower ZT so far. However, situation looks like that progress in theoretical study of organic thermoelectric effect lags far behind experimental investigation in the last 30 years, but has been changed remarkably until the recent five years. Here, we have tried to describe organic thermoelectric materials and theoretical approaches, which allow to calculate characteristics of charge carrier transport processes responsible for thermoelectric effect in organic semiconductors. We hope that these contexts can be helpful to improve thermoelectric effect in organic materials and provide motivation for growth of thermoelectric applications of organic semiconductors. We believe that quest for green energy sources will stimulate intensive research and development works in the field of novel organic thermoelectric materials and devices that will result in serious improvement in thermoelectric efficiency of organic thermoelectric materials and enable development of novel high-performance and affordable organic thermoelectric devices.

## Abbreviations

where δ½εði, kÞ−εði, k

<sup>M</sup>ðk, <sup>k</sup>′

′

4. Conclusion and outlook

thermoelectric devices.

<sup>Þ</sup> is not relative with <sup>k</sup> and <sup>k</sup>′

110 Thermoelectrics for Power Generation - A Look at Trends in the Technology

Þ� is Dirac delta function, and <sup>θ</sup> is angle between <sup>k</sup> and <sup>k</sup>′

Shockley's method, scattering is assumed to be isotropic, and matrix element of interactions

Calculated dependences of Seebeck coefficient on charge carriers' concentration are shown in Figure 13. Calculated dependences of Seebeck coefficient display different properties such as positive S values for holes and negative S values for electrons. Seebeck coefficient value is isotropic at first glance, and it decreases rapidly as charge carriers' concentration increases.

In the past decades, the research on organic thermoelectric materials has made great progress. Rich variety of novel organic materials has been synthesized and applied in thermoelectric devices, and thermoelectric performances of organic semiconductors have been promoted greatly. However, as compared to inorganic thermoelectric materials, organic thermoelectric materials still exhibit lower ZT so far. However, situation looks like that progress in theoretical study of organic thermoelectric effect lags far behind experimental investigation in the last 30 years, but has been changed remarkably until the recent five years. Here, we have tried to describe organic thermoelectric materials and theoretical approaches, which allow to calculate characteristics of charge carrier transport processes responsible for thermoelectric effect in organic semiconductors. We hope that these contexts can be helpful to improve thermoelectric effect in organic materials and provide motivation for growth of thermoelectric applications of organic semiconductors. We believe that quest for green energy sources will stimulate intensive research and development works in the field of novel organic thermoelectric materials and devices that will result in serious improvement in thermoelectric efficiency of organic thermoelectric materials and enable development of novel high-performance and affordable organic

Figure 13. Seebeck coefficient for (a) H2Pc, (b) CuPc, (c) NiPc, (d) TiOPc calculated as a function of the charge carriers

concentration at 298 K [47]. a, b and c denote a, b and c crystal axes, respectively.

.

. In Bardeen and


## Author details

Nianduan Lu\*, Ling Li and Ming Liu

\*Address all correspondence to: lunianduan@ime.ac.cn

Key Laboratory of Microelectronic Devices & Integrated Technology, Institute of Microelectronics of Chinese Academy of Sciences, Beijing, China

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Provisional chapter
