**Review of Research on the Thermoelectric Material ZnSb** Review of Research on the Thermoelectric

Xin Song and Terje G. Finstad Xin Song and Terje G. Finstad

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

http://dx.doi.org/10.5772/65661

#### Abstract

Material ZnSb

The thermoelectric material ZnSb has been studied intensively in recent years and has shown promising features. The other zinc-antimonide compound, Zn4Sb3 has remarkable low thermal conductivity, but it is accompanied with phase transitions at moderate temperature and has inherent stability problems. Compared to that, ZnSb is relatively phase stable and has a relative high charge carrier mobility and Seebeck coefficient, thus yielding a decent power factor. Meanwhile, its thermal conductivity can be reduced by means of nanostructuring, thus giving a good figure of merit at moderate temperatures, 400–600K. Many researchers have dedicated their efforts to study and improve ZnSb properties, and the figure of merit has been reported to be above one. Still, ZnSb as a thermoelectric material has features and behaviours that are not well-understood. The behaviour and properties of its intrinsic defects are not understood, but have interested researchers in recent years. This chapter intends to offer a comprehensive review on ZnSb to the readers. By combining own experiences from research on thermoelectric materials, the authors address the prospect for improving the thermoelectric properties of ZnSb and the concerns of transferring lab results to manufacturing.

Keywords: zinc antimonide, impurity band conduction, intrinsic defects, vacancies, p-type

## 1. Introduction

The thermoelectric effect in ZnSb has been known for almost two centuries. The first documented encounter can be traced back to the original work of Seebeck on thermoelectric current generation on different materials and alloy pairs in 1819–1827 [1, 2]. Quantitative measurements of the Seebeck voltage of ZnSb have been carried out by Becquerel in 1866 [3],

© 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.

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

and thermoelectric generators using Zn-Sb alloy were fabricated for practical purposes since 1870 [4]. From the early twentieth century, many attempted to solve the crystal structure, but were barely successful [5–7], until Almin, finally, in 1948 determined the crystal structure of ZnSb together with CdSb [8]. A large interest in ZnSb followed and was benefitted by the progress on semiconductors since the 1950s. Figure 1 shows a thermoelectric device made by ZnSb in the 1950s. It shows a solar thermoelectric generator prototype built by p-ZnSb and n-Bi91Sb9 with an overall efficiency of 0.63% [9]. Around the same time, a thermoelectric refrigerator made of n-PbTe and p-ZnSb was demonstrated in the USSR in the 1950s [10]. However, research reporting on ZnSb faded in the 1970s, and there was little improvement in terms of its efficiency. In recent years, renewed attention appeared due to a nanostructuring boom in material science, and the thermoelectric properties of ZnSb have been intensively studied and improved. There are also other energy-related applications of ZnSb actively being explored, such as electrodes for rechargeable Li-ion batteries [11], or phase change memory cells [12].

Figure 1. Solar thermoelectric generator. (Reprinted from [9], with the permission of AIP Publishing.) (a) Open circuit emf (Seebeck coefficient) as a function of temperature on ZnSb-alloys comparing with other thermal couples. Materials: (1) ZnSb (Sn, Ag, Bi)-Bi91Sb9, (2) ZnSb (Sn, Ag, Bi)-constantan, (3) Bi91Sb9Sn5-Bi91Sb9, (4) Chromel P-constantan. (b) Thermoelectric efficiency on aforesaid materials; (c) Solar radiation thermopile contained 25 junctions built by p-ZnSb in plot (a) and (b) and n-Bi91Sb9. Above: front surface exposed to the sun; below: rear view shows the thermoelectric junctions.

Table 1 lists some reported figure of merit zT. The performance of ZnSb strongly depends on doping concentration and operation temperature. In addition, preparation-induced defects (phase impurity, oxidation and grain size) and intrinsic defects (vacancies, interstitials, clusters) influence strongly the material's performance. These need to be controlled in order to bring further progress, and in general, handling of the material has a learning curve and a detailed understanding of the material, per se, is needed.


Table 1. List of reported zT of ZnSb.

and thermoelectric generators using Zn-Sb alloy were fabricated for practical purposes since 1870 [4]. From the early twentieth century, many attempted to solve the crystal structure, but were barely successful [5–7], until Almin, finally, in 1948 determined the crystal structure of ZnSb together with CdSb [8]. A large interest in ZnSb followed and was benefitted by the progress on semiconductors since the 1950s. Figure 1 shows a thermoelectric device made by ZnSb in the 1950s. It shows a solar thermoelectric generator prototype built by p-ZnSb and n-Bi91Sb9 with an overall efficiency of 0.63% [9]. Around the same time, a thermoelectric refrigerator made of n-PbTe and p-ZnSb was demonstrated in the USSR in the 1950s [10]. However, research reporting on ZnSb faded in the 1970s, and there was little improvement in terms of its efficiency. In recent years, renewed attention appeared due to a nanostructuring boom in material science, and the thermoelectric properties of ZnSb have been intensively studied and improved. There are also other energy-related applications of ZnSb actively being explored, such as electrodes for rechargeable Li-ion batteries [11], or

Table 1 lists some reported figure of merit zT. The performance of ZnSb strongly depends on doping concentration and operation temperature. In addition, preparation-induced defects (phase impurity, oxidation and grain size) and intrinsic defects (vacancies, interstitials, clusters) influence strongly the material's performance. These need to be controlled in order to bring further progress, and in general, handling of the material has a learning curve and a

Figure 1. Solar thermoelectric generator. (Reprinted from [9], with the permission of AIP Publishing.) (a) Open circuit emf (Seebeck coefficient) as a function of temperature on ZnSb-alloys comparing with other thermal couples. Materials: (1) ZnSb (Sn, Ag, Bi)-Bi91Sb9, (2) ZnSb (Sn, Ag, Bi)-constantan, (3) Bi91Sb9Sn5-Bi91Sb9, (4) Chromel P-constantan. (b) Thermoelectric efficiency on aforesaid materials; (c) Solar radiation thermopile contained 25 junctions built by p-ZnSb in plot (a) and (b) and n-Bi91Sb9. Above: front surface exposed to the sun; below: rear view shows the thermoelectric

detailed understanding of the material, per se, is needed.

phase change memory cells [12].

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

junctions.

## 2. Crystal structure of ZnSb

#### 2.1. Crystallographic structure and covalent bonds

The crystallographic structure of ZnSb has been determined by Almin [8]. According to this determination, ZnSb has orthorhombic crystal structure, oP16 and belongs to the space group Pbca no. 61. The structure of ZnSb has been studied and confirmed by different techniques, albeit gave slightly different interatomic distances [25–28]. Figure 2 shows the crystal structure of ZnSb that was generated by the structural data from Mozharivskyj [27].

The crystal structure can be viewed as a deformed zinc blende structure. The distorted edgesharing ZnSb4 tetrahedra generate a peculiar five-fold coordination of each atom, as seen in Figure 2a: one of the same kind and four of the other kind. In the context of bonding and its relation to conduction, all atoms in the crystal structure are tied together in a network—a point, we will return to below.

Another way to systematize the structure is to group the atoms together in planar rhomboid rings of Zn2Sb2 that have short Zn-Zn bonds connected to two different longer Zn-Sb bonds, as seen in Figure 2a. These motifs are also tied together in a network that completes the crystal structure. The crystal structure can be recognized in atomic scale by scanning transmission electron microscopy (STEM), as shown in Figure 2b.

The interatomic distances for each bond are also annotated in Figure 2a. The bonds in ZnSb have been categorized in three groups, shown in Figure 2c and d: the bonds i–vi are covalent bonds for building up the tetrahedron; the bonds vii and viii form the Zn2Sb2-ring; and the bonds ix1-6 are the dimers that connect the Zn2Sb2-rings. The angles between each Sb-Zn-Sb bond are also annotated in Figure 2d. Notice that the angles are close to those in regular tetrahedron, 109.5°. Therefore, even though the structure has five-fold coordination, one can still expect that ZnSb satisfies the tetrahedron rules to some extent. One of them is the electron count per bond. ZnSb has seven valence electrons per formula unit, whereas a regular tetrahedral binary semiconductor has eight valence electrons. Such electron-poor valence often indicates a metallic bond. Yet, ZnSb behaves as a semiconductor. The clue about its semiconducting property is probably due to the sp<sup>3</sup> -hybrid orbitals in the tetrahedron, that often represents a semiconducting bond [30]. The counting rules cannot be applied on a per-bond-basis without considering the complete network. Therefore, all the atoms in the crystal structure are bonded together in a network. ZnSb, thereby, has been classified as an electron-poor framework semiconductor (EPFS) [26, 31]. A quite similar interpretation for the structure has been applied to the related compounds CdSb [30, 32–34] and ZnAs [35].

Figure 2. Crystal structure, bonding and coordination environment of ZnSb. (Reprinted with author's permission from [29]. ©X. Song, 2016.) (a) Structure in a 1×2×3 cell generated by Mozharivskyj's data [27]. Both the deformed tetrahedra and the Zn2Sb2-ring, as well as the interatomic distances between the nearest neighbours are annotated. (b) Highresolution scanning transmission electron microscopic (HR-STEM) imaging reveals atomic scale structure that is recognized corresponding to (a) and (c). (c) 3×1×3 cell shows the Zn2Sb2-ring network. Each ring has six nearest neighbours, connected by bonds ix1-6. (d) The angles between Sb-Zn-Sb are similar to that of the standard tetrahedron, 109.5°. The bonds i-vi are covalent bonds for building up the tetrahedron, while vii and viii are the bonds to form Zn2Sb2-ring; bonds ix1-6 in (c) are the dimers, that connect the Zn2Sb2-rings.

Valence electrons in ZnSb have a certain distribution. Figure 3 shows the theoretical ab-initio calculations by GGA-PBE (Generalized Gradient Approximation with Perdew-Burke-Ernzerhof exchange functionals) of the so-called deformation charge [36].

The results show that a Zn atom transfers a small average fraction of 0.26 electrons to Sb along Zn-Sb bond [37], which is expected due to the difference in Pauling electronegativity between Zn (1.65eV) and Sb (1.96eV). Essentially, the same transfer was found in the calculations of Benson et al. [38]. On the other hand, X-ray photoelectron spectroscopy (XPS) and electron energy loss spectroscopy (EELS) measurements indicated a shift of a Zn Auger peak and softening of EELS fine structure could be caused by a small net charge transfer of 0.1 electron from Zn to Sb [39]. The apparent difference between reported experiments and calculations can be related to experimental uncertainties and different volumes that were chosen for the calculation.

Figure 3. Deformation charge density distribution in electron per Å<sup>2</sup> in the plane of a Zn2Sb2-ring calculated by GGA– PBE. The colour map indicates the isocharge density lines: red indicates accumulation of electrons, whereas blue shows loss of electrons in the relaxed structure of the compound compared with the number of electrons in the free atoms [36]. (DOI:10.1088/0953-8984/26/36/365401. © IOP Publishing. Reproduced with permission. All rights reserved.)

#### 2.2. Electronic structure

#### 2.2.1. Band calculations

bonds for building up the tetrahedron; the bonds vii and viii form the Zn2Sb2-ring; and the bonds ix1-6 are the dimers that connect the Zn2Sb2-rings. The angles between each Sb-Zn-Sb bond are also annotated in Figure 2d. Notice that the angles are close to those in regular tetrahedron, 109.5°. Therefore, even though the structure has five-fold coordination, one can still expect that ZnSb satisfies the tetrahedron rules to some extent. One of them is the electron count per bond. ZnSb has seven valence electrons per formula unit, whereas a regular tetrahedral binary semiconductor has eight valence electrons. Such electron-poor valence often indicates a metallic bond. Yet, ZnSb behaves as a semiconductor. The clue

dron, that often represents a semiconducting bond [30]. The counting rules cannot be applied on a per-bond-basis without considering the complete network. Therefore, all the atoms in the crystal structure are bonded together in a network. ZnSb, thereby, has been classified as an electron-poor framework semiconductor (EPFS) [26, 31]. A quite similar interpretation for the structure has been applied to the related compounds CdSb [30, 32–34]

Valence electrons in ZnSb have a certain distribution. Figure 3 shows the theoretical ab-initio calculations by GGA-PBE (Generalized Gradient Approximation with Perdew-Burke-

Figure 2. Crystal structure, bonding and coordination environment of ZnSb. (Reprinted with author's permission from [29]. ©X. Song, 2016.) (a) Structure in a 1×2×3 cell generated by Mozharivskyj's data [27]. Both the deformed tetrahedra and the Zn2Sb2-ring, as well as the interatomic distances between the nearest neighbours are annotated. (b) Highresolution scanning transmission electron microscopic (HR-STEM) imaging reveals atomic scale structure that is recognized corresponding to (a) and (c). (c) 3×1×3 cell shows the Zn2Sb2-ring network. Each ring has six nearest neighbours, connected by bonds ix1-6. (d) The angles between Sb-Zn-Sb are similar to that of the standard tetrahedron, 109.5°. The bonds i-vi are covalent bonds for building up the tetrahedron, while vii and viii are the bonds to form Zn2Sb2-ring; bonds

The results show that a Zn atom transfers a small average fraction of 0.26 electrons to Sb along Zn-Sb bond [37], which is expected due to the difference in Pauling electronegativity between Zn (1.65eV) and Sb (1.96eV). Essentially, the same transfer was found in the calculations of Benson et al. [38]. On the other hand, X-ray photoelectron spectroscopy (XPS) and electron energy loss spectroscopy (EELS) measurements indicated a shift of a Zn Auger peak and softening of EELS fine structure could be caused by a small net charge transfer of 0.1 electron

Ernzerhof exchange functionals) of the so-called deformation charge [36].

ix1-6 in (c) are the dimers, that connect the Zn2Sb2-rings.


about its semiconducting property is probably due to the sp<sup>3</sup>

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

and ZnAs [35].

The band structure of ZnSb has been calculated by ab-initio methods by many groups in recent years [2, 26, 31, 36–42]. The calculations are based upon density functional theory (DFT), but with varying detailed approximations and trade-offs between computational cost and accuracy. By comparing different calculated band diagrams, one can see some features that are common for most of the calculations and expect to filter out methodological errors in the different reports. Figure 4 shows calculation of ZnSb band diagram.

The zero energy position corresponds to the largest energy of filled states. Thus, the states below 0 correspond to the valence band, while those above correspond to the conduction band. The value of the band gap is severely underestimated by the computational approximations. By using more accurate methods but at the expense of increased computation time, such as HSE-hybrid functional (Heyd-Scuseria-Ernzerhof), the band gap was calculated to be around 0.5eV [37]. This value is close to the experimental value for single crystal ZnSb. On the other hand, the shape of the bands may be less affected by computational approximations. The band diagram in Figure 4 shares some of the features found in most of the calculations listed. The band gap is indirect with the maximum of the valence band along the symmetry line Γ-Χ and the minimum of the conduction band along Γ-Z. One can see that the conduction band contains more satellites within 0.5eV of the minimum than pockets of the maximum in the valence band. Thus, one can expect ZnSb would have acted better as an n-type material than a p-type material, if stable n-type doping could have been achieved.

Figure 4. Band diagram of ZnSb showing energy states along high symmetry directions in k-space calculated by Berland et al. [2] using GGA—PBE. The Brillouin zone for orthorhombic lattice with the high symmetry symbols are shown in inset for indication. (Reprinted with author's permission from [29]. ©X. Song, 2016.)

It is worth mentioning the band diagram that was calculated by Yamada in 1978 by using pseudopotentials [43]. The maximum of the valence band was found to be on the line from Γ-Χ at k = (0.93π/a, 0.0), which is close to the DFT values, and the band gap was 0.6eV. However, a minimum of the conduction band is located at k= (0.47π/a, 0.0) along Γ-Χ, which is not in agreement with most DFT calculations, and it is hard to determine experimentally due to the difficulty in preparing n-type ZnSb.

#### 2.2.2. Experimental band gap

The band gap has been measured by different methods. Values of 0.5–0.53eV for single crystal ZnSb, which were measured by optical absorption, have been reported [44, 45]. These values are essentially identical when considering the uncertainties, and 0.5eV has been considered to be a reference value for single crystal ZnSb. Many research have also determined the thermodynamic band gap from the temperature dependence of the charge carrier concentration in the intrinsic regime. The charge carrier concentration is determined from the Hall coefficient, RH. A linear fit of lnRHT 3 <sup>2</sup> vs. <sup>1</sup> <sup>T</sup> will yield the activation energy, which is half of the thermodynamic energy gap. (This assumes an effective density of states proportional to T 3 2.). Values of 0.47– 0.65eV have been reported in the literature for single crystal ZnSb based upon Hall effect measurements [46, 47].

For polycrystalline ZnSb, the band gap is often reported to be around 0.31–0.35eV [13, 48], which is smaller than that of single crystal material. It is justified to discuss whether the band gap really is different, or if it is due to that the idealizations of the measurement methods do not hold for polycrystalline material. One of the methods that has been used for estimating the band gap is to measure the temperature dependence of the Seebeck coefficient. By determining the temperature, Tmax, for the maximum of the absolute value of the Seebeck coefficient, αmax, the band gap can be estimated from the Goldsmid formula, Eg ¼ 2qαmaxTmax [49]. This method works well for many semiconductors, for instance Zr-NiSn half-Heusler [50]. However, there have been reports on some systems that the Goldsmid formula does not apply [51, 52]. ZnSb may be one of them. Guo and Luo have reported that the Goldsmid formula returned a value of Eg =0.3eV for their polycrystalline ZnSb samples [23]. However, Böttger et al. justified that for the samples that have a band gap of 0.3eV obtained by Goldsmid formula, the temperature-dependent resistivity was fitted better with a value of 0.44eV [53]. It is fair to state that it depends upon the context whether it is best to reconsider the band gap value for polycrystalline or reconsider the idealizations used in the measurement methods.

We should also keep in mind that heavily doping may influence the density of states near the band edges, forming tails that are extending into the band gap. The defect states in the band gap also influence the Eg values. This is a well-documented phenomenon (for Si) [54], even if the precision in a detailed quantitative understanding may be lacking. We have reported that the maximum of the Seebeck coefficient of ZnSb could be varied considerably by the presence of defect states in the band gap [52].

#### 2.2.3. Effective mass and density of states

line Γ-Χ and the minimum of the conduction band along Γ-Z. One can see that the conduction band contains more satellites within 0.5eV of the minimum than pockets of the maximum in the valence band. Thus, one can expect ZnSb would have acted better as an n-type material

It is worth mentioning the band diagram that was calculated by Yamada in 1978 by using pseudopotentials [43]. The maximum of the valence band was found to be on the line from Γ-Χ at k = (0.93π/a, 0.0), which is close to the DFT values, and the band gap was 0.6eV. However, a minimum of the conduction band is located at k= (0.47π/a, 0.0) along Γ-Χ, which is not in agreement with most DFT calculations, and it is hard to determine experimentally due to the

Figure 4. Band diagram of ZnSb showing energy states along high symmetry directions in k-space calculated by Berland et al. [2] using GGA—PBE. The Brillouin zone for orthorhombic lattice with the high symmetry symbols are shown in inset

The band gap has been measured by different methods. Values of 0.5–0.53eV for single crystal ZnSb, which were measured by optical absorption, have been reported [44, 45]. These values

difficulty in preparing n-type ZnSb.

for indication. (Reprinted with author's permission from [29]. ©X. Song, 2016.)

2.2.2. Experimental band gap

than a p-type material, if stable n-type doping could have been achieved.

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

The idealized single parabolic band (SPB) model is convenient for analysing experimental results. The model has been successful for finding the optimum doping concentration of many thermoelectric materials [55–57]. When applied to Seebeck measurements on ZnSb with different doping concentrations, it has been observed that Pisarenko plot (the Seebeck coefficient vs. the charge carrier concentration) does not follow the SPB model with a single density of states effective mass m�, which was determined to be (0.42–0.49)×m0, where m<sup>0</sup> is free electron mass [15, 53], but rather a different mass fit for different ranges of doping concentrations. A previous study by Böttger et al. has suggested that deviations from idealized SPB behaviour could be induced by impurity band states [53]. We have showed that deviations from simple SPB behaviour at varying doping concentration could be modelled by introducing an impurity band [52]. One may comment that the best fit with varying m� is not necessary to imply that the energy band curvature varies. It suffices that the temperature-dependent position of the Fermi level varies differently than that in an idealized SPB case.

## 3. Electrical properties and doping effect

#### 3.1. Electrical properties and scattering mechanisms

Table 2 summarizes the band gap, the charge carrier concentration and other electrical and thermal properties reported for ZnSb in the literature.

Given the crystal structure, single crystal ZnSb exhibits anisotropic conduction, which is strongly dependent on the anisotropic effective mass [58]. Böttger et al. determined each mass tensor component from band diagram calculations [53]. Different components were given by m� <sup>a</sup> ¼ 0:1811m0; m� <sup>b</sup> ¼ 0:4913m0; m� <sup>c</sup> ¼ 0:0837m0. The results agree with the anisotropic Hall mobility and the highest electrical conductivity is measured along the c-axis [15, 45]. Anisotropic energy surface has also been observed by optical absorption indicating that the constant energy surface in k-space in ZnSb is a spheroid [59].

There is much literature devoted to scattering mechanisms in semiconductors [65], while there are fewer reports dealing with that topic specifically for ZnSb. It is expected that ZnSb has similar behaviour to those semiconductors which have been much studied and follows similar trends. ZnSb appears to have favourably small polarity due to small electronegativity difference between Zn and Sb. This would in turn lead to a negligible polar optical phonon scattering compared to III–V and II–VI compounds where polar optical phonon scattering may be dominant. Roughly, transport in ZnSb is dominated by impurity scattering at low temperature, while at higher temperature, when lattice vibrations are stronger, longitudinal acoustic phonon scattering dominates (deformation potential scattering). The hole mobility varies with temperature as μ∝T<sup>r</sup> , thus a plot of lnμ vs. T will give the scattering factor r that implies the scattering mechanism. A value of -1 to -1.5 typically indicates that longitudinal acoustic phonon scattering dominates. In Figure 5a, the slopes of the Hall mobility approaches -1.5 as the doping concentration decreases. It indicates that acoustic phonon scattering dominates within the temperature range. The deviation from -1.5 for each individual curve is attributed to additional ionized impurity scattering [66]. It is also seen that the higher hole concentration corresponds to an increase in ionized impurity scattering, which limits the hole mobility.

Not only the intentional dopants, but also defects, that are ionized or neutralized, screened or unscreened, contribute to scattering. Likely scattering centres are Zn vacancies, interstitials, internal strain, grain boundaries and dislocations. Figure 5b shows the resistivity for an unprocessed ZnSb ingot that was obtained directly from solidification and hot-pressed ZnSb pellets with different dopant concentrations. The temperature coefficient, <sup>d</sup><sup>ρ</sup> dT, for the unprocessed ingot is positive, which is commonly observed for metals and semiconductors in a certain temperature range where phonon scattering dominates. For the processed samples, either with or without Ag, the temperature coefficient <sup>d</sup><sup>ρ</sup> dT is negative. The reason for the negative temperature coefficient could be the dominant Coulomb scattering due to charged defects or impurities.


the energy band curvature varies. It suffices that the temperature-dependent position of the

Table 2 summarizes the band gap, the charge carrier concentration and other electrical and

Given the crystal structure, single crystal ZnSb exhibits anisotropic conduction, which is strongly dependent on the anisotropic effective mass [58]. Böttger et al. determined each mass tensor component from band diagram calculations [53]. Different components were given by m�<sup>a</sup> ¼ 0:1811m0; m�<sup>b</sup> ¼ 0:4913m0; m�<sup>c</sup> ¼ 0:0837m0. The results agree with the anisotropic Hall

tropic energy surface has also been observed by optical absorption indicating that the constant

There is much literature devoted to scattering mechanisms in semiconductors [65], while there are fewer reports dealing with that topic specifically for ZnSb. It is expected that ZnSb has similar behaviour to those semiconductors which have been much studied and follows similar trends. ZnSb appears to have favourably small polarity due to small electronegativity difference between Zn and Sb. This would in turn lead to a negligible polar optical phonon scattering compared to III–V and II–VI compounds where polar optical phonon scattering may be dominant. Roughly, transport in ZnSb is dominated by impurity scattering at low temperature, while at higher temperature, when lattice vibrations are stronger, longitudinal acoustic phonon scattering dominates (deformation potential scattering). The hole mobility varies with

scattering mechanism. A value of -1 to -1.5 typically indicates that longitudinal acoustic phonon scattering dominates. In Figure 5a, the slopes of the Hall mobility approaches -1.5 as the doping concentration decreases. It indicates that acoustic phonon scattering dominates within the temperature range. The deviation from -1.5 for each individual curve is attributed to additional ionized impurity scattering [66]. It is also seen that the higher hole concentration corresponds to an increase in ionized impurity scattering, which limits the hole mobility.

Not only the intentional dopants, but also defects, that are ionized or neutralized, screened or unscreened, contribute to scattering. Likely scattering centres are Zn vacancies, interstitials, internal strain, grain boundaries and dislocations. Figure 5b shows the resistivity for an unprocessed ZnSb ingot that was obtained directly from solidification and hot-pressed ZnSb

ingot is positive, which is commonly observed for metals and semiconductors in a certain temperature range where phonon scattering dominates. For the processed samples, either with

> d ρ

coefficient could be the dominant Coulomb scattering due to charged defects or impurities.

T will give the scattering factor

d ρ

dT is negative. The reason for the negative temperature

c-axis [15, 45]. Aniso-

r that implies the

dT, for the unprocessed

Fermi level varies differently than that in an idealized SPB case.

mobility and the highest electrical conductivity is measured along the

k-space in ZnSb is a spheroid [59].

, thus a plot of ln

μ vs.

pellets with different dopant concentrations. The temperature coefficient,

3. Electrical properties and doping effect

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

3.1. Electrical properties and scattering mechanisms

thermal properties reported for ZnSb in the literature.

energy surface in

temperature as

μ ∝ T r

or without Ag, the temperature coefficient

Figure 5. (a) Hall mobility along the c-axis as a function of temperature for p-type ZnSb at various hole concentrations (1) 3×1016cm-3; (2) 4×1017cm-3; (3) 5.5×1017cm-3; (4) 1×1019cm-3. (Reprinted with permission from [15]. Copyright (1966) by the American Physical Society.) (b) Resistivity vs. temperature of ball-milled and hot-pressed samples with varying silver content. Inset: unprocessed sample (Ingot) [16]. (Reprinted with permission of Springer.)

#### 3.2. Doping effects

The most direct purpose of doping is to vary the charge carrier concentration. A broad range of dopant elements has been reported for ZnSb. The selection of dopant is often rationalized based on the same valence electron counting scheme that is applied to the elemental group IV, III–V or II–VI tetrahedrally bonded semiconductors. These considerations are applied for acceptors, while donors are challenging. One will have acceptors by replacing group I elements for Zn or group IV elements for Sb. It is expected that donors can be substitutes for group III elements on Zn sites and group VI elements on Sb sites. In all cases, there may be an issue with doping efficiency, i.e. not all the added dopant atoms will be electrically active. It is common and qualitatively well-understood for other semiconductors that this inefficiency involves segregation (solid solubility limit), clustering of dopant atoms and/or agglomeration of complexes of dopant atoms and point defects. A theoretical calculation predicts that the optimum hole concentration for the thermoelectric efficiency of ZnSb is around 2×1019cm-3 [53], which is achievable in p-type ZnSb. For donors in ZnSb, there may also be additional issues to what has been mentioned above.

#### 3.2.1. Acceptors

#### 3.2.1.1. IZn—acceptors as elements of group I

CuZn, AuZn, AgZn all yield p-type conduction [47, 67]. Most of the reported charge carrier concentrations are below the optimum value, and probably depend upon the details of sample preparation. However, the highest hole concentration that have been reported for Ag doping is 4×1019cm-3 (for 0.02at.% Ag) [19] while that for Cu is 2×1019cm-3 (for 0.1at.% Cu) [15, 21, 64]. There are several interesting behaviours that involve additional states in the band gap when doping with Cu. Some details can be seen in [52].

## 3.2.1.2. IVSb—acceptors as the elements of group IV

Hole concentrations around (4–14)×1018cm-3 were obtained in materials with a content of (0.06–3) at.% Sn [53, 68]. The hole concentration variations with Sn doping concentrations where apparently opposite for these two studies. The highest hole concentration of 14×1018 cm-3 was obtained for content 0.1at.% Sn [68] and yielded the highest mobility. It was suggested that two different doping mechanisms are effective in different temperature ranges involving different intrinsic defects, Sn on different lattice sites and their variation with temperature [68].

## 3.2.1.3. IZnIVSb—co-doping

Hole concentrations of (2–2.5)×1019cm-3 have been reported by co-doping of group I (0.15at.% Cu or Ag)/IV (0.6at.% Pb, Sn, or Ge)/Cd [20, 21]. The measured transport coefficients at different regions indicate two types of impurity acceptor: one embedded into Zn sites, and another into Sb sites. Here, Cd is not expected to act as an acceptor, but for increasing the phonon scattering and thereby reducing the thermal conductivity. A similar intended function has been applied by adding P to increase alloy phonon scattering in the Cu doped ZnSb [18, 69].

#### 3.2.2. Donors

3.2. Doping effects

3.2.1. Acceptors

issues to what has been mentioned above.

3.2.1.1. IZn—acceptors as elements of group I

The most direct purpose of doping is to vary the charge carrier concentration. A broad range of dopant elements has been reported for ZnSb. The selection of dopant is often rationalized based on the same valence electron counting scheme that is applied to the elemental group IV, III–V or II–VI tetrahedrally bonded semiconductors. These considerations are applied for acceptors, while donors are challenging. One will have acceptors by replacing group I elements for Zn or group IV elements for Sb. It is expected that donors can be substitutes for group III elements on Zn sites and group VI elements on Sb sites. In all cases, there may be an issue with doping efficiency, i.e. not all the added dopant atoms will be electrically active. It is common and qualitatively well-understood for other semiconductors that this inefficiency involves segregation (solid solubility limit), clustering of dopant atoms and/or agglomeration of complexes of dopant atoms and point defects. A theoretical calculation predicts that the optimum hole concentration for the thermoelectric efficiency of ZnSb is around 2×1019cm-3 [53], which is achievable in p-type ZnSb. For donors in ZnSb, there may also be additional

Figure 5. (a) Hall mobility along the c-axis as a function of temperature for p-type ZnSb at various hole concentrations (1) 3×1016cm-3; (2) 4×1017cm-3; (3) 5.5×1017cm-3; (4) 1×1019cm-3. (Reprinted with permission from [15]. Copyright (1966) by the American Physical Society.) (b) Resistivity vs. temperature of ball-milled and hot-pressed samples with varying silver

content. Inset: unprocessed sample (Ingot) [16]. (Reprinted with permission of Springer.)

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

CuZn, AuZn, AgZn all yield p-type conduction [47, 67]. Most of the reported charge carrier concentrations are below the optimum value, and probably depend upon the details of sample n-Type ZnSb is desired because (i) thermoelectric modules are preferably built of parallel legs of n-type and p-type materials, and it is preferable to use the same material (ZnSb) for minimizing the thermal stress; (ii) theoretically, n-type ZnSb is believed to be a much better thermoelectric material than p-type [36, 40, 42]. However, no real successful stable n-type doping has been achieved. But, temporary n-type behaviours have been reported by doping with group III and group VI elements.

## 3.2.2.1. IIIZn—donors as elements of group III

Group III elements have been used as donors to yield n-type conduction in CdSb [70]. It was later reported that ZnSb could also be made n-type by In doping, probably substituting Zn as InZn. AlZn and GaZn also exhibited temporary n-type behaviour [71, 72]. However, the n-type conduction did not always occur. Justi et al. did not achieve n-type ZnSb with Ga despite several attempts with single and polycrystalline ZnSb [14]. Niedziolka et al. predicted theoretically by DFT calculations that boron would electronically be a good candidate for n-type ZnSb, but did not succeed to synthesize the material and ascribed it to the high formation energy of a boron atom on a Zn site [36].

## 3.2.2.2. VISb—donors as elements of group VI

Some success with Te doping has been reported. Ueda et al. reported that a Te content in very narrow window around 2at.% yielded n-type, possibly by forming substitutions of Te atoms on Sb sites, TeSb; while at lower concentration (<1at.%) and higher concentrations (>3at.%), the samples are always p-type. Excess doping with Te results in precipitation of the ZnTe phase and a change in conduction from n- to p-type [73]. No n-type doping was observed by S doping [29].

#### 3.2.2.3. n-Type to p-type transition

A temporary n-type behaviour with a transition to p-type has been reported. Explanations for these behaviours are related to such factors as oxygen migration on internal surfaces or grain boundaries [71]. Schneider has reported an n-type to p-type transition in n-type ZnxCd1-xSb every time when an oxygen gas was flushed into the sample container, and relaxed back to ntype after a certain time [71]. Another factor entering into explanations are Zn vacancies acting as acceptors and their migration [36, 42, 74]. A similar transition from n-type to p-type also occurs in the related compound CdSb, which has been attributed to Cd-vacancies [75].

## 4. Zn vacancies and intrinsic defects

The theoretical intrinsic charge carrier concentration of perfect ZnSb at room temperature is approximately 2×1014cm-3 given by pi <sup>¼</sup> <sup>2</sup> <sup>2</sup>πm�kBT h2 <sup>3</sup> 2 eη , where <sup>η</sup> <sup>¼</sup> <sup>−</sup> Eg <sup>2</sup>kBT, and taking Eg ¼ 0:53 eV and m� ¼ 0:42×m<sup>0</sup> [15]. However, the experimental measurements show that the charge carrier concentration of the best single crystals at room temperature is around (1–2)×1016cm-3 [15, 46, 61, 62] and up to ∼1018cm-3 for polycrystalline samples without intended dopants [14, 45]. This deviation is considered due to the intrinsic defects, giving a net hole concentration. The most favoured intrinsic defects in ZnSb are Zn vacancies, which are believed to yield ptype conduction [42, 74]. The intrinsic defects in ZnSb have been calculated on by DFT methods [42, 74]. The calculations gave much lower formation energies for Zn vacancies than other intrinsic defects, meaning that Zn vacancies will out-number other intrinsic defects by orders of magnitude. Discrete vacancy defect states are considered to accept electrons from (or donate electrons to) the bands, if they are negatively (or positively) charged. The charge state of the defect will depend on the Fermi level for electrons. This can, in principle, be calculated from the condition of electrical charge conservation (charge neutrality). Figure 6 shows a conceptual schematic model of a Zn vacancy in different charge states. It is based upon a combination of interpretation of Bjerg et al.'s work [74] and a popularization of Fairs Vacancy model for silicon [76].

The vacancy can in principle have any charge states, but only -2, -1 and 0 seem readily accessible by doping and temperature variation. The formation energy for VZn- in this configuration was calculated to be 0.32eV. The net hole concentration in ZnSb without any doping was then calculated from the requirement of charge neutrality and assuming equilibrium number of vacancies in different charge states (-1 and -2 dominated). The net hole concentration in this configuration was calculated to be 8.8×1017cm-3 at room temperature, which is in the range of the experimental Hall concentrations measured by Böttger et al. (4–10)×1017cm-3 [16]. One should also compare the calculated net hole concentration to the hole concentration of undoped single crystal ZnSb that is significantly lower than 8.8×1017cm-3. This apparent discrepancy indicates that exact values of formation energies should be used with caution. However, the concepts and the idea of VZn as a very important defect seem valid.

3.2.2.2. VISb—donors as elements of group VI

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3.2.2.3. n-Type to p-type transition

4. Zn vacancies and intrinsic defects

model for silicon [76].

approximately 2×1014cm-3 given by pi <sup>¼</sup> <sup>2</sup> <sup>2</sup>πm�kBT

doping [29].

Some success with Te doping has been reported. Ueda et al. reported that a Te content in very narrow window around 2at.% yielded n-type, possibly by forming substitutions of Te atoms on Sb sites, TeSb; while at lower concentration (<1at.%) and higher concentrations (>3at.%), the samples are always p-type. Excess doping with Te results in precipitation of the ZnTe phase and a change in conduction from n- to p-type [73]. No n-type doping was observed by S

A temporary n-type behaviour with a transition to p-type has been reported. Explanations for these behaviours are related to such factors as oxygen migration on internal surfaces or grain boundaries [71]. Schneider has reported an n-type to p-type transition in n-type ZnxCd1-xSb every time when an oxygen gas was flushed into the sample container, and relaxed back to ntype after a certain time [71]. Another factor entering into explanations are Zn vacancies acting as acceptors and their migration [36, 42, 74]. A similar transition from n-type to p-type also

The theoretical intrinsic charge carrier concentration of perfect ZnSb at room temperature is

h2 <sup>3</sup> 2 eη

eV and m� ¼ 0:42×m<sup>0</sup> [15]. However, the experimental measurements show that the charge carrier concentration of the best single crystals at room temperature is around (1–2)×1016cm-3 [15, 46, 61, 62] and up to ∼1018cm-3 for polycrystalline samples without intended dopants [14, 45]. This deviation is considered due to the intrinsic defects, giving a net hole concentration. The most favoured intrinsic defects in ZnSb are Zn vacancies, which are believed to yield ptype conduction [42, 74]. The intrinsic defects in ZnSb have been calculated on by DFT methods [42, 74]. The calculations gave much lower formation energies for Zn vacancies than other intrinsic defects, meaning that Zn vacancies will out-number other intrinsic defects by orders of magnitude. Discrete vacancy defect states are considered to accept electrons from (or donate electrons to) the bands, if they are negatively (or positively) charged. The charge state of the defect will depend on the Fermi level for electrons. This can, in principle, be calculated from the condition of electrical charge conservation (charge neutrality). Figure 6 shows a conceptual schematic model of a Zn vacancy in different charge states. It is based upon a combination of interpretation of Bjerg et al.'s work [74] and a popularization of Fairs Vacancy

The vacancy can in principle have any charge states, but only -2, -1 and 0 seem readily accessible by doping and temperature variation. The formation energy for VZn- in this configuration was calculated to be 0.32eV. The net hole concentration in ZnSb without any doping was then calculated from the requirement of charge neutrality and assuming equilibrium

, where <sup>η</sup> <sup>¼</sup> <sup>−</sup> Eg

<sup>2</sup>kBT, and taking Eg ¼ 0:53

occurs in the related compound CdSb, which has been attributed to Cd-vacancies [75].

Figure 6. Schematic drawing of occupancy of localized states associated with the Zn vacancy in ZnSb. (Reprinted with author's permission from [29]. ©X. Song, 2016.) The vacancy will have different charge states -1, -2, -3 dependent upon the position of the Fermi level EF with respect to the levels E<sup>−</sup><sup>1</sup> <sup>V</sup> , <sup>E</sup><sup>−</sup><sup>2</sup> <sup>V</sup> and <sup>E</sup><sup>−</sup><sup>3</sup> <sup>V</sup> . EV is the valence band onset and EC is the conduction band (CB) onset.

There have been many reports on changes in charge carrier concentration after heat treatments, both for single crystal and polycrystalline ZnSb. Many observed a slow recovery to the initial values of the charge carrier concentration [15, 20, 44, 45, 47, 61, 77]. Andronik et al. specifically attributed this change to Frenkel defects [77]: by Zn atoms leaving their lattice sites and becoming vacancy-interstitial pairs, VZn-ZnI. By assuming that all of the measured changes in charge carrier concentration were due to Frenkel defect formation, the activation energy of the process could be determined. The Frenkel defect concentration n<sup>ϕ</sup> was assumed to be given by n<sup>ϕ</sup> ¼ ffiffiffiffiffiffiffiffiffi NN′ <sup>p</sup> e − <sup>E</sup><sup>ϕ</sup> 2kBT , where n<sup>ϕ</sup> ¼ ni−n<sup>0</sup> is the concentration of Frenkel defect, n<sup>0</sup> and ni are the concentration before and after heating, respectively, N is the concentration of atoms, N′ is the concentration of interstitials (there are more than one interstitial position in the lattice), E<sup>ϕ</sup> is the formation energy of a Frenkel pair. The formation energy was determined from experiments to be 0.5eV. This experimental value seems in the range of formation energies calculated by Bjerg et al. [74]. On the other hand, the formation energy for a Zn vacancy calculated by Jund et al. gave a different value of 0.8eV [42]. This calculation used a Zn64Sb64 supercell with 128 lattice sites and compared it to the energy of a Zn63Sb64 supercell at 0K, which corresponds to a vacancy concentration of 1.5at.%.

Recently, we have studied evaporation of Zn by thermogravimetry and Zn vacancy created during vaporization [29]. The net hole concentration was measured to be about 6×1018cm-3, corresponding to a vacancy concentration of about 0.03at.%. Schematically, two processes in series were considered as:

$$\mathbf{ZnSb(s)} \nRightarrow \mathbf{Zn\_{1-x}Sb(s) + x \cdot Zn(g)},\tag{1}$$

$$\text{ZnSb}(s) \Leftarrow \text{Zn}(g) + \text{Sb}(s). \tag{2}$$

Reaction (1) occurs when the VZn was created but within the dilute limit, while reaction (2) applies to a situation where the Zn vacancy concentration is beyond the solubility limit and ZnSb decomposes into Sb phase and Zn vapour.

## 5. Impurity band conduction

In an idealized semiconductor, which is well-approximated by pure Si crystals [78], the charge carrier concentration shows the so-called freeze out at low (cryogenic) temperatures: the dopant atoms are not ionized and the charge carrier concentration goes towards zero, characterized by an infinite Hall coefficient in Hall measurements. However, the Hall coefficient in undoped ZnSb has shown a turning point at low temperatures, typically below 50K, as seen in Figure 7, and then a decrease with further cooling, which is explained by impurity band conduction [79]. Here, the term impurity band is most likely tied to defects, but observed phenomena are similar to what can be observed for high doping concentration in semiconductors. Impurity band conduction has been reported in many materials [80–82]. It was also observed for ZnSb by Justi et al. in the 1960s [14]. Recently, several others have reported on impurity bands in ZnSb [53, 79, 83].

Let us here analyse sketchily the conditions for observing the characteristics shown in Figure 7. The specifics of this observation are given in [79]. The changes in hole concentration as the sample was cooled is in principle similar to that of a textbook low doping concentration semiconductor, where the charge carriers are frozen out of the valence band. The valence band of the sample in Figure 7 will be nearly empty (for holes) at the lowest temperature. The holes are transferred to the acceptor-based impurity band. However, the holes are mobile in the impurity band and contribute to conduction and Hall effect. Thus, the Hall coefficient decreases with cooling to the lowest temperatures. In order to get conduction in the impurity band, some donor compensating centres are needed. (Without donor level, the impurity band would be full of holes, i.e. empty for electrons and there is no conduction).

from experiments to be 0.5eV. This experimental value seems in the range of formation energies calculated by Bjerg et al. [74]. On the other hand, the formation energy for a Zn vacancy calculated by Jund et al. gave a different value of 0.8eV [42]. This calculation used a Zn64Sb64 supercell with 128 lattice sites and compared it to the energy of a Zn63Sb64 supercell

Recently, we have studied evaporation of Zn by thermogravimetry and Zn vacancy created during vaporization [29]. The net hole concentration was measured to be about 6×1018cm-3, corresponding to a vacancy concentration of about 0.03at.%. Schematically, two processes in

Reaction (1) occurs when the VZn was created but within the dilute limit, while reaction (2) applies to a situation where the Zn vacancy concentration is beyond the solubility limit and

In an idealized semiconductor, which is well-approximated by pure Si crystals [78], the charge carrier concentration shows the so-called freeze out at low (cryogenic) temperatures: the dopant atoms are not ionized and the charge carrier concentration goes towards zero, characterized by an infinite Hall coefficient in Hall measurements. However, the Hall coefficient in undoped ZnSb has shown a turning point at low temperatures, typically below 50K, as seen in Figure 7, and then a decrease with further cooling, which is explained by impurity band conduction [79]. Here, the term impurity band is most likely tied to defects, but observed phenomena are similar to what can be observed for high doping concentration in semiconductors. Impurity band conduction has been reported in many materials [80–82]. It was also observed for ZnSb by Justi et al. in the 1960s [14]. Recently, several others have reported on

Let us here analyse sketchily the conditions for observing the characteristics shown in Figure 7. The specifics of this observation are given in [79]. The changes in hole concentration as the sample was cooled is in principle similar to that of a textbook low doping concentration semiconductor, where the charge carriers are frozen out of the valence band. The valence band of the sample in Figure 7 will be nearly empty (for holes) at the lowest temperature. The holes are transferred to the acceptor-based impurity band. However, the holes are mobile in the impurity band and contribute to conduction and Hall effect. Thus, the Hall coefficient decreases with cooling to the lowest temperatures. In order to get conduction in the impurity band, some donor compensating centres are needed. (Without donor level, the impurity band would be full of holes, i.e. empty for electrons and there is

ZnSbðsÞ⇌Zn1<sup>−</sup>xSbðsÞ þ x � ZnðgÞ, (1)

ZnSbðsÞ⇌ZnðgÞ þ SbðsÞ: (2)

at 0K, which corresponds to a vacancy concentration of 1.5at.%.

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

ZnSb decomposes into Sb phase and Zn vapour.

5. Impurity band conduction

impurity bands in ZnSb [53, 79, 83].

no conduction).

series were considered as:

Figure 7. The Hall coefficient of an undoped hot-pressed ZnSb sample. (Reprinted with author's permission from [29]. ©X. Song, 2016.) The Hall coefficient in ideal cases is inversely proportional to the charge carrier concentration. If there was regular freeze-out of the charge carriers, the Hall coefficient goes to infinity at low temperatures. However, in the presented case of undoped ZnSb, there is a turning point in the Hall coefficient, which was interpreted as a signature of an impurity band.

We turn to a situation where the doping concentration is much higher than that of the sample in Figure 7, and first consider the large difference in characteristic features of the change in the charge carrier concentration with temperature. Figure 8 compares the Hall concentration of the charge carrier and the Hall mobility (inset) at low temperature for high (0.3at.% Cu) and lower concentration (no Cu), respectively (data in Refs. [52, 79]). One can see that the characteristic feature of impurity band conduction vanished in the highly doped sample at low temperature. The situation is qualitatively as follows: A highly doped sample is equivalent to a degenerate semiconductor, where the hole concentration is high and the Fermi level is located in the valence band. The native impurity band would be full of holes and so would the top of the valence band. At the lowest temperatures, the conduction will occur within the valence band. Therefore, one cannot have a similar change with temperature as in the case of undoped ZnSb where there was a vanishing conduction in the valence band at the lowest temperature.

Figure 8. Temperature dependence of the Hall concentration of charge carriers at the temperature lower than 300K of highly doped ZnSb (0.3at.% Cu content) and undoped ZnSb. (Reprinted with author's permission from [29]. ©X. Song, 2016.). Inset: the Hall mobility.

#### 5.1. The impurity band in ZnSb—its nature, origin and specific points of interest

The nature and theoretical treatment of general impurity band can be found in textbooks [84]. The band states are considered to come from interactions, which set in for concentrations above a certain value of defect species, such as dopant atoms, impurities or intrinsic crystal defects.

The formation of impurity band is illustrated in Figure 9 for an n-type semiconductor. Electrons at a donor level can be transferred to a neighbour donor by thermal activation and tunnelling, but without entering into states in the conduction band. One would then have the hopping regime for transport in the material as illustrated in Figure 9a. When the donor concentration increases further, the wave functions of the donor states overlap and can form a band, where one has impurity band conduction, as illustrated in Figure 9b.

The mobility in the impurity band is typically small because the band is relatively narrow, and as a consequence, one would have a small dispersion curvature in Eðk ⇀ Þ and large effective mass. In a semiconductor, at low temperature, conduction can occur dominantly in the impurity band if there are some compensating levels, such that the impurity band is not fully occupied. At a particular higher concentration, there may be a smear of the impurity band and the conduction band, as illustrated in Figure 9c. Beyond this concentration, the Mott transition, which is a sharp transition from insulator to metal behaviour, can take place.

Figure 9. Schematics of impurity state/band and conduction band (CB) for n-type semiconductor at low impurity concentration, medium concentration and high concentration at random impurity distribution. Band diagrams illustrate the hopping conduction and impurity band conduction. (Reprint with author's permission from [84]. ©E. Fred Schubert, 2015). Inset: dimensional schematic calculated density of states for high impurity concentration. E<sup>0</sup> is assumed to be the onset of the conduction band; DCðEÞ is the number of conduction band and DimðEÞ is the density of states of impurities in periodically arrangement. (Reprinted with permission from [85]. Copyright (1953) American Chemical Society.)

Usually, the Mott criterion for when the transition occurs is NI≥0:014a<sup>−</sup><sup>3</sup> <sup>B</sup> , where NI is the atomic concentration of impurities and aB is the Bohr radius of the impurity. There are several different treatments yielding essentially the same numbers [84]. The most considered situations are those of high concentrations of shallow donors or acceptors. Here, the Mott criterion gives the insulator-metal transition. However, one can create impurity bands with a certain energy anywhere in the band gap. Some of the concentrations for the Mott transition then approximately correspond to the concentration to have an impurity band. Rawat et al. have suggested a Yb mid-gap impurity band in PbTe affecting the thermoelectric properties [86].

5.1. The impurity band in ZnSb—its nature, origin and specific points of interest

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

band, where one has impurity band conduction, as illustrated in Figure 9b.

as a consequence, one would have a small dispersion curvature in Eðk

defects.

2016.). Inset: the Hall mobility.

The nature and theoretical treatment of general impurity band can be found in textbooks [84]. The band states are considered to come from interactions, which set in for concentrations above a certain value of defect species, such as dopant atoms, impurities or intrinsic crystal

Figure 8. Temperature dependence of the Hall concentration of charge carriers at the temperature lower than 300K of highly doped ZnSb (0.3at.% Cu content) and undoped ZnSb. (Reprinted with author's permission from [29]. ©X. Song,

The formation of impurity band is illustrated in Figure 9 for an n-type semiconductor. Electrons at a donor level can be transferred to a neighbour donor by thermal activation and tunnelling, but without entering into states in the conduction band. One would then have the hopping regime for transport in the material as illustrated in Figure 9a. When the donor concentration increases further, the wave functions of the donor states overlap and can form a

The mobility in the impurity band is typically small because the band is relatively narrow, and

⇀

Þ and large effective

With the doping concentrations for optimum thermoelectric performance that typically is ∼1019cm-3, it is reasonable to expect that the formation of impurity bands is rather common in thermoelectric materials. Also, impurity band formation is just one of several high doping effects one should expect, such as the Mott transition, band tailing and band gap renormalization [84]. Thus, one should discuss thermoelectric material in the framework of the theory related to heavily doped semiconductors.

When it comes to ZnSb specifically, it has been estimated that the impurity band may exist for the impurity concentrations that are well within the observed doping concentrations. We have determined the critical impurity concentration in ZnSb to be about 6×1017cm-3 in previous study, which is around the acceptor concentrations used in the model to fit the low temperature measurements [79]. For the doping concentration of 1018–1019cm-3 in ZnSb, one can expect impurity bands to form. For undoped or very lightly doped material, we suggested that point defects, especially Zn vacancies can be expected to be involved in impurity bands. From the discussion of vacancy formation in Section4, it appears likely that a high concentration of vacancies can be created by annealing, even to some extent they could combine with any other possible impurities or defects in impurity band. The impurities will likely be dependent on the specific dopants and the preparation technique. For example, oxygen is expected to be an impurity in ball-milled material and the amount introduced will depend upon the atmosphere during processing. Presently, one cannot make a conclusion about the importance of oxygen in this context and the solid solubility of oxygen is unknown. Fedorov et al. observed evidence for impurity levels in the band gap associated with different combinations of group I (Ag or Cu) and group IV (Sn or Ge) acceptor elements, which all were similar to each other, but different to those of the single acceptor element [21]. Temperature-dependent transport coefficients were also measured that were interpreted as a temperature-dependent energy state being present with a level in the valence band. The energy states were considered as hybridized states formed by mixing characteristics of the valence band and the impurity band. In a general case, a temperature-dependent level can have a similar effect as a defect chemistry reaction involving growth and decrease with temperature of the population of two defect species having different energy, as suggested in Ref. [52].

#### 5.2. Impact of impurity band on thermoelectric properties

An impurity band will have an effect on the transport properties and the thermoelectric device properties. It may not be immediately transparent how. The conduction in the impurity band is perhaps a minor effect in this context. The most important effect may be on the Seebeck coefficient.

#### 5.2.1. Effect on conduction

The effect of impurity bands on the electrical conductivity is expected to be largest when holes in the valence band (for p-type) do not contribute to the conduction [53]. This is expected to have a strong effect for samples where the doping is below degenerate, but sufficiently close to the Mott criterion, and in addition at low temperatures. It is expected, that in a thermoelectric material, the mobility of the charge carriers in an impurity band is much lower than that in the valence band, thus the impurity band should only have a modest effect on the electrical conductivity when valence band conduction is strong.

#### 5.2.2. Effect upon Seebeck—effective density of states mass

The density of states effective mass may be affected by an impurity band. The density of states may be changed by several high doping effects including the formation of impurity bands. Qualitatively a smear of the impurity band and valence band is expected. Thus, even though the conduction of impurity band is often only observable at low temperature, the Seebeck coefficient can be affected above room temperature. The details to calculate the transport coefficients can be found in Ref. [79]. The Seebeck coefficient is sensitive to the position of the Fermi level and how the density of states varies with energy. Both these factors can be affected by an impurity band. There have been reports on change of density of states effective mass with varying doping concentration [53]. From a Pisarenko plot, one can find the density of states effective mass by fitting measured data. In Ref. [52], we obtained the best fitting by assuming an impurity band. Further, it was shown that camel-shaped curves of Seebeck coefficient with temperature, which is unusual in ZnSb, could be modelled by a temperaturedependent impurity band. It has been suggested that if one could engineer the energy structure of impurity band, then one could have a tool to enhance the thermoelectric performance [87].

Another impact of the impurity band may be on the n-type to p-type transition. This was suggested by Schneider by the observation of a sharp increase in the electrical conductivity on a temporary n-type and following n-type to p-type transition [71]. On a similar topic, though with different statements, Fedorov et al. rationalized the difficulty in doping ZnSb ntype by the formation of an impurity band close to the conduction band [21].

## 6. ZnSb synthesis techniques

determined the critical impurity concentration in ZnSb to be about 6×1017cm-3 in previous study, which is around the acceptor concentrations used in the model to fit the low temperature measurements [79]. For the doping concentration of 1018–1019cm-3 in ZnSb, one can expect impurity bands to form. For undoped or very lightly doped material, we suggested that point defects, especially Zn vacancies can be expected to be involved in impurity bands. From the discussion of vacancy formation in Section4, it appears likely that a high concentration of vacancies can be created by annealing, even to some extent they could combine with any other possible impurities or defects in impurity band. The impurities will likely be dependent on the specific dopants and the preparation technique. For example, oxygen is expected to be an impurity in ball-milled material and the amount introduced will depend upon the atmosphere during processing. Presently, one cannot make a conclusion about the importance of oxygen in this context and the solid solubility of oxygen is unknown. Fedorov et al. observed evidence for impurity levels in the band gap associated with different combinations of group I (Ag or Cu) and group IV (Sn or Ge) acceptor elements, which all were similar to each other, but different to those of the single acceptor element [21]. Temperature-dependent transport coefficients were also measured that were interpreted as a temperature-dependent energy state being present with a level in the valence band. The energy states were considered as hybridized states formed by mixing characteristics of the valence band and the impurity band. In a general case, a temperature-dependent level can have a similar effect as a defect chemistry reaction involving growth and decrease with temperature of the population of two defect species

An impurity band will have an effect on the transport properties and the thermoelectric device properties. It may not be immediately transparent how. The conduction in the impurity band is perhaps a minor effect in this context. The most important effect may be on the Seebeck coefficient.

The effect of impurity bands on the electrical conductivity is expected to be largest when holes in the valence band (for p-type) do not contribute to the conduction [53]. This is expected to have a strong effect for samples where the doping is below degenerate, but sufficiently close to the Mott criterion, and in addition at low temperatures. It is expected, that in a thermoelectric material, the mobility of the charge carriers in an impurity band is much lower than that in the valence band, thus the impurity band should only have a modest effect on the electrical

The density of states effective mass may be affected by an impurity band. The density of states may be changed by several high doping effects including the formation of impurity bands. Qualitatively a smear of the impurity band and valence band is expected. Thus, even though the conduction of impurity band is often only observable at low temperature, the Seebeck coefficient can be affected above room temperature. The details to calculate the transport coefficients can be found in Ref. [79]. The Seebeck coefficient is sensitive to the position of the Fermi level and how the density of states varies with energy. Both these factors can be affected

having different energy, as suggested in Ref. [52].

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

5.2.1. Effect on conduction

5.2. Impact of impurity band on thermoelectric properties

conductivity when valence band conduction is strong.

5.2.2. Effect upon Seebeck—effective density of states mass

Common synthesis methods for most of bulk thermoelectric materials can be categorized into three groups according to different processing steps, namely stoichiometric melts (SM), powder metallurgic method (PM), pseudo-pulverized and intermixed elements sintering method (Pseudo-PIES), as shown in Figure 10.

Polycrystalline ZnSb ingots can be synthesized by the so-called SM methods, i.e. melting of the elemental zinc and antimony followed by solidification in air or quenching in cold water. The purity of the starting elemental zinc and antimony materials has a significant impact on the resulting electrical properties. For example, starting materials with purities of 99.99% and 99.9999% allows to obtain the charge carrier concentration of ∼10<sup>19</sup> and ∼1016cm-3, respectively, on undoped polycrystalline ZnSb [14]. Since ZnSb does not melt congruently, solidification will result in a mix of the phases, Zn4Sb3, ZnSb and Sb. This mix can be homogenized by sufficient heat treatments to reach the thermodynamic equilibrium state with a single uniform ZnSb phase [14, 15]. Another problem with the solidification is that the sample contains cracks that significantly influence on the electron transport [13].

The solidified ingots are often milled into fine powder and pressed to pellets, which is a procedure that includes the basic ingredients of standard powder metallurgy (PM). Milling offers access to nanosized grains, thus providing possibility to enhance the thermoelectric properties. Earlier studies show that different milling techniques led to a trend of grain size as 80.0, 44.6 and 32.4nm for manually grinding, dry-milling and wet-milling [16], as well as 10 nm for cryo-milling [88], respectively.

The PIES method (pulverized and intermixed elements sintering method) has been introduced into preparation of thermoelectric (Bi/Sb)2(Te/Se)3 materials, where all the elements are initially mixed and milled to fine powder before hot-pressing (no melting process) [89]. The electrical conductivity of the sample that was synthesized by this method has been reported about 5 times higher than that for the SM sample [90]. Distinguished from a typical PIES method, we often used pseudo-PIES for ZnSb, which partially mixed the dopant element with SM ingot in ball-milling, and then processed hot-pressing.

Figure 10. Flow chart of synthesis procedures. (Reprinted with author's permission from [29]. ©X. Song, 2016.)

There are different kinds of compaction techniques that follows powder metallurgy and have been used for fabrication of ZnSb samples. The most common ones are cold-pressing (at room temperature with ultra-pressure 2–10GPa [83, 91]), hot-pressing (>450°C with pressure of 20– 300MPa [16, 19, 20, 35]), and spark plasma sintering (SPS) (the electrical current is passed through the sample with 5min reaction time at 350–450°C [83, 92]). One important difference among hot-presses is the manipulation of secondary phases; both removal and proportioning are possible, and obviously depends upon the temperature and duration, but also on details of the instrument design and the environment of the ZnSb powder. Xiong et al. have reported that the volume fraction of Sb phase was estimated to be ∼2wt.% by Rietveld refinement in a hotpressed sample [19] at 673K in vacuum followed by an evacuated quartz ampoule and annealed at 673K for 80h. A recent study on SPS-samples showed also that Sb phase domains were distributed along the samples, accompanied with Zn4Sb3 on the surface [92]. Another difference is the final grain size of pellets. We have reported that rapid hot-press helped to minimize the grain size due to shorter cooling time [88].

Another important consideration of the synthesis technique is the ability to produce large amounts of thermoelectric materials in a cost-effective way. Considering that one of the favourable aspects of ZnSb from a commercial point of view is the low materials cost, there have been several efforts where the cost efficiency of the synthesis technique is important [92–94].

## 7. From laboratory to fabrication

Figure 10. Flow chart of synthesis procedures. (Reprinted with author's permission from [29]. ©X. Song, 2016.)

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

ZnSb practical devices have been produced [9, 95], and there has been a promising achievement on thermoelectric performance of ZnSb in the laboratory. However, it is still challenging to transfer the achievement from laboratory to modern manufacturing. Progress in synthesis from different points of view have also to go through many tests regarding machinability, mechanical stability, thermal stability, thermal cycling and long-term stability, as well as compatibility with targeted fabrication techniques. Several of these issues are expected to contribute to—as well as benefit from—a further fundamental understanding of ZnSb, when practical solutions on short and long timescales are targeted. On a short to medium timescale, ZnSb can take advantage of new fabrication technologies that has been developed, but using traditional approaches for the device functionality. On a longer perspective, ZnSb may also be brought further into the explorations of new nanotechnology approaches to improve the performance of possible future generations of thermoelectrics.

One hindrance towards an ideal thermoelectric module made entirely of ZnSb is the inability to synthesis of stable n-type ZnSb. Although theoretical modelling shows favourable electronic structure of n-type ZnSb, there seems to be no promising paved routes to success. The direct synthesis of n-type ZnSb by doping would need a breakthrough. From an optimistic point of view that may arise indirectly from various other investigations on ZnSb, perhaps through defect engineering or a combination of different approaches, for example, modulation doping by embedded higher band gap materials with the appropriate band offsets for supply of electrons combined with compensation of Zn vacancy acceptors. A practical compromising route towards module-making is using another semiconductor than ZnSb for the n-type leg, for instance Mg2Sn1-xSix that matches ZnSb well in expected operation temperature, has the same environmentally friendly profile [20], as well as a low cost on raw materials. There might also be other suitable material candidates. Any practical problems with thermal expansion mismatch of materials in a module would have to be solved. Previous experiences with ZnSb modules have made it necessary to dope or add elements to ZnSb in order to achieve suitable mechanical properties. Fortunately, there has been a large development in packaging technology for electronic devices in the last couple of decades. New options for substrates and bonding techniques may be offered and meet the requirements on thermal expansion of the semiconductors.

The thermal stability of the synthesized ZnSb needs to be tested and probably be improved. This is one area where both fundamental studies and practical solutions may enter. ZnSb samples are subjected to Zn evaporation at high temperatures. The evaporation depends naturally very much on the ambient and the surface conditions. It is possible that protective layers can be applied to minimize evaporation. The situation has some similarities to that of several binary electronic materials, such as III–V materials, where one of the elements have a much higher vapour pressure, than what can be tolerated at the desired processing temperature. For GaAs, dielectric films SiO2 and Si3N4 have been used for the purpose of preventing arsenic evaporation. A similar approach with a conformal deposition of a protective dielectric layer may be advantageous for ZnSb. Thermal stability also has to do with the thermal generation of point defects and their diffusion at elevated temperatures. The understanding of the phenomena is unsatisfactory from an academic point of view, in particular on the level of defect chemistry and electronic structure, but there are many experimental observations of the simple electrical parameters. Several authors have reported that after a heat treatment of ZnSb, the electrical conductivity and the charge carrier concentration increased, while the Seebeck coefficient decreased. The change was followed by a slow recovery towards the initial values at room temperature [15, 20, 44, 45, 47, 61, 77]. The characteristics can be related it to the VZn-ZnI Frenkel pair formation at elevated temperatures, and the recovery caused by their slower recombination at lower temperature. The vacancy concentration was linked to hole concentration. It was rationalized that these hysteresis effects would not be significant at high doping concentrations [15]. The doping effect on the vacancy concentration was then not considered. A detailed understanding of the vacancies, interstitials and their energy levels, ionization and formation energies is needed to understand the influence for higher doping concentration. The influence of more complicated defects can also be a large challenge. There are also reports on various temperature-cycling phenomena [52, 96, 97], involving the doping atoms and energy levels of these. Some of these effects may differ for different synthesis details.

The thermal stability is referring to all properties of the material, including the thermal conductivity. We have reported grain growth induced by heating, particularly in nanostructured bulk samples [88]. The grain growth will naturally induce a change of thermal conductivity due to the dependence on phonon scattering. To which extent, it constitutes a practical problem depends upon the targeted operation temperature. Approaches to minimize grain growth usually consist of adding atoms that segregate in grain boundaries, thereby preventing grain growth. This is an area that needs further study.

There are various routes that can make ZnSb a part of long-term exploration to improve thermoelectrics by nanostructures (not just nanograins). Some of them may use ways of depositing films of ZnSb, such as by MOCVD, sputtering [98, 99] and electroplating [11, 100], etc. By these techniques, it could be feasible to make composites and layered structures in a controlled way with different materials with suitable band offsets for energy filtering [101]. Possibilities of making high quality epitaxial films may also be attractive for fundamental material property studies. One might also do band engineering in the material by introducing misfit stress. Thin-film deposition may also offer a possibility to grow template nanostructures and exploiting the possibilities of quantum confinement in ZnSb and study the conduction band properties of ZnSb by injection into nanostructures.

## Acknowledgements

route towards module-making is using another semiconductor than ZnSb for the n-type leg, for instance Mg2Sn1-xSix that matches ZnSb well in expected operation temperature, has the same environmentally friendly profile [20], as well as a low cost on raw materials. There might also be other suitable material candidates. Any practical problems with thermal expansion mismatch of materials in a module would have to be solved. Previous experiences with ZnSb modules have made it necessary to dope or add elements to ZnSb in order to achieve suitable mechanical properties. Fortunately, there has been a large development in packaging technology for electronic devices in the last couple of decades. New options for substrates and bonding techniques

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

may be offered and meet the requirements on thermal expansion of the semiconductors.

differ for different synthesis details.

growth. This is an area that needs further study.

The thermal stability of the synthesized ZnSb needs to be tested and probably be improved. This is one area where both fundamental studies and practical solutions may enter. ZnSb samples are subjected to Zn evaporation at high temperatures. The evaporation depends naturally very much on the ambient and the surface conditions. It is possible that protective layers can be applied to minimize evaporation. The situation has some similarities to that of several binary electronic materials, such as III–V materials, where one of the elements have a much higher vapour pressure, than what can be tolerated at the desired processing temperature. For GaAs, dielectric films SiO2 and Si3N4 have been used for the purpose of preventing arsenic evaporation. A similar approach with a conformal deposition of a protective dielectric layer may be advantageous for ZnSb. Thermal stability also has to do with the thermal generation of point defects and their diffusion at elevated temperatures. The understanding of the phenomena is unsatisfactory from an academic point of view, in particular on the level of defect chemistry and electronic structure, but there are many experimental observations of the simple electrical parameters. Several authors have reported that after a heat treatment of ZnSb, the electrical conductivity and the charge carrier concentration increased, while the Seebeck coefficient decreased. The change was followed by a slow recovery towards the initial values at room temperature [15, 20, 44, 45, 47, 61, 77]. The characteristics can be related it to the VZn-ZnI Frenkel pair formation at elevated temperatures, and the recovery caused by their slower recombination at lower temperature. The vacancy concentration was linked to hole concentration. It was rationalized that these hysteresis effects would not be significant at high doping concentrations [15]. The doping effect on the vacancy concentration was then not considered. A detailed understanding of the vacancies, interstitials and their energy levels, ionization and formation energies is needed to understand the influence for higher doping concentration. The influence of more complicated defects can also be a large challenge. There are also reports on various temperature-cycling phenomena [52, 96, 97], involving the doping atoms and energy levels of these. Some of these effects may

The thermal stability is referring to all properties of the material, including the thermal conductivity. We have reported grain growth induced by heating, particularly in nanostructured bulk samples [88]. The grain growth will naturally induce a change of thermal conductivity due to the dependence on phonon scattering. To which extent, it constitutes a practical problem depends upon the targeted operation temperature. Approaches to minimize grain growth usually consist of adding atoms that segregate in grain boundaries, thereby preventing grain The authors acknowledge support by the Norwegian Research Council under contract NFR11- 40-6321 (NanoThermo) and the University of Oslo. The authors also thank to Dr. Patricia Almeida Carvalho for her contribution to transmission electron microscopic imaging.

## Author details

Xin Song\* and Terje G. Finstad

\*Address all correspondence to: xins@fys.uio.no

Department of Physics, University of Oslo, Oslo, Norway

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**Provisional chapter**

## **Silver-Antimony-Telluride: From First-Principles Calculations to Thermoelectric Applications Silver-Antimony-Telluride: From First-Principles Calculations to Thermoelectric Applications**

## Yaron Amouyal Yaron Amouyal

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

http://dx.doi.org/10.5772/66086

#### **Abstract**

Silver-antimony-telluride (AgSbTe2 ) based compounds have emerged as a promising class of materials for thermoelectric (TE) power generation at the mid-temperature range. This Chapter demonstrates utilization of first-principles calculations for predicting TE properties of AgSbTe2 -based compounds and experimental validations. Predictive calculations of the effects of La-doping on vibrational and electronic properties of AgSbTe2 compounds are performed applying the density functional theory (DFT), and temperature-dependent TE transport coefficients are evaluated applying the Boltzmann transport theory (BTE). Experimentally, model ternary (AgSbTe<sup>2</sup> ) and quaternary (3 at. % La-AgSbTe<sup>2</sup> ) compounds were synthesized, for which TE transport coefficients were measured, indicating that thermal conductivity decreases due to La-alloying. The latter also reduces electrical conductivity and increases Seebeck coefficients. All trends correspond with those predicted from first-principles. Thermal stability issues are essential for TE device operation at service conditions, e.g. changes of matrix composition and second-phase precipitation, and are also addressed in this study on both computational and experimental aspects. It is shown that La-alloying affects TE figure-of-merit positively, e.g., improving from 0.35 up to 0.50 at 260 °C. We highlight the universal aspects of this approach that can be applied for other TE compounds. This enables us screening their performance prior to synthesis in laboratory.

**Keywords:** silver-antimony-telluride, first-principles calculations, thermoelectric transport properties, Boltzmann transport theory, lattice dynamics, thermal stability

## **1. Introduction**

It is of utmost technological importance to develop predictive tools that will provide us with information about design of materials' functional properties. In this context, density functional theory (DFT) first-principle calculations offer us such possibilities [1–4], allowing us

© 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. © 2016 The Author(s). Licensee InTech. This chapter is distributed under the terms of the Creative Comm ons 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.

calculation of structural, interfacial, vibrational, and electronic properties. Knowledge of these properties and how they depend on temperature and material's composition are essential to assess total thermoelectric (TE) performance of thermoelectric device. Among recently investigated TE materials, silver-antimony-telluride (AgSbTe2 )-based alloys have emerged as a promising class of materials for TE power generation in low- to mid-temperature range. These compounds are derivatives of lead-antimony-silver-telluride (LAST)-based alloys of AgPbmSbTe2+m form [5–9], which exhibit large TE figure-of-merit *ZT* values ranging from 1.3 to 1.7 [5, 10, 11], which are associated with the intrinsically good TE properties of AgSbTe2 -phase.

AgSbTe2 -based alloys serve not only for TE power conversion or cooling, but also for nonvolatile electronic memory, being classified as phase change materials, as demonstrated in thorough investigation by Wuttig and coworkers [12–15]. They have attracted scientific interest owing to their special nature of interatomic bonding and vibrational properties [16–18]. On TE aspect, their superior performance is associated mainly to glass-like, intrinsically low values of lattice thermal conductivities, as low as 0.6 W m−1 K−1 [19]. This anomaly is associated either to strong anharmonicity of interatomic forces [20, 21] or to relatively large variance of interatomic forces prevailing between Ag+ and Sb3+ cations, encouraging phonon scattering [22]. Additionally, resonant bonding yields high level of structural instability, that is accompanied, for instance, by spontaneous phase decomposition [23, 24]. This, intriguingly, what makes AgSbTe2 -based alloys good materials for both TE and phase change applications. Owing to these peculiarities, these alloys have recently been investigated extensively, either experimentally [19, 25–30] or computationally [18, 22, 31–33].

Despite of relatively high *ZT* values of AgSbTe2 phase, it is still challenging to increase them to the range of 2–3. Reaching at this limit will enable us employing this material for energy conversion at power levels >500 W [34]. Reduction in lattice thermal conductivity is a conventional way to enhance TE performance and is achieved by either doping with solute elements [35] or formation of second phases to stimulate phonon scattering [36–38]. These lattice defects affect, of course, electronic properties, mainly electrical conductivity and Seebeck coefficient. Attempts to improve TE properties of AgSbTe<sup>2</sup> -based alloys by doping with different elements [19, 25, 39–47], as well as, by formation of second phase precipitates [46, 48–51], proved to be successful, as reported in the exhaustive studies of Zhang et al., Du et al., and Mohanraman et al. Alloying with second phase forming elements raises imperative question about material's thermal stability, when employed in TE generators under service conditions, with engineering implications [51–53].

Among efforts to improve TE properties of AgSbTe<sup>2</sup> -based alloys, Min et al. reported on improvement of electron transport properties due to La-doping [27]. Positive effects on PbTe compound due to La-doping were recorded, as well [54, 55]. In their recent study, Min et al. introduce a complete analysis of TE properties of AgSbTe2 doped with La of different concentrations [56].

Notwithstanding the aforementioned successful experimental and computational attempts, a set of experimental routines, that is initiated and directed by predictions from first principles for complete TE performance or any other computational procedure, is missing.

A significant step in this direction is introduced by our previous investigations of AgSbTe<sup>2</sup> based phase, involving both computational and experimental aspects [57, 58]. Vibrational properties of both AgSbTe2 -based and La-doped-AgSbTe<sup>2</sup> alloys, including frequency-dependent vibrational density of states functions (v-DOS), temperature-dependent heat capacity, sound velocities, and Debye temperatures were evaluated employing lattice dynamics firstprinciples calculations. It was reported that La-doping reduces average sound velocity and varies v-DOS of AgSbTe2 -based phase [57, 58]. Quantitatively, lattice thermal conductivity of La0.125Ag0.875SbTe2 alloy was calculated to be lower by ca. 14%, than that of AgSbTe2 -based phase at 300 K [58]. Experimental validations of these effects of La-alloying on reducing lattice thermal conductivity were made, as well [58].

This chapter introduces a refined approach of evaluating temperature-dependent lattice thermal conductivity from data obtained *ab-initio*, as well as, calculations of electronic transport coefficients. Most importantly, this chapter presents experimental validations for the entire dataset obtained from first-principles, including thermal and electrical measurements.

## **2. Chapter outline**

calculation of structural, interfacial, vibrational, and electronic properties. Knowledge of these properties and how they depend on temperature and material's composition are essential to assess total thermoelectric (TE) performance of thermoelectric device. Among recently

a promising class of materials for TE power generation in low- to mid-temperature range. These compounds are derivatives of lead-antimony-silver-telluride (LAST)-based alloys of AgPbmSbTe2+m form [5–9], which exhibit large TE figure-of-merit *ZT* values ranging from 1.3 to

volatile electronic memory, being classified as phase change materials, as demonstrated in thorough investigation by Wuttig and coworkers [12–15]. They have attracted scientific interest owing to their special nature of interatomic bonding and vibrational properties [16–18]. On TE aspect, their superior performance is associated mainly to glass-like, intrinsically low values of lattice thermal conductivities, as low as 0.6 W m−1 K−1 [19]. This anomaly is associated either to strong anharmonicity of interatomic forces [20, 21] or to relatively large variance

ing [22]. Additionally, resonant bonding yields high level of structural instability, that is accompanied, for instance, by spontaneous phase decomposition [23, 24]. This, intriguingly,

Owing to these peculiarities, these alloys have recently been investigated extensively, either

to the range of 2–3. Reaching at this limit will enable us employing this material for energy conversion at power levels >500 W [34]. Reduction in lattice thermal conductivity is a conventional way to enhance TE performance and is achieved by either doping with solute elements [35] or formation of second phases to stimulate phonon scattering [36–38]. These lattice defects affect, of course, electronic properties, mainly electrical conductivity and Seebeck

ent elements [19, 25, 39–47], as well as, by formation of second phase precipitates [46, 48–51], proved to be successful, as reported in the exhaustive studies of Zhang et al., Du et al., and Mohanraman et al. Alloying with second phase forming elements raises imperative question about material's thermal stability, when employed in TE generators under service conditions,

improvement of electron transport properties due to La-doping [27]. Positive effects on PbTe compound due to La-doping were recorded, as well [54, 55]. In their recent study, Min et al.

Notwithstanding the aforementioned successful experimental and computational attempts, a set of experimental routines, that is initiated and directed by predictions from first principles

for complete TE performance or any other computational procedure, is missing.



1.7 [5, 10, 11], which are associated with the intrinsically good TE properties of AgSbTe2

)-based alloys have emerged as

and Sb3+ cations, encouraging phonon scatter-

phase, it is still challenging to increase them



doped with La of different concen-


investigated TE materials, silver-antimony-telluride (AgSbTe2

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

of interatomic forces prevailing between Ag+

Despite of relatively high *ZT* values of AgSbTe2

with engineering implications [51–53].

trations [56].

experimentally [19, 25–30] or computationally [18, 22, 31–33].

coefficient. Attempts to improve TE properties of AgSbTe<sup>2</sup>

Among efforts to improve TE properties of AgSbTe<sup>2</sup>

introduce a complete analysis of TE properties of AgSbTe2

AgSbTe2

what makes AgSbTe2

This chapter consists primarily of original computational and experimental data along with data, that were reported by us earlier [57, 58], and is aimed at drawing a complete picture depicting the role of lanthanum-alloying in silver-antimony-telluride-based alloys on a broad TE view. Herein, we demonstrate how alloying of AgSbTe2 (P4/mmm) alloy with lanthanum solute atoms brings about significant reduction in thermal conductivity with positive effects on TE power factor, as well; thus, achieving improved *ZT* values. This is achieved by DFT calculations of structural, interfacial, vibrational, and electronic properties performed for La-free and La-doped alloys, followed by experimental validation implemented by thermal and electronic transport measurements.

Computational procedures are divided into the following steps:


this context, the molar formation energies of both phases and the free energies of their interfaces with AgSbTe2 -matrix are simulated to predict their thermal stability and nucleation sequence.

**5.** Additionally, to address the influence of deviations from AgSbTe<sup>2</sup> -stoichiometry on electron transport properties, the latter is simulated for two off-stoichiometric model alloys Ag3 SbTe4 and AgSb3 Te4 .

Experimental procedures are divided into the following steps:


## **3. Research methods**

This section provides a brief description of computational and experimental methods applied in this research.

#### **3.1. First-principles calculation**

The primary calculations are performed for AgSbTe2 stoichiometric phase. To address, however, both optional cases of second-phase nucleation and deviations from stoichiometric composition, as described in Section 2, the following phases are simulated, as well: Sb2 Te3 , Sb8 Te3 , Ag3 SbTe4 , and AgSb3 Te4 .

#### *3.1.1. The base AgSbTe2 phase—structural and vibrational calculations*

Silver-antimony-telluride of AgSbTe2 stoichiometry is commonly known to introduce a cubic lattice structure; however, it was suggested, that it may coexist with tetragonal and rhombohedral forms [59]. The following optional space group symmetries: cubic (Pm-3m, No. 221), tetragonal (P4/mmm, No. 123), and rhombohedral (R-3m, No. 166) have been simulated from first-principles [57]. Calculations of temperature-dependent Helmholtz free energy for these three polymorphs indicate that P4/mmm polymorph is the most stable one at temperatures above 400 K, whose energy exhibits close proximity to that of Pm-3m polymorph. Based on calculated v-DOS function for P4/mmm model alloy consisting of 4 atoms per simulation cell, **Figure 1a**, it was decided to test effects of doping with lanthanum atoms (to be discussed further below). To represent effects of La-doping with effective concentration of La atoms, that is close to realistic doping levels, a model compound of Ag7 LaSb<sup>8</sup> Te16 stoichiometry was constructed having the same P4/mmm space group symmetry as of the original AgSbTe2 lattice. In this compound, consisting of 32 atoms per simulation cell, **Figure 1b**, La-atom substitutes for 1 ⁄ <sup>8</sup> of Ag-atoms, so that, the resulting concentration is 3.125 at.% La. Computational parameters concerning structural relaxation and vibrational properties are provided in detail [57]. The effects of La-doping on vibrational and thermal properties will be discussed further below.

this context, the molar formation energies of both phases and the free energies of their

tron transport properties, the latter is simulated for two off-stoichiometric model alloys

) and quaternary (3 at.% La-AgSbTe<sup>2</sup>

**2.** Differential scanning calorimetry (DSC) tests are implemented for both La-free and La-doped alloys to address thermal stability issues and how they are influenced by

**3.** Temperature-dependent thermal conductivity of both alloys is determined to realize effects

**4.** Similarly, both temperature-dependent electrical conductivity and Seebeck coefficients are measured for ternary and quaternary alloys to realize effects of La-doping and to compare

**5.** Finally, to assess whether La-doping contributes to conversion efficiency, TE power factor

This section provides a brief description of computational and experimental methods applied

ever, both optional cases of second-phase nucleation and deviations from stoichiometric com-

lattice structure; however, it was suggested, that it may coexist with tetragonal and rhombohedral forms [59]. The following optional space group symmetries: cubic (Pm-3m, No. 221),

position, as described in Section 2, the following phases are simulated, as well: Sb2

 *phase—structural and vibrational calculations*

of La-doping and to compare them with those predicted from first-principles.

and figure-of-merit are evaluated for La-free and La-doped materials.

vacuum melting followed by quenching and hot-pressing. The appropriate conditions

**5.** Additionally, to address the influence of deviations from AgSbTe<sup>2</sup>

Experimental procedures are divided into the following steps:




) alloys are synthesized by

stoichiometric phase. To address, how-

stoichiometry is commonly known to introduce a cubic

Te3 , Sb8 Te3 ,

interfaces with AgSbTe2

and AgSb3

enabling formation of AgSbTe2

**1.** Model ternary (AgSbTe2

Te4 .

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

them with those predicted from first-principles.

The primary calculations are performed for AgSbTe2

Te4 .

ation sequence.

Ag3 SbTe4

are found.

La-additions.

**3. Research methods**

**3.1. First-principles calculation**

, and AgSb3

Silver-antimony-telluride of AgSbTe2

*3.1.1. The base AgSbTe2*

in this research.

Ag3 SbTe4

**Figure 1.** The lattice structures of model alloys discussed in this study and their space group symmetries: (a) AgSbTe<sup>2</sup> (P4/mmm); (b) Ag7 LaSb<sup>8</sup> Te16 (P4/mmm); (c) Sb2 Te3 (R-3m); (d) Sb8 Te3 (R-3m); (e) (AgSbTe2 ) 2 (cubic P1); (f) Ag3 SbTe4 (cubic P1); and (g) AgSb3 Te4 (cubic P1).

#### *3.1.2. The base AgSbTe2 phase—electronic calculations*

To simulate the effects of La-doping on electrical conductivity and Seebeck coefficient, electronic band structures are calculated for both lattices from first principles. A plane-wave basis set is implemented in Vienna *ab-initio* simulation package (VASP) [60–62] and *MedeA*® software environment [63]. The exchange-correlation electronic energy is expressed by means of generalized gradient approximation (GGA) using PBEsol energy functional [64] and projector augmented wave (PAW) potentials, which are utilized to represent core electron density [65]. Sampling of Brillouin zone is carried out using a set of uniform Monkhorst-Pack *k*-point mesh with density ranges between 0.14 and 0.17 Å−1 and smearing method of linear-tetrahedron with Blöchl corrections [66]. To represent Kohn-Sham electronic wave functions, the plane waves are spanned with 400 eV energy cutoff for the structural relaxation or electronic calculations, respectively. Electronic optimization procedures are performed applying 10−5 eV energy convergence threshold.

The calculated 0 K band structures are used for evaluation of temperature-dependent electrical conductivity, electronic component of thermal conductivity, and Seebeck coefficient, applying near-equilibrium Boltzmann transport theory with constant relaxation time approximation, as implemented in BoltzTrap code [67].

The partial electrical conductivity tensor, *σ*′ *αβ*(*i*, **k** ) , represented for *i*th energy band and a given **k**-point, is obtained from Cartesian component of electron group velocity by derivation of *i*th energy band, *ε<sup>i</sup>*,*<sup>k</sup>* , with respect to *α*- and *β* -components of electron's wave vector [68]. *σ*′ *αβ* (*i*, **k** ) is then given by:

$$
\sigma\_{\
u\phi}^{'}(\mathbf{i}, \mathbf{k}) \equiv e^2 \,\pi\_{\ll k} \frac{1}{\hbar^2} \frac{\partial^2 \varepsilon\_{ik}}{\partial k\_a \partial k\_\[} \,' \tag{1}
$$

where *e* is electron unit charge, ℏ is reduced Planck constant, and *τ<sup>i</sup>*,*<sup>k</sup>* is electron relaxation time, which is assumed to be constant. This yields temperature and chemical potential, *μ* , dependent electrical conductivity tensor with respect to *α*- and *β*-components, summed over N-energy bands: 0 \_

$$\sigma\_{a\phi}(T,\mu \,) = \frac{1}{\Omega} \sum\_{l=1}^{N} [\sigma\_{a\phi}^{\prime}(\varepsilon\_{\,)}] \left[ -\frac{\partial f\_{0}(T,\varepsilon,\mu \,)}{\partial \varepsilon} \right] \text{d}\,\varepsilon\_{\,\,\,\nu} \tag{2}$$

where *Ω* is characteristic unit cell volume and *f* 0 (*T*, *ε*, *μ* )is equilibrium Fermi-Dirac distribution function [69]. The electronic component of thermal conductivity tensor, *κ<sup>e</sup>* , is, accordingly, expressed by: 0 \_

$$\kappa\_{a\emptyset}^{\varepsilon}(T\_{\prime}\,\mu\,) = \frac{1}{e^{2}T\Omega} \sum\_{l=1}^{N} [\sigma\_{\,\,a\emptyset}^{\prime}(\varepsilon\_{\,l}) \cdot (\varepsilon\_{\,l} - \mu\,)^{2}] \left[ -\frac{\partial f\_{0}(T,\varepsilon,\mu)}{\partial \varepsilon} \right] \mathbf{d}\,\,\varepsilon\_{\,l}\,. \tag{3}$$

Finally, the explicit expression for Seebeck coefficient tensor, *Sij* , is given by [70, 71]:

$$
\boldsymbol{\kappa}\_{\text{ayl}}^{\prime}(\boldsymbol{\Gamma}, \boldsymbol{\mu}) = \frac{1}{\varepsilon^2 T \Omega} \sum\_{i \in \mathcal{I}} \boldsymbol{\sigma}\_{\text{ayl}}(\boldsymbol{\varepsilon}\_i) \cdot (\boldsymbol{\varepsilon}\_i - \boldsymbol{\mu}) \left[ \frac{\boldsymbol{\gamma}\_{\text{cyl}}}{\partial \varepsilon} \right] \mathbf{d} \,\boldsymbol{\varepsilon}\_i. \tag{3}
$$

Finally, the explicit expression for Sebeck coefficient tensor,  $\boldsymbol{S}\_{\boldsymbol{\beta}'}$  is given by [70, 71]:

$$
\boldsymbol{\mathcal{S}}\_{\boldsymbol{\psi}}(\boldsymbol{\Gamma}, \boldsymbol{\mu}) = [\boldsymbol{\sigma}]\_{\text{ul}}^{-1} \frac{1}{\varepsilon \Gamma \Omega} \sum\_{i=1}^{N} [\boldsymbol{\sigma}\_{\text{,i}}^{\prime}(\boldsymbol{\varepsilon}\_i) \cdot (\boldsymbol{\varepsilon}\_i - \boldsymbol{\mu}) \left[ \frac{\partial f\_0(\boldsymbol{T}, \boldsymbol{\varepsilon}, \boldsymbol{\mu})}{\partial \varepsilon} \right] \mathbf{d} \,\boldsymbol{\varepsilon}\_i. \tag{4}
$$

#### *3.1.3. The Sb2 Te3 and Sb8 Te3 phases*

*3.1.2. The base AgSbTe2*

energy convergence threshold.

of *i*th energy band, *ε<sup>i</sup>*,*<sup>k</sup>*

(*i*, **k** ) is then given by:

N-energy bands:

ingly, expressed by:

*καβ*

*Sij*

imation, as implemented in BoltzTrap code [67].

The partial electrical conductivity tensor, *σ*′

*σ*′

*σαβ*(*T*, *<sup>μ</sup>* ) = \_\_1

where *Ω* is characteristic unit cell volume and *f*

*e*

(*T*, *μ* ) = \_\_\_\_\_ <sup>1</sup>

(*T*, *μ* ) = [*σ*]

Finally, the explicit expression for Seebeck coefficient tensor, *Sij*

*αi* <sup>−</sup><sup>1</sup> \_\_\_\_ 1 *eT<sup>Ω</sup>* ∑ *i*=1 *N* ∫ *σ*′

*<sup>e</sup>* <sup>2</sup> *<sup>T</sup><sup>Ω</sup>* <sup>∑</sup> *i*=1 *N* ∫ *σ*′

 *phase—electronic calculations*

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

To simulate the effects of La-doping on electrical conductivity and Seebeck coefficient, electronic band structures are calculated for both lattices from first principles. A plane-wave basis set is implemented in Vienna *ab-initio* simulation package (VASP) [60–62] and *MedeA*® software environment [63]. The exchange-correlation electronic energy is expressed by means of generalized gradient approximation (GGA) using PBEsol energy functional [64] and projector augmented wave (PAW) potentials, which are utilized to represent core electron density [65]. Sampling of Brillouin zone is carried out using a set of uniform Monkhorst-Pack *k*-point mesh with density ranges between 0.14 and 0.17 Å−1 and smearing method of linear-tetrahedron with Blöchl corrections [66]. To represent Kohn-Sham electronic wave functions, the plane waves are spanned with 400 eV energy cutoff for the structural relaxation or electronic calculations, respectively. Electronic optimization procedures are performed applying 10−5 eV

The calculated 0 K band structures are used for evaluation of temperature-dependent electrical conductivity, electronic component of thermal conductivity, and Seebeck coefficient, applying near-equilibrium Boltzmann transport theory with constant relaxation time approx-

given **k**-point, is obtained from Cartesian component of electron group velocity by derivation

time, which is assumed to be constant. This yields temperature and chemical potential, *μ* , dependent electrical conductivity tensor with respect to *α*- and *β*-components, summed over

*αβ*( *ε<sup>i</sup>* )[− 

0

*αβ*( *ε<sup>i</sup>* ) ⋅ ( *ε<sup>i</sup>* − *μ* ) 2

*<sup>j</sup>α*( *ε<sup>i</sup>* ) <sup>⋅</sup> ( *ε<sup>i</sup>* <sup>−</sup> *<sup>μ</sup>* )[<sup>−</sup>

∂ *f*

0 \_ (*T*, *ε*, *μ* )

> [−  ∂ *f*

> > ∂ *f*

0 \_ (*T*, *ε*, *μ* )

0 \_ (*T*, *ε*, *μ* )

\_\_\_1 ℏ2 <sup>∂</sup><sup>2</sup> *<sup>ε</sup>* \_\_\_\_\_\_*<sup>i</sup>*,*<sup>k</sup>* ∂ *kα* ∂ *k<sup>β</sup>*

*αβ*(*i*, **k** ) = *e* <sup>2</sup> *τ<sup>i</sup>*,*<sup>k</sup>*

where *e* is electron unit charge, ℏ is reduced Planck constant, and *τ<sup>i</sup>*,*<sup>k</sup>*

*<sup>Ω</sup>* ∑ *i*=1 *N* ∫ *σ*′

tion function [69]. The electronic component of thermal conductivity tensor, *κ<sup>e</sup>*

, with respect to *α*- and *β* -components of electron's wave vector [68]. *σ*′

*αβ*(*i*, **k** ) , represented for *i*th energy band and a

, (1)

<sup>∂</sup>*<sup>ε</sup>* ]<sup>d</sup> *<sup>ε</sup><sup>i</sup>* , (2)

<sup>∂</sup>*<sup>ε</sup>* ]<sup>d</sup> *<sup>ε</sup><sup>i</sup>* . (3)

<sup>∂</sup>*<sup>ε</sup>* ]<sup>d</sup> *<sup>ε</sup><sup>i</sup>* . (4)

, is given by [70, 71]:

(*T*, *ε*, *μ* )is equilibrium Fermi-Dirac distribu-

is electron relaxation

, is, accord-

*αβ*

Nonmagnetic DFT calculations are performed for Sb2 Te3 and Sb8 Te3 crystal structures having (R-3m) space group symmetry, which incorporate 15 and 33 atoms per simulation cell, respectively. Both lattice structures are rendered in **Figure 1c** and **d**, respectively. A computational routine similar to aforementioned one is implemented with several differences. GGA approximation is applied for a set of uniform 9 × 9 × 9 Monkhorst-Pack *k*-point mesh, and plane waves are spanned with either 400 or 350 eV energy cutoff for structural relaxation or electronic calculations, respectively. Electronic optimization procedures are performed applying 10−6 eV energy convergence threshold.

Structural relaxation procedures are first performed, allowing variation of cell volume and atom positions at all degrees of freedom, setting a convergence threshold of 10−4 eV Å−1 for Hellman-Feynman forces. The resulting lattice parameters obtained for relaxed crystal structures are: a = b = 4.34 Å and c = 31.21 Å for Sb2 Te3 ; and: a = b = 4.37 Å and c = 64.93 Å for Sb8 Te3 , which are in good agreement with data reported in the literature [72, 73]. Then, electronic band structure calculations are performed for both relaxed structures.

Band structures are calculated in the same manner as mentioned above, allowing calculations of temperature-dependent electrical conductivity, electronic component of thermal conductivity, and Seebeck coefficient values. These calculations yield p-type behavior for both structures, and we fine-tune the positions of electronic chemical potential to reside at the top of the valence bands. This yields Seebeck coefficient values that are very similar to those measured by us experimentally for pure Sb2 Te3 standard. Additionally, we set electron relaxation time to be 8 fs, so as to fit electrical conductivity values calculated for Sb<sup>2</sup> Te3 with those measured for the same standards. We, then, apply the same relaxation time for Sb8 Te3 , as well.

To address bulk and interfacial energetic aspects related with nucleation of Sb2 Te3 and Sb8 Te3 phases in AgSbTe2 phase, we have simulated formation energies of Sb2 Te3 and Sb8 Te3 phases and their interfaces with AgSbTe2 phase. Molar formation energy of model SbpTeq cell, *E*\_ *Sbp Teq tot* , is calculated using the following expression [57]:

is calculated using the following expression [57]:

$$\underline{E}\_{St, \Gamma\_{\epsilon}}^{\prime} = \frac{\underline{E}\_{St, \Gamma\_{\epsilon}}^{\prime \prime} - p \times \mu\_{sb}^{\prime} - q \times \mu\_{\epsilon}^{\prime}}{p + q} \tag{5}$$

where *E*\_ *Sbp Teq tot* is cell's molar total energy and *μSb o* and *μTe o* are chemical potentials of Sb- and Te-atoms in their standard states, which are evaluated to be −397.72 and −303.12 kJ mol−1, respectively. The free energy of silver-antimony-telluride (AST)/antimony-telluride (SBT) interface is calculated constructing a slab model having AST/SBT generic form, and using the following expression [74]:

$$\mathcal{V} = \frac{1}{2A} \{ \mathbf{E}'\_{\rm SAT/SBT} - \mathbf{n}\_{\rm SAT} \mathbf{E}'\_{\rm SAT} - \mathbf{n}\_{\rm SAT} \mathbf{E}'\_{\rm SAT} \} \, , \tag{6}$$

where *A* is AST/SBT interface cross-sectional area, *EAST*/*SBT f* is calculated formation energy of slab model, *E*\_ *AST f* and *E*\_ *SBT f* are calculated molar formation energies of AST and SBT sub-cells, and *nAST* and *nSBT* are their number of moles in the entire model slab, respectively.

#### *3.1.4. Ag3 SbTe4 and AgSb3 Te4 model compounds*

To simulate the effects of deviations from stoichiometric AgSbTe<sup>2</sup> composition, we construct three model alloys based on P4/mmm space group symmetry, which is reduced to cubic P1 symmetry, by setting equal lattice parameter of a = 6.113 Å for all. The resulting structures simulated are: (AgSbTe2 )2 , Ag3 SbTe4 , and AgSb3 Te4 , which appear in **Figure 1e, f,** and **g,** respectively. All three structures contain 8 atoms per unit cell and Sb/Ag ratios of 1, 1/3, and 3, respectively. To calculate band structures of these three model alloys, spin-orbit (SO) magnetic calculations were performed utilizing a similar GGA/PAW routine as described above for uniform 7 × 7 × 7 Monkhorst-Pack *k*-point mesh and 400 eV energy cutoff to represent Kohn-Sham electronic wave functions, applying 10−6 eV energy convergence threshold. SO coupling is often being considered in band structure calculations [32, 70, 75]. TE transport properties were calculated according to the procedure detailed by Eqs. (1)–(4).

## **3.2. Experimental procedure**

#### *3.2.1. Materials synthesis*

Experimental procedures implemented in this study are intended to validate the effects of La-alloying on TE performance, as predicted from first principles. They include synthesis of two model alloys, La-free and La-alloyed, having molar ratios (Ag:Sb:Te:La) of 18:29:53:0 and 15.75:29:53:2.25, respectively. Generally, synthesis procedures comprise vacuum melting and iced-water quenching, followed by uniaxial hot-pressing at two distinct temperatures, 540 and 500°C, yielding two series of 12.7 mm dia. pellets referenced below as Series A and Series B, respectively. The difference between these two series of alloys is manifested by their phase contents and average composition in matrix. These factors significantly affect TE performance, as will be discussed further below. A detailed description of the experimental procedures appears elsewhere [58].

#### *3.2.2. Materials and thermoelectric property characterization*

Materials characterization procedures include microstructure, phase identification, and composition analysis employing scanning electron microscopy and X-ray diffraction [58]. Assessment of alloys' thermal stability is investigated using SETARAM 1600 DSC with a scanning rate of 25 K min−1 at temperatures ranging from room temperature through 973 K.

Temperature-dependent electrical conductivity, σ(T), and Seebeck coefficient, S(T) (thermopower), of these pellets are measured in temperature range from 300 to ~700 K employing *Nemesis®* SBA-458 apparatus (Netzsch GmbH), which is designed for simultaneous measurements of electrical conductivity and thermopower for planar geometry [76–78].

*MicroFlash®* LFA-457 laser flash analyzer (LFA; Netzsch GmbH) is utilized to measure directly of thermal diffusivity, α(T), of pellets in the same temperature range applying pulse-corrected Cowan approximation to consider heat loss of the samples [79], yielding instrumental accuracy of 2%. Material's density, *ρ*, is measured at room temperature, and density's dependence on temperature is neglected. Temperature-dependent heat capacity, Cp(T), is simultaneously measured in LFA by comparative method using pure Al<sup>2</sup> O3 —reference sample having similar geometry [76]. The resulting accuracy of evaluation of thermal conductivity values is equal to 10%. Pellets' thermal conductivity values, κ, are then determined by measuring their temperature-dependent thermal diffusivity and heat capacity, as well as, density; κ is then expressed by [80]:

$$\kappa(\mathbf{T}) = \left. \alpha(\mathbf{T}) \cdot \boldsymbol{\rho} \cdot \mathbf{C}\_p(\mathbf{T}) \,. \tag{7}$$

## **4. Effects of La-alloying on thermoelectric performance**

In this section, we introduce the concept resting behind La-alloying: its origin and implications, predictions from first principles, and experimental validations. Comparative discussion of the results in view of TE performance is provided.

#### **4.1. Predictions from first-principles**

#### *4.1.1. The AgSbTe2 (P4/mmm) phase*

*3.1.4. Ag3*

*SbTe4*

tures simulated are: (AgSbTe2

**3.2. Experimental procedure**

cedures appears elsewhere [58].

*3.2.2. Materials and thermoelectric property characterization*

*3.2.1. Materials synthesis*

 *and AgSb3*

*Te4*

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

 *model compounds*

SbTe4

properties were calculated according to the procedure detailed by Eqs. (1)–(4).

three model alloys based on P4/mmm space group symmetry, which is reduced to cubic P1 symmetry, by setting equal lattice parameter of a = 6.113 Å for all. The resulting struc-

, and AgSb3

respectively. All three structures contain 8 atoms per unit cell and Sb/Ag ratios of 1, 1/3, and 3, respectively. To calculate band structures of these three model alloys, spin-orbit (SO) magnetic calculations were performed utilizing a similar GGA/PAW routine as described above for uniform 7 × 7 × 7 Monkhorst-Pack *k*-point mesh and 400 eV energy cutoff to represent Kohn-Sham electronic wave functions, applying 10−6 eV energy convergence threshold. SO coupling is often being considered in band structure calculations [32, 70, 75]. TE transport

Experimental procedures implemented in this study are intended to validate the effects of La-alloying on TE performance, as predicted from first principles. They include synthesis of two model alloys, La-free and La-alloyed, having molar ratios (Ag:Sb:Te:La) of 18:29:53:0 and 15.75:29:53:2.25, respectively. Generally, synthesis procedures comprise vacuum melting and iced-water quenching, followed by uniaxial hot-pressing at two distinct temperatures, 540 and 500°C, yielding two series of 12.7 mm dia. pellets referenced below as Series A and Series B, respectively. The difference between these two series of alloys is manifested by their phase contents and average composition in matrix. These factors significantly affect TE performance, as will be discussed further below. A detailed description of the experimental pro-

Materials characterization procedures include microstructure, phase identification, and composition analysis employing scanning electron microscopy and X-ray diffraction [58]. Assessment of alloys' thermal stability is investigated using SETARAM 1600 DSC with a scanning rate of 25 K min−1 at temperatures ranging from room temperature through 973 K.

Temperature-dependent electrical conductivity, σ(T), and Seebeck coefficient, S(T) (thermopower), of these pellets are measured in temperature range from 300 to ~700 K employing *Nemesis®* SBA-458 apparatus (Netzsch GmbH), which is designed for simultaneous measure-

*MicroFlash®* LFA-457 laser flash analyzer (LFA; Netzsch GmbH) is utilized to measure directly of thermal diffusivity, α(T), of pellets in the same temperature range applying pulse-corrected Cowan approximation to consider heat loss of the samples [79], yielding instrumental accuracy of 2%. Material's density, *ρ*, is measured at room temperature, and density's dependence on temperature is neglected. Temperature-dependent heat capacity, Cp(T), is simultaneously

ments of electrical conductivity and thermopower for planar geometry [76–78].

Te4

composition, we construct

, which appear in **Figure 1e, f,** and **g,**

To simulate the effects of deviations from stoichiometric AgSbTe<sup>2</sup>

) 2 , Ag3

## *4.1.1.1. Structural and vibrational properties*

P4/mmm form of AgSbTe2 phase is found to be the most stable one compared to all three polymorphs at temperatures larger than 400 K and exhibits Helmholtz free energy values with close proximity to those of cubic polymorph [57]. Frequency-dependent v-DOS, *gp* (*ω*), calculated for this compound applying Debye approximation exhibits two major peaks at ca. 2.0 and 2.7 THz, and discloses interesting feature. Whereas, 2.7 THz peak comprises equal contributions from lattice vibrations of all sublattice sites, 2.0 THz one is primarily ascribed to vibrations of Ag-sublattice site atoms [57, 58]. This opens up the option of tuning v-DOS pattern by introducing point defects, a discipline for which the term *phonon engineering* has been coined [35]. Particularly, substitutions for Ag-sublattice sites by elements of different mass or atomic radius are expected to modify v-DOS with respect to that of pure AgSbTe2 phase by suppressing its major v-DOS peak. This, consequently, will reduce lattice thermal conductivity. La has been suggested as optional substitution atom due to its relatively large mass and atomic radius compared to average values of AgSbTe2 , that is, 138.91 a.m.u. and 187 pm vs. 121.21 a.m.u. and 143.98 pm, respectively, giving rise to enhanced phonon scattering by point defects [81–84]. Furthermore, La-alloying has commercial outcomes, since La is the most inexpensive element compared to constituents of AgSbTe2 alloy and is one of the less inexpensive ones among *energy-critical elements* [85].

Three substitutional options were tested, in which La substitutes for Ag, Sb, or Te, and it was found that substitution at Ag-sublattice sites is the most energetically preferred state for P4/mmm symmetry [57]. Accordingly, La-doped structure was constructed, in which one La-atom substitutes for 1/8. of Ag-atoms, and is shown in **Figure 1b**. First, v-DOS was calculated for La-doped structure and 2.0 THz peak was suppressed, as expected. Second, phonon dispersion curves were calculated for both AgSbTe2 and LaAg<sup>7</sup> Sb8 Te16 alloys close to Γ-point along c-crystallographic direction, indicating, that the slopes of the one longitudinal and two transverse acoustic modes of AgSbTe2 -lattice are greater, than those of La-alloyed one [57]. Quantitatively, average sound velocities derived for pure and La-alloyed materials are 1727 and 1046 m s−1, respectively. Moreover, temperature-dependent heat capacity functions were determined for both structures, yielding slightly lower values for La-alloyed material. Both values of sound velocity and heat capacity that are found to decrease due to La-alloying imply, that La-alloying should reduce lattice thermal conductivity [57]. Additional calculations employing Debye approximation for low-temperature range of heat capacity yield Debye temperatures and sound velocities for both pure and La-alloyed materials, which are 112 K and 1684 m s−1 vs. 104 K and 1563 m s−1, respectively [58]. It is noteworthy that evaluation of sound velocity in this manner is considered to be more physically reliable, since it represents the entire space of lattice directions, rather than individual one. It is, therefore, expected that this way of calculation should yield thermal conductivity values, that fit experimental data better than the former way does.

#### *4.1.1.2. Effects of La-doping on thermal conductivity*

Average sound velocity, *vs* , and Debye temperature, *θD* , evaluated from first-principles serve as input, that is required to evaluate lattice thermal conductivity, *κ<sup>p</sup>* . To this end, one possibility is to employ Callaway model for lattice thermal conductivity [86, 87], which has become conventional, particularly in the field of TE materials [36–38, 88–93]. In present case, however, there is no need to employ Callaway model for several reasons. First, Callaway model is specified for low temperatures, where contributions of either Normal (N)- or Umklapp (U)-processes are at the same order of magnitude. For temperatures adequately higher than Debye temperature (e.g., *θD* ≈ 112 K for AgSbTe<sup>2</sup> alloy) [30, 57], only U-processes dominate. Second, Callaway model considers *gp* (*ω*) and *Cp* (*T*) functions that are simplistically approximated based on Debye model [94]. In present case, however, the explicit *gp* (*ω*) and *Cp* (*T*) functions have already been calculated for both pure and La-alloyed materials. Alternatively, the following expression for lattice thermal conductivity is employed [94–96]:

$$
\kappa\_p = \frac{1}{3} C\_v v\_s^2 \,\tau \,\,\,\,\,\tag{8}
$$

where *τ* is phonon relaxation time. To first approximation, it has been assumed that La-doping influences mostly sound velocity and heat capacity and has negligible effect on *τ*. The ratio of *Cv vs* 2 -products obtained for LaAg<sup>7</sup> Sb8 Te16 andAgSbTe2 alloys, therefore, reflects the lower limit of relative reduction in thermal conductivity due to La-alloying. Applying dispersion curves close to Γ-point along c-crystallographic direction, it is predicted, that *κ<sup>p</sup>* should decrease by factor of ca. 2.7 due to La-doping. Alternatively, applying sound velocity values derived from Debye approximation, *κ<sup>p</sup>* is expected to decrease by ca. 14% at room temperature due to La-doping [58].

A more thorough and accurate treatment of expression (8) considers the effects of La-alloying on *τ*, as well. To evaluate *τ*, contributions of two major scattering mechanisms are taken into account. The first one is phonon-phonon inelastic interactions, i.e., U-processes, that prevail for these alloys above room temperature. Relaxation time for U-processes, *τU*, is represented by [96, 97]:

$$
\pi\_{\mathcal{U}}^{-1} \approx \frac{\hbar \,\gamma^2}{M \,\mathrm{v}\_\*^{-2} \theta\_D} \,\omega^2 \, T \, e^{\left(\frac{\theta\_d}{M}\right)} \,\tag{9}
$$

where *γ* is Grüneisen parameter that reflects the degree of lattice anharmonicity [69], and *M* is average atomic mass of alloy. Second, to account for internal composition inhomogeneity or compositional modulations at unit-cell length scales, that are typical for such materials [5, 8, 16, 91], the boundary scattering mechanism is employed for characteristic period *l*, represented by relaxation time *τB* , so that [96]:

$$
\pi\_{\rm B}^{-1} \approx \frac{\nu\_s}{I} \,. \tag{10}
$$

To consider dependence of v-DOS on phonon frequency, frequency-averaged expression for *τU* is introduced, so that *gp* (*ω*) serves as weighting function:

$$
\left< \tau\_{\mathcal{U}}^{-1} \right>\_{\omega} = \frac{\hbar \gamma^2}{M \nu\_\* \,^2 \theta\_0 \,\omega\_0} T \, e^{\left(\frac{\theta\_0}{\mathcal{N}}\right)} \Big|\_{0}^{\omega\_p} \omega^2 \, \mathcal{g}\_p(\omega) d\omega \,\, \,\tag{11}
$$

where *ωD* is Debye frequency. Equivalent relaxation time is then expressed as:

$$
\tau^{-1} = \left< \tau\_{\ll}^{-1} \right>\_{\omega} + \tau\_{\gg}^{-1} \,. \tag{12}
$$

The resulting values of lattice thermal conductivity for LaAg<sup>7</sup> Sb8 Te16 and AgSbTe2 alloys are obtained from Eq. (8) by substituting the respective physical magnitudes for both alloys in Eqs. (9)–(11) [19, 20, 30, 57, 58, 92] with *l* ≈ 1 nm [5, 8, 16, 91]. Lattice thermal conductivity for LaAg<sup>7</sup> Sb8 Te16 and AgSbTe2 alloys calculated as function of temperature appear in **Figure 2**.

It is shown that thermal conductivity exhibits realistic values, that correspond with data documented in the literature [19, 20, 25, 98] with marked decrease due to La-doping, ranging between relative values of 11 and 19%, depending on temperature.

#### *4.1.1.3. Effects of La-doping on electrical properties*

Γ-point along c-crystallographic direction, indicating, that the slopes of the one longitudinal

[57]. Quantitatively, average sound velocities derived for pure and La-alloyed materials are 1727 and 1046 m s−1, respectively. Moreover, temperature-dependent heat capacity functions were determined for both structures, yielding slightly lower values for La-alloyed material. Both values of sound velocity and heat capacity that are found to decrease due to La-alloying imply, that La-alloying should reduce lattice thermal conductivity [57]. Additional calculations employing Debye approximation for low-temperature range of heat capacity yield Debye temperatures and sound velocities for both pure and La-alloyed materials, which are 112 K and 1684 m s−1 vs. 104 K and 1563 m s−1, respectively [58]. It is noteworthy that evaluation of sound velocity in this manner is considered to be more physically reliable, since it represents the entire space of lattice directions, rather than individual one. It is, therefore, expected that this way of calculation should yield thermal conductivity values, that fit experi-

ity is to employ Callaway model for lattice thermal conductivity [86, 87], which has become conventional, particularly in the field of TE materials [36–38, 88–93]. In present case, however, there is no need to employ Callaway model for several reasons. First, Callaway model is specified for low temperatures, where contributions of either Normal (N)- or Umklapp (U)-processes are at the same order of magnitude. For temperatures adequately higher than

(*ω*) and *Cp*

tions have already been calculated for both pure and La-alloyed materials. Alternatively, the

3 *Cv vs*

Te16 andAgSbTe2

where *τ* is phonon relaxation time. To first approximation, it has been assumed that La-doping influences mostly sound velocity and heat capacity and has negligible effect on *τ*. The ratio of

of relative reduction in thermal conductivity due to La-alloying. Applying dispersion curves

by factor of ca. 2.7 due to La-doping. Alternatively, applying sound velocity values derived

A more thorough and accurate treatment of expression (8) considers the effects of La-alloying on *τ*, as well. To evaluate *τ*, contributions of two major scattering mechanisms are taken into account. The first one is phonon-phonon inelastic interactions, i.e., U-processes, that prevail

mated based on Debye model [94]. In present case, however, the explicit *gp*

following expression for lattice thermal conductivity is employed [94–96]:

Sb8

close to Γ-point along c-crystallographic direction, it is predicted, that *κ<sup>p</sup>*


, and Debye temperature, *θD* , evaluated from first-principles serve

. To this end, one possibil-

(*ω*) and *Cp*

(*T*) func-

should decrease

alloy) [30, 57], only U-processes dominate.

<sup>2</sup> *τ* , (8)

alloys, therefore, reflects the lower limit

is expected to decrease by ca. 14% at room temperature due to

(*T*) functions that are simplistically approxi-

and two transverse acoustic modes of AgSbTe2

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

mental data better than the former way does.

Average sound velocity, *vs*

*Cv vs* 2

*4.1.1.2. Effects of La-doping on thermal conductivity*

Debye temperature (e.g., *θD* ≈ 112 K for AgSbTe<sup>2</sup>

*<sup>κ</sup><sup>p</sup>* <sup>=</sup> \_\_1

Second, Callaway model considers *gp*


from Debye approximation, *κ<sup>p</sup>*

La-doping [58].

as input, that is required to evaluate lattice thermal conductivity, *κ<sup>p</sup>*

It was shown that La-alloying reduces lattice thermal conductivity values, which affects TE performance positively. To address, however, the total effects of La-alloying on TE performance, evaluation of electrical conductivity and Seebeck coefficient is essential. This goal was achieved from first-principles applying Boltzmann transport theory as described above for LaAg<sup>7</sup> Sb8 Te16 and AgSbTe2 alloys. The results are plotted in **Figure 3** in temperature range 50–1000 K.

It is found that La-doping results in reduction in electrical conductivity (e.g., from ca. 1800 down to 250 S cm−1 at room temperature) and, at the same time, increase in Seebeck coefficient, e.g., from ca. 4 up to 40 µV K−1 at room temperature. For the sake of comparison, Jovovic and Heremans reported on experimental measurements of electrical conductivity and Seebeck coefficients of stoichiometric and doped AgSbTe<sup>2</sup> alloys at temperatures up to 400 K [19, 98]. For example, they report on electrical resistivity value of 5 × 10−5 Ohm m at 100 K for stoichiometric AgSbTe2 alloy, which is equivalent to 200 S cm−1.

They report also on electrical resistivity that increases with temperature, indicating charge carriers scattering. Additionally, electrical resistivity may either increase or decrease with doping, depending on dopant's chemical identity. In the present case, electrical conductivity values are significantly larger, e.g., ca. 1900 S cm−1 at 100 K, and are decreasing with temperature, where La-doping reduces conductivity. Seebeck coefficient values reported by Jovovic et al. exhibit general trend of increase with temperature, which corresponds to trend calculated in the present case. Also, they report on general trend of increase in Seebeck coefficient values due to doping (except doping with AgTe), in agreement with the present study for La. Complementary trend is reported by Du et al. [25, 99]. Most interestingly, effects of La-doping on electrical properties of AgSbTe<sup>2</sup> alloy are reported by Min et al. [27]. They report on trends that are qualitatively similar to those of the present study. First, La-doping was also reported to reduce electrical conductivity, e.g., from ca. 400 S cm−1 for undoped AgSbTe2 down to 66 S cm−1 for 3 at.% La-doping at room temperature. Second, La-doping increases Seebeck coefficients, e.g., from ca. 90 µV·K−1 for undoped AgSbTe2 up to ca. 220 µV K−1 for 3 at.% La-doping at room temperature. Quantitatively, values of electrical conductivity calculated in this study are considered to be large with respect to the above cited studies. Conversely, Seebeck coefficient values calculated in this study are considered to be smaller than those reported by the above studies. We note, however, that such calculations are most meaningful for comparative purposes, since they rest upon values, that should be calibrated against experimental data, such as electronic chemical potential and relaxation times.

**Figure 2.** The lattice thermal conductivity values calculated from first-principles for AgSbTe<sup>2</sup> (pure AST; filled red circles) and LaAg<sup>7</sup> Sb8 Te16 (La-doped AST; empty red circles) alloys in temperature range 300–1000 K.

**Figure 3.** Electrical conductivity and Seebeck coefficient values calculated for AgSbTe<sup>2</sup> (pure AST; filled black squares and blue circles, respectively) and LaAg<sup>7</sup> Sb8 Te16 (La-doped AST; empty black squares and blue circles, respectively) alloys in temperature range 50–1000 K from first-principles applying Boltzmann transport theory.

It is indicated that the effects of La-doping on electrical conductivity and Seebeck coefficient are opposite to each other. Evaluation of TE power factor (PF; *S* <sup>2</sup> *σ*) is, therefore, necessary in order to realize how La affects TE power conversion. **Figure 4** displays PF calculated for LaAg<sup>7</sup> Sb8 Te16 and AgSbTe2 alloys in temperature range 50–1000 K.

It is shown that La-doping has considerably positive effect on PF. This also corresponds with the data reported by Min et al. [27], specifically for low La-concentration regime. We note that, moreover, La-doping reduces lattice thermal conductivity, as shown in **Figure 2**. We conclude that La-alloying should improve energy conversion efficiency of AgSbTe<sup>2</sup> (P4/mmm), as reflected by increased TE figure-of-merit.

#### *4.1.2. Formation of Sb2 Te3 and Sb8 Te3 (R-3m) phases*

and Heremans reported on experimental measurements of electrical conductivity and Seebeck

For example, they report on electrical resistivity value of 5 × 10−5 Ohm m at 100 K for stoichio-

They report also on electrical resistivity that increases with temperature, indicating charge carriers scattering. Additionally, electrical resistivity may either increase or decrease with doping, depending on dopant's chemical identity. In the present case, electrical conductivity values are significantly larger, e.g., ca. 1900 S cm−1 at 100 K, and are decreasing with temperature, where La-doping reduces conductivity. Seebeck coefficient values reported by Jovovic et al. exhibit general trend of increase with temperature, which corresponds to trend calculated in the present case. Also, they report on general trend of increase in Seebeck coefficient values due to doping (except doping with AgTe), in agreement with the present study for La. Complementary trend is reported by Du et al. [25, 99]. Most interestingly, effects of

report on trends that are qualitatively similar to those of the present study. First, La-doping was also reported to reduce electrical conductivity, e.g., from ca. 400 S cm−1 for undoped

K−1 for 3 at.% La-doping at room temperature. Quantitatively, values of electrical conductivity calculated in this study are considered to be large with respect to the above cited studies. Conversely, Seebeck coefficient values calculated in this study are considered to be smaller than those reported by the above studies. We note, however, that such calculations are most meaningful for comparative purposes, since they rest upon values, that should be calibrated against experimental data, such as electronic chemical potential and relaxation times.

increases Seebeck coefficients, e.g., from ca. 90 µV·K−1 for undoped AgSbTe2

**Figure 2.** The lattice thermal conductivity values calculated from first-principles for AgSbTe<sup>2</sup>

Te16 (La-doped AST; empty red circles) alloys in temperature range 300–1000 K.

down to 66 S cm−1 for 3 at.% La-doping at room temperature. Second, La-doping

alloys at temperatures up to 400 K [19, 98].

alloy are reported by Min et al. [27]. They

up to ca. 220 µV

(pure AST; filled red circles)

coefficients of stoichiometric and doped AgSbTe<sup>2</sup>

La-doping on electrical properties of AgSbTe<sup>2</sup>

AgSbTe2

and LaAg<sup>7</sup>

Sb8

metric AgSbTe2 alloy, which is equivalent to 200 S cm−1.

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

The single δ-phase is Sb-rich phase based on AgSbTe<sup>2</sup> alloy. Since it has limited solubility to Sb with relatively moderate slope of Sb-solvus, it is likely to decompose to δ+Sb<sup>2</sup> Te3 phase mixture [28, 29, 100–103], whereas Sb2 Te3 is equilibrium phase and may appear as different homologous forms [72, 73, 104–107]. Precipitation of antimony-telluride second phase in δ-matrix is expected to affect TE performance due to contributions from both matrix and precipitate phases or variation of the average matrix composition. In the following sections, we address both aspects. Section 4.1.2.1 introduces the issue of precipitation sequence based on bulk/interfacial energetic considerations, and Section 4.1.2.2 predicts the effects of phase formation on electronic properties. Then, Section 4.1.3 deals with compositional variations in the matrix and their effects on electronic properties.

**Figure 4.** Thermoelectric power factor (PF) calculated for AgSbTe2 (pure AST; filled black squares) and LaAg<sup>7</sup> Sb8 Te16 (La-doped AST; empty black squares) alloys in temperature range 50–1000 K from first-principles applying Boltzmann transport theory.

#### *4.1.2.1. The precipitation sequence: energetic aspects*

Nucleation of Sb2 Te3 and Sb8 Te3 phases from Sb-saturated δ-AgSbTe<sup>2</sup> matrix has been observed, which can be associated to different experimental conditions. To account for the sequence of phase formation, information on both bulk and interfacial energetics is required. The formation energies of Sb2 Te3 and Sb8 Te3 (R-3m) phases, calculated according to Eq. (5), are −62 and −56.6 kJ mol−1, respectively. This implies that Sb2 Te3 is more energetically favorable, assuming, that Sb2 Te3 precipitates are adequately large, so that, interfaces do not play significant role. To address the role of interfaces, free energies of Sb2 Te3 /AgSbTe2 and Sb8 Te3 /AgSbTe2 interfaces are evaluated. To this end, two slab models of (Sb2 Te3 ) 2 /(AgSbTe2 ) 5 /(Sb2 Te3 ) 2 (40 atoms) and (AgSbTe2 ) 3 / (Sb8 Te3 ) 6 /(AgSbTe2 ) 3 (90 atoms) forms are constructed, respectively, consisting of two interfaces each, exhibiting (111 ) AgSbTe2 ∥ (0001 ) SbpTeq and 〈<sup>10</sup>¯〉 1AgSbTe 2 <sup>∥</sup> 〈¯ 2 110〉Sb pTeq orientation relationship, which was observed experimentally [100]. Both structures are displayed in **Figure 5**.

It is noted that two interfaces presented in both slabs shown in **Figure 5a** and **b** consist of different Sb- and Te-terminating planes, so that interfacial free energies calculated according to Eq. (6) represent an average value for both terminations. Correction factor is, therefore, applied to represent interfacial free energy of low-energy Sb-termination. The resulting values for Sb2 Te3 / AgSbTe2 and Sb8 Te3 /AgSbTe2 interfaces are *γ* = 208 and 175 mJ m−2, respectively. These values are considered to be relatively low compared to those of intermetallic compounds and are comparable with those of pure metals [108]. This is, however, not surprising, considering the extremely small atomic misfit between the (111) AgSbTe2 and (0001) SbpTeq crystallographic planes [100], which encourages formation of Sb2 Te3 or Sb8 Te3 precipitates in the form of long lamellae along these planes [28, 29, 57, 58, 100–103]. These low values of interfacial free energy also initiate fast nucleation, thanks to low activation energy for nucleation, which is proportional to *γ*<sup>3</sup> [109].

**Figure 5.** Two slab models of (a) (Sb2 Te3 )2 /(AgSbTe2 )5 /(Sb2 Te3 )2 (40 atoms) and (b) (AgSbTe2 )3 /(Sb8 Te3 )6 /(AgSbTe2 )3 (90 atoms) including two Sb2 Te3 /AgSbTe2 and Sb8 Te3 /AgSbTe2 interfaces each, respectively. All interfaces, marked by arrows, are of ( 111 ) AgSbTe 2 ∥ ( 0001 ) Sb p Te q and 〈10 ¯ 1 〉 AgSbTe2 ∥ 〈 ¯2110 〉 Sb p Te q orientation relationship.

Interestingly, Sb2 Te3 phase exhibits lower value of formation energy and higher value of interfacial free energy compared to those of Sb8 Te3 phase. This implies that Sb8 Te3 is metastable phase that may form prior to the nucleation of Sb2 Te3 equilibrium phase [28, 29, 100–103]. Suggested nucleation sequence is, therefore, supersaturated-δ → supersaturated-δ + Sb<sup>8</sup> Te3 → equilibrium-δ + Sb<sup>2</sup> Te3 .

#### *4.1.2.2. Effects of Sb<sup>2</sup> Te3 and Sb8 Te3 formation on electronic properties*

*4.1.2.1. The precipitation sequence: energetic aspects*

**Figure 4.** Thermoelectric power factor (PF) calculated for AgSbTe2

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

and Sb8

Te3

Te3

∥ (0001 )

phases from Sb-saturated δ-AgSbTe<sup>2</sup>

(R-3m) phases, calculated according to Eq. (5), are −62 and −56.6 kJ

Te3

<sup>∥</sup> 〈¯ 2 110〉Sb pTeq

interfaces are *γ* = 208 and 175 mJ m−2, respectively. These values are

precipitates in the form of long lamellae along these

and Sb8

) 5 /(Sb2 Te3 ) 2

(90 atoms) forms are constructed, respectively, consisting of two interfaces

is more energetically favorable, assuming, that Sb2

/AgSbTe2

(pure AST; filled black squares) and LaAg<sup>7</sup>

which can be associated to different experimental conditions. To account for the sequence of phase formation, information on both bulk and interfacial energetics is required. The formation

(La-doped AST; empty black squares) alloys in temperature range 50–1000 K from first-principles applying Boltzmann

precipitates are adequately large, so that, interfaces do not play significant role. To address

/AgSbTe2

and 〈<sup>10</sup>¯〉 1AgSbTe 2

It is noted that two interfaces presented in both slabs shown in **Figure 5a** and **b** consist of different Sb- and Te-terminating planes, so that interfacial free energies calculated according to Eq. (6) represent an average value for both terminations. Correction factor is, therefore, applied to represent interfacial free energy of low-energy Sb-termination. The resulting values for Sb2

considered to be relatively low compared to those of intermetallic compounds and are comparable with those of pure metals [108]. This is, however, not surprising, considering the extremely

and (0001)

planes [28, 29, 57, 58, 100–103]. These low values of interfacial free energy also initiate fast nucle-

SbpTeq

/(AgSbTe2

Te3

SbpTeq

Te3

which was observed experimentally [100]. Both structures are displayed in **Figure 5**.

AgSbTe2

ation, thanks to low activation energy for nucleation, which is proportional to *γ*<sup>3</sup>

Te3 ) 2 matrix has been observed,

interfaces are evalu-

orientation relationship,

(40 atoms) and (AgSbTe2

crystallographic planes [100], which

[109].

Te3

Sb8 Te16

> ) 3 /

Te3 /

Te3

and Sb8

mol−1, respectively. This implies that Sb2

the role of interfaces, free energies of Sb2

ated. To this end, two slab models of (Sb2

AgSbTe2

/AgSbTe2

Te3 or Sb8 Te3

) 3

Te3

/(AgSbTe2

and Sb8

encourages formation of Sb2

Te3

small atomic misfit between the (111)

each, exhibiting (111 )

Nucleation of Sb2

transport theory.

energies of Sb2

(Sb8 Te3 ) 6

AgSbTe2

In view of aforementioned prospect for the presence of either of Sb2 Te3 - or Sb8 Te3 -phases in AgSbTe2 -matrix, calculations of transport coefficients of these phases provide us with predictions of the effects such phase mixture on TE performance. **Figure 6** displays electrical conductivity and Seebeck coefficients calculated in temperature range 50–1000 K.

It is shown that both electrical conductivity and Seebeck coefficient values of Sb<sup>2</sup> Te3 phase are larger than those of Sb8 Te3 phase in wide temperature range, e.g., ca. 2100 S cm−1 and 85 µV K−1 for Sb2 Te3 compared to 1380 S cm−1 and 29 µV K−1 for Sb8 Te3 at 300 K, respectively. Moreover, comparison of these results with the data shown in **Figure 3** for AgSbTe2 -matrix implies that precipitation of Sb2 Te3 phase yields positive influence on TE performance: both electrical conductivity and Seebeck coefficient increase. It is strikingly indicated that the effects of Sb<sup>2</sup> Te3 precipitation are even greater, than those of La-doping. It is, therefore, concluded that the desirable material from TE viewpoint is La-doped, Sb-supersaturated δ-AgSbTe<sup>2</sup> -matrix that is aged for a certain duration to form considerable amount of Sb2 Te3 phase. The effects of Sb<sup>8</sup> Te3 phase on TE performance are, conversely, inferior to those of Sb2 Te3 phase. Sb8 Te3 is, however, metastable phase and is not expected to prevail for long durations at elevated temperatures (e.g., under service conditions of TE generator) due to low thermal stability.

**Figure 6.** Electrical conductivity and Seebeck coefficient values calculated for Sb<sup>2</sup> Te3 (filled black squares and blue circles, respectively) and Sb8 Te3 (empty black squares and blue circles, respectively) compounds in temperature range 50–1000 K from first-principles applying Boltzmann transport theory.

#### *4.1.3. Effects of off-stoichiometry on electronic properties of the AgSbTe<sup>2</sup> phase*

An additional effect taking place during precipitation of any SbpTeq phase from Sb-supersaturated δ-matrix is enrichment of δ-matrix with Ag-atoms and depletion of Sb. To simulate these compositional variations, two off-stoichiometric model alloys are constructed, namely Ag3 SbTe4 and AgSb3 Te4 , in addition to stoichiometric AgSbTe2 phase. These model compounds, appearing in **Figure 1e, g,** and **f,** exhibit Sb/Ag ratios of 1/3, 3, and 1, respectively. **Figure 7** displays electrical conductivity and Seebeck coefficient values calculated in temperature range 50–1000 K.

It is shown, that increase in Sb/Ag ratio results in decrease in electrical conductivity simultaneously with increase in Seebeck coefficient. This trend corresponds well with study of Jovovic and Heremans [19], who reported on decrease in both Seebeck coefficient and electrical resistivity due to additions of 2% AgTe to stoichiometric AgSbTe2 -phase, i.e., reducing Sb/Ag ratio. It should be noted that comparison of this trend with data reported in the literature is not straightforward, since compositional changes involve in practice not only Sb/Ag ratio, but also ratio of Te to any of the other species. Additionally, deviations from given stoichiometry often involve formation of second phases, which is not directly simulated here. For instance, Zhang et al. reported on dependence of TE properties on composition for Ag2−ySby Te1+y -based alloys and found that electrical conductivity increases, while Seebeck coefficient decreases with *y*-values increasing from 1.26 up to 1.38 [101].

Most importantly, this predicted effect of Sb/Ag ratio on electrical properties has major implications on the temporal evolution of TE performance of the material during aging heat treatments (below Sb-solvus), or of TE generator during service. Since SbpTeq phases nucleate from Sb-supersaturated δ-matrix during heat treatments, Sb/Ag ratio in δ-matrix decreases. This should be accompanied by increase in electrical conductivity concurrently with decrease in Seebeck coefficient.

**Figure 7.** Electrical conductivity and Seebeck coefficient values calculated for Ag<sup>3</sup> SbTe4 (left-half-filled black squares and blue circles, respectively), (AgSbTe2 )2 (empty black squares and blue circles, respectively), and AgSb3 Te4 (right-halffilled black squares and blue circles, respectively) alloys in temperature range 50–1000 K from first-principles applying Boltzmann transport theory.

## **5. Experimental results**

*4.1.3. Effects of off-stoichiometry on electronic properties of the AgSbTe<sup>2</sup>*

**Figure 6.** Electrical conductivity and Seebeck coefficient values calculated for Sb<sup>2</sup>

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

Te4

tivity due to additions of 2% AgTe to stoichiometric AgSbTe2

with *y*-values increasing from 1.26 up to 1.38 [101].

namely Ag3

respectively) and Sb8

SbTe4

Te3

ture range 50–1000 K.

and AgSb3

K from first-principles applying Boltzmann transport theory.

An additional effect taking place during precipitation of any SbpTeq

Sb-supersaturated δ-matrix is enrichment of δ-matrix with Ag-atoms and depletion of Sb. To simulate these compositional variations, two off-stoichiometric model alloys are constructed,

compounds, appearing in **Figure 1e, g,** and **f,** exhibit Sb/Ag ratios of 1/3, 3, and 1, respectively. **Figure 7** displays electrical conductivity and Seebeck coefficient values calculated in tempera-

It is shown, that increase in Sb/Ag ratio results in decrease in electrical conductivity simultaneously with increase in Seebeck coefficient. This trend corresponds well with study of Jovovic and Heremans [19], who reported on decrease in both Seebeck coefficient and electrical resis-

It should be noted that comparison of this trend with data reported in the literature is not straightforward, since compositional changes involve in practice not only Sb/Ag ratio, but also ratio of Te to any of the other species. Additionally, deviations from given stoichiometry often involve formation of second phases, which is not directly simulated here. For instance,

alloys and found that electrical conductivity increases, while Seebeck coefficient decreases

Most importantly, this predicted effect of Sb/Ag ratio on electrical properties has major implications on the temporal evolution of TE performance of the material during aging heat treat-

Sb-supersaturated δ-matrix during heat treatments, Sb/Ag ratio in δ-matrix decreases. This

Zhang et al. reported on dependence of TE properties on composition for Ag2−ySby

ments (below Sb-solvus), or of TE generator during service. Since SbpTeq

 *phase*


, in addition to stoichiometric AgSbTe2 phase. These model

Te3

(empty black squares and blue circles, respectively) compounds in temperature range 50–1000

phase from

(filled black squares and blue circles,

Te1+y -based

phases nucleate from

It was shown above how first-principles calculations provide us with information about all aspects concerning TE transport behavior, including thermal and electrical conductivity and Seebeck coefficient. Most importantly, this assists us in tailoring the material by introducing lattice defects to enhance its TE performance. In the following section, we introduce experimental procedures taken for validating the above predictions. Comparing between both aspects is, moreover, very instructive not only on engineering aspects, but also on universal aspect, by realizing how to implement computational tools to predict properties of other materials.

#### **5.1. Microstructure and implications on thermoelectric behavior**

As mentioned above, two classes of La-alloyed AgSbTe<sup>2</sup> -based materials were prepared by uniaxial hot-pressing at 540 or 500°C, and are classified as Series A and Series B, respectively. The ideal case for testing the effects of La-doping is single δ-phase dissolving La homogeneously. This, however, is difficult to achieve. Hot-pressing at 540°C, that is, above Sb-solvus, expected to yield the desirable single δ-phase that does not contain Sb<sup>2</sup> Te3 precipitates [101–103]. These Sb2 Te3 precipitates, indeed, were not observed in Series A samples; however, La-rich precipitates having stoichiometry close to LaTe<sup>2</sup> were observed [110]. As a result, δ-matrix was found to be depleted of La [58], which does not allow us comparison between La-free and La-doped samples. Conversely, samples of Series B, that were hot-pressed at 500°C, exhibit considerable amount of Sb2 Te3 phase, which is expected; however, LaTe<sup>2</sup> precipitates are dissolved, so that δ-matrix contains adequately large amount of La, close to its nominal concentration. Series B is, therefore, more suitable to exemplify the effects of La-doping. Moreover, as predicted from first-principles, the presence of Sb<sup>2</sup> Te3 precipitates, in addition to La solute atoms, has positive effects on electronic transport.

#### **5.2. Thermal analysis**

Thermal conductivity measurements performed for both Series A and Series B indicate the expected trend. First, all thermal conductivity values lie in the range 0.6–0.8 W m−1 K−1 [58]. Second, samples of Series A did not exhibit any considerable difference between La-free and La-doped materials [58]. This is associated to depletion of δ-matrix from La solute atoms, so that, matrix composition of La-doped and La-free materials is practically the same. Third, and most importantly, it was found that thermal conductivity of La-doped materials is significantly lower than those of La-free materials of Series B, e.g., 0.8 W m−1 K−1 for La-free and 0.6 W m−1 K−1 for La-doped samples at 500 K. This is strikingly corroborated by predictions from first-principles, both qualitatively and quantitatively, as shown in **Figure 2**. It is also noteworthy that both values coincide at temperatures larger than 650 K, which can be associated with phase transition [58, 101–103]. Thorough discussion of thermal conductivity values measured for Series A and Series B materials and their relationship with microstructure appears elsewhere [58]. To address this issue of phase transition, DSC measurements were implemented for both La-free and La-doped samples, **Figure 8**.

**Figure 8.** Differential scanning calorimetry (DSC) signals collected upon heating from La-free (continuous black curve) and La-doped (dashed red curve) samples.

Endothermic peak at around 630–650 K is observed for La-free material, which is associated with Ag2 Te + Sb2 Te3 → δ-AgSbTe<sup>2</sup> phase transition at 360°C [101–103]. La-doped material, however, does not exhibit this transition. This corresponds well with thermal conductivity behavior reported by us earlier [58], in which temperature-dependent thermal conductivity of La-doped materials show up continuous trend, whereas La-free materials exhibit sharp drop of thermal conductivity around this temperature. This implies that La-additions help in stabilizing δ-phase against decomposition, which is expected to contribute to stability of TE device operation at service conditions. Sharp endothermic peak at ca. 860 K, which is common for both La-free and La-doped materials, is associated to melting.

#### **5.3. Electrical property measurements**

**Figure 8.** Differential scanning calorimetry (DSC) signals collected upon heating from La-free (continuous black curve)

to be depleted of La [58], which does not allow us comparison between La-free and La-doped samples. Conversely, samples of Series B, that were hot-pressed at 500°C, exhibit considerable

δ-matrix contains adequately large amount of La, close to its nominal concentration. Series B is, therefore, more suitable to exemplify the effects of La-doping. Moreover, as predicted from

Thermal conductivity measurements performed for both Series A and Series B indicate the expected trend. First, all thermal conductivity values lie in the range 0.6–0.8 W m−1 K−1 [58]. Second, samples of Series A did not exhibit any considerable difference between La-free and La-doped materials [58]. This is associated to depletion of δ-matrix from La solute atoms, so that, matrix composition of La-doped and La-free materials is practically the same. Third, and most importantly, it was found that thermal conductivity of La-doped materials is significantly lower than those of La-free materials of Series B, e.g., 0.8 W m−1 K−1 for La-free and 0.6 W m−1 K−1 for La-doped samples at 500 K. This is strikingly corroborated by predictions from first-principles, both qualitatively and quantitatively, as shown in **Figure 2**. It is also noteworthy that both values coincide at temperatures larger than 650 K, which can be associated with phase transition [58, 101–103]. Thorough discussion of thermal conductivity values measured for Series A and Series B materials and their relationship with microstructure appears elsewhere [58]. To address this issue of phase transition, DSC measurements were implemented

precipitates are dissolved, so that

precipitates, in addition to La solute atoms, has positive

phase, which is expected; however, LaTe<sup>2</sup>

Te3

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

and La-doped (dashed red curve) samples.

amount of Sb2

Te3

first-principles, the presence of Sb<sup>2</sup>

for both La-free and La-doped samples, **Figure 8**.

effects on electronic transport.

**5.2. Thermal analysis**

It was predicted from first-principles that La-doping reduces electrical conductivity and increases Seebeck coefficient, **Figure 3**. Measurements of electrical conductivity and Seebeck coefficients were carried out for both Series A and Series B materials. The samples of Series B are of our interest, since they dissolve La-atoms in δ-matrix; we will, therefore, introduce these results first. **Figure 9** displays experimentally collected electrical conductivity and Seebeck coefficient values of La-free and La-doped materials of Series B.

It is shown that electrical conductivity values decrease, e.g., from ca. 1400 down to 900 S cm−1 at room temperature, and Seebeck coefficient increase, e.g., from ca. 30 up to 70 µV K−1 at room temperature, due to La-doping. This behavior is, qualitatively, the same as that observed for calculated values shown in **Figure 3**. Moreover, temperature dependence, that is, electrical conductivity decreasing and Seebeck coefficient increasing with temperature for both La-free and La-doped materials, is identical to that indicated by calculated values shown in **Figure 3**. There are two major differences between experimental and calculated values appearing in **Figures 3** and **9**, respectively. First, the absolute values of measured Seebeck coefficient values are greater than calculated ones. Also, difference of electrical conductivity between La-doped and La-free materials is smaller for measured dataset than for calculated ones. This is probably due to difficulty to simulate low dopant concentrations in DFT [70]. Second, it is noteworthy that both values of electrical conductivity and Seebeck coefficients measured for La-free and La-doped materials converge at temperatures >650 K, **Figure 9**. Interestingly, these convergences occur due to sharp deviations of the values featured by La-free material, whereas the values of La-doped materials preserve their continuous trendline. This observation corresponds well with the behavior shown by DSC curves in **Figure 8**, where La-free compound decomposes at around 650 K, whereas La-doped compound seem to preserve its thermal stability. This also corresponds with converging thermal conductivities of the samples of Series B as discussed above [58]. Following our comparative discussion in Section 4.1.1.3, experimental values of electrical properties are found to be closer to experimental values reported in the literature than to calculated values [19, 25, 27, 98, 99].

To complement our understanding of the effects of La-doping on electronic properties, we measured temperature-dependent electrical conductivity and Seebeck coefficient values for the samples of Series A, as well. The results are plotted against temperature in **Figure 10**.

Comparison between the results attained for alloys of Series A and Series B is very instructive. As noted, the samples of Series A exhibited formation of LaTe<sup>2</sup> -like precipitates, which "drain out" La atoms from δ-matrix, resulting in matrix compositions, that are nearly identical to each other for La-free and La-doped materials. For this reason, thermal conductivity values measured for La-free and La-doped materials seem to be practically identical in wide temperature range [58]. It is, therefore, not surprising to observe the same behavior for electrical properties, **Figure 10**.

It is indicated, that both electrical conductivity and Seebeck coefficient values measured for La-free and La-doped materials seem to be very close to each other in the entire temperature range, probably due to nearly identical matrix compositions for La-free and La-doped materials. Additionally, electrical conductivity and Seebeck coefficients featured by La-doped alloys exhibit relatively continuous temperature-dependent behavior, whereas values, measured for La-free alloys exhibit curled behavior. This, again, can be explained in terms of poor thermal stability of La-free materials, as discussed above.

**Figure 9.** Electrical conductivity and Seebeck coefficient values measured for La-free (pure AST; filled black squares and blue circles, respectively) and La-doped (La-doped AST; empty black squares and blue circles, respectively) alloys of Series B in temperature range 300–673 K.

#### **5.4. Implications for thermoelectric power conversion**

It has been shown that La-doping has unequivocally positive effect on reducing lattice thermal conductivity, both computationally and experimentally. The effects on electrical properties, particularly electrical conductivity and Seebeck coefficient, are opposing each other. To assess the effects of La-doping on device's power capacity, TE PFs of La-free and La-doped materials of Series B are evaluated based on the data displayed in **Figure 9**. The results are shown in **Figure 11**.

Comparison between the results attained for alloys of Series A and Series B is very instruc-

"drain out" La atoms from δ-matrix, resulting in matrix compositions, that are nearly identical to each other for La-free and La-doped materials. For this reason, thermal conductivity values measured for La-free and La-doped materials seem to be practically identical in wide temperature range [58]. It is, therefore, not surprising to observe the same behavior

It is indicated, that both electrical conductivity and Seebeck coefficient values measured for La-free and La-doped materials seem to be very close to each other in the entire temperature range, probably due to nearly identical matrix compositions for La-free and La-doped materials. Additionally, electrical conductivity and Seebeck coefficients featured by La-doped alloys exhibit relatively continuous temperature-dependent behavior, whereas values, measured for La-free alloys exhibit curled behavior. This, again, can be explained in terms of poor thermal

It has been shown that La-doping has unequivocally positive effect on reducing lattice thermal conductivity, both computationally and experimentally. The effects on electrical properties, particularly electrical conductivity and Seebeck coefficient, are opposing each

**Figure 9.** Electrical conductivity and Seebeck coefficient values measured for La-free (pure AST; filled black squares and blue circles, respectively) and La-doped (La-doped AST; empty black squares and blue circles, respectively) alloys of


tive. As noted, the samples of Series A exhibited formation of LaTe<sup>2</sup>

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

for electrical properties, **Figure 10**.

stability of La-free materials, as discussed above.

**5.4. Implications for thermoelectric power conversion**

Series B in temperature range 300–673 K.

It is clearly shown that La-doping affects positively PF for temperatures lower than 500 K, e.g., PF determined for room temperature increases from ca. 200 to 400 µW m−1 K−2 due to La-doping. At higher temperatures, PFs of La-free and La-doped materials are practically identical. The maximum PF values observed are around 1000 µW m−1 K−2. This trend is similar to that reported by Min et al. [27], that is, PF increasing from 300 up to 1500 µW m−1 K−2 in respective temperature range from room temperature to 400°C for AgSbTe2 alloy.

La-doping was tested by them for different compositions, where composition yielding the greatest PF values is AgSb0.99La0.01Te2 , with PF values around 1000–1200 µW m−1 K−2 in the entire temperature range. Particularly, this La-doped material exhibits superior PF values up to ca. 325°C. This trend is similar to that reported by us in this study.

**Figure 10.** Electrical conductivity and Seebeck coefficient values measured for La-free (pure AST; filled black squares and blue circles, respectively) and La-doped (La-doped AST; empty black squares and blue circles, respectively) alloys of Series A in temperature range 300–773 K.

Finally, determination of TE figure-of-merit for both La-free and La-doped materials will provide us with the ultimate indication whether La-doping enhances TE power conversion efficiency. Based on thermal and electrical properties measured for Series A and Series B, temperature-dependent *ZT* values were determined and appear in **Figure 12**.

Most importantly, it is shown that La-doping increases *ZT* values markedly, **Figure 12b**, e.g., from ca. 0.3 to 0.45 at 473 K. This improvement is due to decrease in thermal conductivity in almost the entire temperature range and increase in PF at low-temperature regime due to La-doping. Above 600 K, again, both values of La-free and La-doped alloys converge due to poor thermal stability of La-free materials. *ZT* values of La-free and La-doped materials shown in **Figure 12b** correspond with those reported by Zhang et al. [101], where the effects of La-doping are comparable to those of stoichiometric variations about AgSbTe<sup>2</sup> composition. Similar values are reported by Mohanraman et al. [43] and Jovovic and Heremans [19] for Bi-doping, as well as, for Pb-doping [19]. Chen et al. obtain similar *ZT* values for Ge-doping [111] and for Sn-doping [112], depending on concentration. *ZT* values reported in the present study are, however, lower than those reported by Du et al. [25, 99], probably owing to different processing conditions yielding higher electrical conductivity values [113].

The picture, revealed for alloys of Series A, is, however, different; it is shown in **Figure 12a** that La-doping has little or no effect on *ZT*. This is, again, not surprising and follows the trends featured by Series A alloys for electrical conductivity and Seebeck coefficient, **Figure 9**, and thermal conductivity [58] associated to depletion of La-atoms from δ-matrix in La-alloyed materials hot-presses at 540°C.

**Figure 11.** Thermoelectric power factor (PF) values evaluated for La-free (pure AST; filled black squares) and La-doped (La-doped AST; empty black squares) alloys of Series B in temperature range 300–673 K.

**Figure 12.** Thermoelectric figure of merit (ZT) values evaluated for La-free (pure AST; filled blue squares) and La-doped (La-doped AST; empty blue squares) alloys of (a) Series A and (b) Series B in temperature range 300–673 K.

#### **6. Summary and concluding remarks**

Most importantly, it is shown that La-doping increases *ZT* values markedly, **Figure 12b**, e.g., from ca. 0.3 to 0.45 at 473 K. This improvement is due to decrease in thermal conductivity in almost the entire temperature range and increase in PF at low-temperature regime due to La-doping. Above 600 K, again, both values of La-free and La-doped alloys converge due to poor thermal stability of La-free materials. *ZT* values of La-free and La-doped materials shown in **Figure 12b** correspond with those reported by Zhang et al. [101], where the effects

tion. Similar values are reported by Mohanraman et al. [43] and Jovovic and Heremans [19] for Bi-doping, as well as, for Pb-doping [19]. Chen et al. obtain similar *ZT* values for Ge-doping [111] and for Sn-doping [112], depending on concentration. *ZT* values reported in the present study are, however, lower than those reported by Du et al. [25, 99], probably owing to different processing conditions yielding higher electrical conduc-

The picture, revealed for alloys of Series A, is, however, different; it is shown in **Figure 12a** that La-doping has little or no effect on *ZT*. This is, again, not surprising and follows the trends featured by Series A alloys for electrical conductivity and Seebeck coefficient, **Figure 9**, and thermal conductivity [58] associated to depletion of La-atoms from δ-matrix in La-alloyed

**Figure 11.** Thermoelectric power factor (PF) values evaluated for La-free (pure AST; filled black squares) and La-doped

(La-doped AST; empty black squares) alloys of Series B in temperature range 300–673 K.

composi-

of La-doping are comparable to those of stoichiometric variations about AgSbTe<sup>2</sup>

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

tivity values [113].

materials hot-presses at 540°C.

This chapter introduced the following findings. Computationally, total energy calculations for different polymorphs of AgSbTe<sup>2</sup> phase yield their Helmholtz free energies, implying, that P4/mmm space group symmetry is the most stable one at temperatures adequately higher than room temperatures. Predictions of the effects of doping on thermal conductivity are established on calculations of vibrational properties, such as phonon dispersion and density of states, from first-principles. Based on specific features in v-DOS curve, it is hypothesized that La-substitution for Ag-sites should result in reduced lattice thermal conductivity. These calculations predict reduction in average sound velocity from 1684 to 1563 m s−1 and of Debye temperature from 112 to 104 K due to La-doping. Applying Umklapp mechanism for phonon scattering with frequency-averaged inverse relaxation time, which is combined with boundary scattering, yields temperature-dependent functional forms for lattice thermal conductivity. Marked decrease due to La-doping, ranging between relative values of 11 and 19% depending on temperature, are observed. Then, calculations of electronic band structures of both La-free and La-doped lattices are performed, yielding TE transport coefficients applying Boltzmann transport theory. It is found that La-doping results in reduction in electrical conductivity (e.g., from ca. 1800 down to 250 S cm−1 at room temperature) at the same time with increase in Seebeck coefficient, e.g., from ca. 5 up to 40 µV K−1 at room temperature.

Attempts to infer conclusions with practical implications from DFT calculations must consider engineering aspects that extend further beyond single phase state having high symmetry unit cell, that maintains its physical properties with time. For example, considerations, such as long-term device operation under elevated service temperatures, should be taken into account. Such case requires original solution for simplified (or, sometimes, over-simplified) approach offered by DFT. Particularly, for the case of thermal stability, exposure of Sb-rich δ-phase to elevated temperatures results in precipitation of SbpTeq -based phases at the same time with decrease in Sb/Ag ratio in δ-matrix. In this manner, thermal stability issues can be addressed by dividing the realistic conditions into a set of simplified problems, each can be handled by DFT. To this end, we first consider the case in which Sb<sup>2</sup> Te3 and Sb8 Te3 phases precipitate inside AgSbTe2 -matrix. It is found that both electrical conductivity and Seebeck coefficient values of Sb<sup>2</sup> Te3 -phase are larger, than those of Sb8 Te3 -phase in wide temperature range, e.g., ca. 2100 S cm−1 and 85 µV K−1 for Sb2 Te3 compared to1380 S cm−1 and 29 µV K−1 for Sb8 Te3 at 300 K, respectively. Moreover, it is estimated that precipitation of Sb2 Te3 -phase in AgSbTe2 -matrix is expected to improve the total values of both electrical conductivity and Seebeck coefficient. Concerning nucleation sequence of Sb<sup>2</sup> Te3 and Sb8 Te3 phases in AgSbTe2 , their molar formation energies and interfacial free energies were calculated, suggesting that Sb8 Te3 nucleates first as metastable phase, prior to the formation of equilibrium Sb2 Te3 phase. Second, to address the influence of deviations from AgSbTe<sup>2</sup> stoichiometry on electron transport properties, off-stoichiometric model alloys Ag<sup>3</sup> SbTe4 and AgSb3 Te4 were simulated. It is found that increase in Sb/Ag ratio results in decrease in electrical conductivity simultaneously with increase in Seebeck coefficient. Considering both effects of Sb<sup>2</sup> Te3 precipitation accompanied by simultaneous decrease in Sb/Ag ratio in δ-matrix taking place with aging time at temperatures below δ-solvus, it is expected that electrical conductivity of two-phase δ+Sb<sup>2</sup> Te3 alloy should increase with aging time, disregarding effects, such as electron boundary scattering. Interestingly, these two effects have opposite consequences regarding Seebeck coefficient, so that, it is difficult to assess resulting Seebeck coefficient.

Experimentally, model ternary (AgSbTe2 ) and quaternary (3 at.% La-AgSbTe<sup>2</sup> ) alloys were synthesized by vacuum melting followed by quenching and hot-pressing. The appropriate conditions enabling formation of AgSbTe2 -matrix that dissolves La-atoms with no La-rich precipitates were established. DSC tests enable observation of Ag2 Te+Sb2 Te3 →δ-AgSbTe<sup>2</sup> phase transition at 360°C for La-free alloys only, indicating improvement of alloy's thermal stability due to La-additions. Temperature-dependent thermal conductivity of both alloys indicate reduction in thermal conductivity as a result of La-alloying from 0.92 to 0.71 W m−1 K−1 at 573 K, which corresponds with the trend predicted from first-principles. Measurements of temperature-dependent electrical conductivity and Seebeck coefficients indicate that La-doping reduces electrical conductivity and increases Seebeck coefficients, as predicted from firstprinciples. Eventually, it is shown that La-doping has positive effects on TE figure-of-merit *ZT*, which is improved, e.g., from 0.35 up to 0.50 at 260°C.

We demonstrate how first-principles calculations serve as trustworthy tool for predicting TE performance of materials, screening the best candidates for application in TE devices. It is noteworthy that such DFT routines prove to be very efficient by prediction of TE properties in a way saving expensive and time-consuming experiments. The resulting materials that seem to possess improved performance are, eventually, processed in laboratory. We show how simple physical considerations can be implemented in DFT calculations and lead to improvement of power conversion efficiency. La-doping improves the alloys' thermal stability and reduces their thermal conductivity, as well as enhances TE power factor in certain temperature range. As a result, the total TE figure-of-merit improves significantly. We, finally, emphasize the universal aspects of this approach that can be applied for other TE materials, as well.

## **Acknowledgements**

tivity are established on calculations of vibrational properties, such as phonon dispersion and density of states, from first-principles. Based on specific features in v-DOS curve, it is hypothesized that La-substitution for Ag-sites should result in reduced lattice thermal conductivity. These calculations predict reduction in average sound velocity from 1684 to 1563 m s−1 and of Debye temperature from 112 to 104 K due to La-doping. Applying Umklapp mechanism for phonon scattering with frequency-averaged inverse relaxation time, which is combined with boundary scattering, yields temperature-dependent functional forms for lattice thermal conductivity. Marked decrease due to La-doping, ranging between relative values of 11 and 19% depending on temperature, are observed. Then, calculations of electronic band structures of both La-free and La-doped lattices are performed, yielding TE transport coefficients applying Boltzmann transport theory. It is found that La-doping results in reduction in electrical conductivity (e.g., from ca. 1800 down to 250 S cm−1 at room temperature) at the same time with increase in Seebeck coefficient, e.g., from ca. 5 up to 40

Attempts to infer conclusions with practical implications from DFT calculations must consider engineering aspects that extend further beyond single phase state having high symmetry unit cell, that maintains its physical properties with time. For example, considerations, such as long-term device operation under elevated service temperatures, should be taken into account. Such case requires original solution for simplified (or, sometimes, over-simplified) approach offered by DFT. Particularly, for the case of thermal stability, exposure

at the same time with decrease in Sb/Ag ratio in δ-matrix. In this manner, thermal stability issues can be addressed by dividing the realistic conditions into a set of simplified problems,


Te3 and


and Sb8

Te3

SbTe4


alloy should increase with aging time, disre-

Te3

Te3

compared to1380 S cm−1

Te3


, their molar formation energies and interfacial free energies were cal-

were simulated. It is found that increase in Sb/Ag ratio results in decrease

phase. Second, to address the influence of deviations from AgSbTe<sup>2</sup>

precipitation accompanied by simultaneous decrease in Sb/Ag ratio

at 300 K, respectively. Moreover, it is estimated that precipitation


nucleates first as metastable phase, prior to the formation

of Sb-rich δ-phase to elevated temperatures results in precipitation of SbpTeq

Te3

conductivity and Seebeck coefficient. Concerning nucleation sequence of Sb<sup>2</sup>

stoichiometry on electron transport properties, off-stoichiometric model alloys Ag<sup>3</sup>

in electrical conductivity simultaneously with increase in Seebeck coefficient. Considering

in δ-matrix taking place with aging time at temperatures below δ-solvus, it is expected that

garding effects, such as electron boundary scattering. Interestingly, these two effects have opposite consequences regarding Seebeck coefficient, so that, it is difficult to assess resulting

Te3

temperature range, e.g., ca. 2100 S cm−1 and 85 µV K−1 for Sb2

Te3

each can be handled by DFT. To this end, we first consider the case in which Sb<sup>2</sup>

µV K−1 at room temperature.

phases precipitate inside AgSbTe2

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

Te3

and Seebeck coefficient values of Sb<sup>2</sup>


Te3

Te3

electrical conductivity of two-phase δ+Sb<sup>2</sup>

and 29 µV K−1 for Sb8

phases in AgSbTe2

of equilibrium Sb2

both effects of Sb<sup>2</sup>

Seebeck coefficient.

and AgSb3

culated, suggesting that Sb8

Te4

Sb8 Te3

of Sb2 Te3 The author wishes to acknowledge generous support from the Israel Science Foundation (ISF), Grant no. 698/13, as well as, from the German-Israeli Foundation for Research and Development (GIF), Grant no. I-2333-1150.10/2012. Partial support from the Nancy and Stephen Grand Technion Energy Program (GTEP), the Russell Berrie Nanotechnology Institute (RBNI), Technion, and the Adelis Foundation for renewable energy research are greatly acknowledged, as well.

## **Author details**

Yaron Amouyal

Address all correspondence to: amouyal@technion.ac.il

Department of Materials Science and Engineering, Technion—Israel Institute of Technology, Haifa, Israel

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#### **Nanostructured State-of-the-Art Thermoelectric Materials Prepared by Straight-Forward Arc-Melting Method Nanostructured State-of-the-Art Thermoelectric Materials Prepared by Straight-Forward Arc-Melting Method**

Federico Serrano-Sánchez, Mouna Gharsallah, Julián Bermúdez, Félix Carrascoso, Norbert M. Nemes, Oscar J. Dura, Marco A. López de la Torre, José L. Martínez, María T. Fernández-Díaz and José A. Alonso Julián Bermúdez, Félix Carrascoso, Norbert M. Nemes, Oscar J. Dura, Marco A. López de la Torre, José L. Martínez, María T. Fernández-Díaz and José A. Alonso

Federico Serrano-Sánchez, Mouna Gharsallah,

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

http://dx.doi.org/10.5772/65115

#### **Abstract**

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

S.: Enhanced thermoelectric performance of AgSbTe2

based alloys with a small amount of GeTe addition. J. Phys. D: Appl. Phys.

thermo-

synthesized by high pressure and

AgSbTe2

Thermoelectric materials constitute an alternative to harvest sustainable energy from waste heat. Among the most commonly utilized thermoelectric materials, we can mention Bi2Te3 (hole and electron conductivity type), PbTe and recently reported SnSe intermetallic alloys. We review recent results showing that all of them can be readily prepared in nanostructured form by arc-melting synthesis, yielding mechanically robust pellets of highly oriented polycrystals. These materials have been characterized by neutron powder diffraction (NPD), scanning electron microscopy (SEM) and electronic and thermal transport measurements. Analysis of NPD patterns demonstrates near-perfect stoichiometry of above-mentioned alloys and fair amount of anharmonicity of chemical bonds. SEM analysis shows stacking of nanosized sheets, each of them presumably single-crystalline, with large surfaces parallel to layered slabs. This nanostructuration affects notably thermoelectric properties, involving many surface boundaries (interfaces), which are responsible for large phonon scattering factors, yielding low thermal conductivity. Additionally, we describe homemade apparatus developed for the simultaneous measurement of Seebeck coefficient and electric conductivity at elevated temperatures.

**Keywords:** thermoelectrics, nanostructuration, lattice thermal conductivity, thermopower, neutron powder diffraction

© 2017 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. © 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.

## **1. Introduction**

Thermoelectric materials possess the remarkable capability to transform temperature differen‐ ces between two ends of a material sample directly and reversibly into a electrical potential difference. Waste heat recovery, which implies around 70% of primary energy production, exploited as a new source of power generation, could mean significant progress worldwide [1, 2]. Thermoelectric generators are able to perform this task, but currently they are not yet cost‐ effective. Several advantages featured by thermoelectric power generation devices, such as the absence of moving parts, reliability, endurance, quiet operation and no pollutant emission, make these devices valuable from an energy and environmental point of view and useful in a wide range of applications.

The dimensionless figure of merit *ZT* = (*S*<sup>2</sup> *σ*)*T*/*k*, where *S* stands for Seebeck coefficient, *σ* is the electrical conductivity and *κ* is the total thermal conductivity, evaluates thermoelectric performance of materials and serves as a reference value in thermoelectric materials research [3–8]. Maximization of ZT requires high Seebeck coefficient and low electrical resistivity and thermal conductivity values. This physical value is closely linked to the power generation efficiency of thermoelectric devices:

$$\varepsilon = \frac{T\_H - T\_c}{T\_H} \frac{\sqrt{1 + ZT\_M}^{-1} - 1}{\sqrt{1 + ZT\_M} + \frac{T\_c}{T\_H}},\tag{1}$$

where *TH*, *TC* and *TM* are the temperature of the hot and cold ends and the average temperature. From this, we can abstract, that larger mean ZT along with larger temperature differences return better conversion efficiencies. Current commercial devices based on BiTe alloys reach efficiencies of ~6%, while new materials based on recent advances to improve ZT are expected to reach ~12–17%. These approaches are mainly focused on lowering lattice thermal conduc‐ tivity by bulk nanostructuring and enhancing the power factor, S2 σ, by band engineering.

Experiments with nanostructured thermoelectric materials prove that highly efficient ther‐ moelectric energy conversion could be forthcoming [9, 10]. Bulk samples, containing nanoscale constituents or inhomogeneity, exhibit enhanced thermoelectric phenomena, which are connected with the latest advances in optimizing thermoelectric figure of merit. Materials featuring these characteristics have been found among compounds, where nano‐inclusions are inherently formed by using preparation methods to induce the nanostructured morphology. The main effect of nanostructuration is to affect the lattice thermal conductivity. Phonons are effectively scattered, when separation of defects or grain‐sizes is similar to phonons' mean‐ free path. Consequently, bearing in mind the difference in electronic scattering length, structural unit‐cells, comparable in size to heat carrying phonon wavelength, will improve the performance. On the other hand, quantum confinement effects could allow to treat *S*, *σ* and *k* quasi‐independently and achieve higher power factors, defined as *S*<sup>2</sup> *σ* product [10–14].

Usually, thermoelectric nanocomposites are prepared initially and then assembled into bulk solids. Several methods for nanostructuring bulk materials have been developed; the most commonly used are spark plasma sintering (SPS), hot pressing, ball milling and wet chemical reactions [15]. All of them present different advantages and disadvantages, but they share drawbacks of long reaction and sample preparation times. For instance, it is expected, that the SPS method will be very beneficial for the reduction in lattice thermal conductivity due to retention of low-dimensional grains. On the other hand, it requires long annealing times and, as expected, results in more pronounced equiaxed morphology of powder particles with decrease in their size [16]. Chemical methods are convenient in terms of particle size, shape and crystallinity; nevertheless, removal of insulating organic capping ligands from nanocrystals is essential before consolidation into bulk pellets, and most of the chemically prepared materials present lower ZT values due to unsuitable charge carriers' concentrations and low intergranular connectivity achieved during compaction [17, 18].

Our present work deals with a straightforward and fast technique based on arc-melting synthesis. We have been able to prepare by this technique different families of thermoelectric materials including Bi2−xSbxTe3 and Bi2(Te1−xSex)3 alloys, SnSe and related alloys, PbTe and GeSe compounds [19–21]. This method yields highly nanostructured samples prepared in really short times, which require no further processing and are directly implementable into devices. Highly oriented polycrystalline pellets are obtained with extremely low thermal conductivity, probably linked to the nanostructured nature of polycrystalline domains. This chapter describes synthesis by arc-melting and structural and thermoelectric characterization of these materials. Structural characterization has been carried out by X-ray diffraction (XRD) and neutron powder diffraction (NPD), which complements the study of thermoelectric properties and is used as the basis for density functional theory (DFT) calculations. Therefore, we review transport results of various bismuth telluride and tin selenide-related alloys, as well as, some other alloys. Bi2Te3 forms the basis for the most widely used thermoelectrics near room temperature. Arc-melting is a good technique affording rapid production with various doping and alloying. But how good is the resulting material? Thermoelectric property measurements by various procedures can reveal it.

## **2. Experimental section**

**1. Introduction**

range of applications.

efficiency of thermoelectric devices:

e

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

tivity by bulk nanostructuring and enhancing the power factor, S2

quasi‐independently and achieve higher power factors, defined as *S*<sup>2</sup>

Thermoelectric materials possess the remarkable capability to transform temperature differen‐ ces between two ends of a material sample directly and reversibly into a electrical potential difference. Waste heat recovery, which implies around 70% of primary energy production, exploited as a new source of power generation, could mean significant progress worldwide [1, 2]. Thermoelectric generators are able to perform this task, but currently they are not yet cost‐ effective. Several advantages featured by thermoelectric power generation devices, such as the absence of moving parts, reliability, endurance, quiet operation and no pollutant emission, make these devices valuable from an energy and environmental point of view and useful in a wide

The dimensionless figure of merit *ZT* = (*S*<sup>2</sup> *σ*)*T*/*k*, where *S* stands for Seebeck coefficient, *σ* is the electrical conductivity and *κ* is the total thermal conductivity, evaluates thermoelectric performance of materials and serves as a reference value in thermoelectric materials research [3–8]. Maximization of ZT requires high Seebeck coefficient and low electrical resistivity and thermal conductivity values. This physical value is closely linked to the power generation

<sup>1</sup> <sup>1</sup> ,

(1)

σ, by band engineering.

*σ* product [10–14].

+ +

where *TH*, *TC* and *TM* are the temperature of the hot and cold ends and the average temperature. From this, we can abstract, that larger mean ZT along with larger temperature differences return better conversion efficiencies. Current commercial devices based on BiTe alloys reach efficiencies of ~6%, while new materials based on recent advances to improve ZT are expected to reach ~12–17%. These approaches are mainly focused on lowering lattice thermal conduc‐

Experiments with nanostructured thermoelectric materials prove that highly efficient ther‐ moelectric energy conversion could be forthcoming [9, 10]. Bulk samples, containing nanoscale constituents or inhomogeneity, exhibit enhanced thermoelectric phenomena, which are connected with the latest advances in optimizing thermoelectric figure of merit. Materials featuring these characteristics have been found among compounds, where nano‐inclusions are inherently formed by using preparation methods to induce the nanostructured morphology. The main effect of nanostructuration is to affect the lattice thermal conductivity. Phonons are effectively scattered, when separation of defects or grain‐sizes is similar to phonons' mean‐ free path. Consequently, bearing in mind the difference in electronic scattering length, structural unit‐cells, comparable in size to heat carrying phonon wavelength, will improve the performance. On the other hand, quantum confinement effects could allow to treat *S*, *σ* and *k*

1

*<sup>T</sup> <sup>T</sup> <sup>H</sup> <sup>c</sup> ZTM TH*


*T T ZT H c <sup>M</sup>*

#### **2.1. Preparation by arc-melting**

Intermetallic alloys of different above-mentioned families were prepared in an Edmund Buhler Compact Arc Melter MAM-1 (**Figure 1a**). Stoichiometric amounts of grinded mixture of reacting elements were pelletized in a glove box. Pellets were molten under Ar atmosphere in water-cooled Cu crucible (**Figure 1b**), leading to intermetallic ingots (**Figure 1c**), which can be ground to powder for structural characterization or cut with a diamond saw in bar-shaped samples for transport measurements. Complete characterization of these novel materials has included structural study by XRD and NPD and detailed examination of thermoelectric parameters.

**Figure 1.** (a) Compact arc-melting furnace utilized for synthesis of nanostructured materials. (b) Water-cooled copper crucible, where sample can be quenched after melting process. (c) Typical aspect of as-grown ingots of intermetallic alloys.

#### **2.2. Structural characterization**

Initial characterization of products was carried out by laboratory XRD (Cu Kα, λ = 1.5406 Å). NPD diagrams were collected either at HRPT diffractometer of SINQ (The Swiss Spallation Neutron Source) spallation source at Paul Scherrer Institut or at D2B high-resolution diffractometer at Institut Laue-Langevin, Grenoble. Patterns were collected at room temperature with a wavelength of 1.494 Å (HRPT) or 1.594 Å (D2B). The high-flux mode was used (Δd/d ≈ 5 × 10−4); typical collection time was 2 h. For some selected samples (Sn0.8Ge0.2Se), temperaturedependent NPD experiment was also carried out at D2B diffractometer. About 2 g of the sample was contained in a vanadium can and placed in the isothermal zone of the furnace with a vanadium resistor operating under vacuum (PO2 ≈ 10−6 torr). Measurements were carried out upon heating at 25, 200, 420 and 580°C, and NPD data were collected in diffractometer D2B. Diffraction data were analyzed by Rietveld method with FULLPROF program [22]. Line shape of diffraction peaks was generated by pseudo-Voigt function. The following parameters were refined: background points, zero shift, half-width, pseudo-Voigt, scale factor and unit-cell parameters. Positional and occupancy factors and anisotropic displacement factors were also refined for NPD data. Coherent scattering lengths for Bi, Te, Sn, Ge and Se were 8.532, 5.800, 6.225, 8.185 and 7.970 fm, respectively. A preferred orientation correction was applied, considering platelets perpendicular to the [001] for Bi2Te3-related alloys and the [100] direction for SnSe-related alloys.

## **2.3. Microstructural characterization**

Surface texture of as-grown pellets is studied by field emission SEM (FE-SEM) in ZEISS 55 model. FE-SEM provides very focused energy electron beam, which improves greatly the spatial resolution and allows working at very low potentials, (from 0.02 to 5 kV); this helps to minimize effects of charge load on nonconductive samples and to avoid any damage to electron beam sensitive samples. It offers typical SEM image of surface topography of the sample with large depth of field. It is best suited for middle and low resolutions with high acceleration potential. It is mainly used to browse with low magnification looking for points of interest and to study samples with much topographical information. It also carries a secondary electron detector in lens: located inside the electron column, and it works with low-energy secondary electrons and offers higher resolution images. It is very sensitive to surface characteristics of the sample, so it is very suitable for surface characterization of any material.

#### **2.4. Transport measurements**

**Figure 1.** (a) Compact arc-melting furnace utilized for synthesis of nanostructured materials. (b) Water-cooled copper crucible, where sample can be quenched after melting process. (c) Typical aspect of as-grown ingots of intermetallic

Initial characterization of products was carried out by laboratory XRD (Cu Kα, λ = 1.5406 Å). NPD diagrams were collected either at HRPT diffractometer of SINQ (The Swiss Spallation Neutron Source) spallation source at Paul Scherrer Institut or at D2B high-resolution diffractometer at Institut Laue-Langevin, Grenoble. Patterns were collected at room temperature with a wavelength of 1.494 Å (HRPT) or 1.594 Å (D2B). The high-flux mode was used (Δd/d ≈ 5 × 10−4); typical collection time was 2 h. For some selected samples (Sn0.8Ge0.2Se), temperaturedependent NPD experiment was also carried out at D2B diffractometer. About 2 g of the sample was contained in a vanadium can and placed in the isothermal zone of the furnace with a vanadium resistor operating under vacuum (PO2 ≈ 10−6 torr). Measurements were carried out upon heating at 25, 200, 420 and 580°C, and NPD data were collected in diffractometer D2B. Diffraction data were analyzed by Rietveld method with FULLPROF program [22]. Line shape of diffraction peaks was generated by pseudo-Voigt function. The following parameters were refined: background points, zero shift, half-width, pseudo-Voigt, scale factor and unit-cell parameters. Positional and occupancy factors and anisotropic displacement factors were also refined for NPD data. Coherent scattering lengths for Bi, Te, Sn, Ge and Se were 8.532, 5.800, 6.225, 8.185 and 7.970 fm, respectively. A preferred orientation correction was applied, considering platelets perpendicular to the [001] for Bi2Te3-related alloys and the [100] direction

alloys.

**2.2. Structural characterization**

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

for SnSe-related alloys.

#### *2.4.1. Physical properties measurement system (PPMS)*

Three basic properties of thermoelectric materials (Seebeck coefficient, electrical resistivity and thermal conductivity) can be characterized simultaneously over a broad temperature range, between 2 and 400 K, by the thermal transport option (TTO) of the physical properties measurement system (PPMS) of Quantum Design Inc. This system allows for four electrical and thermal contacts with the sample. It uses two small thin-film temperature sensors (Cernox) mounted on small brass holders to measure both voltage and temperature drop across the sample. It uses another small brass piece with 2 kOhm resistive chip heater both to inject electrical current for resistivity measurement and to supply a known amount of heating power for Seebeck and thermal conductivity measurements. The fourth contact of the samples is the large brass baseplate of the sample holder, which thermally anchors it to the cryostat.

Measurements are carried out as follows: we use bar-shaped samples with 10 × 3 × 2 mm3 dimensions, prepared either by directly cutting from as-prepared ingots or by directly coldpressing it after arc-melting in a properly shaped die. Four copper leads are wrapped around the bar and then fixed with silver epoxy. We use the following thermal protocol: cool the sample from 300 K to low temperature (either 2 K or 10 K), then warm it to 395 K and then cool it again to base temperature. We use slow sweep rate of 0.3 K/min (over 2 days for each sample) and gather data continuously. Electrical resistivity is measured by applying sinusoidal current with typical frequency of 17 Hz and amplitude between 10 μA and 10 mA. Seebeck coefficient is then measured by establishing a temperature gradient of typically 3% of the sample sink temperature. Here, the only important source of experimental error may arise from the fact, that Cernox temperature sensors are not touching the sample directly, but are thermally connected to it via a few millimeter-length of copper wires. Thermal conductivity is measured by dynamically modeling the temperature gradient on the sample between two Cernox sensors as known heater power (between 10 μW and 50 mW, adjusted to achieve 3% gradient) is supplied, and then removed, to one end of the sample. Above ~150 K, errors related to radiative heat losses become important. These are ameliorated to a certain extent by careful application of the correction software of TTO. Another, less important, source of heat losses is conduction through copper wires of voltage/temperature gradient leads. Finally, convective heat losses are minimized by the high vacuum option of PPMS, establishing pressure below 10−5 torr.

For Hall coefficient measurements, we use thin pellets (~1 mm thick, 10 mm diameter) in van der Pauw geometry, with four contacts placed along the perimeter, and pass a DC current with alternating sign to eliminate thermoelectric voltages along diagonal. Measured voltage is still dominated by ohmic resistance, which is then removed by comparing values obtained in large positive and negative magnetic fields.

#### *2.4.2. High-temperature Seebeck coefficient measured in micro-miniature refrigerator (MMR) device*

Seebeck coefficient is the ratio of voltage difference produced from applied temperature gradient. In principle, this concept is easy to understand, and one might think that this thermoelectric property is easy to measure. However, it can be difficult to evaluate [23, 24]. Basically, a temperature gradient is established between hot and cold ends of the sample and then the voltage drop, appearing between them, is measured. If the temperature gradient is kept constant during measurement, the method is called steady-state method.

Here we describe a method used by the commercial system of MMR Technologies Inc. (MMR device). This system allows measuring Seebeck coefficient of semiconductors and metals between 70 and 730 K. This method employs two pairs of thermocouples. One pair is formed by junctions of copper and reference material (constantan) with a well-known value of Seebeck coefficient. The other pair is formed of junctions of copper and sample, in which Seebeck coefficient is to be determined (**Figure 2a**). This method requires that both materials, reference and sample, have similar thermal conductance in order to ensure similar thermal transport through both of them. Thus, constantan wires with different diameters are used as a reference to allow evaluating materials with very different thermal conductivities.

**Figure 2.** (a) Seebeck thermal stage supplied by MMR technologies. Black line indicates place of unknown sample and red line indicates that of reference sample. (b) Chamber with refrigerator, which provides temperature range between 70 and 730 K.

Another interesting characteristic of the method provided by MMR system is the double reference measurement technique, which gives more accurate and reproducible results. By using this feature, the equipment subtracts any instrumental offset voltage due to thermovoltage effects from wires or connections. Different stages, made up of alumina or polyamide, allow covering a broad temperature range of measurement from 70 to 730 K (**Figure 2a** and **b**).

#### *2.4.3. High-temperature transport device: high-temperature Seebeck measurements in homemade apparatus*

of the correction software of TTO. Another, less important, source of heat losses is conduction through copper wires of voltage/temperature gradient leads. Finally, convective heat losses are minimized by the high vacuum option of PPMS, establishing pressure below 10−5 torr. For Hall coefficient measurements, we use thin pellets (~1 mm thick, 10 mm diameter) in van der Pauw geometry, with four contacts placed along the perimeter, and pass a DC current with alternating sign to eliminate thermoelectric voltages along diagonal. Measured voltage is still dominated by ohmic resistance, which is then removed by comparing values obtained in large

*2.4.2. High-temperature Seebeck coefficient measured in micro-miniature refrigerator (MMR) device* Seebeck coefficient is the ratio of voltage difference produced from applied temperature gradient. In principle, this concept is easy to understand, and one might think that this thermoelectric property is easy to measure. However, it can be difficult to evaluate [23, 24]. Basically, a temperature gradient is established between hot and cold ends of the sample and then the voltage drop, appearing between them, is measured. If the temperature gradient is

Here we describe a method used by the commercial system of MMR Technologies Inc. (MMR device). This system allows measuring Seebeck coefficient of semiconductors and metals between 70 and 730 K. This method employs two pairs of thermocouples. One pair is formed by junctions of copper and reference material (constantan) with a well-known value of Seebeck coefficient. The other pair is formed of junctions of copper and sample, in which Seebeck coefficient is to be determined (**Figure 2a**). This method requires that both materials, reference and sample, have similar thermal conductance in order to ensure similar thermal transport through both of them. Thus, constantan wires with different diameters are used as a reference

**Figure 2.** (a) Seebeck thermal stage supplied by MMR technologies. Black line indicates place of unknown sample and red line indicates that of reference sample. (b) Chamber with refrigerator, which provides temperature range between

Another interesting characteristic of the method provided by MMR system is the double reference measurement technique, which gives more accurate and reproducible results. By using this feature, the equipment subtracts any instrumental offset voltage due to thermo-

kept constant during measurement, the method is called steady-state method.

to allow evaluating materials with very different thermal conductivities.

positive and negative magnetic fields.

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

70 and 730 K.

As commented above, measurement of Seebeck coefficient seems like one of the less challenging tasks: create temperature gradient, measure voltage … What could be simpler? Yet, at elevated temperatures, this poses a challenge, mainly due to large, hard to control, temperature gradients. The largest systematic errors arise from the fact, that it is virtually impossible to detect temperatures at exactly the same spot where voltage difference is measured. Additional difficulty is strong chemical and metallurgic reactivity of typical thermoelectric materials at temperatures above a few hundred degree celsius, limiting the choice of building blocks for any instrument. Even such precious workhorse material as Pt is out of the question.

There are two main approaches to measure Seebeck effect in thermoelectric materials: integral and differential methods [24]. In the integral method, one end is maintained at a fixed temperature *T*1, while another end is heated to induce, sometimes large, temperature gradient Δ*T* = *T*2 − *T*1. According to the definition of Seebeck coefficient, we can write:

$$V\_{TC} = V\_T(T\_1, T\_2) - V\_C(T\_1, T\_2) = \int\_{T\_1}^{T\_2} (S\_T(T) - S\_C(T)) dT,\tag{2}$$

where *VT* and *ST* are, respectively, Seebeck voltage and Seebeck coefficient of the thermoelectrics, while *VC* and *SC* are those of connecting lead. Normally, these conductors are metals with low Seebeck coefficient, such as Cu or Pt with known thermoelectric properties. Thus, it is possible to infer Seebeck voltage of interest, *VT*, from voltage measured, *VTC*, using the following expression:

$$V\_{TC} + V\_C(T\_1, T\_2) = V\_T(T\_1, T\_2) = \int\_{T\_1}^{T\_2} S\_T(T)dT.\tag{3}$$

In the differential technique, small thermal gradient is used to estimate Seebeck coefficient at mean sample temperature. We can distinguish two approaches to this technique. In the DC method, constant thermal gradient is maintained, while mean temperature is varied, whereas in the AC method mean temperature is stabilized followed by the change in temperature gradient, usually in a sinusoidal form [25].

In the following, we describe a high-temperature homemade instrument to measure Seebeck coefficient with both integral and differential techniques. We based our design on the system described in Ref. [25], with some modifications, which are indicated below. Typical sample dimensions are pellets of around 10 mm diameter and 2 mm thickness, also ideal for laser flash measurements of thermal diffusivity.

**Figure 3** shows the design scheme of measurement. This instrument is composed of two thermocouples, two blocks of niobium (Nb), two cartridge heaters with built-in thermocouples and a radiation furnace with yet another thermocouple. The whole assembly is placed in a vacuum chamber equipped with turbo-pump station and operates in a vacuum of around 7.5 × 10−7 torr and between 300 and 950 K. Baseplate can be water-cooled. We now describe important components of the homemade system.

**Figure 3.** The top panel shows the main pieces of homemade instrument: vacuum chamber with turbo-pump station, furnace assembly and electronics for temperature control and voltage measurements. Screenshot of data acquisition software shows typical data resulting in differential AC measurement.

#### *2.4.3.1. Thermocouples*

Thermocouples are used to measure both temperature of the sample at either side and Seebeck voltage. These consist of two different wires, one of chromel and another of niobium, of 0.1 mm diameter, inserted in a four-bore ceramic tube (1.2 mm diameter with 0.2 mm bores) in such a way that where these wires cross Nb ones make contacts with the sample [25]. Thus, the difference between temperature and voltage measurements is minimized to the diameter of Nb wire. These four-bore ceramic tubes are mounted on spring-loaded mechanisms to press them dynamically against the sample. Springs are located outside the hot-zone to maintain their elasticity. We found, that this system works well enough without the sophisticated strain gauge mechanism of Ref. [25]. Niobium is a good choice for its low Seebeck coefficient—we use two Nb leads to detect Seebeck voltage of the sample.

#### *2.4.3.2. Niobium blocks*

Niobium blocks form the basis of apparatus. These cylinders, whose diameter and length are 20 mm, have two functions: they house cartridge heaters (and thus heat the sample differen-

tially) and thermocouples, and press the sample during the measurement. After finding copper to be a poor choice due to its reactivity, we chose niobium for its chemical inertness against typical thermoelectric materials and for its good thermal conductivity. An advantage of using a typical metallic block instead of a ceramic one, as in Ref. [25], is that they can act as a pair of electrical contacts, to inject electrical current in 4-probe resistivity measurement, while ohmic voltage can be measured on contacts used for Seebeck voltage. Metallic blocks are also easier to machine. These blocks are electrically insulated from the rest of the equipment by ceramic (MACOR®) collars and are pressed against the sample by two sets of three springs on support bars.

#### *2.4.3.3. Cartridge heaters*

**Figure 3** shows the design scheme of measurement. This instrument is composed of two thermocouples, two blocks of niobium (Nb), two cartridge heaters with built-in thermocouples and a radiation furnace with yet another thermocouple. The whole assembly is placed in a vacuum chamber equipped with turbo-pump station and operates in a vacuum of around 7.5 × 10−7 torr and between 300 and 950 K. Baseplate can be water-cooled. We now describe

**Figure 3.** The top panel shows the main pieces of homemade instrument: vacuum chamber with turbo-pump station, furnace assembly and electronics for temperature control and voltage measurements. Screenshot of data acquisition

Thermocouples are used to measure both temperature of the sample at either side and Seebeck voltage. These consist of two different wires, one of chromel and another of niobium, of 0.1 mm diameter, inserted in a four-bore ceramic tube (1.2 mm diameter with 0.2 mm bores) in such a way that where these wires cross Nb ones make contacts with the sample [25]. Thus, the difference between temperature and voltage measurements is minimized to the diameter of Nb wire. These four-bore ceramic tubes are mounted on spring-loaded mechanisms to press them dynamically against the sample. Springs are located outside the hot-zone to maintain their elasticity. We found, that this system works well enough without the sophisticated strain gauge mechanism of Ref. [25]. Niobium is a good choice for its low Seebeck coefficient—we

Niobium blocks form the basis of apparatus. These cylinders, whose diameter and length are 20 mm, have two functions: they house cartridge heaters (and thus heat the sample differen-

important components of the homemade system.

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

software shows typical data resulting in differential AC measurement.

use two Nb leads to detect Seebeck voltage of the sample.

*2.4.3.1. Thermocouples*

*2.4.3.2. Niobium blocks*

Cartridge heaters create controlled temperature gradient across the sample. They are inserted into niobium blocks off-center and are in good thermal contact with them. Cartridge heaters (from Watlow Ltd, 6.3 mm diameter, 25 mm length, 150 W) have individually incorporated Jtype thermocouples. This enables us to smoothly control temperature gradient across the sample, even though cartridge heaters can deviate from the sample temperature by tens of degrees. We use programmable DC power supplies to control the temperature of cartridge heaters with high accuracy. Power supplies act as highly linear power amplifiers at the output of simple PID temperature controllers. Use of 0–5 V DC control logic helps us avoid introducing electronic noise into measurement, which would be rather troublesome in the typical solid state relay (SSR) scheme.

#### *2.4.3.4. Furnace*

The sample and Nb-blocks are surrounded by a small tubular furnace to establish the average temperature and crucially to reduce radiative heat losses. Homemade furnace is composed of an aluminum oxide tube of 34 mm internal diameter with rolled-up Kanthal wire. This heating element is surrounded by mineral fiber and stainless steel sheet with low emissivity. After placing the sample between the Nb-blocks, the whole furnace can slide up on three steel posts to position.

#### *2.4.3.5. Breakout connector*

The system has several thermocouples, and one of the crucial advantages of such an instrument, according to Ref. [25], is the possibility to easily swap and test different thermocouple wires for various samples. However, this poses technical challenge: these thermocouple wires must be run through the vacuum chamber. Although there exist commercial feedthroughs for thermocouples, these are costly and would eliminate flexibility to change the type of wire used. Therefore, we installed a break-out connector (DB-25) within the vacuum chamber and use copper wires from this post toward feedthrough (also DB-25, gold-plated pins) and outside toward electronics. As the break-out connector gets warm during operation (up to 80°C), we monitor its temperature with a resistive sensor (Pt100) and use this as "cold junction" in thermocouple measurements, in order to minimize spurious thermoelectric voltages.

#### *2.4.3.6. Electronics*

Seebeck voltage, thermocouples monitoring the sample temperature and any resistance measurements (such as Pt100 of breakout connector or the sample itself) are measured by Keithley-2700 scanning multimeter. Other thermocouples (cartridge heaters, furnace) are connected to three West-P6100 PID controllers. Their 0–5 V DC programming output acts on DeltaES150 DC power supplies. Smooth voltage output reduces electronic noise on sensitive Seebeck voltage and resistivity measurements from heating system.

#### *2.4.3.7. Data acquisition and temperature set-point control*

Data acquisition and temperature set-point control are handled by a LabVIEW program, which communicates via GPIB with multimeter and via RS485 serial protocol with PID controllers.

Salient features of this instrument are its operating range from slightly above room temperature up to 900 K and its flexibility to perform three different types of measurement schemes: quasi-integral, differential DC and differential AC. Each scheme has its own compromise between accuracy and overall required time for Seebeck coefficient measurements.

**•** *Quasi-integral* method is based on integral method and provides quick measurements, with low accuracy. We apply a step input to one heater, while the other is turned off. Although temperature of neither side of the sample is fixed, it is possible to extract the whole temperature-dependent Seebeck coefficient curve as polynomial function:

$$S(T) = S\_0 + S\_1 \cdot T + S\_2 \cdot T^2 + S\_3 \cdot T^3 + S\_4 \cdot T^4 + S\_5 \cdot T^5 + \dotsb \tag{4}$$

According to Eq. (3) Seebeck voltage is:

$$V\_T \left( T\_1, T\_2 \right) = S\_0 \cdot \left( T\_2 - T\_1 \right) + \frac{S\_1}{2} \cdot \left( T\_2^2 - T\_1^2 \right) + \frac{S\_2}{3} \cdot \left( T\_2^3 - T\_1^3 \right) + \frac{S\_3}{4} \cdot \left( T\_2^4 - T\_1^4 \right) + \dots \tag{5}$$

Therefore, from broad set of data, *Sn* polynomial coefficients can be numerically approximated. This technique does not generate particularly accurate results, but in as little as one hour, full *S*(*T*) curve may be obtained up to 900 K, which is very helpful for screening purposes, when faced with large number of samples. The peculiarity of this technique is that resulting *S*(*T*) curves are completely (and thus perplexingly) smooth, since they result from Eq. (4). Also, near the lowest and highest measured temperatures, *S*(*T*) curves behave anomalously due to the way the numerical fit works. In a sense, integral method is closest to real-life operation with large temperature differences present.

**•** *Differential DC* method is the closest to definition of Seebeck coefficient:

$$S(T) = \frac{dV}{dT} \,. \tag{6}$$

This method provides more accurate results than quasi-integral one, but is somewhat slower. We maintain more-or-less constant temperature gradient of a few degrees using cartridge heaters, while raising overall temperature smoothly with the furnace. This method also works without the surrounding furnace, but temperature differences between cartridge heaters and respective sample sides are quite large (several tens of degrees). It is also difficult to gauge any systematic errors arising from voltage and temperature offsets. Differential DC method is the closest operation mode to MMR system.

*2.4.3.6. Electronics*

Seebeck voltage, thermocouples monitoring the sample temperature and any resistance measurements (such as Pt100 of breakout connector or the sample itself) are measured by Keithley-2700 scanning multimeter. Other thermocouples (cartridge heaters, furnace) are connected to three West-P6100 PID controllers. Their 0–5 V DC programming output acts on DeltaES150 DC power supplies. Smooth voltage output reduces electronic noise on sensitive

Data acquisition and temperature set-point control are handled by a LabVIEW program, which communicates via GPIB with multimeter and via RS485 serial protocol with PID controllers.

Salient features of this instrument are its operating range from slightly above room temperature up to 900 K and its flexibility to perform three different types of measurement schemes: quasi-integral, differential DC and differential AC. Each scheme has its own compromise

**•** *Quasi-integral* method is based on integral method and provides quick measurements, with low accuracy. We apply a step input to one heater, while the other is turned off. Although temperature of neither side of the sample is fixed, it is possible to extract the whole tem-

> 2345 01 2 3 4 5 *ST S S T S T S T S T S T* ( ) = + ×+ × + × + × + × +L (4)

*S S <sup>S</sup> V TT S T T T T T T T T* (5)

Therefore, from broad set of data, *Sn* polynomial coefficients can be numerically approximated. This technique does not generate particularly accurate results, but in as little as one hour, full *S*(*T*) curve may be obtained up to 900 K, which is very helpful for screening purposes, when faced with large number of samples. The peculiarity of this technique is that resulting *S*(*T*) curves are completely (and thus perplexingly) smooth, since they result from Eq. (4). Also, near the lowest and highest measured temperatures, *S*(*T*) curves behave anomalously due to the way the numerical fit works. In a sense, integral method is closest to real-life operation

between accuracy and overall required time for Seebeck coefficient measurements.

( ) ( ) ( ) ( ) 1 2 22 33 44 <sup>3</sup> 12 0 2 1 2 1 2 1 2 1 , () <sup>234</sup> *<sup>T</sup>* = × - + × - + × - + × - +¼

perature-dependent Seebeck coefficient curve as polynomial function:

**•** *Differential DC* method is the closest to definition of Seebeck coefficient:

( ) <sup>=</sup> . *dV S T*

*dT* (6)

Seebeck voltage and resistivity measurements from heating system.

*2.4.3.7. Data acquisition and temperature set-point control*

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

According to Eq. (3) Seebeck voltage is:

with large temperature differences present.

**•** *Differential AC* is the slowest method, but also the most accurate, as described in Ref. [25]. It takes several hours (easily a full day) to obtain a few Seebeck coefficient data points, for example, every 50 K. This is because furnace and cartridge heater temperatures must be stabilized first and this takes a long time at high temperatures, and then cartridge heater temperatures are oscillated (with a period of tens of minutes) to obtain complete data sets (e.g., in **Figure 4**). The great advantage of this method is that any voltage offsets arising from stray thermoelectric emfs or temperature offsets, for example, due to miscalibration of thermocouples, are eliminated by linear regression to collected data. Differential AC method is reminiscent of the operation mode of PPMS.

**Figure 4.** Typical temperature-dependent Seebeck coefficient data gathered with both differential DC method (full symbols) and integral method (lines) for low Seebeck metals, aluminum and copper, commercial p-type Bi2Te3 ingot and test pellet of SnSe produced by arc-melting.

We end this section by presenting a few temperature-dependent Seebeck coefficient curves for test materials. We used pieces of commercial aluminum and copper to check effects of voltage and temperature offsets. These metals have minimal Seebeck coefficient values at room temperature, around 3.5 μV K−1 for Al and 6.5 μV K−1 for Cu. These would vary by only a few μV K−1 in the studied temperature range. We found, that differential DC method gives Seebeck coefficient values differing by less than 10 μV K−1, as absolute error. Relative error is less flattering, as for example, in the case of Al we measure negative values. Interestingly, integral method yields 5–6 μV K−1 for Cu, very close to tabulated value. Nevertheless, instrument is designed to study thermoelectric materials with large Seebeck coefficient values. We can take

±10 μV K−1 as a rough estimate for systematic errors of the instrument. Results for commercial ingot of p-type Bi2Te3 above 100 μV K−1, with characteristic maximum above 400 K, are similar to expected behavior. Finally, preliminary data from a pellet of SnSe produced by arc-melting and measured by quasi-integral method are also shown. These values are quite a bit lower than expected. The reason is still to be explored, but it is probably related to the fact, that data were recorded upon second heating run, and the sample may have suffered some chemical alteration. Whatever the case may be, it demonstrates the capabilities of the instrument.

#### *2.4.4. Thermal conductivity: laser flash thermal diffusivity method*

So-called laser flash thermal diffusivity technique is a useful method to determine thermal properties of bulk samples and also thin films. This method allows measuring thermal diffusivity (*α*) of a sample in very broad temperature range (80–2500 K) and diffusivity (0.001– 10 cm2 /s) range. For a given material, *α* is directly related to the speed at which the material can change its temperature. Thus, thermal conductivity of the sample is obtained from measurements of diffusivity (*α*), specific heat (*Cp*) and density (ρ) of the sample by means of this relation:

$$
\kappa = \alpha \cdot C\_P \cdot \rho. \tag{7}
$$

Commonly used systems, which measure *α*, usually allow also measuring *Cp*. In spite of this feature, it is recommended to measure specific heat by means of a separate technique, like differential scanning calorimetry (DSC), in order to obtain more accurate estimation of the final value. However, at high temperature, where the specific heat reaches a constant value, diffusivity provides the essential parameter to estimate thermal conductivity.

As shown in **Figure 5a**, use of this method to measure α implies illumination of one face of the sample by a laser pulse of length below 1 ms. An infrared (IR) detector placed behind rear face detects the signal, which is proportional to temperature rise. Thermal diffusivity value is obtained from IR signal rise against time. Example of IR signal profile vs. time is shown in **Figure 5b** corresponding to a graphite reference sample. Original Parker method [27] considers adiabatic conditions, and therefore, diffusivity value is obtained from thickness of the sample and time (t1/2), where IR signal profile reaches half of maximum rise:

$$\alpha = 0.1388 \left( \bigvee\_{l\_{1/2}}^{L^2} \right), \tag{8}$$

where *L* is the thickness of the sample. This method is valid only for adiabatic conditions; however, different methods have been designed in order to consider effects of finite laser pulse time and radiative losses in nonadiabatic conditions [27–30]. Correction fits and evaluation models based on this method are also provided by manufacturers of state-of-the-art thermal diffusivity measuring systems.

Nanostructured State-of-the-Art Thermoelectric Materials Prepared by Straight-Forward Arc-Melting Method http://dx.doi.org/10.5772/65115 193

**Figure 5.** (a) Schematic illustration of laser flash method (adapted from *Thermoelectric Handbook: Macro to Nano*) [26], (b) signal profile and model fitted of graphite reference sample obtained in Laser flash system Linseis LFA 1000.

In addition, laser flash method imposes certain requirements on samples to be measured. It is mandatory to prepare plate samples with flat parallel planes to ensure correct acquisition of temperature profile at the rear face of the sample. Another important point about the sample preparation is to ensure the highest emissivity/absorption in the rear/front surface of the sample. For this purpose, thin coating of graphite well adhered over the sample's surface is commonly used (see **Figure 6a**).

**Figure 6.** Different parts and sample holder (a, b), carrousel for six samples (c), and general view of laser flash equipment: Linseis LFA 1000 (d).

#### *2.4.5. Thermal conductivity: 3ω method*

±10 μV K−1 as a rough estimate for systematic errors of the instrument. Results for commercial ingot of p-type Bi2Te3 above 100 μV K−1, with characteristic maximum above 400 K, are similar to expected behavior. Finally, preliminary data from a pellet of SnSe produced by arc-melting and measured by quasi-integral method are also shown. These values are quite a bit lower than expected. The reason is still to be explored, but it is probably related to the fact, that data were recorded upon second heating run, and the sample may have suffered some chemical alteration. Whatever the case may be, it demonstrates the capabilities of the instrument.

So-called laser flash thermal diffusivity technique is a useful method to determine thermal properties of bulk samples and also thin films. This method allows measuring thermal diffusivity (*α*) of a sample in very broad temperature range (80–2500 K) and diffusivity (0.001–

> r

Commonly used systems, which measure *α*, usually allow also measuring *Cp*. In spite of this feature, it is recommended to measure specific heat by means of a separate technique, like differential scanning calorimetry (DSC), in order to obtain more accurate estimation of the final value. However, at high temperature, where the specific heat reaches a constant value,

As shown in **Figure 5a**, use of this method to measure α implies illumination of one face of the sample by a laser pulse of length below 1 ms. An infrared (IR) detector placed behind rear face detects the signal, which is proportional to temperature rise. Thermal diffusivity value is obtained from IR signal rise against time. Example of IR signal profile vs. time is shown in **Figure 5b** corresponding to a graphite reference sample. Original Parker method [27] considers adiabatic conditions, and therefore, diffusivity value is obtained from thickness of the sample

> 2 1/2

è ø *L*

where *L* is the thickness of the sample. This method is valid only for adiabatic conditions; however, different methods have been designed in order to consider effects of finite laser pulse time and radiative losses in nonadiabatic conditions [27–30]. Correction fits and evaluation models based on this method are also provided by manufacturers of state-of-the-art thermal

0.1388 , æ ö <sup>=</sup> ç ÷

= · ·. *CP* (7)

*t* (8)

ka

diffusivity provides the essential parameter to estimate thermal conductivity.

and time (t1/2), where IR signal profile reaches half of maximum rise:

a

diffusivity measuring systems.

/s) range. For a given material, *α* is directly related to the speed at which the material can change its temperature. Thus, thermal conductivity of the sample is obtained from measurements of diffusivity (*α*), specific heat (*Cp*) and density (ρ) of the sample by means of

*2.4.4. Thermal conductivity: laser flash thermal diffusivity method*

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

10 cm2

this relation:

Alternative procedure to determine thermal conductivity is the so-called 3ω (3 omega) method [31]. We sandwiched a thin gold wire (diameter *d* = 25 μm) between two identical, disk-shaped commercial Bi2Te3 samples. We used BN spray to electrically insulate the wire from the sample. This is a slight variation in the original method as heating/sensing wire is completely surrounded by the material. This method relies on applying AC current along the gold thread (heater) at frequency *ω*, which generates thermal oscillations finally resulting in a voltage at the third harmonic (3*ω*), which is closely related to thermal conductivity (κ):

$$V\_{3\alpha\phi} = -\frac{V\_{1\alpha\phi}^3 \cdot \mathcal{B}}{8\pi \cdot l \cdot \kappa \cdot R\_0} \cdot \left[ \ln(2\alpha) + \ln\left(\frac{d^2}{4\alpha}\right) - 2 \cdot \ln(2) \right] - i \cdot \frac{V\_{1\alpha\phi}^2 \cdot \mathcal{B}}{16 \cdot l \cdot \kappa \cdot R\_0} \,,\tag{9}$$

where *V*1*<sup>ω</sup>* is the amplitude of the ohmic voltage, *l* is the length of the heater, *β* is the temperature coefficient of gold, *R*0 is the nominal wire electrical resistance, *α* is the thermal diffusivity of the sample. This formula is valid as long as thermal penetration depth, 2 is greater than five times the wire radius. Performing linear fit to above expression, of *V*3*<sup>ω</sup>* vs ln(2*ω*), thermal conductivity can be determined.

Here we present the results of this frequency-dependent third harmonic measurement for commercial p-type Bi2Te3 at 300 K [31]. Performing linear fit to the expression indicated in this section, of *V*3*<sup>ω</sup>* vs ln(2*ω*), as shown in **Figure 7**, thermal conductivity obtained is *κ* = 1.32 W m−1 K−1 at 300 K, matching reasonably well the results with TTO method of PPMS.

**Figure 7.** 3ω method for extracting thermal conductivity of commercial p-type Bi2Te3 at room temperature, with frequency-dependent third harmonic voltage, V3ω (full symbols), and its phase shift (empty symbols) and with respect to logarithmic frequency (inset).

#### **2.5. DFT calculations**

We calculated the electronic density of states based on the experimentally determined unit cells in generalized gradient approximation (GGA) DFT scheme with Perdue-Burke-Emzerhof (PBE) pseudopotentials in CASTEP using Materials Studio package [32, 33]. We considered 1×2×2 minimal supercells replacing between 0 and 4 Sn atoms with Ge or Sb out of 16. For Sb alloying, we also considered structures with one Sn atom missing. We checked two different configurations for each composition.

## **3. Results and discussion**

## **3.1. Bi2Te3**

completely surrounded by the material. This method relies on applying AC current along the gold thread (heater) at frequency *ω*, which generates thermal oscillations finally resulting in a voltage at the third harmonic (3*ω*), which is closely related to thermal conductivity (κ):

> ( ) ( ) 3 2 2 1 1

é ù æ ö × × =- × + - × - × ê ú ç ÷

a

ç ÷ ×× × ê ú ×× × ë û è ø

where *V*1*<sup>ω</sup>* is the amplitude of the ohmic voltage, *l* is the length of the heater, *β* is the temperature coefficient of gold, *R*0 is the nominal wire electrical resistance, *α* is the thermal diffusivity of the sample. This formula is valid as long as thermal penetration depth, 2 is greater than five times the wire radius. Performing linear fit to above expression, of *V*3*<sup>ω</sup>* vs ln(2*ω*), thermal

Here we present the results of this frequency-dependent third harmonic measurement for commercial p-type Bi2Te3 at 300 K [31]. Performing linear fit to the expression indicated in this section, of *V*3*<sup>ω</sup>* vs ln(2*ω*), as shown in **Figure 7**, thermal conductivity obtained is *κ* = 1.32 W m−1 K−1 at 300 K, matching reasonably well the results with TTO method of

**Figure 7.** 3ω method for extracting thermal conductivity of commercial p-type Bi2Te3 at room temperature, with frequency-dependent third harmonic voltage, V3ω (full symbols), and its phase shift (empty symbols) and with respect to

We calculated the electronic density of states based on the experimentally determined unit cells in generalized gradient approximation (GGA) DFT scheme with Perdue-Burke-Emzerhof

w

*V V <sup>d</sup> V i*

0 0 ln 2 ln 2 ln 2 , <sup>8</sup> <sup>4</sup> <sup>16</sup>

*l R l R* (9)

 w  b

k

3

w

conductivity can be determined.

logarithmic frequency (inset).

**2.5. DFT calculations**

PPMS.

w

p k

b

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

Pristine Bi2Te3 was successfully prepared by arc-melting as reported in Ref. [20]. Bi2Te3 both n-type and p-type presents the best thermoelectric properties for applications near room temperature. Consequently, preparation of these compounds by arc-melting and verification of their thermoelectric properties was an interesting milestone. We found, that samples present high electrical conductivity, while they retain low thermal conductivity, which is strongly affected by morphology. On the other hand, Seebeck coefficient values are similar to previously reported results.

As shown in **Figure 8**, typical microstructure of samples can be described as piles of stacked sheets parallel to plane defined by **b** and **c** crystallographic axis, providing easy cleavage of materials. Thickness of individual sheets is well below 0.1 μm (typically 20–40 nm). Thermoelectric properties of these materials are strongly influenced by this micro- or nanostructuration, involving many surface boundaries (interfaces) that are responsible for scattering of both charge carriers and phonons.

**Figure 8.** Typical microstructure of Bi2Te3 prepared by arc-melting, showing nanostructuration in sheets perpendicular to crystallographic c axis. Magnification (a) 7000×, (b) 25,000×, (c) 50,000×, and (d) 80,000×.

Transport properties in pure Bi2Te3 were measured in PPMS device [20] and high-temperature device (described in Section 2.4.3) on cold-pressed pellets. In the temperature range between 300 and 540 K, absolute value of Seebeck coefficient increases continuously until a maximum of −93 μV K−1, as shown in **Figure 9a**. These measurements were repeated in different samples.

**Figure 9.** Temperature dependences of (a) Seebeck coefficient and (b) electrical resistivity of Bi2Te3 prepared by arcmelting.

Published data for undoped Bi2Te3 offer a wide range of Seebeck coefficient values from −50 to −260 μV K−1 [15, 34–36] depending on material's nature and charge carriers concentration. Compounds prepared by wet chemical methods demonstrate similar Seebeck coefficient values [18, 34], whereas for samples prepared by ball-milling and hot-pressing technique, this coefficient is as high as −190 μV K−1 [37]. In bismuth telluride samples, charge carriers concentration is strongly affected by antisite BiTe and TeBi defects, which are randomly created during synthesis process. This feature yields a wide range of Seebeck coefficient values measured in samples prepared by different methods [15, 34–39].

Electrical resistivity (**Figure 9b**) suggests semimetallic behavior, and, thus, we observe an increase in electrical resistivity with temperature. As temperature increases, charge carrier' scattering is augmented. We found resistivity values of 2 μOhm m at 320 K, whereas for samples prepared by mechanical alloying and SPS or hot pressing, they display higher values of 30 and 7 μOhm m, respectively [37, 38]. Samples synthesized by chemical processes show resistivity values between 13 and 5 μOhm m [34, 39]. These results indicate improvement compared to other preparation procedures. The number of thermally excited charge carriers increases with temperature, as shown by Hall concentration measurements. Charge carriers' density at 310 K is equal to 7.46 × 1018 cm−3, similar to other literature values [35]. Hall mobility of charge carriers is calculated by *μH* = *RH σ*, resulting in 4514 cm2 V−1 s−1, which is an extremely high value due to low resistivity. Preferred orientation of sheets might be the main cause of this great electron mobility along measurement direction, resulting from the exceptionally anisotropic nature of Bi2Te3, with in-plane conductivity [40] over double that of out of plane.

Low thermal conductivity is critical for good thermoelectric performance. Thermal conductivity vs temperature is displayed in **Figure 10a** for Bi2Te3. At 365 K, thermal conductivity reaches its minimum value of 1.2 W m−1 K−1 after decreasing along the whole temperature range. This is an excellent value for Bi2Te3 bulk material, comparable to one of the lowest values presented in literature of 0.9 W m−1 K−1, Ref. [15]. It implies good compromise with excellent electrical resistivity and its electronic contribution to thermal conductivity. Layered nanostructured morphology of pellets is probably playing important role in reducing thermal conductivity, where abundant grain boundaries along phonon path (between layers or block of layers) increase phonon scattering. This effect compensates for improved electrical resistivity. Other procedures leading to nanostructured samples, i.e., ball-milling and hot pressing, yield thermal conductivity value of 1.2 W m−1 K−1 at 330 K [37], while for chemical synthesis values of 0.8 W m−1 K−1 at 380 K are obtained [34], however, in alloys with higher electrical resistivity. Eventually, then, our arc-melting technique produces Bi2Te3 with ZT approaching 0.3 (**Figure 10b**).

**Figure 9.** Temperature dependences of (a) Seebeck coefficient and (b) electrical resistivity of Bi2Te3 prepared by arc-

Published data for undoped Bi2Te3 offer a wide range of Seebeck coefficient values from −50 to −260 μV K−1 [15, 34–36] depending on material's nature and charge carriers concentration. Compounds prepared by wet chemical methods demonstrate similar Seebeck coefficient values [18, 34], whereas for samples prepared by ball-milling and hot-pressing technique, this coefficient is as high as −190 μV K−1 [37]. In bismuth telluride samples, charge carriers concentration is strongly affected by antisite BiTe and TeBi defects, which are randomly created during synthesis process. This feature yields a wide range of Seebeck coefficient values measured in

Electrical resistivity (**Figure 9b**) suggests semimetallic behavior, and, thus, we observe an increase in electrical resistivity with temperature. As temperature increases, charge carrier' scattering is augmented. We found resistivity values of 2 μOhm m at 320 K, whereas for samples prepared by mechanical alloying and SPS or hot pressing, they display higher values of 30 and 7 μOhm m, respectively [37, 38]. Samples synthesized by chemical processes show resistivity values between 13 and 5 μOhm m [34, 39]. These results indicate improvement compared to other preparation procedures. The number of thermally excited charge carriers increases with temperature, as shown by Hall concentration measurements. Charge carriers' density at 310 K is equal to 7.46 × 1018 cm−3, similar to other literature values [35]. Hall mobility

high value due to low resistivity. Preferred orientation of sheets might be the main cause of

V−1 s−1, which is an extremely

samples prepared by different methods [15, 34–39].

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

of charge carriers is calculated by *μH* = *RH σ*, resulting in 4514 cm2

melting.

**Figure 10.** (a) Thermal conductivity measured in PPMS device; inset shows pellet used with TTO setup and (b) figure of merit of Bi2Te3 prepared by arc-melting.

## **3.2. Bi2Te3 based alloys: Bi2(Te1−xSex)3**

Preparation of Bi2Te3-Bi2Se3 solid solutions by alloying Bi2Se3 with Bi2Te3, where stronger Se-Bi interactions are created, enlarges band-gap energy and forms new donor levels. This may lead to enhanced electrical conductivity [41–43] and improve thermoelectric performance. Besides, decrease in lattice thermal conductivity is expected due to point defects induced by alloying. On the other hand, Bi2(Te1−xSex)3 alloys are extremely susceptible to anisotropic effects, which have been notable disadvantages in preparation of bulk samples that have not been able to keep high electrical resistivity. Attempts for preparation of oriented grains in bulk samples have been made to overcome this issue [44].

We prepared Bi2(Te0.8Se0.2)3 pellets by arc-melting. NPD study was essential to investigate structural details of this doped sample. Neutrons are particularly suitable to study these intermetallic alloys having texturized nature of powder, which gives XRD patterns with large and untreatable preferred orientation effects. Neutrons provide bulk analysis, with good penetration; also the way of filling sample holders, (vanadium cylinders), helps to reduce unwanted preferred orientation, which is additionally minimized by rotation of sample holders. Moreover, lack of form factors for neutrons as diffraction probe enables accessing remote regions of reciprocal space, thus yielding accurate anisotropic displacement factors, which may give hints of the origin of phonon propagation across these materials, characterized by low thermal conductivity.

For Bi2(Te0.8Se0.2)3, NPD data were collected at RT at HRPT diffractometer of SINQ spallation source at PSI with *λ* = 1.494 Å. Crystal structure refinement was carried out in Bi2Te3-type model [45] in hexagonal setting of rhombohedral R-3m space group (no. 166), *Z* = 3, with Bi located at 6*c* (00z) Wyckoff site and Te/Se distributed at random over two different crystallographic sites, (Te,Se)1 at 3*a* positions and (Te,Se)2 at 6*c*. There was excellent agreement between observed and calculated profiles, as shown in **Figure 11**; minor preferred orientation correction was effective in improving refinement for all reflections in the whole angular range, reaching low Bragg discrepancy factors of 5.15%. **Tables 1** and **2** include lattice and atomic parameters and anisotropic displacements factors, as well as discrepancy factors after refinement. Unitcell parameters are **a** = 4.3315(1) Å and **c** = 30.208(7) Å. Unit-cell size is substantially smaller than that of parent Bi2Te3 compound (with unit-cell parameters: **a** = 4.385915 (6) Å, **c** = 30.495497 (1) Å, upon incorporation of smaller Se atoms.

**Figure 12** shows two views of refined crystal structure of Bi2(Te0.8Se0.2)3, along c axis (left panel) and perpendicular to c axis (right panel). It consists of hexagonal close-packed sheets, each layer being composed of fivefold stacking sequence of covalently bonded (Te,Se)2-Bi-(Te,Se)1- Bi-(Te,Se)2 atoms, whereas interatomic forces between adjacent layers ((Te,Se)2-(Te,Se)2 interactions) are mainly van der Waals type. As a consequence, crystals of these alloys are easily cleaved perpendicular to **c**-direction. Bi atoms are coordinated to 3 (Te,Se)1 at distances of 3.129(7) Å and 3 (Te,Se)2 at 3.102(9) Å in distorted octahedral configuration. Distance between terminal (Te,Se)2 of adjacent layers is 3.634(9) Å. It is noteworthy that anisotropic displacement ellipsoids are strongly flattened with short axis perpendicular to bonding directions, i.e., along [110] directions as shown in the left panel in **Figure 12**.

**Figure 11.** NPD profiles for Bi2(Te0.8Se0.2)3. Crosses are experimental points, solid line is calculated fit and difference is at the bottom. Vertical marks correspond to allowed Bragg reflections.


Unit-cell parameters: a = 4.3315 (4) Å, c = 30.208 (5) Å, 490.83 (10) Å3 , Z = 3. Ueq and Uij are, respectively, the equivalent and anisotropic atomic displacement parameters. Discrepancy factors after refinement are also included.

**Table 1.** Structural parameters for Bi2(Te0.8Se0.2)3 refined in R-3m space group (hexagonal setting) from NPD data collected at RT with λ = 1.494 Å.


**Table 2.** Anisotropic displacement parameters (Å2 ).

**3.2. Bi2Te3 based alloys: Bi2(Te1−xSex)3**

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

have been made to overcome this issue [44].

(1) Å, upon incorporation of smaller Se atoms.

[110] directions as shown in the left panel in **Figure 12**.

by low thermal conductivity.

Preparation of Bi2Te3-Bi2Se3 solid solutions by alloying Bi2Se3 with Bi2Te3, where stronger Se-Bi interactions are created, enlarges band-gap energy and forms new donor levels. This may lead to enhanced electrical conductivity [41–43] and improve thermoelectric performance. Besides, decrease in lattice thermal conductivity is expected due to point defects induced by alloying. On the other hand, Bi2(Te1−xSex)3 alloys are extremely susceptible to anisotropic effects, which have been notable disadvantages in preparation of bulk samples that have not been able to keep high electrical resistivity. Attempts for preparation of oriented grains in bulk samples

We prepared Bi2(Te0.8Se0.2)3 pellets by arc-melting. NPD study was essential to investigate structural details of this doped sample. Neutrons are particularly suitable to study these intermetallic alloys having texturized nature of powder, which gives XRD patterns with large and untreatable preferred orientation effects. Neutrons provide bulk analysis, with good penetration; also the way of filling sample holders, (vanadium cylinders), helps to reduce unwanted preferred orientation, which is additionally minimized by rotation of sample holders. Moreover, lack of form factors for neutrons as diffraction probe enables accessing remote regions of reciprocal space, thus yielding accurate anisotropic displacement factors, which may give hints of the origin of phonon propagation across these materials, characterized

For Bi2(Te0.8Se0.2)3, NPD data were collected at RT at HRPT diffractometer of SINQ spallation source at PSI with *λ* = 1.494 Å. Crystal structure refinement was carried out in Bi2Te3-type model [45] in hexagonal setting of rhombohedral R-3m space group (no. 166), *Z* = 3, with Bi located at 6*c* (00z) Wyckoff site and Te/Se distributed at random over two different crystallographic sites, (Te,Se)1 at 3*a* positions and (Te,Se)2 at 6*c*. There was excellent agreement between observed and calculated profiles, as shown in **Figure 11**; minor preferred orientation correction was effective in improving refinement for all reflections in the whole angular range, reaching low Bragg discrepancy factors of 5.15%. **Tables 1** and **2** include lattice and atomic parameters and anisotropic displacements factors, as well as discrepancy factors after refinement. Unitcell parameters are **a** = 4.3315(1) Å and **c** = 30.208(7) Å. Unit-cell size is substantially smaller than that of parent Bi2Te3 compound (with unit-cell parameters: **a** = 4.385915 (6) Å, **c** = 30.495497

**Figure 12** shows two views of refined crystal structure of Bi2(Te0.8Se0.2)3, along c axis (left panel) and perpendicular to c axis (right panel). It consists of hexagonal close-packed sheets, each layer being composed of fivefold stacking sequence of covalently bonded (Te,Se)2-Bi-(Te,Se)1- Bi-(Te,Se)2 atoms, whereas interatomic forces between adjacent layers ((Te,Se)2-(Te,Se)2 interactions) are mainly van der Waals type. As a consequence, crystals of these alloys are easily cleaved perpendicular to **c**-direction. Bi atoms are coordinated to 3 (Te,Se)1 at distances of 3.129(7) Å and 3 (Te,Se)2 at 3.102(9) Å in distorted octahedral configuration. Distance between terminal (Te,Se)2 of adjacent layers is 3.634(9) Å. It is noteworthy that anisotropic displacement ellipsoids are strongly flattened with short axis perpendicular to bonding directions, i.e., along

**Figure 12.** Two projections of crystal structure, along c axis (left panel) and perpendicular to c axis (right panel). Strongly anisotropic displacement ellipsoids (95% probability), with the short axis along [110] direction are illustrated.

Transport properties were evaluated in our homemade apparatus (Section 2.4.5). Seebeck coefficient vs temperature curve is plotted in **Figure 13a**.

Slow decrease in S is observed between 300 and 550 K, where average value is −75 μV K−1. There is small improvement in thermopower regarding pure Bi2Te3 samples, but it is still low in contrast to other Bi2(Te1−xSex)3 alloys, where values of −190 μV K−1 are reported [46] or even −259 μV K−1 at room temperature in samples with optimized composition [47]. Hall concentration of charge carriers is determined as 3.1 × 1019 cm−3 at 300 K (inset in **Figure 13a**), which is somewhat higher than in pure Bi2Te3 [20, 35], as a result of donor feature of Bi2(Te1−xSex)3 alloys.

As expected, temperature dependence of electrical resistivity (**Figure 13b**) exhibits the same semimetallic behavior as pure compound, but abrupt reduction in resistivity is observed at 530 K, until minimum value of 55 μOhm m is reached. Compared with pure compound (Section 3.1), with extremely low electrical resistivity (2 μOhm m at 300 K) prepared by arcmelting, these results indicate deterioration of thermoelectric performance. The drop in electrical conduction is possibly a consequence of the enormous anisotropy of this alloy, meaning that orientations of layered structures are not aligned for improved electron mobility. Analogous relationship between charge carriers scattering, doping and electrical conductivity is reported by Ajay Soni et al. [47] for Bi2Te2.2Se0.8 nanocomposite, which shows metallic and semiconductor behavior throughout their measurement range with values around 75 μOhm m at room temperature.

**Figure 12.** Two projections of crystal structure, along c axis (left panel) and perpendicular to c axis (right panel). Strongly anisotropic displacement ellipsoids (95% probability), with the short axis along [110] direction are illustrated.

Transport properties were evaluated in our homemade apparatus (Section 2.4.5). Seebeck

Slow decrease in S is observed between 300 and 550 K, where average value is −75 μV K−1. There is small improvement in thermopower regarding pure Bi2Te3 samples, but it is still low in contrast to other Bi2(Te1−xSex)3 alloys, where values of −190 μV K−1 are reported [46] or even −259 μV K−1 at room temperature in samples with optimized composition [47]. Hall concentration of charge carriers is determined as 3.1 × 1019 cm−3 at 300 K (inset in **Figure 13a**), which is somewhat higher than in pure Bi2Te3 [20, 35], as a result of donor feature of Bi2(Te1−xSex)3

As expected, temperature dependence of electrical resistivity (**Figure 13b**) exhibits the same semimetallic behavior as pure compound, but abrupt reduction in resistivity is observed at 530 K, until minimum value of 55 μOhm m is reached. Compared with pure compound (Section 3.1), with extremely low electrical resistivity (2 μOhm m at 300 K) prepared by arcmelting, these results indicate deterioration of thermoelectric performance. The drop in electrical conduction is possibly a consequence of the enormous anisotropy of this alloy, meaning that orientations of layered structures are not aligned for improved electron mobility. Analogous relationship between charge carriers scattering, doping and electrical conductivity is reported by Ajay Soni et al. [47] for Bi2Te2.2Se0.8 nanocomposite, which shows metallic and semiconductor behavior throughout their measurement range with values around 75 μOhm m

coefficient vs temperature curve is plotted in **Figure 13a**.

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alloys.

at room temperature.

**Figure 13.** Temperature dependences of (a) Seebeck coefficient and (b) electrical resistivity for Bi2(Te0.8Se0.2)3 measured in homemade apparatus.

**Figure 14** shows dependence of total thermal conductivity on temperature determined in PPMS device.

Expected Umklapp maximum at low temperature appears with subsequent decrease over the whole measurement range until minimum value of 0.8 W m−1 K−1 is reached at 300 K. This is better (lower) thermal conductivity than reported for pristine nanostructured Bi2Te3 obtained by arc-melting, reaching 1.2 W m−1 K−1 at 365 K [20]. Excellent present values could be related to stronger anisotropy, higher electrical resistivity and point defects induced by alloying. In Bi2Te3-Bi2Se3 alloys produced by encapsulated melting and hot pressing, the best thermal conductivity value was equal to 1.04 W m−1 K−1 at 323 K [46], while for samples made by largescale zone melting, values of 1.2 W m−1 K−1 at 323 K are observed [48].

In samples prepared by polyol method followed by SPS, which leads to nanocomposite materials, low values of thermal conductivity are found: 0.9 W m−1 K−1 at 300 K for Bi2Te2.2Se0.8 and 0.7 W m−1 K−1 at 300 K for Bi2Te2.7Se0.3 nanocomposites [47]. The literature survey shows, that our thermal conductivity values are among the best reported, which is probably related to the nanostructuration effects, that we describe for arc-melted samples, with advantage of the simplicity of our one-step straightforward method.

**Figure 14.** Temperature dependence of thermal conductivity of Bi2(Te0.8Se0.2)3 measured in PPMS device. Extremely low thermal conductivity of 0.8 W m−1 K−1 is observed at 300 K.

#### **3.3. SnSe and related alloys**

Tin selenide and its various alloys show good thermoelectric performance at temperatures well above the maximum attainable in PPMS. Therefore, the main use of these results, measured with PPMS, is to guide us in search for candidate compositions. However, as we show, we found surprisingly high values of Seebeck coefficient, whereas thermal conductivity of tin selenide produced by arc-melting is considerably lower than that of single crystals. Both are highly promising results for thermoelectric materials.

#### *3.3.1. Structural characterization*

We have prepared by simple and straightforward arc-melting technique highly textured SnSe samples with record Seebeck coefficient values and extremely low thermal conductivity [19]. Test NPD study was essential to investigate structural details of SnSe, since this bulk study is by far much less sensitive to the preferred orientation effects. Not only pristine SnSe, but other several novel series of SnSe-based alloys, namely Sn1−xMxSe (M = Sb, Ge) prepared by arcmelting, have been investigated by neutron diffraction. We will illustrate these studies with description of *in situ* structural evolution of Sn0.8Ge0.2Se in the temperature range of maximum thermoelectric efficiency. NPD data were collected in diffractometer D2B. Measurements were taken at 25, 200, 420 and 580°C*.*

conductivity value was equal to 1.04 W m−1 K−1 at 323 K [46], while for samples made by large-

In samples prepared by polyol method followed by SPS, which leads to nanocomposite materials, low values of thermal conductivity are found: 0.9 W m−1 K−1 at 300 K for Bi2Te2.2Se0.8 and 0.7 W m−1 K−1 at 300 K for Bi2Te2.7Se0.3 nanocomposites [47]. The literature survey shows, that our thermal conductivity values are among the best reported, which is probably related to the nanostructuration effects, that we describe for arc-melted samples, with advantage of

**Figure 14.** Temperature dependence of thermal conductivity of Bi2(Te0.8Se0.2)3 measured in PPMS device. Extremely low

Tin selenide and its various alloys show good thermoelectric performance at temperatures well above the maximum attainable in PPMS. Therefore, the main use of these results, measured with PPMS, is to guide us in search for candidate compositions. However, as we show, we found surprisingly high values of Seebeck coefficient, whereas thermal conductivity of tin selenide produced by arc-melting is considerably lower than that of single crystals. Both are

We have prepared by simple and straightforward arc-melting technique highly textured SnSe samples with record Seebeck coefficient values and extremely low thermal conductivity [19]. Test NPD study was essential to investigate structural details of SnSe, since this bulk study is by far much less sensitive to the preferred orientation effects. Not only pristine SnSe, but other

scale zone melting, values of 1.2 W m−1 K−1 at 323 K are observed [48].

the simplicity of our one-step straightforward method.

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

thermal conductivity of 0.8 W m−1 K−1 is observed at 300 K.

highly promising results for thermoelectric materials.

**3.3. SnSe and related alloys**

*3.3.1. Structural characterization*

**Figure 15** illustrates NPD patterns of Sn0.8Ge0.2Se at 420 and 580°C*.* Crystal structure can be Rietveld-refined in orthorhombic *Pnma* space group below 420°C. At this temperature, an orthorhombic (*Pnma*) to orthorhombic (*Cmcm*) phase transition takes place. **Figure 16** shows phase diagram displaying temperature dependence of unit-cell parameters of both orthorhombic phases. A dramatic rearrangement of atoms is observed along with phase transitions, bearing a more ordered structure. **Figure 17** displays crystal structures at room temperature, 200, 420 and 580°C. It is noteworthy, that change in displacement ellipsoids directions with temperature presents its largest axis along **c** direction in *Pnma* space group, while at high temperature it is oriented along **b** axis in *Cmcm* space group. In *Pnma*, structure consists of trigonal pyramids SnSn3 forming layers perpendicular to [100] direction, with thermal ellipsoids oriented within the layers, whereas across the transition to *Cmcm* the coordination environment changes to tetragonal pyramid, where large Sn ellipsoids in the basal squareplane adopt a configuration with the longest axis perpendicular to four closer chemical bonds, oriented along **b** axis of orthorhombic structure. Such high thermal displacements indicate strong rattling effect of Sn in a pentacoordinated cage, accounting for the observed decrease in thermal conductivity and good thermoelectric performance of this material.

**Figure 15.** Observed (crosses), calculated (full line) and difference (at the bottom) NPD profiles for Sn0.8Ge0.2Se at 420 °C, just below the phase transition. Vertical markers correspond to allowed Bragg reflections.

**Figure 16.** Phase diagram showing thermal evolution of unit-cell parameters.

**Figure 17.** Crystal structures of orthorhombic phases at 25 (upper left), 200 (upper right), 420 (bottom left) and 580°C (bottom right).

#### *3.3.2. Thermoelectric characterization*

**Figure 16.** Phase diagram showing thermal evolution of unit-cell parameters.

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

(bottom right).

**Figure 17.** Crystal structures of orthorhombic phases at 25 (upper left), 200 (upper right), 420 (bottom left) and 580°C

We first discuss our results on pure (i.e., unalloyed) SnSe, produced by arc-melting. The barshaped sample was cut directly from as-produced ingot as described above. **Figure 18** shows transport properties obtained in PPMS between 2 and 380 K. Seebeck coefficient (in middle panel) exhibits monotonic increase in positive (i.e., p-type) values reaching a maximum of 668 μV K−1 [19]. At the time, this was the highest Seebeck coefficient value reported in SnSe. We have observed this behavior in various samples on repeated measurements, consistently. While preliminary studies reported values only around 50 μV K−1 [49], the ground-breaking single crystal results of Zhao et al. [50] reach around 580 μV K−1, quite independent of crystallographic direction [50]. Meanwhile, other reported values of polycrystalline samples are close to this value [51–53]. Uncontrolled differences in hole concentration may play a role in these variations. Zhao et al. [50] found, that Seebeck coefficient value reaches its maximum in SnSe around 525 K. When we extrapolate our results (limited below 400 K in PPMS), we could expect as much as 800 μV K−1, and as we show below, indeed, we do find such high values with MMR device (described in Section 2.4.2).

Temperature dependence of electrical resistivity is shown in the bottom panel of **Figure 18**; Hall concentration of charge carriers at 300 K is 7.95 × 1015 cm-3 [19]. Resistivity decreases exponentially with temperature, as expected for a semiconductor. We consistently find, that resistivity of SnSe and its alloys produced by arc-melting is rather high. This is a persistent problem of the technique, which we must address in the future. Nevertheless, we must also bear in mind, that these results from PPMS are limited to a temperature range well below that, where SnSe functions as a good thermoelectric. For comparison, our arc-melting produced pellet has bulk resistivity at room temperature (295 K) of around 64 mOhm m, significantly higher than expected: the single crystals of Zhao et al. [50] have 1 mOhm m within bc plane and 5 mOhm m along a-direction, whereas Sassi et al. [52] report 11 mOhm m along the pressing direction in polycrystals and 5 mOhm m perpendicular to it. Hall effect measurements at 300 K yields p-type hole concentration of 7.95 × 1015 cm−3. This is much lower than that of typical thermoelectrics and, indeed, of other SnSe reports (e.g., 4 × 1017 cm−3 by Zhao et al. [50]). Again, this is a persistent finding in our SnSe alloys: free charge carriers' concentration is much lower than expected, indicating the presence of strong traps for charge carriers. It also explains large electrical resistivity along with strong nanostructuration, producing abundant grain boundaries. Surprisingly, large Seebeck coefficient value is also related to low charge density, through Pisarenko relation [54].

Thermal conductivity of SnSe is shown in the top panel of **Figure 18**. It is overwhelmingly dominated by lattice contribution, due to low charge carriers' concentration.

Thermal conductivity peaks around 25 K due to UmKlapp scattering and then starts to decrease monotonically throughout the measurement range, reaching a value as low as 0.2 W m−1 K−1 at 395 K. This is a strikingly low value. Admittedly, direct heat-flow technique employed by PPMS is strongly affected by heat loss problems discussed above and these become acute above room temperature. Nevertheless, values are highly reliable below 100 K, and they are consistently very low there, too, in several samples. The intrinsic lattice thermal conductivity of SnSe is very low, probably an outcome of anharmonicity of chemical bonds. High Grüneisen parameters and strong phonon-phonon interactions are expected as a result of the presence of lone-electron pairs of both Se2− and Sn2+ ions [49, 55]. In fact, lone pairs of p-block elements play an important role deforming lattice vibration, which results in strong anharmonicity; significantly, anisotropic vibrations of both Sn and Se atoms are determined by NPD, with the main ellipsoid axes directed along chemical bonds (**Figure 17**), which is also indicative of such anharmonicity, as vibrations are hindered out of bonding direction by voluminous electron pairs filling empty space in the crystal structure. Moreover, thermal conductivity is significantly lower than those reported in single crystals (1.8 W m−1 K−1) [50, 56] and even lower compared to those recently reported for polycrystalline samples [52]. Extremely small values measured in the present material are most likely related to strong texture obtained during synthesis process, that leads to layered nanostructuration along **a** axis (**Figure 17**). This is particularly effective to boost phonon scattering at nanoscale, thus resulting in record low thermal conductivity for this polycrystalline material.

**Figure 18.** Temperature dependence of (top) thermal conductivity, (middle) Seebeck coefficient, (bottom) electrical resistivity of stoichiometric SnSe.

A second set of measurements of Seebeck coefficient at high temperature were carried out at MMR device, by comparing Seebeck effect of SnSe material with that of constantan wire, as described in Section 2.4.2. Seebeck coefficient was measured using 1 × 1 × 8 mm3 bar-shaped SnSe samples and reference constantan wire of 0.125 mm diameter. Reproducibility of measurements was confirmed by repeating them after making new contacts both on the sample and on reference constantan wire. This procedure warrants accuracy better than 5% over the whole temperature range.

**Figure 19** shows Seebeck coefficient as function of temperature *S*(*T*) measured using the method described above for SnSe. Initially, *S*(*T*) increases with *T* from room temperature up to 400 K, where it reaches about 840 μV K−1. Between 400 and 500 K, Seebeck coefficient is almost temperature independent, and above 500 K *S*(*T*) decreases monotonically up to the maximum experimental temperature, which is lower than temperature corresponding to structural transition from *Pnma* to *Cmcm*, described above from NPD data. These values are slightly higher than those reported by Zhao et al. [50] on single-crystalline samples. This enhancement can be related to nanostructuration of the sample and presence of high density of boundaries.

parameters and strong phonon-phonon interactions are expected as a result of the presence of lone-electron pairs of both Se2− and Sn2+ ions [49, 55]. In fact, lone pairs of p-block elements play an important role deforming lattice vibration, which results in strong anharmonicity; significantly, anisotropic vibrations of both Sn and Se atoms are determined by NPD, with the main ellipsoid axes directed along chemical bonds (**Figure 17**), which is also indicative of such anharmonicity, as vibrations are hindered out of bonding direction by voluminous electron pairs filling empty space in the crystal structure. Moreover, thermal conductivity is significantly lower than those reported in single crystals (1.8 W m−1 K−1) [50, 56] and even lower compared to those recently reported for polycrystalline samples [52]. Extremely small values measured in the present material are most likely related to strong texture obtained during synthesis process, that leads to layered nanostructuration along **a** axis (**Figure 17**). This is particularly effective to boost phonon scattering at nanoscale, thus resulting in record low

**Figure 18.** Temperature dependence of (top) thermal conductivity, (middle) Seebeck coefficient, (bottom) electrical re-

A second set of measurements of Seebeck coefficient at high temperature were carried out at MMR device, by comparing Seebeck effect of SnSe material with that of constantan wire, as

SnSe samples and reference constantan wire of 0.125 mm diameter. Reproducibility of measurements was confirmed by repeating them after making new contacts both on the sample and on reference constantan wire. This procedure warrants accuracy better than 5% over the

bar-shaped

described in Section 2.4.2. Seebeck coefficient was measured using 1 × 1 × 8 mm3

thermal conductivity for this polycrystalline material.

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

sistivity of stoichiometric SnSe.

whole temperature range.

**Figure 19.** High-temperature Seebeck coefficient as function of temperature for SnSe measured in MMR device.

Morphology of the material produced by arc-melting is highly granular, nanostructured. This raises obvious concern about transport measurements. Do we measure intrinsic properties of the materials or are the data heavily distorted by grain-boundary effects? We can get an idea about this by comparing the three transport properties for the same material in two measurements. First, the sample is cut directly from the arc-molten ingot with a diamond saw and measured. Second, the material is directly cold-pressed after arc-melting and then measured. In both cases, the crystal structure, the platelet-like nanostructure and bulk bar-shaped form of samples are the same. What changes is the microstructure. The cold-pressed sample is denser with better grain-to-grain contacts. This is expected to raise both electrical and thermal conductivities. We use Sb-alloyed SnSe as an example. Thermal conductivity of SnSe and its alloys is not affected by the changed morphology. We also found that above room temperature, value of electrical resistivity has been improved by an order of magnitude, and Seebeck coefficient remains unchanged (not shown). This experiment demonstrates, that we are looking at the intrinsic thermal properties, whereas electrical connectivity of the material is in need of improving: measurements do not reflect the intrinsic electrical properties for tin selenide alloys.

Why would electrical and thermal conductivities respond differently to cold-pressing? Electrical conductivity is improved upon increasing grain-to-grain contacts and contact area. However, thermal conductivity is not affected. The reason is related to the nature of phonon scattering and the phonon mean-free path. We can estimate this by comparing low-temperature thermal conductivity (below UmKlapp peak) and specific heat (inset in the top panel of **Figure 20**), using phenomenological relation for phonon diffusion: = 1 <sup>3</sup> ××, that relates thermal conductivity to specific heat at constant volume *CV*, sound velocity (*v*) and phonon mean-free path (*l*). By ignoring the rather complex phonon dispersion of SnSe and using

phonon velocities as given by Zhao et al. [50], we can estimate phonon mean-free path to be between 2 and 10 nm; effectively at low temperature, it is limited by the nanostructured grainsize, but at higher temperatures intrinsic properties dominate.

**Figure 20.** Temperature dependence of (top) thermal conductivity, (middle) Seebeck coefficient and (bottom) electrical resistivity and (inset) specific heat and thermal conductivity comparison at low temperature of Sb0.2Sn0.8Se alloy.

The idea to study alloys of SnSe with SbSe is to control Fermi level and concentration of free charge carriers. To our dismay, we found, that SnSbSe alloys display very high resistivity, higher even, than nominally stoichiometric SnSe, with very low Hall concentration of charge carriers. We did manage to achieve n-type, negative, Seebeck coefficient. Indeed, absolute value of negative Seebeck coefficient reaches 100–200 μV K−1, depending on composition and temperature. These results are summarized for Sb0.2Sn0.8Se in **Figure 20**. Furthermore, for this composition, Hall effect measurements resulted in p-type, with hole concentration 3 × 1016 cm−3 at room temperature. Expected free electron concentration, from *ab initio* calculations of electronic density of states (**Figure 21**), is around 3 × 1021 cm−3 and obviously n-type for this level of Sb fraction in the compound. In order to resolve the apparent contradiction between measured and calculated free electron concentration and measured signs of Hall and Seebeck coefficients, we reconsidered the electronic structure calculation in view of strong Sn deficiency revealed by Rietveld refinement of NPD data. In our calculations, we use 1 × 2 × 2 minimal supercells with 16 Sn and 16 Se sites. Of these, we replace up to 3 Sn with Sb to approximate experimental alloying and remove one Sn to represent observed Sn site deficiency. Resulting band structure shows a striking narrow band in the gap above the valence band, appearing as a sharp peak in the density of states (DOS). This acts as shallow energy charge trap that localizes electrons transferred from Sb substitutes. Thus, Fermi level remains stuck in this band for a wide range of Sb concentration, invalidating our expectation of simple rigid-band charge transfer model. The complicated band structure is then responsible for different signs of Hall and Seebeck coefficients, too.

Why would electrical and thermal conductivities respond differently to cold-pressing? Electrical conductivity is improved upon increasing grain-to-grain contacts and contact area. However, thermal conductivity is not affected. The reason is related to the nature of phonon scattering and the phonon mean-free path. We can estimate this by comparing low-temperature thermal conductivity (below UmKlapp peak) and specific heat (inset in the top panel of

thermal conductivity to specific heat at constant volume *CV*, sound velocity (*v*) and phonon mean-free path (*l*). By ignoring the rather complex phonon dispersion of SnSe and using phonon velocities as given by Zhao et al. [50], we can estimate phonon mean-free path to be between 2 and 10 nm; effectively at low temperature, it is limited by the nanostructured grain-

**Figure 20.** Temperature dependence of (top) thermal conductivity, (middle) Seebeck coefficient and (bottom) electrical resistivity and (inset) specific heat and thermal conductivity comparison at low temperature of Sb0.2Sn0.8Se alloy.

The idea to study alloys of SnSe with SbSe is to control Fermi level and concentration of free charge carriers. To our dismay, we found, that SnSbSe alloys display very high resistivity, higher even, than nominally stoichiometric SnSe, with very low Hall concentration of charge

1

<sup>3</sup> ××, that relates

**Figure 20**), using phenomenological relation for phonon diffusion: =

size, but at higher temperatures intrinsic properties dominate.

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

**Figure 21.** Electronic density of states of stoichiometric and Sn-deficient SnSe and Sb-SnSe with compositions indicated in labels. Fermi level is placed at E = 0, and thus band structures shift around with doping level.

The great advantage of arc-melting synthesis is that it affords a way to rapidly assay various compositions for thermoelectric properties. By introducing atoms of different radii, we can modify electronic structure, even without obvious charge transfer, this is so-called band engineering, for example, modification of bandwidth. Obvious candidates to do this are columnar neighbors of tin, lead and germanium. In the following we present results first on SnPbSe alloys and then on SnGeSe alloys. In both series, we found p-type Seebeck coefficient values.

Studying three different SnPbSe alloy compositions with up to 30% Pb substitution on Sn site has shown no improvement on any of thermoelectric properties (**Figure 22**). Electrical resistivity increases by several orders of magnitude, as we have seen for SnSbSe alloys, too. Indeed, it is so high, that resistance of samples surpasses few MOhm limit of PPMS electronics at low temperature. The Seebeck coefficient value reaches up to 600 μV K−1 at 400 K, which is high, but no higher, than in stoichiometric SnSe produced by arc-melting. Finally, thermal conductivity shows the same UmKlapp peak at low temperature as SnSe and Sb0.2Sn0.8Se with no overall reduction.

**Figure 22.** Temperature dependences of (top) thermal conductivity, (middle) Seebeck coefficient and (bottom) electrical resistivity of SnSe alloyed with Pb.

In contrast, by going to smaller ionic radius, SnGeSe alloy has several beneficial effects, although electrical resistivity is still too high. Most importantly, as shown in **Figure 23**, Seebeck coefficient value surpasses 1000 μV K−1 for low GeSe fraction. Curious, nonmonotonic change of Seebeck coefficient with increase in GeSe fraction is supported by electronic structure calculations, based on experimentally determined crystal structures. These reveal, that semiconducting gap also varies nonmonotonously with Ge substitution, first increasing with respect to the gap of SnSe and then decreasing with more Ge (**Figure 24**). Large Seebeck coefficient value is caused partly by low charge carriers concentration, as indicated by resistivity, that is 1–2 orders of magnitude above that of stoichiometric SnSe, following Pisarenko relation.

Nanostructured State-of-the-Art Thermoelectric Materials Prepared by Straight-Forward Arc-Melting Method http://dx.doi.org/10.5772/65115 211

SnPbSe alloys and then on SnGeSe alloys. In both series, we found p-type Seebeck coefficient

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

Studying three different SnPbSe alloy compositions with up to 30% Pb substitution on Sn site has shown no improvement on any of thermoelectric properties (**Figure 22**). Electrical resistivity increases by several orders of magnitude, as we have seen for SnSbSe alloys, too. Indeed, it is so high, that resistance of samples surpasses few MOhm limit of PPMS electronics at low temperature. The Seebeck coefficient value reaches up to 600 μV K−1 at 400 K, which is high, but no higher, than in stoichiometric SnSe produced by arc-melting. Finally, thermal conductivity shows the same UmKlapp peak at low temperature as SnSe and Sb0.2Sn0.8Se with

**Figure 22.** Temperature dependences of (top) thermal conductivity, (middle) Seebeck coefficient and (bottom) electrical

In contrast, by going to smaller ionic radius, SnGeSe alloy has several beneficial effects, although electrical resistivity is still too high. Most importantly, as shown in **Figure 23**, Seebeck coefficient value surpasses 1000 μV K−1 for low GeSe fraction. Curious, nonmonotonic change of Seebeck coefficient with increase in GeSe fraction is supported by electronic structure calculations, based on experimentally determined crystal structures. These reveal, that semiconducting gap also varies nonmonotonously with Ge substitution, first increasing with respect to the gap of SnSe and then decreasing with more Ge (**Figure 24**). Large Seebeck coefficient value is caused partly by low charge carriers concentration, as indicated by resistivity, that is 1–2 orders of magnitude above that of stoichiometric SnSe, following

values.

no overall reduction.

resistivity of SnSe alloyed with Pb.

Pisarenko relation.

**Figure 23.** Sn1−xGexSe (x = 0, 0.1, 0.2, 0.3) temperature dependences (top) thermal conductivity, (middle) Seebeck coeffi‐ cient and (bottom) electrical resistivity—exhibiting characteristic semiconducting behavior. Two independent measure‐ ments are shown for x = 0.1 and 0.3. Below 150–200 K electrical resistance of Ge‐doped SnSe samples increases beyond the limits (few MOhm) of the electronics of PPMS, and this influences Seebeck voltage, too (from Ref. [21]).

**Figure 24.** Calculated electronic density of states (DOS) of SnSe, black solid line, Sn0.88Ge0.12Se, red dashed line, and Sn0.81Ge0.19Se, blue dotted line (from Ref. [21]).

#### *3.3.3. Thermal conductivity results from laser flash thermal diffusivity method*

**Figure 25** shows total thermal conductivity (κ) obtained by laser flash diffusivity method for different thermoelectric compounds: SnSe, Sn0.8Ge0.2Se and Sn0.8Sb0.2Se; PbTe is used as a reference.

**Figure 25.** Thermal conductivity values of SnSe, Sn0.8Ge0.2Se, Sn0.8Sb0.2Se and PbTe obtained by laser flash diffusivity method.

Lead telluride, PbTe, is a well-known thermoelectric material, that, due to its band gap of about 0.3 eV, is useful in intermediate temperature range of operation. Its thermal conductivity falls from room temperature with a 1/T dependence, which is a fingerprint of the enhancement of phonon-phonon interactions with increasing temperature. This behavior, together with its band-gap value, makes PbTe one of the most competitive thermoelectric materials for generators above 500 K. However, several efforts are being made to enhance its efficiency. The main ways to drive this goal are enhancement of thermoelectric properties by nanostructuring and modifications in the density of states to create resonant states in the conduction band [57].

The pure SnSe and related alloys (Sn0.8Ge0.2Se, Sn0.8Sb0.2Se) display significantly lower thermal conductivities in the high-temperature region. At room temperature, values of total thermal conductivity are 0.89 and 0.7 W m−1 K−1 for SnSe and Sn0.8Sb0.2Se compounds, respectively. These values are further reduced with increasing temperature, reaching 0.4 W m−1 K−1 at 675 K. It is noteworthy, that above-described thermal conductivities determined in PPMS are considerably lower than values obtained by an indirect procedure, from thermal diffusivity.

Total thermal conductivity has two contributions, lattice thermal conductivity (κ*lat*), due to phonon transport, and charge carriers' thermal conductivity (κ*ch*), due to thermal transport of charge carriers (electrons and/or holes). As a first approximation, Wiedemann-Franz law [26] allows reasonable estimation of charge carriers thermal conductivity as a function of temperature, *κch* = (*L*0*T*) ⁄ *ρ*, where *L0* is the Lorentz number and *ρ* is the electrical resistivity. For the case of SnSe family, total thermal conductivity is almost fully dominated by lattice thermal conductivity. In fact, ratio of thermal conductivity due to charge carriers to total thermal conductivity is approximately 10−4. The different anisotropic direction of both measurements might be related to the differences in the magnitude of determined thermal conductivity with respect to the direct measure provided by PPMS.

## **4. Conclusions**

*3.3.3. Thermal conductivity results from laser flash thermal diffusivity method*

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

reference.

method.

**Figure 25** shows total thermal conductivity (κ) obtained by laser flash diffusivity method for different thermoelectric compounds: SnSe, Sn0.8Ge0.2Se and Sn0.8Sb0.2Se; PbTe is used as a

**Figure 25.** Thermal conductivity values of SnSe, Sn0.8Ge0.2Se, Sn0.8Sb0.2Se and PbTe obtained by laser flash diffusivity

Lead telluride, PbTe, is a well-known thermoelectric material, that, due to its band gap of about 0.3 eV, is useful in intermediate temperature range of operation. Its thermal conductivity falls from room temperature with a 1/T dependence, which is a fingerprint of the enhancement of phonon-phonon interactions with increasing temperature. This behavior, together with its band-gap value, makes PbTe one of the most competitive thermoelectric materials for generators above 500 K. However, several efforts are being made to enhance its efficiency. The main ways to drive this goal are enhancement of thermoelectric properties by nanostructuring and modifications in the density of states to create resonant states in the conduction band [57].

The pure SnSe and related alloys (Sn0.8Ge0.2Se, Sn0.8Sb0.2Se) display significantly lower thermal conductivities in the high-temperature region. At room temperature, values of total thermal conductivity are 0.89 and 0.7 W m−1 K−1 for SnSe and Sn0.8Sb0.2Se compounds, respectively. These values are further reduced with increasing temperature, reaching 0.4 W m−1 K−1 at 675 K. It is noteworthy, that above-described thermal conductivities determined in PPMS are considera-

Total thermal conductivity has two contributions, lattice thermal conductivity (κ*lat*), due to phonon transport, and charge carriers' thermal conductivity (κ*ch*), due to thermal transport of charge carriers (electrons and/or holes). As a first approximation, Wiedemann-Franz law [26] allows reasonable estimation of charge carriers thermal conductivity as a function of temperature, *κch* = (*L*0*T*) ⁄ *ρ*, where *L0* is the Lorentz number and *ρ* is the electrical resistivity. For the case of SnSe family, total thermal conductivity is almost fully dominated by lattice thermal conductivity. In fact, ratio of thermal conductivity due to charge carriers to total thermal conductivity is approximately 10−4. The different anisotropic direction of both measurements

bly lower than values obtained by an indirect procedure, from thermal diffusivity.

We have described a fast one-step procedure to prepare nanostructured intermetallic alloys belonging to the families of well-known Bi2Te3 and recently described SnSe, all of them showing similar nanostructure consisting of stacks of nanosheets, that perturb propagation of phonons and provide extremely low thermal conductivity. Crystal structure studies from NPD data reveal anisotropic displacement parameters, probably due to the presence of lone-electron pairs of the p-block elements (Bi, Te, Sn, Se…) also contributing to low lattice thermal conductivity. Seebeck coefficient values are enhanced in SnSe system, reaching extraordinary high values close to 1000 μV K−1 in SnGeSe alloys. As a drawback of nanostructuration, electrical resistivity values are much higher in this system than those described in single crystalline samples, probably arising from many grain boundaries, which perturb charge carriers path. We describe also a simple apparatus for the measurement of high-temperature transport properties, ideally conceived to determine *S* and *σ* in disk-shaped pellets directly obtained from the intermetallic ingots. The use of Nb pistons, chemically inert to reactive p elements like Bi, Te or Se, is particularly suitable given the weak S factor for Nb, yielding reproducible results for known materials like Cu or Al.

#### **Abbreviations**


## **Acknowledgements**

We thank the financial support of the Spanish Ministry of Science and Innovation to the project MAT2013-41099-R and by JCCM through Project PPII-2014-019-P. We thank the Institut Laue-Langevin (ILL) and Paul Scherrer Institut (PSI) for providing the neutron beam time.

## **Author details**

Federico Serrano-Sánchez1 , Mouna Gharsallah1,2, Julián Bermúdez1 , Félix Carrascoso1 , Norbert M. Nemes1 , Oscar J. Dura3 , Marco A. López de la Torre3 , José L. Martínez1 , María T. Fernández-Díaz4 and José A. Alonso1\*

\*Address all correspondence to: ja.alonso@icmm.csic.es

1 Institute of Materials Science of Madrid, Madrid, Spain

2 National School of Engineers, Sfax University, Tunisia

3 Department of Applied Physics and INEI, University of Castilla La Mancha, Ciudad Real, Spain

4 Institut Laue Langevin, Grenoble, France

## **References**


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**Acknowledgements**

**Author details**

Norbert M. Nemes1

Spain

**References**

Federico Serrano-Sánchez1

María T. Fernández-Díaz4

, Oscar J. Dura3

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

\*Address all correspondence to: ja.alonso@icmm.csic.es

1 Institute of Materials Science of Madrid, Madrid, Spain

2 National School of Engineers, Sfax University, Tunisia

4 Institut Laue Langevin, Grenoble, France

10.1007/978-1-4899-5723-8

Florida; 2012.

and José A. Alonso1\*

We thank the financial support of the Spanish Ministry of Science and Innovation to the project MAT2013-41099-R and by JCCM through Project PPII-2014-019-P. We thank the Institut Laue-

, Mouna Gharsallah1,2, Julián Bermúdez1

3 Department of Applied Physics and INEI, University of Castilla La Mancha, Ciudad Real,

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#### **Nanometer Structured Epitaxial Films and Foliated Layers Based on Bismuth and Antimony Chalcogenides with Topological Surface States Nanometer Structured Epitaxial Films and Foliated Layers Based on Bismuth and Antimony Chalcogenides with Topological Surface States**

Lidia N. Lukyanova, Yuri A. Boikov, Oleg A. Usov, Mikhail P. Volkov and Viacheslav A. Danilov Lidia N. Lukyanova, Yuri A. Boikov, Oleg A. Usov, Mikhail P. Volkov and Viacheslav A. Danilov

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

http://dx.doi.org/10.5772/65750

#### **Abstract**

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The thermoelectric and galvanomagnetic properties of nanometer structured epitaxial films and foliated layers based on bismuth and antimony chalcogenides were investi‐ gated, and an increase in the figure of merit Z up to 3.85 × 10‐3 K‐1 was observed in the Bi0.5Sb1.5Te3 films over the temperature range of 180–200 K. It is shown that an increase in the Seebeck coefficient and the change in the slope on temperature, associated with changes in the effective scattering parameter of charge carriers and strong anisotropy of scattering in the films, lead to enhance power factor due to the growth of the effective mass of the density of states. These features are consistent with the results of research of oscillation effects in strong magnetic fields at low temperatures and research of Raman scattering at normal and high pressures in the foliated layers of solid solutions (Bi, Sb)2(Te, Se)3, in which the topological Dirac surface states were observed. The unique properties of topological surface states in the investigated films and layers make topological insulators promising material for innovation nanostructured thermoelec‐ trics.

**Keywords:** thermoelectric films, topological surface states, power factor, scattering on interphase, block boundaries

## **1. Introduction**

Thermoelectrics based on bismuth and antimony chalcogenides are well known and have been extensively studied for their excellent thermoelectric properties [1–3]. Recently, the nanostruc‐

© 2017 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. © 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.

tured (Bi,Sb)2(Te,Se)3 epitaxial films were shown to possess an enhanced thermoelectric figure of merit Z compared to corresponding bulk crystals due to mechanical stresses and intensive phonon scattering at the grain boundaries. Lattice thermal conductivity of heteroepitaxial nanostructured films may be substantially diminished, as compared to corresponding bulk crystals, due to acoustic phonon scattering by grain and interface boundaries. Boundaries and strain may be easily induced in thin Bi2Te3‐based films grown on mismatched substrates. In contrast to point defects, which suppress heat transfer by short wave phonons, grain and interface boundaries are efficient in scattering of long wave ones. That is why, investigation of thin films with different structure and level of mechanical stresses looks quite important for development of thermoelectric materials with enhanced performance.

At the current stage, a new property of these materials, known as topological insulator, became one of the important subjects of the investigations [4–6]. These novel quantum states are the result of the electronic band inversion due to strong spin‐orbit interaction, so the bulk becomes insulating and the surface displays an unusual metallic electronic surface state of Dirac fermions with linear dispersion and spin texture that ensures high mobility of charge carriers due to the lack of backscattering on defects. The nanostructured films of topological materials [7, 8] theoretically proved the possibility of formation of topological excitons that can condense in a wide temperature range with the appearance of superfluidity and thus a significant increase in the mobility of the charge carriers. Currently, there is only a preliminary report on the pilot study of the heterostructure Sb2Te3/Bi2Te3, which assumes the realization of exciton condensation [9]. The theoretical model [10] for topological thermoelectrics based on the Landauer transport theory shows that the value of the Seebeck coefficient and thermoelectric efficiency is determined by the ratio of the mean free path of Dirac fermions to the mean free path of bulk electrons. According to the proposed model, an increase in the contribution of the surface states and the energy dependence of the lifetime of the electronic states provide the maximum amount of the Seebeck coefficient and the increase in the thermoelectric efficiency. Experimental research of transport of thin films (Bi1‐xSbx)2Te3 [11] carried out in a wide range of compositions, and temperatures have confirmed validity of this model. It follows that the study of surface states of Dirac fermions is promising for thermoelectricity to improve the energy conversion efficiency of nanostructured thermoelectrics. This chapter includes the thermoelectric properties under normal conditions and under high pressure, galvanomagnetic and optical properties of nanostructured films based on Bi2Te3, obtained by different methods, in order to determine the possible effect of the topological surface states of Dirac fermions depending on the composition, the Seebeck coefficient and temperature.

## **2. Features of formation and structure of the grown (Bi,Sb)2Te3 films**

Because of incongruent evaporation/sublimation of (Bi,Sb)2Te3 solid solutions and pronounced volatility of tellurium at temperatures higher than 400°C, formation of stoichiometric epitaxial films of bismuth and antimony chalcogenides is a nontrivial task. Hot wall technique [12, 13] was used to grow stoichiometric Bi0.5Sb1.5Te3 layers with a thickness of 30–500 nm.

Structure of the grown thermoelectric films was investigated by X‐ray (Philips X'pert MRD, CuKα1, ω/2Θ‐ and φ‐scans). Surface morphology of the grown (Bi,Sb)2Te3 films was studied by atomic force microscopy (Nanoscope IIIa, tipping mode). Nanostructured epitaxial thermo‐ electric films of (Bi,Sb)2Te3 were grown by hot wall technique on mica (muscovite) substrates. Usage of a mica substrate promotes small in‐plane misorientation of the blocks in the BST film, but relatively high deposition temperature is in a favor of low density of defects in their volume. Thickness of the grown thermoelectric layers was in the range of 30–500 nm. Substrate temperature during thermoelectric film formation was roughly 70°C less then temperature of sublimating stoichiometric Bi0.5Sb1.5Te3 burden. X‐ray ω/2Θ scans were traced for the grown Bi0.5Sb1.5Te3 films when plane including incident and reflected Roentgen beams was in plane normal to (000.1) of mica or (101.5) of the thermoelectric layer (see **Figures 1** and **2**). From obtained scans follow that c‐axis in the (Bi,Sb)2Te3 films grown on mica by hot wall technique was normal to substrate plane. Driving force for preferential orientation of c‐axis in the grown films along normal to a substrate plane was substantial anisotropy of a surface free energy of the bismuth and antimony chalcogenides. From X‐ray, φ*‐*scan traced for a (101.5) Bi0.5Sb1.5Te3 reflex, see insert in **Figure 1**, follows that thermoelectric films grown on mica were well in‐ plane preferentially oriented as well. In‐plane disorientation of blocks in the films was ∼0.3°. (The estimation obtained from full width at half of a maximum of a peak on the φ**‐**scan. Roughly, equidistant system of growth steps was clear detectable at the film surface (see **Figure 2**), at AFM image of free surface of the (Bi,Sb)2Te3 film grow on mica. Height of the growth steps was about 1 nm.

tured (Bi,Sb)2(Te,Se)3 epitaxial films were shown to possess an enhanced thermoelectric figure of merit Z compared to corresponding bulk crystals due to mechanical stresses and intensive phonon scattering at the grain boundaries. Lattice thermal conductivity of heteroepitaxial nanostructured films may be substantially diminished, as compared to corresponding bulk crystals, due to acoustic phonon scattering by grain and interface boundaries. Boundaries and strain may be easily induced in thin Bi2Te3‐based films grown on mismatched substrates. In contrast to point defects, which suppress heat transfer by short wave phonons, grain and interface boundaries are efficient in scattering of long wave ones. That is why, investigation of thin films with different structure and level of mechanical stresses looks quite important for

At the current stage, a new property of these materials, known as topological insulator, became one of the important subjects of the investigations [4–6]. These novel quantum states are the result of the electronic band inversion due to strong spin‐orbit interaction, so the bulk becomes insulating and the surface displays an unusual metallic electronic surface state of Dirac fermions with linear dispersion and spin texture that ensures high mobility of charge carriers due to the lack of backscattering on defects. The nanostructured films of topological materials [7, 8] theoretically proved the possibility of formation of topological excitons that can condense in a wide temperature range with the appearance of superfluidity and thus a significant increase in the mobility of the charge carriers. Currently, there is only a preliminary report on the pilot study of the heterostructure Sb2Te3/Bi2Te3, which assumes the realization of exciton condensation [9]. The theoretical model [10] for topological thermoelectrics based on the Landauer transport theory shows that the value of the Seebeck coefficient and thermoelectric efficiency is determined by the ratio of the mean free path of Dirac fermions to the mean free path of bulk electrons. According to the proposed model, an increase in the contribution of the surface states and the energy dependence of the lifetime of the electronic states provide the maximum amount of the Seebeck coefficient and the increase in the thermoelectric efficiency. Experimental research of transport of thin films (Bi1‐xSbx)2Te3 [11] carried out in a wide range of compositions, and temperatures have confirmed validity of this model. It follows that the study of surface states of Dirac fermions is promising for thermoelectricity to improve the energy conversion efficiency of nanostructured thermoelectrics. This chapter includes the thermoelectric properties under normal conditions and under high pressure, galvanomagnetic and optical properties of nanostructured films based on Bi2Te3, obtained by different methods, in order to determine the possible effect of the topological surface states of Dirac fermions

development of thermoelectric materials with enhanced performance.

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

depending on the composition, the Seebeck coefficient and temperature.

**2. Features of formation and structure of the grown (Bi,Sb)2Te3 films**

was used to grow stoichiometric Bi0.5Sb1.5Te3 layers with a thickness of 30–500 nm.

Because of incongruent evaporation/sublimation of (Bi,Sb)2Te3 solid solutions and pronounced volatility of tellurium at temperatures higher than 400°C, formation of stoichiometric epitaxial films of bismuth and antimony chalcogenides is a nontrivial task. Hot wall technique [12, 13]

**Figure 1.** X‐ray ω/2Θ scan traced for the grown Bi0.5Sb1.5Te3 film when plane including incident and reflected Roentgen beams was in plane normal to (000.1) plane of substrate. Insert plots φ‐scan of a (101.5) reflex from the same film.

**Figure 2.** X‐ray ω/2Θ scan traced for the grown Bi0.5Sb1.5Te3 film when plane including incident and reflected Roentgen beams was normal to (101.5) plane of the thermoelectric layer. AFM image of free surface of the grown thermoelectric layer is shown on insert.

#### **3. Thermoelectric properties**

Efficiency of thermoelectric energy conversion is dependent on figure of merit (*Z*) of the used materials (Z = *S*<sup>2</sup>  σ*/κ*, where S—Seebeck coefficient, σ—electrical conductivity, and *κ*—thermal conductivity) with electron and hole conductance. Thermoelectric properties of bismuth telluride and related solid solution Bi0.5Sb1.5Te3 heteroepitaxial nanostructured films were investigated below room temperature. The temperature dependences of the Seebeck coefficient S and the electroconductivity σ of the Bi2Te3 and Bi0.5Sb1.5Te3 films are shown in **Figure 3**. The electrical conductivity of bulk samples grows more sharply with temperature decrease for both Bi2Te3 and Bi0.5Sb1.5Te3 solid solution than for films (**Figure 3**, curves 6, 8 and 5, 7). The observed decrease in electrical conductivity in the films is related to the influence of scattering on interphase and intercrystallite grain boundaries.

The temperature dependences of the Seebeck coefficient (**Figure 3**), unlike such electrical conductivity dependences, are located higher for films than for bulk Bi2Te3 (curves 1, 2) and Bi0.5Sb1.5Te3 (curves 3, 4). The highest power factor values were obtained in submicrometer Bi0.5Sb1.5Te3 film at S = 242 μV K‐1 over the temperature range of 80–300 K and in the Bi0.5Sb1.5Te3 film at S = 234 μV K‐1 over the range of 130–260 K (**Figure 4**, curves 5, 3). An enhancement of the Seebeck coefficient and change in its temperature dependence slope both indicate the changes of charge carrier scattering mechanisms in grown films [14, 15] compared those to the bulk thermoelectric materials (**Figure 4**, curves 1–5 and curves 6–9).

**Figure 3.** Temperature dependences of the Seebeck coefficient S (1–9), electroconductivity σ (10–18) in heteroepitaxial films (1–5, 10–14), and bulk samples (6–9 and 15–18) of Bi0.5Sb1.5Te3 (1–3, 6–9, 10–12, 16–18) and Bi2Te3 (4, 5, 13, 14).

**Figure 2.** X‐ray ω/2Θ scan traced for the grown Bi0.5Sb1.5Te3 film when plane including incident and reflected Roentgen beams was normal to (101.5) plane of the thermoelectric layer. AFM image of free surface of the grown thermoelectric

Efficiency of thermoelectric energy conversion is dependent on figure of merit (*Z*) of the used

conductivity) with electron and hole conductance. Thermoelectric properties of bismuth telluride and related solid solution Bi0.5Sb1.5Te3 heteroepitaxial nanostructured films were investigated below room temperature. The temperature dependences of the Seebeck coefficient S and the electroconductivity σ of the Bi2Te3 and Bi0.5Sb1.5Te3 films are shown in **Figure 3**. The electrical conductivity of bulk samples grows more sharply with temperature decrease for both Bi2Te3 and Bi0.5Sb1.5Te3 solid solution than for films (**Figure 3**, curves 6, 8 and 5, 7). The observed decrease in electrical conductivity in the films is related to the influence of scattering

The temperature dependences of the Seebeck coefficient (**Figure 3**), unlike such electrical conductivity dependences, are located higher for films than for bulk Bi2Te3 (curves 1, 2) and Bi0.5Sb1.5Te3 (curves 3, 4). The highest power factor values were obtained in submicrometer Bi0.5Sb1.5Te3 film at S = 242 μV K‐1 over the temperature range of 80–300 K and in the Bi0.5Sb1.5Te3 film at S = 234 μV K‐1 over the range of 130–260 K (**Figure 4**, curves 5, 3). An

 σ*/κ*, where S—Seebeck coefficient, σ—electrical conductivity, and *κ*—thermal

layer is shown on insert.

materials (Z = *S*<sup>2</sup>

**3. Thermoelectric properties**

on interphase and intercrystallite grain boundaries.

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

**Figure 4.** Temperature dependences of power factor S2 σ for heteroepitaxial films (1–5) and bulk samples (6–9) of Bi0.5Sb1.5Te3 (1–3, 6–9) and Bi2Te3 (4, 5) for S (μV K‐1) at room temperatures: 1—214, 2—224, 3—242, 4—203, 5—234, 6— 214, 7—207, 8—233, 9—221.

The results of the study of galvanomagnetic and thermoelectric properties in epitaxial films have been used to determine the average effective mass of the density of states m/m0 and mobility μ0 of charge carriers taking into account the effective scattering parameter in the model with an isotropic relaxation time similar to the bulk thermoelectrics [14, 16, 17]. Calculations of the effective mass m/m0 and mobility m0 have showed that the effective mass of the films is higher than in the bulk samples (**Figure 5**, curves 1–5 and 6, 7) with slight reduction of the mobility in the films (**Figure 5**, curves 13, 14). From the study of the galvano‐ magnetic properties, the behavior of the effective mass and mobility in the films was found to depend on the scattering mechanism of charge carriers and the parameters of the ellipsoidal constant energy surfaces [13, 18].

**Figure 5.** Temperature dependences of the density‐of‐states effective mass m/m0 (1–7) and charge carrier mobilitym0 (8–14) for films (1–5, 8–12) and bulk samples (6, 7, 13, 14) of Bi0.5Sb1.5Te3 (1–3, 6–7, 8–10, 13–14) and Bi2Te3 (4, 5, 11, 12).

The product (m/m0) 3/2μ0, proportional to the figure of merit Z, is higher for films than bulk thermoelectrics due to growth of the effective mass of the density states, which determines an increase in power factor of the films (**Figure 6**). At temperatures below 200 K, an increase in the (m/m0) 3/2μ0 was observed in the solid solution Bi0.5Sb1.5Te3 at a value of the Seebeck coefficient S = 242 μV K‐1 at room temperature (**Figure 6**, curve 3).

An estimated value of the figure of merit Z in heteroepitaxial Bi0.5Sb1.5Te3 film increases to 3.85 × 10‐3 K‐1 over the temperature range of 180–200 K. Such increase in Z is approximately by 60% compared to conventional bulk materials and by 20% compared with multicomponent bulk thermoelectrics optimized for temperatures below 200 K [19, 20]. Reduction in thermal conductivity in the Bi0.5Sb1.5Te3 films can reach 20–30% due to additional scattering of charge carriers in the intercrystallite and interphase boundaries [3, 21] that give an additional rise in the figure of merit.

Nanometer Structured Epitaxial Films and Foliated Layers Based on Bismuth and Antimony Chalcogenides... http://dx.doi.org/10.5772/65750 225

**Figure 6.** Temperature dependence of the (m/m0) 3/2 μ0 parameter for films (1–5) and bulk samples (6, 7) of Bi0.5Sb1.5Te3 (1–3, 5–7) and Bi2Te3 (4).

#### **4. Mechanisms of charge carriers scattering**

The results of the study of galvanomagnetic and thermoelectric properties in epitaxial films have been used to determine the average effective mass of the density of states m/m0 and mobility μ0 of charge carriers taking into account the effective scattering parameter in the model with an isotropic relaxation time similar to the bulk thermoelectrics [14, 16, 17]. Calculations of the effective mass m/m0 and mobility m0 have showed that the effective mass of the films is higher than in the bulk samples (**Figure 5**, curves 1–5 and 6, 7) with slight reduction of the mobility in the films (**Figure 5**, curves 13, 14). From the study of the galvano‐ magnetic properties, the behavior of the effective mass and mobility in the films was found to depend on the scattering mechanism of charge carriers and the parameters of the ellipsoidal

**Figure 5.** Temperature dependences of the density‐of‐states effective mass m/m0 (1–7) and charge carrier mobilitym0 (8–14) for films (1–5, 8–12) and bulk samples (6, 7, 13, 14) of Bi0.5Sb1.5Te3 (1–3, 6–7, 8–10, 13–14) and Bi2Te3 (4, 5, 11, 12).

thermoelectrics due to growth of the effective mass of the density states, which determines an increase in power factor of the films (**Figure 6**). At temperatures below 200 K, an increase in

An estimated value of the figure of merit Z in heteroepitaxial Bi0.5Sb1.5Te3 film increases to 3.85 × 10‐3 K‐1 over the temperature range of 180–200 K. Such increase in Z is approximately by 60% compared to conventional bulk materials and by 20% compared with multicomponent bulk thermoelectrics optimized for temperatures below 200 K [19, 20]. Reduction in thermal conductivity in the Bi0.5Sb1.5Te3 films can reach 20–30% due to additional scattering of charge carriers in the intercrystallite and interphase boundaries [3, 21] that give an additional rise in

coefficient S = 242 μV K‐1 at room temperature (**Figure 6**, curve 3).

3/2μ0, proportional to the figure of merit Z, is higher for films than bulk

3/2μ0 was observed in the solid solution Bi0.5Sb1.5Te3 at a value of the Seebeck

constant energy surfaces [13, 18].

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

The product (m/m0)

the figure of merit.

the (m/m0)

The charge carrier scattering mechanisms of Bi2Te3 and solid solution Bi0.5Sb1.5Te3 films were investigated from analysis of the galvanomagnetic coefficients including transverse and longitudinal components of magnetoresistivity tensor rijkl, electroresistivity rij, and Hall coefficient rijk within many‐valley model of energy spectrum for isotropic scattering mecha‐ nism [14, 18, 22]. A relaxation time for isotropic carrier scattering depends on energy E by power law: τ = τ0 Er , where τ0 is an energy independent factor and r is the scattering parameter. The least square analysis of experimental galvanomagnetic coefficients for isotropic scattering mechanism permits to determine the degeneracy parameter βd [13, 15]. The dependence of βd on temperature obtained in magnetic field at B = 10 T is in agreement with that at B = 14 T (**Figure 7**, curves 1, 2).

The parameter βd depends on temperature more sharply in the film than in the bulk Bi2‐xSbxTe3 solid solutions (**Figure 7**, points 3, 4). The temperature dependence of the βd of the films is supposed to be explained by an additional charge carrier scattering on interphase and inter‐ crystallite boundaries of monocrystalline grains of the films. As shown in **Figure 8**, the depend‐ ence of the degeneracy parameter βd on the reduced Fermi level η shows that the βd values in films are less than in bulk materials. Therefore, the degeneracy of films is smaller than bulk thermoelectrics [13].

The effective scattering parameter reff and the reduced Fermi level η were calculated by Nelder‐ Mead least square method from the temperature dependences of the degeneracy parameter βd and the Seebeck coefficient S [14, 24]. As compared to bulk materials, the values of the parameter reff are considerably different from the value r = ‐0.5, specific for an acoustic phonon scattering mechanism due to sharper energy dependence of electron relaxation time in the films, that is, explained by an additional charge carriers scattering on interphase and inter‐ crystallite boundaries of epitaxial films (**Figure 8**).

**Figure 7.** Temperature dependence of the degeneracy parameter βd (1–2) in the Bi0.5Sb1.5Te3 film. βd is (1) 10 T and (2) 14  T. Points for bulk solid solutions: 3 [23], 4 [14].

**Figure 8.** The degeneracy parameter βd (1–6) and the effective scattering parameter reff (7–12) on reduced Fermi level η in Bi2Te3 (1, 7), Bi0.5Sb1.5Te3 (2, 8) films, and Bi2‐xSbxTe3‐ySey (x = 1.2, y = 0.09), (3, 4, 9, 10); Bi2‐xSbxTe3‐ySey (x = 1.3, y = 0.07), (5, 11); Bi2‐xSbxTe3 (x = 1.6), (6, 12) bulk solid solutions.

The materials under study exhibit both anisotropy of the transport properties and anisotropy of charge carrier scattering. In a six‐valley model of the energy spectrum with anisotropic scattering of charge carriers, the components of the relaxation time tensor () can be presented as <sup>=</sup> ϕ() where ϕ(ε) is an isotropic function depending on μ and τij is an anisotropic multiplier that is independent on energy. The ratios of the () tensor components were determined in the temperature interval from 10 to 300 K [15, 17, 25, 26]. The relation between the τ (ε) components was found as follows: τ22 > τ11 > τ33, and charge carrier scattering along bisector directions was dominant in the film as in the bulk thermoelectrics at low temperatures [17, 25, 27]. The ratio τ22/τ11 in the Bi2‐xSbxTe3 film is increased along bisector axes, but the ratio τ33/τ11 is diminished along the trigonal direction in contrast to corresponding bulk thermoelectrics at low [17, 25] and room [27] temperatures. The value τ23 is near the same as τ11 for the films, while for bulk materials τ23 is less than τ11. These specific features of charge carriers scattering lead to increase in the slope of the Seebeck coefficient dependence on temperature (**Figure 3**) and to enhance the thermoelectric power factor for films. Optimization of structure and charge state of the grains and/or interface boundaries might be in favor of a large thermoelectric power factor and figure of merit.

## **5. Thermoelectric properties under high pressure**

**Figure 7.** Temperature dependence of the degeneracy parameter βd (1–2) in the Bi0.5Sb1.5Te3 film. βd is (1) 10 T and (2) 14 

**Figure 8.** The degeneracy parameter βd (1–6) and the effective scattering parameter reff (7–12) on reduced Fermi level η in Bi2Te3 (1, 7), Bi0.5Sb1.5Te3 (2, 8) films, and Bi2‐xSbxTe3‐ySey (x = 1.2, y = 0.09), (3, 4, 9, 10); Bi2‐xSbxTe3‐ySey (x = 1.3, y = 0.07),

The materials under study exhibit both anisotropy of the transport properties and anisotropy of charge carrier scattering. In a six‐valley model of the energy spectrum with anisotropic scattering of charge carriers, the components of the relaxation time tensor () can be presented as <sup>=</sup> ϕ() where ϕ(ε) is an isotropic function depending on μ and τij is an anisotropic multiplier that is independent on energy. The ratios of the () tensor components

T. Points for bulk solid solutions: 3 [23], 4 [14].

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

(5, 11); Bi2‐xSbxTe3 (x = 1.6), (6, 12) bulk solid solutions.

The thermoelectric properties of *n‐*Bi2Te3‐*x‐y*Se*x*S*y* solid solutions with atomic substitutions in the tellurium sublattice at (*x* = 0.27, 0.3, *y* = 0, and *x* = *y* = 0.09) and p‐Bi2Te3 were studied under pressure of 8 GPa on submicron layer samples at room temperature using the technique described in Ref. [28–30]. It was found that the Seebeck coefficient decreases and the electro‐ conductivity increases with increasein pressure, but the power factor S2 σ increases for all compositions, and becomes maximum at pressures of 3–4 GPa (**Figure 9**). The effective mass m/m0 and mobility μ0 in the *n‐*Bi2Te3‐*x‐y*Se*x*S*y* and p‐Bi2Te3 films were obtained taking into account of the change in the scattering mechanism depending on the solid solution composi‐ tion and carrier density [14, 31]. With increasing pressure *P*, the effective mass m/m0 [29] in the n‐ and p‐type compositions decreases (**Figure 10**). For *p‐*Bi2Te3 and for composition at x =  y = 0.09, the dependence of m/m0 and μ0 on *P* has an inflection at pressures about 3–4 GPa [29, 30]. These inflections in the dependences of m/m0 and μ0 on *P*, observed at nearly the same pressure as for the maximum value of power factor S2 σ, were explained by the influence of topological phase transition at room temperature (**Figure 10**, curves 3, 7).

The existence of the topological transition in Bi2Te3 is confirmed by precise diffraction studies of the pressure dependence of lattice parameters [32], abrupt change in the elasticity modulus and its derivative [33], and the change in the Fermi surface section from study of de Haas‐van Alphen [32, 34]. This topological transition in Bi2Te3 was also confirmed by study of Raman spectroscopy under high pressure [35]. The maximum of the product (m/m0) 3/2μ0, proportional to the figure of merit, was observed at about the same pressure range as for the topological transition (**Figure 11**). The estimations of the thermal conductivity κ in the *n*‐ and *p*‐type materials show that increase in κ in the pressure range ∼3–4 GPa is not higher than 50% [36]. But the power factor of *n‐*Bi2Te3‐x‐ySexSy solid solutions and the p‐type compositions Bi2‐*x*Sb*x*Te3 [29] increases under pressure more significantly, and thus, enhancement of the figure of merit values can reach 50–70% taking into account the influence of topological transition at room temperature.

**Figure 9.** Pressure dependences of power factor of the *n‐*Bi2Te3‐*x‐y*Se*x*S*y* solid solution layers; *x*, *y* are (1) 0.27, 0; (2) 0.3, 0; (3) 0.09, 0.09 and p‐Bi2Te3 (4).

**Figure 10.** Pressure dependences of the effective mass m/m0 and the mobility μ0 of the *n‐*Bi2Te3‐*x‐y*Se*x*S*y* solid solutions; *x*, *y* are (1, 5) 0.27, 0; (2, 6) 0.3, 0; (3, 7) 0.09, 0.09 and p‐Bi2Te3 (4, 8).

**Figure 11.** Pressure dependences of the product (m/m0) 3/2μ0 of the *n*‐Bi2Te3‐*x‐y*Se*x*S*y* solid solutions; *x*, *y* are (1) 0.27, 0; (2) 0.3, 0; (3) 0.09, 0.09 and p‐Bi2Te3 (4).

## **6. Quantum oscillations of magnetoresistance**

**Figure 9.** Pressure dependences of power factor of the *n‐*Bi2Te3‐*x‐y*Se*x*S*y* solid solution layers; *x*, *y* are (1) 0.27, 0; (2) 0.3, 0;

**Figure 10.** Pressure dependences of the effective mass m/m0 and the mobility μ0 of the *n‐*Bi2Te3‐*x‐y*Se*x*S*y* solid solutions; *x*,

3/2μ0 of the *n*‐Bi2Te3‐*x‐y*Se*x*S*y* solid solutions; *x*, *y* are (1) 0.27, 0; (2)

*y* are (1, 5) 0.27, 0; (2, 6) 0.3, 0; (3, 7) 0.09, 0.09 and p‐Bi2Te3 (4, 8).

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

**Figure 11.** Pressure dependences of the product (m/m0)

0.3, 0; (3) 0.09, 0.09 and p‐Bi2Te3 (4).

(3) 0.09, 0.09 and p‐Bi2Te3 (4).

Quantum oscillations of the magnetoresistance associated with surface electronic states in three‐dimensional topological insulators have been studied in *p‐*type Bi2Te3 films [37] in strong magnetic fields from 6 to 14 T at low temperatures (**Figure 12**). The main parameters of surface charge carriers in the films (**Tables 1** and **2**) were determined by analyzing the temperature dependences of normalized amplitude of magnetoresistance oscillations [38]. The phase shift of oscillation period, evaluated by extrapolation of dependence of the Landau level indexes (n = 2, 3, 4, 5) (**Figure 12**) on inverse magnetic field in the limit of 1/B = 0, was found to be consistent with the value of π Berry phase, which is characteristic of surface states of Dirac fermions with linear dispersion [37]. The obtained parameters of the surface states of charge carriers in the nanostructured materials under consideration are important for the develop‐ ment of new high‐performance thermoelectrics. The parameters of the surface states of Dirac fermions, such as the mean free path and the energy dependence of lifetime of the charge carriers at the surface, the Fermi energy and respective position of the Fermi level, have a specific influence on the Seebeck coefficient and power factor.

**Figure 12.** Magnetoresistance dependence ρxx (1–3) on magnetic field B and quantum oscillations Δρxx(4–6) dependence on inverse magnetic field 1/B; ρxx at the temperatures: 1, 4–1.6 K, 2, 5–4.2 K, 3, 6–10 K and the Landau level index (*n* = 2, 3, 4, 5) corresponding to the minimum amplitudes of the oscillations.


**Table 1.** Cyclotron resonance frequency *ν*, Fermi velocity *v*F, Fermi energy *EF*, charge carrier mobility *μ*, mean free path of charge carriers *lF*, the relaxation time *τ*, and Dingle temperature *TD* of the Bi2Te3 films.


**Table 2.** Frequency of quantum oscillations of the magnetoresistance *F*, cross section of the Fermi surface *S*(*kF*), Fermi wave vector *kF*, and surface concentration of charge carriers *nFs* in the Bi2Te3 films.

#### **7. Raman spectra**

The resonance Raman scattering and morphology of an interlayer van der Waals surface (0001) in thin layer films of chalcogenides based on bismuth and antimony were studied in depend‐ ence on the composition, the Seebeck coefficient, and the thickness of the samples. Raman spectra of optical phonons Eg 2 , A1u2 , and A1g2 in thin layers of binary compound *n*‐Bi2Te3 and alloys Bi2Te3‐ySey, Bi2‐xSbxTe3‐ySey, in heteroepitaxial films of *p*‐Bi2Te3 and chemically foliated solid solutions Bi2‐xSbxTe3‐ySey are shown in **Figures 13** and **14**. The morphology of the interlayer surfaces (0001) of these samples was studied by atomic force microscopy.

**Figure 13.** Raman spectra of mechanically split thin layers of n‐Bi2Te3 (1‐1, 1‐2), n‐Bi2Te2.88Se0.12 (2‐1, 2‐2) and n‐ Bi2Te2.7Se0.3 (3‐1, 3‐2, 4‐1, 4‐2). (1‐1, 1‐2): S = ‐270 μV K‐1, Rq = 0.45 nm, Ha = 1.75 nm. (2‐1, 2‐2): S = ‐285 μV K‐1, Rq = 3.8 nm, Ha = 8 nm. (3‐1, 3‐2): S = ‐305 μV K‐1, Rq = 4.6 nm, Ha = 15 nm. (4‐1, 4‐2): S = ‐315 μV K‐1, Rq = 2.9 nm, Ha = 2.3 nm.

Nanometer Structured Epitaxial Films and Foliated Layers Based on Bismuth and Antimony Chalcogenides... http://dx.doi.org/10.5772/65750 231

*F***, T** *S(kF)***, nm‐2** *kF***, nm** *nFs***× 1012, cm‐2**

**Table 2.** Frequency of quantum oscillations of the magnetoresistance *F*, cross section of the Fermi surface *S*(*kF*), Fermi

The resonance Raman scattering and morphology of an interlayer van der Waals surface (0001) in thin layer films of chalcogenides based on bismuth and antimony were studied in depend‐ ence on the composition, the Seebeck coefficient, and the thickness of the samples. Raman

alloys Bi2Te3‐ySey, Bi2‐xSbxTe3‐ySey, in heteroepitaxial films of *p*‐Bi2Te3 and chemically foliated solid solutions Bi2‐xSbxTe3‐ySey are shown in **Figures 13** and **14**. The morphology of the

**Figure 13.** Raman spectra of mechanically split thin layers of n‐Bi2Te3 (1‐1, 1‐2), n‐Bi2Te2.88Se0.12 (2‐1, 2‐2) and n‐ Bi2Te2.7Se0.3 (3‐1, 3‐2, 4‐1, 4‐2). (1‐1, 1‐2): S = ‐270 μV K‐1, Rq = 0.45 nm, Ha = 1.75 nm. (2‐1, 2‐2): S = ‐285 μV K‐1, Rq = 3.8 nm,

Ha = 8 nm. (3‐1, 3‐2): S = ‐305 μV K‐1, Rq = 4.6 nm, Ha = 15 nm. (4‐1, 4‐2): S = ‐315 μV K‐1, Rq = 2.9 nm, Ha = 2.3 nm.

in thin layers of binary compound *n*‐Bi2Te3 and

, and A1g2

interlayer surfaces (0001) of these samples was studied by atomic force microscopy.

24 0.23 0.27 0.58 30 [39] 0.29 0.30 0.72 41.7 [40] 0.40 0.36 1.0 50 [39] 0.48 0.39 1.21

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

wave vector *kF*, and surface concentration of charge carriers *nFs* in the Bi2Te3 films.

2 , A1u2

**7. Raman spectra**

spectra of optical phonons Eg

**Figure 14.** Raman spectra of the thin films of n‐Bi1.6Sb0.4Te2.91Se0.09 (5‐1, 5‐2), p‐Bi2Te3 (6‐1, 6‐2) and foliated Bi0.9Sb1.1Te2.94Se0.06 (7‐1, 7‐2) solid solution. (5‐1, 5‐2): S = ‐280 μV K‐1, Rq = 0.36 nm, Ha = 1.55 nm. (6‐1, 6‐2): Rq = 0.56 nm, Ha = 1.8 nm. (7‐1, 7‐2): S = ‐280 μV K‐1. (7‐1) dissolution time t = 150 h, Rq = 36 nm, Ha = 180 nm. (7‐2) t = 200 h, Rq = 26 nm, Ha = 80 nm.

The roughness Rq and Ha corresponding to the maximum of the distribution function of nanofragment heights on the surface of samples [41] are indicated in the captions of **Figures 13** and **14**.

The appearance of the inactive phonons A1u2 in the Raman spectra, caused by a violation of the inversion symmetry of the crystal, was revealed at decreasing sample thickness and also at high pressure for which topological phase transition in Bi2Te3 [35] was observed. Therefore, the occurrence of the A1u2 was explained by the behavior of surface electronic states of Dirac fermions [42, 43]. The relative intensities I(A1u2 )/I(Eg 2 ) have maximal values in the most thin layers of solid solutions of n‐Bi2Te2.7Se0.3, n‐Bi1.6Sb0.4Te2.91Se0.09, and epitaxial film of the p‐B2Te3 with high Seebeck coefficients (**Figure 15**) with high quality of the interlayer (0001) surface with small roughness Rq and Ha values (**Figures 13** and **14**). In the samples n‐Bi2Te2.88Se0.12, prepared by the Czochralski technique and by the chemical foliated p‐Bi0.9Sb1.1Te2.94S0.06 the ratio I(A1u2 )/I(Eg2), is quite lower (**Figure 15**, curves 2, 7). So the ratio I(A1u2 )/I(Eg2) is strongly affected by the used technology, composition and thickness of the samples. The analysis of the Raman spectra of bismuth telluride and its solid solutions allows to optimize the Seebeck coefficients, composition, sample thickness, and morphology of the surface, which provide the significant role of surface states of Dirac fermions at room temperature.

**Figure 15.** The dependence of the relative intensities I(A1u2 )/I(Eg 2 ) on the thickness of the layers of n‐Bi2Te3 (1), n‐ Bi2Te2.88Se0.12 (2), n‐Bi2Te2.7Se0.3 (3, 4), n‐Bi1.6Sb0.4Te2.91Se0.09 (5), p‐Bi2Te3 (6), and p‐Bi0.9Sb1.1Te2.94Se0.06 (7).

#### **8. Conclusion**

The thermoelectric and galvanomagnetic properties of heteroepitaxial films based on bismuth telluride, grown by the hot wall epitaxy method, were investigated. The highest power factor was obtained in the Bi0.5Sb1.5Te3 films. An enhancement of the Seebeck coefficient and change in its temperature dependence slope both indicate the variation in the charge carrier scattering mechanisms compared to the bulk thermoelectric materials. The increase in the power factor and (m/m0) 3/2μ0, associated with the increase in the effective mass of density of states m/m0, and the reduction in thermal conductivity lead to an increase in the figure of merit Z in the Bi0.5Sb1.5Te3 films up to 3.85 × 10‐3 K‐1 over the temperature range of 180–200 K. Such increase in Z is approximately more by 60% compared to similar bulk materials. The charge carrier scattering mechanisms of the Bi0.5Sb1.5Te3 films were investigated from the data on galvano‐ magnetic properties for isotropic and anisotropic scattering within many‐valley model of energy spectrum. For isotropic scattering, the degeneracy parameter βd, the effective scattering parameter reff**,** and the reduced Fermi level η were calculated. As compared to bulk materials, the values of the parameter reff are considerably different from r = ‐0.5, specific for an acoustic phonon scattering in the epitaxial films. The difference of the reff values is related to an additional charge carriers scattering on interphase and intercrystallite boundaries in the films.

The account of anisotropy of the carrier scattering mechanism has shown that scattering along bisector crystallographic axes is main as compared with corresponding bulk thermoelectrics. Revealed charge carrier scattering peculiarities affect transport properties of the films and might be in favor of a large thermoelectric power factor and the figure of merit.

The studies of the thermoelectric properties of the n‐Bi2Te3‐x‐ySexSy solid solutions under pressure have shown the increase in power factor and product (m/m0) 3/2μ0, which is determined by the growth of the effective mass m/m0. In the composition *n‐*Bi2Te3‐*x‐y*Se*x*S*y* (x = y = 0.09) and p‐Bi2Te3, the change in the slopes of the pressure dependence of the effective mass and the mobility in the range of 3–4 GPa are coincident with maximum of power factor and explained by an influence of the topological transition. An increase in the thermoelectric figure of merit, as compared to normal conditions, was estimated as 50–70% under pressure due to effect of the topological transitions.

Quantum oscillations of the magnetoresistance were revealed at low temperatures T below 10 K in the range of magnetic field from 6 to 14 T in nanostructured submicron Bi2Te3 films grown by hot wall technique. From the analysis of the magnetoresistance oscillations, the cyclotron resonance frequency, cross‐sectional Fermi surface, Landau level indexes and π Berry phase, effective cyclotron mass, Fermi wave vector, velocity and Fermi energy, surface charge carrier concentration, lifetime, and mobility of charge carriers were evaluated. The estimated parameters of topological electronic surface states of nanostructured chalcogenides of bismuth and antimony are of special interest for development of new high‐performance thermoelec‐ trics, because the Seebeck coefficient and hence power factor are significantly determined by the basic parameters such as charge carriers lifetime, the mean free path of charge carriers, and Fermi energy level position.

The resonance Raman scattering and morphology of the interlayer surface (0001) of bismuth and antimony chalcogenides were studied at room temperature depending on the composi‐ tion, the Seebeck coefficient, and the thickness of the layers. Raman shifts and the relative intensities of phonon modes were studied in mechanical and chemical foliated thin layers and epitaxial films of bismuth telluride and its solid solutions. The increase in relative intensity ratio of Raman inactive phonons I(A1u2 )/I(Eg 2 ), sensitive to the topological surface states, was observed for thin layers of n‐Bi2Te2.7Se0.3 and n‐Bi1.6Sb0.4Te2.91Se0.09 solid solutions at low carrier density with Seebeck coefficient values more than ‐280 μV K‐1 and in epitaxial p‐B2Te3 film grown by the hot wall method on mica with perfect interlayer surface. Thus, the resonance Raman spectra analysis allows to optimize the composition, thickness, Seebeck coefficient values, and morphology of the layers and films with enhanced contribution of the topological surface states at room temperature, which increases the prospects of application of these thermoelectrics.

## **Author details**

**Figure 15.** The dependence of the relative intensities I(A1u2

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

**8. Conclusion**

and (m/m0)

)/I(Eg 2

The thermoelectric and galvanomagnetic properties of heteroepitaxial films based on bismuth telluride, grown by the hot wall epitaxy method, were investigated. The highest power factor was obtained in the Bi0.5Sb1.5Te3 films. An enhancement of the Seebeck coefficient and change in its temperature dependence slope both indicate the variation in the charge carrier scattering mechanisms compared to the bulk thermoelectric materials. The increase in the power factor

and the reduction in thermal conductivity lead to an increase in the figure of merit Z in the Bi0.5Sb1.5Te3 films up to 3.85 × 10‐3 K‐1 over the temperature range of 180–200 K. Such increase in Z is approximately more by 60% compared to similar bulk materials. The charge carrier scattering mechanisms of the Bi0.5Sb1.5Te3 films were investigated from the data on galvano‐ magnetic properties for isotropic and anisotropic scattering within many‐valley model of energy spectrum. For isotropic scattering, the degeneracy parameter βd, the effective scattering parameter reff**,** and the reduced Fermi level η were calculated. As compared to bulk materials, the values of the parameter reff are considerably different from r = ‐0.5, specific for an acoustic phonon scattering in the epitaxial films. The difference of the reff values is related to an additional charge carriers scattering on interphase and intercrystallite boundaries in the films. The account of anisotropy of the carrier scattering mechanism has shown that scattering along bisector crystallographic axes is main as compared with corresponding bulk thermoelectrics. Revealed charge carrier scattering peculiarities affect transport properties of the films and

might be in favor of a large thermoelectric power factor and the figure of merit.

3/2μ0, associated with the increase in the effective mass of density of states m/m0,

Bi2Te2.88Se0.12 (2), n‐Bi2Te2.7Se0.3 (3, 4), n‐Bi1.6Sb0.4Te2.91Se0.09 (5), p‐Bi2Te3 (6), and p‐Bi0.9Sb1.1Te2.94Se0.06 (7).

) on the thickness of the layers of n‐Bi2Te3 (1), n‐

Lidia N. Lukyanova\* , Yuri A. Boikov, Oleg A. Usov, Mikhail P. Volkov and Viacheslav A. Danilov

\*Address all correspondence to: lidia.lukyanova@mail.ioffe.ru

Ioffe Institute, Saint Petersburg, Russia

## **References**


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


#### **Thermoelectric Power Generation by Clathrates Thermoelectric Power Generation by Clathrates**

Andrei V. Shevelkov Andrei V. Shevelkov

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

http://dx.doi.org/10.5772/65600

#### **Abstract**

Clathrate compounds combine aesthetic beauty of their crystal structures with promising thermoelectric properties that have made them one of the most explored family of compounds deemed as base for thermoelectric generators for mid- and hightemperature application. This chapter surveys crystal and electronic structure and structure-related transport properties of selected types of clathrates and discusses their thermoelectric performance and prospects of their future applications.

**Keywords:** thermoelectric materials, thermoelectric power generation, clathrates, phonon glass-electronic crystal, charge carrier transport, heat transport

## **1. Introduction**

No compound is able to outplay properly doped bismuth telluride as material for thermoelectric cooling. Since the pioneer works of A.F. Ioffe in the 1950, this material solely holds the position in the industry [1]. Situation is different, when it comes to thermoelectric power generation, where traditional materials based on Bi2Te3 are giving way to new state-of-the-art materials. Among the latter, there are clathrates; these compounds combine low, glass-like thermal conductivity with high electrical conductivity and Seebeck coefficient and are demanded as perspective thermoelectric materials that convert temperature gradient into electric power [2–4].

Clathrates are different from many other prospective materials for thermoelectric power generators, because they feature the spatial separation of two substructures known as host clathrate framework and rattling guests [4–6]. The framework is based on strong covalent bonds, four for each atom, that ensure effective transport of charge carriers leading to high values of both electrical conductivity and thermopower, whereas the rattling of guests inside oversized cages of the framework causes low thermal conductivity owing to either scattering

© 2017 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. © 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.

of heat-carrying phonons or reducing phonon group velocity due to avoided crossing of rattling modes and branches of acoustic phonons. The spatial host-guest separation provides the base for practical utilization of "phonon glass-electron crystal" (PGEC) concept introduced by Slack, according to which decoupling of heat and charge carriers transport enables their independent optimization [7]. But despite the spatial separation, thermal and charge carriers transport properties are not truly independent, which makes optimization of thermoelectric efficiency a very intricate and delicate task. Recent years have witnessed appreciable progress in enhancing thermoelectric efficiency of clathrates at mid- and high-temperature regions. The phonon engineering approaches, including introduction of rare earth guests and formation of complex superstructures, have led to extremely low thermal conductivity for narrow-gap clathrate semiconductors. New synthetic approaches have enabled accurate tuning of charge carriers' concentration by extremely precise doping, as well as providing very high densities of properly consolidated ceramic materials. Finally, new compositions of clathrates have emerged, that allow combination of reasonably high thermoelectric efficiency and utmost chemical and thermal stability. Already now, there are examples of clathrate compounds displaying high values of figure-of-merit, even surpassing unity at T > 470 K, and further progress is highly expected.

This chapter surveys recent progress in developing thermoelectric materials for power generation on the base of inorganic clathrate compounds. We consider crystal and electronic structures of these compounds, the underlying physics of their thermoelectric properties, synthetic methods of their preparation, and, as a central issue, their thermoelectric performance. Current achievements and future prospects are discussed.

## **2. Clathrates as inclusion compounds**

#### **2.1. Crystal structures**

Clathrates belong to plentiful class of inclusion compounds. Their discovery is traced back to the beginning of the nineteenth century, when Sir Davy observed formation of solid chlorine hydrate upon passing gaseous chlorine through water cooled to +5°C. Other hydrates came soon after, and by the middle of the twentieth century, quite a number of hydrates of various gases and liquids were discovered, and their crystal structures were solved. Despite clear differences in their chemical composition and crystal structures, these compounds shared a single common feature, which is complete sequestering of a guest moiety inside cages of framework. Another distinct feature of those compounds is the absence of strong host-guest bonds. In 1965 [8], Kasper, Hagenmuller, and Pouchard reported two new sodium silicides, whose crystal structures were identical to hydrates of various gases, proving that host-guest size matching had the primary role in their formation and stability, rather than the details of chemical bonding. Since then, almost three hundred compounds belonging to ten structure types were documented [3–5, 9]. They involve almost 50 chemical elements constituting more than 50% of all stable chemical elements (**Figure 1**).

**Figure 1.** "Clathrate Periodic Table."

of heat-carrying phonons or reducing phonon group velocity due to avoided crossing of rattling modes and branches of acoustic phonons. The spatial host-guest separation provides the base for practical utilization of "phonon glass-electron crystal" (PGEC) concept introduced by Slack, according to which decoupling of heat and charge carriers transport enables their independent optimization [7]. But despite the spatial separation, thermal and charge carriers transport properties are not truly independent, which makes optimization of thermoelectric efficiency a very intricate and delicate task. Recent years have witnessed appreciable progress in enhancing thermoelectric efficiency of clathrates at mid- and high-temperature regions. The phonon engineering approaches, including introduction of rare earth guests and formation of complex superstructures, have led to extremely low thermal conductivity for narrow-gap clathrate semiconductors. New synthetic approaches have enabled accurate tuning of charge carriers' concentration by extremely precise doping, as well as providing very high densities of properly consolidated ceramic materials. Finally, new compositions of clathrates have emerged, that allow combination of reasonably high thermoelectric efficiency and utmost chemical and thermal stability. Already now, there are examples of clathrate compounds displaying high values of figure-of-merit, even surpassing unity at T > 470 K, and further

This chapter surveys recent progress in developing thermoelectric materials for power generation on the base of inorganic clathrate compounds. We consider crystal and electronic structures of these compounds, the underlying physics of their thermoelectric properties, synthetic methods of their preparation, and, as a central issue, their thermoelectric perform-

Clathrates belong to plentiful class of inclusion compounds. Their discovery is traced back to the beginning of the nineteenth century, when Sir Davy observed formation of solid chlorine hydrate upon passing gaseous chlorine through water cooled to +5°C. Other hydrates came soon after, and by the middle of the twentieth century, quite a number of hydrates of various gases and liquids were discovered, and their crystal structures were solved. Despite clear differences in their chemical composition and crystal structures, these compounds shared a single common feature, which is complete sequestering of a guest moiety inside cages of framework. Another distinct feature of those compounds is the absence of strong host-guest bonds. In 1965 [8], Kasper, Hagenmuller, and Pouchard reported two new sodium silicides, whose crystal structures were identical to hydrates of various gases, proving that host-guest size matching had the primary role in their formation and stability, rather than the details of chemical bonding. Since then, almost three hundred compounds belonging to ten structure types were documented [3–5, 9]. They involve almost 50 chemical elements constituting more

ance. Current achievements and future prospects are discussed.

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

**2. Clathrates as inclusion compounds**

than 50% of all stable chemical elements (**Figure 1**).

progress is highly expected.

**2.1. Crystal structures**

All clathrate crystal structures are based on closed polyhedra having from 20 to 28 vertices (**Figure 2**). Various combinations of these polyhedra lead to complete filling of the space, which is distinctive feature of clathrates. In this review, we will focus on four clathrates types, known as type-I, type-II, type-III, and type-VIII clathrates, as many of them demonstrate high thermoelectric figure-of-merit, in part stemming from the details of their crystal structure.

**Figure 2.** Clathrate-forming polyhedra: (a) 20-vertex pentagonal dodecahedron; (b) 24-vertex tetrakaidecahedron; (c) 26-vertex pentakaidecahedron; and (d) 28-vertex hexakaidecahedron.

Clathrates of type-I are the most numerous; recent review lists over 100 representatives of this structure type [10]. Their crystal structure consists of two types of polyhedra, 20-vertex dodecahedron and 24-vertex tetrakaidecahedron. The latter polyhedra form three-dimensional cubic array in such a way, that centers of adjacent 6-member rings form close rod packing, as in the crystal structure of Cr3Si, whereas the smaller polyhedra fill the remaining empty space (**Figure 3**). Guest atoms fill the centers of the polyhedra, forming only long, non-covalent contacts with atoms forming polyhedral framework. The resulting crystal structure belongs to cubic space group Pm3n and has general chemical formula E46G8, which emphasizes that there are 46 framework atoms and eight guest atoms per unit cell. Whereas the guest atoms occupy two positions, sixfold inside the larger polyhedral cage and twofold inside the smaller one, and have very large coordination numbers of 24 and 20, respectively, all atoms of the framework (24-fold, 16-fold, and sixfold) have tetrahedron environment.

**Figure 3.** Crystal structure of clathrates: (A) type-I clathrate; (B) two adjacent polyhedra in type-I clathrate; (C) type-II clathrate; (D) type-III clathrate; (E) type-VIII clathrate; and (F) asymmetric cage in type-VIII clathrate.

The nature of chemical elements that form type-I clathrates is quite diverse. In general, type-I clathrates are classified into two groups depending on charge of the framework. The most numerous are anionic clathrates, in which the framework bears negative charge compensated by guest cations. A reverse of the host-guest polarity leads to cationic (also known as inversed) clathrates. As a rule, atoms that form framework come from *p*-block of Mendeleev periodic table; however, inclusion of *d*-metals is also possible. Guest atoms are different depending on charge of the framework. In anionic clathrates, guests are cations of large alkali or alkali earth metals; only a few examples of clathrates hosting rare earth metals are documented [11–13]. In the case of cationic clathrates, halogens and chalcogens of 3–5 periods of Mendeleev table serve as anionic guests.

Type-I clathrates frequently feature deviations from ideal crystal structure described above. This includes mixed occupancy of positions by atoms of different chemical nature, partially vacant positions, splitting of positions into two or three closely lying partial occupied sites, and various types of atom and vacancy ordering that lead to formation of superstructures and reduction in symmetry [10]. In most cases, these crystallographic details affect the electronic structure of clathrates and invoke properties that enhance thermoelectric efficiency.

Other clathrate types are less numerous. Their crystal structures are also built of different highcoordination polyhedra. For instance, type-II clathrate is made of combination of 20-vertex dodecahedra with 28-vertex hexakaidecahedra in such a fashion that cubic face-centered structure is formed (**Figure 3**). Crystal structure of type-III clathrates is the only clathrate structure that contains three types of polyhedra at the time; they are 20-vertex dodecahedra, 24-vertex tetrakaidecahedra, and 26-vertex pentakaidecahedra. They share faces to form a tetragonal crystal structure displayed in **Figure 3**. Type-VIII clathrates are slightly different as they have only one type of polyhedra, which is substantially distorted. It can be viewed as dodecahedron, in which three E–E bonds are broken, and three extra E atoms are inserted instead. The resulting polyhedron has rather low symmetry, but its packing within cubic unit cell brings about clathrate type of the crystal structure. As long as distorted polyhedra cannot fill the entire space, additional 8-vertex polyhedra are left unfilled in this crystal structure (**Figure 3**).

#### **2.2. Application of Zintl scheme and electronic structures**

al cubic array in such a way, that centers of adjacent 6-member rings form close rod packing, as in the crystal structure of Cr3Si, whereas the smaller polyhedra fill the remaining empty space (**Figure 3**). Guest atoms fill the centers of the polyhedra, forming only long, non-covalent contacts with atoms forming polyhedral framework. The resulting crystal structure belongs to cubic space group Pm3n and has general chemical formula E46G8, which emphasizes that there are 46 framework atoms and eight guest atoms per unit cell. Whereas the guest atoms occupy two positions, sixfold inside the larger polyhedral cage and twofold inside the smaller one, and have very large coordination numbers of 24 and 20, respectively, all atoms of the frame-

**Figure 3.** Crystal structure of clathrates: (A) type-I clathrate; (B) two adjacent polyhedra in type-I clathrate; (C) type-II

The nature of chemical elements that form type-I clathrates is quite diverse. In general, type-I clathrates are classified into two groups depending on charge of the framework. The most numerous are anionic clathrates, in which the framework bears negative charge compensated by guest cations. A reverse of the host-guest polarity leads to cationic (also known as inversed) clathrates. As a rule, atoms that form framework come from *p*-block of Mendeleev periodic table; however, inclusion of *d*-metals is also possible. Guest atoms are different depending on charge of the framework. In anionic clathrates, guests are cations of large alkali or alkali earth metals; only a few examples of clathrates hosting rare earth metals are documented [11–13]. In the case of cationic clathrates, halogens and chalcogens of 3–5 periods of Mendeleev table serve

Type-I clathrates frequently feature deviations from ideal crystal structure described above. This includes mixed occupancy of positions by atoms of different chemical nature, partially

clathrate; (D) type-III clathrate; (E) type-VIII clathrate; and (F) asymmetric cage in type-VIII clathrate.

as anionic guests.

work (24-fold, 16-fold, and sixfold) have tetrahedron environment.

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

Chemical composition of clathrates frequently looks unusual in terms of the stoichiometry of phases. For instance, the following compounds displaying promising thermoelectric properties are formulated as Sr8Ga16Ge30, Ba8Ga16Sn30, K8In8Sn38, and Si30P16Te8. These formulas can be rationalized on the basis of Zintl electron-counting scheme, which, in fact, shows that these compounds should behave as semiconductors [14].

Application of Zintl scheme rests on the tetrahedral coordination of all atoms of the framework. They all form four two-center, two-electron (2c–2e) bonds, thus forming electronic octet. Let us consider clathrate compound with formula Ba8Ga16Sn38. Its framework comprises tetrahedrally bonded Ga and Sn atoms, whereas Ba guests compensate for the charge of the framework. Each Sn atom forms four 2c–2e bonds, for which it uses four own electrons and four electrons shared with four neighbors. Therefore, it does not require loss or gain of further electrons, which means that under Zintl scheme its formal oxidation state is zero. Similarly, Ga atom, having three valence electrons, is one electron short of forming four 2c–2e bonds. It must gain one electron to achieve an octet, thus acquiring formal oxidation state of −1. There are 16 Ga atoms per formula, which requires compensating for 16 negative charges. Ba atoms with coordination numbers of 20 and 24 clearly exist as Ba2+ cations. There are eight +2 cations that compensate for the charge of the framework and ensure the overall electroneutrality of Ba8Ga16Sn30.

The overall electroneutrality of clathrate compound along with formation of electron octets makes these compounds semiconductors unless limitations of Zintl scheme are overcome. This may happen under various circumstances, including an introduction of *d*-metal into framework, combination of elements, that would lead to overlap of valence and conduction bands, and energy gain of accepting or expelling an electron in favor of formation of chemical bond of high bond energy, as in the case of Si–Si bond [15]. In such cases, metal-to-insulator transition (MIT) may occur, leading to temperature-dependent properties, with prospective thermoelectric parameters at the verge of MIT.

Electronic structure of clathrates, albeit having little in common with Zintl counting scheme, still shows the propensity of this compounds to behave as semiconductors [14]. Electronic structure of various clathrates has been assessed in numerous reports and discussed in several reviews [3–6]. However, the majority of the studies are dealing with calculations at different levels. For type-I clathrates, it was shown that fulfillment of Zintl rule shows up in the following way: All bonding states and, if necessary, nonbonding states (lone pairs neighboring vacancies) are filled and lie below Fermi level, whereas all antibonding states are empty and compose conduction band. Common feature of band structure is that the states in vicinity of Fermi level are composed predominantly by individual contributions that are the most sensitive to various substitutions within clathrate framework. For instance, in type-I clathrate, Sn24−xInxP22I8 indium orbitals have the largest contribution to the states just below Fermi level [16]. In Sn24P19.3I8, another type-I clathrate, but with vacancies in the positions of phosphorus, lone pairs on tin atoms, that surround vacancies, cluster together to form sharp states at the top of valence band [17] (**Figure 4**). Therefore, minor changes in concentration of vacancies or doping element can substantially alter transport properties of clathrates.

**Figure 4.** Scheme of the band structure of Sn24P19.3I8 presented as density of states (DOS) versus energy. Black, total DOS; green, contribution of 4-bonded Sn; red, contribution of 3 + 3-bonded Sn.

Experimental studies of the electronic structure of clathrates are very rare. This is explained by necessity to have rather large single crystals and clean surface to investigate electronic structure by means of X-ray photoelectron spectroscopy (XPS). Recently, these obstacles were overcome, and comprehensive picture of electronic band structure of type-I clathrate Sn24−xInxAs22I8 was obtained [18]. This study proves that chemical bonding has different nature; within the framework, strong covalent bonds are present, whereas the host-guest interactions have pronounced electrostatic nature with clear transfer of electrons from the framework atoms toward guest iodine species. Further, it is shown that top of valence band is composed of shallow I 5*p*, As 4*p*, In 5*p*, and Sn 5*p* orbitals that are largely mixed (**Figure 5**).

of high bond energy, as in the case of Si–Si bond [15]. In such cases, metal-to-insulator transition (MIT) may occur, leading to temperature-dependent properties, with prospective thermoelec-

Electronic structure of clathrates, albeit having little in common with Zintl counting scheme, still shows the propensity of this compounds to behave as semiconductors [14]. Electronic structure of various clathrates has been assessed in numerous reports and discussed in several reviews [3–6]. However, the majority of the studies are dealing with calculations at different levels. For type-I clathrates, it was shown that fulfillment of Zintl rule shows up in the following way: All bonding states and, if necessary, nonbonding states (lone pairs neighboring vacancies) are filled and lie below Fermi level, whereas all antibonding states are empty and compose conduction band. Common feature of band structure is that the states in vicinity of Fermi level are composed predominantly by individual contributions that are the most sensitive to various substitutions within clathrate framework. For instance, in type-I clathrate, Sn24−xInxP22I8 indium orbitals have the largest contribution to the states just below Fermi level [16]. In Sn24P19.3I8, another type-I clathrate, but with vacancies in the positions of phosphorus, lone pairs on tin atoms, that surround vacancies, cluster together to form sharp states at the top of valence band [17] (**Figure 4**). Therefore, minor changes in concentration of vacancies or doping element can

**Figure 4.** Scheme of the band structure of Sn24P19.3I8 presented as density of states (DOS) versus energy. Black, total

Experimental studies of the electronic structure of clathrates are very rare. This is explained by necessity to have rather large single crystals and clean surface to investigate electronic

DOS; green, contribution of 4-bonded Sn; red, contribution of 3 + 3-bonded Sn.

tric parameters at the verge of MIT.

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

substantially alter transport properties of clathrates.

**Figure 5.** Experimental and calculated electronic band structure of Sn22−x−δInxAs22−yI8 for *x* = 12. Reprinted with permission from Inorg. Chem. 2015, 54, 11542–11549. Copyright 2015 American Chemical Society.

In contrast to majority of clathrate types, where semiconducting properties are hardly violated, in the case of type-II clathrates, metallic behavior is more norm than exception. Most of type-II clathrates feature frameworks made of single kind of atoms, Na24−xSi136 being a typical example [19]. In these clathrates, the strength of Si-Si bond (226 kJ/mol) outplays energy loss associated with filling the bottom of conduction band by electrons upon occupation of the guest sites by sodium. Depending on concentration of the guest atoms, MIT is expected, which may lead to various interesting properties, including high thermoelectric performance [20].

## **3. Sample preparation**

## **3.1. Synthesis and crystal growth**

Synthetic routes to clathrates are different. They largely depend on the nature of elements constituting a particular compound. High-temperature ampoule synthesis is the most common method for preparing clathrate compounds, the exact temperature depending on the chemical system. The highest temperatures are explored in the case of silicon-based clathrates owing to very low reactivity of silicon. Heating up to 1500 K might be necessary to enroll this element into reaction; for instance, type-III clathrate Si130P42Te21 was synthesized by heating the stoichiometric mixture of elemental components at 1425 K for 18 days [21]. Further prolonged annealing with intermediate regrinding is always required to achieve homogeneous product. Lower temperatures, between 800 and 1250 K, are required by less inert germanium. For comparison with the previous example, we note that to synthesize isostructural type-III clathrate Ge130P42Te21, temperature of 953 K was sufficient. Completely different scenario is realized in the case of tin. The latter element has low melting point of 505 K, and preparation of tin-based clathrates is associated with formation of melts rich in tin. This frequently becomes an obstacle, because surface of melted tin becomes covered with poorly reactive compounds, such as Sn4P3 or SnAs, leading to incomplete reaction of precursors [18]. This obstacle can be overcome by introducing vapor transport agents. For instance, elemental iodine or SnI4 tend to facilitate reactions owing to formation of volatile intermediates [22, 23].

Other synthetic methods include flux synthesis, precursor decomposition, high-pressure synthesis, and oxidation in ionic liquids [14]. They are used in selected cases depending on the properties of desired clathrates. Of those methods, flux synthesis is rather intensively used both for synthesis and for crystal growth when such low-melting metals as gallium or tin or even aluminum are included in chemical composition of clathrates. Metals themselves produce flux and at the same time are used as reactants. In some cases, large crystals with mass up to 60 mg were prepared by pulling from the melt [24]. A peculiar variation of this method was used for growing crystals of thermoelectric clathrate Ba8Ga16Sn30, where two *p*-metals, gallium and tin, were used as common flux, and properties of the resulting crystals strongly depended on which metal was taken in excess [25].

#### **3.2. Sample densification**

As clathrates are deemed as prospective thermoelectric materials, the problem of sample densification is put forward. Only for a limited number of clathrates, cold pressing produces samples with the density up to 85% of theoretical. These cases are limited to tin-based compounds that exhibit less rigid clathrate frameworks [26].

In recent years, major success in preparing dense samples of various clathrates has been achieved by using of spark plasma sintering (SPS). This method is based on a simultaneous application of temperature, pressure, and DC pulses to sample under inert atmosphere or vacuum (**Figure 6**). High-energy DC pulses are believed to excite plasma nearest to intergrain contacts, leading to high local overheating and consequent bridging of grains with formation of larger uniform particles. Although the exact mechanism is not known and the very formation of plasma is sometimes questioned, this method has been successfully used for preparation of many types of materials [27]. In particular, SPS allows synthesis of clathrates at lower temperatures and lower pressures compared to standard high-pressure method, which is very advantageous as long as clathrates cannot withstand too high pressure because of readily collapse of their tracery framework [28]. For instance, compact and dense pellets of Ge30P16Se8 could be prepared at temperature of 773 K and pressure of 60 MPa that already provided sample density of 96% relative to theoretical one [29]. Similarly, silicon-based clathrates were densified at significantly harsher condition of 1100 K and 110 MPa to achieve sample density of 95% [21, 30]. In both cases, no degradation of the initial sample was observed, proving that densification does not change composition and structure of clathrates and that concomitant thermoelectric measurements are performed on the samples of desired nature.

**Figure 6.** Scheme of the SPS method.

associated with filling the bottom of conduction band by electrons upon occupation of the guest sites by sodium. Depending on concentration of the guest atoms, MIT is expected, which may lead to various interesting properties, including high thermoelectric performance [20].

Synthetic routes to clathrates are different. They largely depend on the nature of elements constituting a particular compound. High-temperature ampoule synthesis is the most common method for preparing clathrate compounds, the exact temperature depending on the chemical system. The highest temperatures are explored in the case of silicon-based clathrates owing to very low reactivity of silicon. Heating up to 1500 K might be necessary to enroll this element into reaction; for instance, type-III clathrate Si130P42Te21 was synthesized by heating the stoichiometric mixture of elemental components at 1425 K for 18 days [21]. Further prolonged annealing with intermediate regrinding is always required to achieve homogeneous product. Lower temperatures, between 800 and 1250 K, are required by less inert germanium. For comparison with the previous example, we note that to synthesize isostructural type-III clathrate Ge130P42Te21, temperature of 953 K was sufficient. Completely different scenario is realized in the case of tin. The latter element has low melting point of 505 K, and preparation of tin-based clathrates is associated with formation of melts rich in tin. This frequently becomes an obstacle, because surface of melted tin becomes covered with poorly reactive compounds, such as Sn4P3 or SnAs, leading to incomplete reaction of precursors [18]. This obstacle can be overcome by introducing vapor transport agents. For instance, elemental iodine or SnI4 tend

to facilitate reactions owing to formation of volatile intermediates [22, 23].

Other synthetic methods include flux synthesis, precursor decomposition, high-pressure synthesis, and oxidation in ionic liquids [14]. They are used in selected cases depending on the properties of desired clathrates. Of those methods, flux synthesis is rather intensively used both for synthesis and for crystal growth when such low-melting metals as gallium or tin or even aluminum are included in chemical composition of clathrates. Metals themselves produce flux and at the same time are used as reactants. In some cases, large crystals with mass up to 60 mg were prepared by pulling from the melt [24]. A peculiar variation of this method was used for growing crystals of thermoelectric clathrate Ba8Ga16Sn30, where two *p*-metals, gallium and tin, were used as common flux, and properties of the resulting crystals strongly depended

As clathrates are deemed as prospective thermoelectric materials, the problem of sample densification is put forward. Only for a limited number of clathrates, cold pressing produces samples with the density up to 85% of theoretical. These cases are limited to tin-based

**3. Sample preparation**

**3.1. Synthesis and crystal growth**

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

on which metal was taken in excess [25].

compounds that exhibit less rigid clathrate frameworks [26].

**3.2. Sample densification**

## **4. Transport properties**

#### **4.1. Charge carriers transport**

As long as clathrates belong to the family of Zintl compounds, they frequently display activation type of conductivity typical for proper semiconductors. They possess rather high values of electrical conductivity, *σ*, and Seebeck coefficient, *S*, giving rise to moderately high values of power factor, *S*<sup>2</sup> *σ*. The latter describes transport of charge carries and depends largely on details of the band structure of given compounds.

The advantageous property of clathrates is that their crystal structure, in particular, the spatial separation of host and guest substructures, provides opportunities for tuning charge carriers transport almost independently of phonon transport.

Electrical conductivity of type-I clathrates ranges from several S m−1 for ideally balanced compounds to nearly 105 S m−1 for properly doped semiconductors. For instance, Sn20.5As22I8 has room-temperature electrical conductivity just below 1 S m−1, whereas introduction of In as doping element pushes electrical conductivity to 135–461 S m−1 depending on concentration of indium and corresponding vacancies in clathrate framework [16, 31]. Similarly, stoichiometric Si30P16Te8 is not good electrical conductor with room-temperature value of 63.3 S m−1 [32]. However, its band structure can be altered upon creating vacancies in guest positions with concomitant change in the Si:P ratio. As a result, band gap was decreased from 1.24 eV to minimum of 0.12 eV and electrical conductivity was increased up to (1–4) × 104 S m−1 depending on actual composition of clathrate [30]. Importantly, electronic structure and, hence, conducting properties are only weakly sensitive to isovalent substitution, provided that the substituting atoms reside on similar crystallographic sites. For instance, K8M8Sn38 (M = Al, Ga, and In) exhibits almost the same room-temperature conductivity of (6.5–12.5) × 104 S m−1 [33]. In these compounds, small change in electrical conductivity can be attributed to shrinkage of clathrate framework upon going from In to Ga and to Al. Another example of sensitivity of transport properties to the framework structural modification is provided by Sn20Zn4P21.2X8 (X = Br, I). When Br is a guest, the shrinkage of the framework leads to relaxation of atoms residing next to vacancies causing a significant shortage of Sn–P and Zn–P bonds compared to I-based compound. Accordingly, the framework becomes more conductive as band gap decreases from 0.25 to 0.11 eV. As a result, Sn20Zn4P21.2Br8 displays much greater room-temperature conductivity of 250 S m−1 compared to 0.4 S m−1 for I-based analog prepared under the same conditions [23].

Basically, electrical conductivity is product of charge, charge carriers' concentration, and mobility. The former is constant, but two other parameters vary with both temperature and chemical nature of clathrate. However, charge carriers' concentration is intrinsic property of a given composition, whereas their mobility is sensitive to grain boundaries. Therefore, observed conductivity of compound with a given composition may depend upon preparation and compacting methods. Type-I clathrate Sn24P19.3I8 provides example of drastic change in electrical conductivity in response to different preparation routes. As-prepared and coldpressed samples display room-temperature conductivity of 335 S m−1, whereas SPS-treated sample shows much higher conductivity of 6.5 × 103 S m−1 [17, 26]. Temperature-dependent impedance spectroscopy measurements showed that for SPS-compacted sample of high density (92% of theoretical), intergrain contacts start to contribute significantly to total impedance only below 75 K, while above this temperature only activation part could be detected [34].

**4. Transport properties**

**4.1. Charge carriers transport**

values of power factor, *S*<sup>2</sup>

compounds to nearly 105

[23].

on details of the band structure of given compounds.

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

transport almost independently of phonon transport.

As long as clathrates belong to the family of Zintl compounds, they frequently display activation type of conductivity typical for proper semiconductors. They possess rather high values of electrical conductivity, *σ*, and Seebeck coefficient, *S*, giving rise to moderately high

The advantageous property of clathrates is that their crystal structure, in particular, the spatial separation of host and guest substructures, provides opportunities for tuning charge carriers

Electrical conductivity of type-I clathrates ranges from several S m−1 for ideally balanced

has room-temperature electrical conductivity just below 1 S m−1, whereas introduction of In as doping element pushes electrical conductivity to 135–461 S m−1 depending on concentration of indium and corresponding vacancies in clathrate framework [16, 31]. Similarly, stoichiometric Si30P16Te8 is not good electrical conductor with room-temperature value of 63.3 S m−1 [32]. However, its band structure can be altered upon creating vacancies in guest positions with concomitant change in the Si:P ratio. As a result, band gap was decreased from 1.24 eV to

on actual composition of clathrate [30]. Importantly, electronic structure and, hence, conducting properties are only weakly sensitive to isovalent substitution, provided that the substituting atoms reside on similar crystallographic sites. For instance, K8M8Sn38 (M = Al, Ga, and In)

compounds, small change in electrical conductivity can be attributed to shrinkage of clathrate framework upon going from In to Ga and to Al. Another example of sensitivity of transport properties to the framework structural modification is provided by Sn20Zn4P21.2X8 (X = Br, I). When Br is a guest, the shrinkage of the framework leads to relaxation of atoms residing next to vacancies causing a significant shortage of Sn–P and Zn–P bonds compared to I-based compound. Accordingly, the framework becomes more conductive as band gap decreases from 0.25 to 0.11 eV. As a result, Sn20Zn4P21.2Br8 displays much greater room-temperature conductivity of 250 S m−1 compared to 0.4 S m−1 for I-based analog prepared under the same conditions

Basically, electrical conductivity is product of charge, charge carriers' concentration, and mobility. The former is constant, but two other parameters vary with both temperature and chemical nature of clathrate. However, charge carriers' concentration is intrinsic property of a given composition, whereas their mobility is sensitive to grain boundaries. Therefore, observed conductivity of compound with a given composition may depend upon preparation and compacting methods. Type-I clathrate Sn24P19.3I8 provides example of drastic change in electrical conductivity in response to different preparation routes. As-prepared and coldpressed samples display room-temperature conductivity of 335 S m−1, whereas SPS-treated

minimum of 0.12 eV and electrical conductivity was increased up to (1–4) × 104

exhibits almost the same room-temperature conductivity of (6.5–12.5) × 104

*σ*. The latter describes transport of charge carries and depends largely

S m−1 for properly doped semiconductors. For instance, Sn20.5As22I8

S m−1 depending

S m−1 [33]. In these

Importantly, electrical conductivity can be suppressed significantly by significant disorder of crystal structure, which is exemplified by very low value of *σ* ≈ 1 S m−1 at 300 K for Sn20.5As22I8, which is four orders of magnitude smaller than for phosphorus analog. The only reason for such difference is reported to be tremendous disorder in crystal structure of As-based compound, leading to significant scattering of charge carriers on flaws of crystal structure [31].

At high temperatures, many clathrates demonstrate very high electrical conductivity, showing that no other mechanism than activation has any noticeable contribution. There are rare cases of pure metallic properties, where electrical conductivity decreases with temperature as for Na22Si136 [19]; considerably more numerous are examples of clathrates lying at the border of metallic and semiconducting regimes and showing slight increase in electrical conductivity with temperature. For instance, type-III clathrate Si132P42Te21 displays only threefold increase in electrical conductivity upon heating from 300 to 1100 K [35]. At low temperatures, majority of clathrates display very high electrical resistivity. Noticeably, several Si-based clathrates possess transition into superconducting states below 10 K. For instance, type-I clathrate Ba8Si46 has TC of 8 K [36], and type-IX clathrate Ba6Ge25 turns on superconducting below 3.8 K [37].

Type-II clathrates are different from those of other types in displaying metallic type of electrical conductivity, and many of them behave as normal metals. In particular, Cs8Na16Si136 and Cs8Na16Ge136 combine high electrical conductivity manifested by smooth increase in electrical resistivity with temperature-independent Pauli paramagnetism; such combination is typical for good metals [38].

Clathrates demonstrate different types of majority carriers, and therefore, Seebeck coefficient can be positive (holes) or negative (electrons). Absolute values of Seebeck coefficients vary from one clathrate to another and depend on multifold factors. They include band gap width, concentration of charge carriers, degree of the framework disorder, and many others. In most cases, as generally observed for proper semiconductors, the higher the electrical conductivity is, the lower the Seebeck coefficient is, which stems from the opposite trend of their dependence upon charge carriers' concentration [1, 3]. This is exemplified by several clathrates of different structure types. Whereas type-I Sn24P19.3I8 demonstrates at 300 K high electrical conductivity of 6.5 × 103 S × m−1, but also exhibits rather low Seebeck coefficient of only +80 μV × K−1, formally isostructural compound Ge38Sb8I8 displays very high Seebeck coefficient of about +800 μV × K−1, and its electrical conductivity does not exceed 10−1 S × m−1 at the same temperature [39]. Some kind of compromise between values of electrical conductivity and Seebeck coefficient is achieved for charge carriers' concentration of 1019 cm−3. For instance, type-VIII clathrate Ba8Ga16Sn30 doped with small amounts of Cu demonstrates *S =* 350 μV × K−1 coexisting with *σ* = 3 × 104 S × m−1 at 300 K [40].

Important value describing the entire charge carriers' transport is so-called power factor, *PF*, which is related to other properties as *PF* = *S*<sup>2</sup> *σ* [2, 3]. Therefore, for more effective transport of charge carriers, both electrical conductivity and Seebeck coefficient should be maximized, which is impossible for intrinsic semiconductors. Consequently, attempts have been made to optimize charge carriers' concentration by multiple doping and/or vacancy formation. This may lead to altering the band structure by introducing donor and/or acceptor levels, which may be broad enough to cause their overlap with both conduction and valence bands, giving rise to properties of "bad metal" and, provided the optimal tuning is achieved, to metal-to-semiconductor transition. As a result of this strategy, combination of *S =* 170 μV × K−1 with *σ* = 4.75 × 104 S × m−1 at 300 K was achieved for Si46−xPxTe8−y, leading to *PF* = 0.14 × 10−3 W × m−1 × K−2, which is almost four orders of magnitude greater than that for ideally stoichiometric compound Si30P16Te8 [30, 32].

As temperature increases, both electrical conductivity and Seebeck coefficient tend to grow (**Figure 7**), and therefore, power factor also increases; for instance, *PF* for Ge31P15Se8 is three orders of magnitude higher at 650 K compared to 300 K [29].

**Figure 7.** Electrical conductivity σ and Seebeck coefficient S of clathrate Ge31P15Se8 as function of temperature.

#### **4.2. Guest dynamics and heat transport**

Clathrates are famous for their low, glass-like thermal conductivity, which originates from the details of their crystal structure, namely from the motion of guest atoms inside oversized cages of the framework (see **Figure 3b**). Such a motion is known as rattling; it provides pseudolocalized vibrations that are alien to concerted (Debye) vibrations of atoms composing the framework.

Analysis of atomic displacement parameters (ADPs) shows that in all types of clathrate compounds guest atoms have the highest values of ADPs and that absolute values depend on the nature of guest atom and degree of host-guest mismatch. As a rule, temperature dependence of ADPs is linear, which provides an opportunity to estimate characteristic Debye and Einstein temperatures, θD and θE, that are proportional to the slope of <U2 >(T) function, where <U2 > is the mean square atomic displacement either taken for any particular guest atom or averaged over all framework atoms. These characteristic temperatures describe dynamics of clathrate compounds. In particular, θD characterizes the framework; the higher the Debye temperature, the more rigid the framework. Value of θD depends primarily on the nature of atoms composing the framework. Si-based clathrates are known to be the most rigid, and their θD values may exceed 500 K [20]. Frameworks based on tin or germanium are less rigid, and θD value falls in the range of 150–320 K largely depending on the nature and concentration of doping element.

Important value describing the entire charge carriers' transport is so-called power factor, *PF*, which is related to other properties as *PF* = *S*<sup>2</sup> *σ* [2, 3]. Therefore, for more effective transport of charge carriers, both electrical conductivity and Seebeck coefficient should be maximized, which is impossible for intrinsic semiconductors. Consequently, attempts have been made to optimize charge carriers' concentration by multiple doping and/or vacancy formation. This may lead to altering the band structure by introducing donor and/or acceptor levels, which may be broad enough to cause their overlap with both conduction and valence bands, giving rise to properties of "bad metal" and, provided the optimal tuning is achieved, to metal-to-semiconductor transition. As a result of this strategy, combination of

*PF* = 0.14 × 10−3 W × m−1 × K−2, which is almost four orders of magnitude greater than that

As temperature increases, both electrical conductivity and Seebeck coefficient tend to grow (**Figure 7**), and therefore, power factor also increases; for instance, *PF* for Ge31P15Se8 is three

**Figure 7.** Electrical conductivity σ and Seebeck coefficient S of clathrate Ge31P15Se8 as function of temperature.

Clathrates are famous for their low, glass-like thermal conductivity, which originates from the details of their crystal structure, namely from the motion of guest atoms inside oversized cages of the framework (see **Figure 3b**). Such a motion is known as rattling; it provides pseudolocalized vibrations that are alien to concerted (Debye) vibrations of atoms composing the

S × m−1 at 300 K was achieved for Si46−xPxTe8−y, leading to

*S =* 170 μV × K−1 with *σ* = 4.75 × 104

**4.2. Guest dynamics and heat transport**

framework.

for ideally stoichiometric compound Si30P16Te8 [30, 32].

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

orders of magnitude higher at 650 K compared to 300 K [29].

Einstein characteristic temperature provides information on pseudo-localized vibrations of guest atoms inside the framework. In general, its characteristics depend on type of clathrate crystals structure, on atomic mass and size of guest atom, and on host-guest mismatch for given clathrate compound.

Further analysis shows that in all clathrates, ADPs for guest atoms are always greater than for the framework ones. For instance, **Figure 8** displays temperature dependence of ADPs for crystal structure of cationic clathrate, in which framework is composed of silicon and phosphorus atoms in approximate ratio 2:1, whereas tellurium and selenium atoms jointly occupy guest positions.

**Figure 8.** Temperature dependence of ADPs in crystal structure of type-I clathrate [Si,P]46Te6.78Se1.22. Reprinted with permission from Inorg. Chem. 2012, 51, 11396–11405. Copyright 2012 American Chemical Society.

Clearly, ADPs averaged over the framework atoms are the lowest in the structure, ADP for guests in *2a* position comes next, and that for guest in 6*d* position is the highest. The difference between two guest positions is related to structural features. Effective volume of 20-vertex cage centered by 2*a* site is lower than that of 24-vertex cage centered at 6*d*. Moreover, 20-vertex cage is perfectly isotropic, whereas in 24-vertex cage (*cf*. **Figure 2**), motion in the direction of two hexagonal faces and that in perpendicular direction should occur at different frequencies. Such an anisotropy was clearly demonstrated for type-I clathrate Sn24P19.3I8 [41]. **Figure 9** shows that, firstly, ADP of I2 atom residing in the center of 24-vertex cage is the largest in the system. Secondly, whereas motion of I1 atoms is described by single Einstein temperature of 76 K, displacement of I2 is characterized by two Einstein modes because of anisotropy of vibrations. In particular, axial movement in direction to hexagonal faces of tetrakaidecahedron occurs at lower frequency than that in perpendicular direction; respective values of θE are 79 and 63 K.

**Figure 9.** Temperature dependence of ADPs for Sn24P19.3I8. (top) Equivalent ADPs for all atoms. (bottom) Guest atom ADPs in an anisotropic mode. Reprinted with permission from J. Alloys Compd. 2012, 520, 174–179. Copyright 2012 Elsevier.

Guest dynamics can be probed by various methods, ADPs analysis being just a most typical example. Other methods include direct or indirect observation of guest vibration frequencies

by means of Raman spectroscopy, inelastic neutron scattering, resonance ultrasound spectroscopy, heat capacity data, and other tools. Of them, low temperature examination of heat capacity data is frequently used to analyze jointly Debye and Einstein modes. Such analysis was performed for quite a number of clathrates. It was shown that no anomaly is observed below room temperature pointing at the absence of phase transitions, which is corroborated by linearity of *U*(*T*) dependencies. At low temperatures, heat capacity of clathrates does not obey Debye law of cubes owing to significant contributions of Einstein modes. For type-I clathrate Sn24P19.3I8 [41] described above, low-T part of *CP*(*T*) dependence could be circumscribed only by taking into account three different contributions, one Debye and two Einstein, that account for concerted vibrations of the entire framework and for two localized modes (**Figure 10**). Extracted values of θD (265 K) and θE (60 and 78 K) match to values obtained from ADPs [42].

Clearly, ADPs averaged over the framework atoms are the lowest in the structure, ADP for guests in *2a* position comes next, and that for guest in 6*d* position is the highest. The difference between two guest positions is related to structural features. Effective volume of 20-vertex cage centered by 2*a* site is lower than that of 24-vertex cage centered at 6*d*. Moreover, 20-vertex cage is perfectly isotropic, whereas in 24-vertex cage (*cf*. **Figure 2**), motion in the direction of two hexagonal faces and that in perpendicular direction should occur at different frequencies. Such an anisotropy was clearly demonstrated for type-I clathrate Sn24P19.3I8 [41]. **Figure 9** shows that, firstly, ADP of I2 atom residing in the center of 24-vertex cage is the largest in the system. Secondly, whereas motion of I1 atoms is described by single Einstein temperature of 76 K, displacement of I2 is characterized by two Einstein modes because of anisotropy of vibrations. In particular, axial movement in direction to hexagonal faces of tetrakaidecahedron occurs at lower frequency than that in perpendicular direction; respective values of θE are 79 and 63 K.

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

**Figure 9.** Temperature dependence of ADPs for Sn24P19.3I8. (top) Equivalent ADPs for all atoms. (bottom) Guest atom ADPs in an anisotropic mode. Reprinted with permission from J. Alloys Compd. 2012, 520, 174–179. Copyright 2012

Guest dynamics can be probed by various methods, ADPs analysis being just a most typical example. Other methods include direct or indirect observation of guest vibration frequencies

Elsevier.

**Figure 10.** Plot of CP/T3 versus T2 in semi-logarithmic coordinates. Two Einstein (1, 2) and one Debye (3) contributions to total Cp/T3 values (4) are given in comparison with experimental data (filled circles). Reprinted with permission from J. Alloys Compd. 2012, 520, 174–179. Copyright 2012 Elsevier.

Lattice dynamics defines the principal contribution to thermal conductivity of clathrates. Although the majority of clathrates are low-gap semiconductors, they display very low values of thermal conductivity, which ranges at room temperature from 0.4 to 2.0 W × m−1 × K−1. Rattling of guest atoms is the primary reason of reducing thermal conductivity of clathrates due to either lowering of phonon group velocity because of avoided crossing of acoustic modes or resonant scattering of phonons by rattling modes. However, other features of particular clathrate compounds can be added to the mechanism of reducing thermal conductivity. First, vacancy formation within the clathrate framework makes it less rigid leading to reducing Debye temperature, which, in turn, is proportional to velocity of sound, *v*s, that is related to thermal conductivity as *κ*L = 1/3(*vsCPλ*), where *κ*L is lattice part of thermal conductivity, *C*P is heat capacity, and *λ* is phonon mean free path. Second, formation of superstructures gives rise to high unit volumes causing less concerted vibrations of framework atoms, thus reducing thermal conductivity. Third, mass alternation within guest substructure alters phonon mean free path without affecting individual rattling modes, thus also reducing thermal conductivity. Finally, in real systems, any combination of these scenarios is possible.

Mass alternation leads to low thermal conductivity of mixed-guest clathrates Sn24P19.3I8−xBrx (x = 2–4) [26]. For any composition *x*, thermal conductivity is lower than for single-guest compounds, although the latter phases already exhibit low thermal conductivity due to both guest rattling and vacancies within the framework. The lowest value of 0.5 W × m−1 × K−1 is observed at 300 K for composition with I:Br ratio of 1:1 (**Figure 11**), proving that mass alternation is the driving force for reducing thermal conductivity. Mass alternation brings about another peculiar effect as thermal conductivity of such clathrates is glass-like. Whereas for typical crystalline semiconductors thermal conductivity increases until temperature of about 30–50 K and then decreases as *κ* = *f*(*T*−1), glass-like clathrates show smooth increase in thermal conductivity and then temperature-independent regime in the range of about 50–300 K (**Figure 11**).

**Figure 11.** Temperature dependence of thermal conductivity for several clathrates: black, Cs8Sn44; red, Ba8Ga16Ge30; green, Sn24P19.3I8; blue, Sn24P19.3I4Br4; cyan, Sn20.5As22I8.

Recently, it was shown that off-center displacement of guest atoms adds significantly to glasslike character of thermal conductivity; in particular, thermal conductivity of Sr8Ga16Ge30 turns from crystalline-like to glass-like upon increasing off-center displacement of guest atoms sitting on 6*d* site [43].

Clathrate Sn20.5As22I8 displays combination of eightfold cubic superstructure of type-I clathrates with vacancies and mixed occupancies of sites within the framework [31]. In response to structural features, this compound exhibits very low thermal conductivity with roomtemperature value slightly over 0.4 W × m−1 × K−1. Increasing complexity of the crystal structure by partial substitution of indium for tin results in further diminishing of thermal conductivity down to 0.36 W × m−1 × K−1 [16] (**Figure 11**).

Ba8Au16P30 provides an example of peculiar orthorhombic superstructure of type-I structure with fivefold increase in the unit volume. In the region of 40–400 K, this compound demonstrates low, almost temperature-independent, thermal conductivity of 0.6 W × m−1 × K−1 [44]. However, this compound is not Zintl phase. It demonstrates metallic-like electrical conductance with resistivity slightly increasing with increased temperature. Therefore, another mechanism of thermal conductivity has substantial contribution to total thermal conductivity, which is electronic thermal conductivity. The latter is proportional to electrical conductivity, *σ*, according to Wiedemann-Franz equation *κ*e = L0σT, where L0 = 2.45 × 10−8 W × Ohm × K−2 is ideal temperature-independent Lorentz number and T is absolute temperature. It was shown that electronic part of thermal conductivity in Ba8Au16P30 increases from 0.2 W × m−1 × K−1 at 100 K to slightly over 0.5 W × m−1 × K−1 at 400 K, meaning that at the same time lattice part of thermal conductivity decreases in the same interval from about 0.4 to even below 0.2 W × m−1 × K−1 at 400 K, which is the lowest documented value of lattice thermal conductivity for clathrates.

In rare cases, electronic part of thermal conductivity may play dominating role provided clathrate shows properties of good metallic conductor. Type-II clathrate Na24Si136 is example, showing dominating contribution of electronic thermal conductivity amounting at 24 W × m−1 × K−1 at room temperature [20].

#### **4.3. Thermoelectric figure-of-merit**

thermal conductivity. Third, mass alternation within guest substructure alters phonon mean free path without affecting individual rattling modes, thus also reducing thermal conductivity.

Mass alternation leads to low thermal conductivity of mixed-guest clathrates Sn24P19.3I8−xBrx (x = 2–4) [26]. For any composition *x*, thermal conductivity is lower than for single-guest compounds, although the latter phases already exhibit low thermal conductivity due to both guest rattling and vacancies within the framework. The lowest value of 0.5 W × m−1 × K−1 is observed at 300 K for composition with I:Br ratio of 1:1 (**Figure 11**), proving that mass alternation is the driving force for reducing thermal conductivity. Mass alternation brings about another peculiar effect as thermal conductivity of such clathrates is glass-like. Whereas for typical crystalline semiconductors thermal conductivity increases until temperature of about 30–50 K and then decreases as *κ* = *f*(*T*−1), glass-like clathrates show smooth increase in thermal conductivity and then temperature-independent regime in the range of about 50–300 K (**Figure 11**).

**Figure 11.** Temperature dependence of thermal conductivity for several clathrates: black, Cs8Sn44; red, Ba8Ga16Ge30;

Recently, it was shown that off-center displacement of guest atoms adds significantly to glasslike character of thermal conductivity; in particular, thermal conductivity of Sr8Ga16Ge30 turns from crystalline-like to glass-like upon increasing off-center displacement of guest atoms

Clathrate Sn20.5As22I8 displays combination of eightfold cubic superstructure of type-I clathrates with vacancies and mixed occupancies of sites within the framework [31]. In response to structural features, this compound exhibits very low thermal conductivity with roomtemperature value slightly over 0.4 W × m−1 × K−1. Increasing complexity of the crystal structure by partial substitution of indium for tin results in further diminishing of thermal conductivity

Ba8Au16P30 provides an example of peculiar orthorhombic superstructure of type-I structure with fivefold increase in the unit volume. In the region of 40–400 K, this compound demonstrates low, almost temperature-independent, thermal conductivity of 0.6 W × m−1 × K−1 [44]. However, this compound is not Zintl phase. It demonstrates metallic-like electrical conduc-

green, Sn24P19.3I8; blue, Sn24P19.3I4Br4; cyan, Sn20.5As22I8.

down to 0.36 W × m−1 × K−1 [16] (**Figure 11**).

sitting on 6*d* site [43].

Finally, in real systems, any combination of these scenarios is possible.

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

Analysis of transport properties of clathrates leads to conclusion that they possess high electrical conductivity up to 6.5 × 104 S/m, high absolute values of Seebeck coefficient up to ±800 μV/K, and low thermal conductivity down to 0.4 W × m−1 × K−1. Were these values pertinent to single compound, its thermoelectric figure-of-merit would reach unbelievable values largely exceeding *ZT* = 1 at room temperature, which is benchmark of current state-of-the-art thermoelectric materials. However, due to the significant unavoidable coupling of charge carriers and heat transport, *ZT* values for clathrate compounds are quite low at room temperature, scarcely surpassing *ZT* = 0.1. Interestingly, the highest room-temperature *ZT* values are achieved for type-VIII clathrates. For instance, Sb-doped *p*-type Ba8Ga16Sn30 demonstrates *ZT* = 0.6 and 300 K, whereas *n*-type Ba8Ga16Sn30 displays *ZT* = 0.5 at the same temperature [45].

At higher temperature, as both electrical conductivity and Seebeck coefficient tend to grow, whereas thermal conductivity remains essentially constant (combination that is true for the majority of semiconducting clathrates), *ZT* increases with increasing temperature.

Type-I and type-II clathrates are the most studied species. Their thermoelectric properties have been reported in numerous papers, and, in general, it was shown that type-II clathrates rarely show promising thermoelectric properties due to the metallic properties that evoke low Seebeck coefficients of these compounds [6]. On the contrary, type-I clathrates demonstrate higher *ZT* with increasing temperature, with Ba8Ga16Ge30 being the record holder displaying *ZT* = 1.35 at 900 K for Czochralski-pulled crystals [46].

Up to date, type-VIII clathrates demonstrate the highest values of *ZT* at elevated temperatures. These compounds are far less numerous than type-I and type-II counterparts, but, nevertheless, provide good examples of well-studied thermoelectric materials. In mid-temperature region, properly doped Ba8Ga16Sn30 holds the record of the highest *ZT*. For n-type crystals grown from Ga flux and *p*-type crystals grown from Sn-flux display the highest thermoelectric efficiency. When properly doped, these compounds exhibit appreciable high values of *ZT* reaching 1.45 at 500 K for Cu-doped *n*-type material and 1.0 at 480 K for Sb-doped *n*-type material [40, 47]. In general, prominent figures-of-merit can be reached only in the case of doped materials, even if doping is homovalent, but affords appropriate change in electronegativity and host-guest mismatch due to the adjustment of atomic radii. For instance, type-VIII clathrate Sr8Ga18Ge30 does not display intriguing thermoelectric properties; however, partial substitution of Al for Ga affords *ZT* = 0.56 at 800 K [48]. Interestingly, replacement of guest Sr atoms by Eu ones leads to much poorer thermoelectric efficiency despite clearly similar atomic radii of these M2+ cations. The reason of this effect is not clear; probably, it is associated with magnetic structure of Eu-based analog. Moreover, this compound was reported to undergo second-order phase transition upon cooling to below 13 K followed by antiferromagnetic ordering that triggers giant magnetocaloric effect with magnetic entropy of 11.3 J × kg−1 × K−1 [49]. Another example of increasing *ZT* upon introduction of magnetic cation is provided by Ba6.9Ce1.1Au6Si40, for which realization of Kondo interactions is believed to enhance the figure-of-merit by factor of 2 [11].

Because type-VIII clathrates demonstrate relatively poor thermal stability, their possible applications are limited by about 800 K, and they cannot be regarded as candidates for hightemperature thermoelectric power generation. Instead, silicon-based type-I and type-III clathrates are being investigated at high temperatures because of their utmost stability against oxidation in air [35]. In particular, cationic clathrates Si31.9P7.1Te7.0 (type-I) and Si132P40Te21.5 (type-III) are chemically and thermally stable up to 1200 K owing to several nanometers thin layers of phosphorus-doped silicon dioxide, which protects bulk samples from penetrating oxygen, that would lead to oxidation. Reported values of *ZT* for these Si-based clathrates do not exceed 0.4 (**Figure 12**); however, no attempts to increase the figure-of-merit have been performed so far.

**Figure 12.** Figure-of-merit as function of temperature in double-logarithmic coordinates for type-I and type-III clathrates in Si-P-Te system.

Summarizing this section, it is worth noting that thermoelectric figure-of-merit for several clathrates of different structure types reaches 1.4–1.45 in the region of 500–800 K. The main tool for achieving such high values lies in the subtle doping of various low-gap clathrates that causes simultaneous increase in electrical conductivity and Seebeck coefficient caused by proper doping accompanied by minor decrease in thermal conductivity caused by slight mass alteration.

## **5. Conclusion and outlook**

reaching 1.45 at 500 K for Cu-doped *n*-type material and 1.0 at 480 K for Sb-doped *n*-type material [40, 47]. In general, prominent figures-of-merit can be reached only in the case of doped materials, even if doping is homovalent, but affords appropriate change in electronegativity and host-guest mismatch due to the adjustment of atomic radii. For instance, type-VIII clathrate Sr8Ga18Ge30 does not display intriguing thermoelectric properties; however, partial substitution of Al for Ga affords *ZT* = 0.56 at 800 K [48]. Interestingly, replacement of guest Sr atoms by Eu ones leads to much poorer thermoelectric efficiency despite clearly similar atomic radii of these M2+ cations. The reason of this effect is not clear; probably, it is associated with magnetic structure of Eu-based analog. Moreover, this compound was reported to undergo second-order phase transition upon cooling to below 13 K followed by antiferromagnetic ordering that triggers giant magnetocaloric effect with magnetic entropy of 11.3 J × kg−1 × K−1 [49]. Another example of increasing *ZT* upon introduction of magnetic cation is provided by Ba6.9Ce1.1Au6Si40, for which realization of Kondo interactions is believed to enhance the

Because type-VIII clathrates demonstrate relatively poor thermal stability, their possible applications are limited by about 800 K, and they cannot be regarded as candidates for hightemperature thermoelectric power generation. Instead, silicon-based type-I and type-III clathrates are being investigated at high temperatures because of their utmost stability against oxidation in air [35]. In particular, cationic clathrates Si31.9P7.1Te7.0 (type-I) and Si132P40Te21.5 (type-III) are chemically and thermally stable up to 1200 K owing to several nanometers thin layers of phosphorus-doped silicon dioxide, which protects bulk samples from penetrating oxygen, that would lead to oxidation. Reported values of *ZT* for these Si-based clathrates do not exceed 0.4 (**Figure 12**); however, no attempts to increase the figure-of-merit have been performed so

**Figure 12.** Figure-of-merit as function of temperature in double-logarithmic coordinates for type-I and type-III clath-

Summarizing this section, it is worth noting that thermoelectric figure-of-merit for several clathrates of different structure types reaches 1.4–1.45 in the region of 500–800 K. The main tool for achieving such high values lies in the subtle doping of various low-gap clathrates that

figure-of-merit by factor of 2 [11].

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

far.

rates in Si-P-Te system.

Clathrates have been an attractive family of compounds primarily because of their fascinating structures. Within decades, it has become clear that clathrates are unique compounds combining spatial separation of host and guest substructures with very narrow (if any) band gaps, which allows almost independent optimization of charge carriers and thermal transport by tuning charge carriers' concentration and host-guest mismatch. Many chemical elements are known to take part in building clathrates frameworks of several types and serving as guests, making the property tuning plentiful and multifarious. With many instruments in hand, this tuning has already led to discovery of many clathrate compounds with carefully and wisely altered properties. Thermoelectric property optimization has been the central topic of clathrate research and resulted in various intriguing and promising achievements. They include, importantly, thermoelectric figure-of-merit almost reaching *ZT* = 1.5 in mid-T range and discovery of clathrates that demonstrate utmost stability in moist air at higher temperatures.

Nowadays, clathrates, albeit showing promising thermoelectric performance, are still far from commercial production and applications. Waiting for their explorations are elaboration of fabrication methods leading to *n*- and *p*-type legs of thermoelectric device, investigation of their compatibility at working temperature (from 500 to 1100 K), and engineering of contact and isolation layers. However, emerging sphere of automotive thermoelectric power generation requires new and more efficient thermoelectric materials capable of working at mid-T range being environmentally benign, whereas new trends in solar energy harvesting call for new thermoelectric materials exhibiting combination of high efficiency with outstanding chemical and thermal stability.

Nevertheless, clathrate research is an ongoing exploration. More than 300 papers are being published per annum in this decade on the topics ranging from the property optimization to uncovering of the underlying physics to elaboration of synthetic pathways and to discovery of new clathrates and related materials. Whereas the former topic works for near-future applications, the latter one is still of basic research. However, it shows that many new clathrates, including those of rare or even new types, are awaiting their discovery and property investigation.

## **Acknowledgements**

This work is supported in part by the Russian Science Foundation under Grant # 16-12-00004.

## **Author details**

Andrei V. Shevelkov

Address all correspondence to: shev@inorg.chem.msu.ru

Department of Chemistry, Lomonosov Moscow State University, Moscow, Russia

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#### **Efficient Thermoelectric Materials Based on Solid Solutions of Mg2X Compounds (X = Si, Ge, Sn) Efficient Thermoelectric Materials Based on Solid Solutions of Mg2X Compounds (X = Si, Ge, Sn)**

Vladimir K. Zaitsev, Grigoriy N. Isachenko and Alexander T. Burkov Vladimir K. Zaitsev, Grigoriy N. Isachenko and Alexander T. Burkov

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

http://dx.doi.org/10.5772/65864

#### **Abstract**

The silicides have obvious attractive characteristics that make them promising materials as thermoelectric energy converters. The constituting elements are abundant and have low price, many of compounds have good high temperature stability. Therefore, considerable efforts have been made, especially in the past 10 years, in order to develop efficient silicide-based thermoelectric materials. These efforts have culminated in creation of Mg2(Si-Sn) n-type thermoelectric alloys with proven maximum thermoelectric figure of merit *ZT* of 1.3. This success is based on combination of two approaches to maximize the thermoelectric performance: the band structure engineering and the alloying. In this chapter, we review data on crystal and electronic structure as well as on the thermoelectric properties of Mg2X compounds and their solid solutions.

**Keywords:** silicides, magnesium silicide, thermoelectricity, figure of merit

## **1. Introduction**

Among the large family of silicon-based compounds, semiconducting silicides have received particular interest as thermoelectric materials because they are potentially cheap and mostly stable materials. Comparatively, low charge carriers' mobility in these semiconductors is compensated by high electron state density, i.e. high effective mass of charge carriers. Therefore, silicides were the main focus of thermoelectric research community since the 1950s [1]. Investigations of these materials were especially active during the past 10 years. The most important results have been achieved for Mg2X (X = Si, Sn, Ge)-based alloys. Based on the Zaitsev et al. [2] work, n-type Mg2(Si-Sn) solid solutions with thermoelectric figure of merit

© 2017 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. © 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.

(*S* is thermopower or Seebeck coefficient; *σ* is electrical conductivity; κ is thermal conductivity, and *T* is absolute temperature) up to 1.3 were obtained by several research groups [3–7]. Many researchers believe that there is possibility for further improvement. Now considerable efforts are directed to the development of a matching p-type material.

Already in the 1960s, it was shown that Mg2X compounds (X = Si, Ge, Sn) and their solid solutions are promising compounds for thermoelectric energy conversion [8, 9]. Very high values of *ZT* are reported in Refs. [10, 11]. However, later the interest to these compounds has been almost vanished until the last decade. A new wave of research activity on Mg2X compounds was initiated by information about high figure of merit achieved in Mg2Si-Mg2Sn solid solutions and growing interest to environment-friendly materials for thermoelectric energy conversion.

The maximum conversion efficiency of thermoelectric generator *η* is determined by dimensionless figure of merit *ZT* [12]:

$$\eta = \frac{T\_H - T\_C}{T\_H} \frac{\sqrt{\overline{ZT} + 1} - 1}{\sqrt{\overline{ZT} + 1} + \frac{T\_C}{T\_H}},\tag{1}$$

where *TH* and *TC* are temperatures at hot and at cold junctions of thermoelectric generator thermopile. is the dimensionless figure of merit, averaged over working temperature range Δ*T* = *TH* – *TC*. The semiconductor physics theory gives the following estimate for parameter *Z* [13]:

$$Z\_{\text{max}} = \frac{(m^\*)^{\frac{3}{2}}\mu}{\kappa\_{\text{lat}}},\tag{2}$$

where *m*\* is the effective mass of electron state density (DOS), *µ* is the free charge carriers' mobility, and *κ*lat is the lattice thermal conductivity. One can see that a good thermoelectric material will have heavy effective mass, high charge carriers' mobility, and low lattice thermal conductivity. However, in fact coefficients determining Z are strongly interdependent. Thermoelectric materials with high DOS typically have low mobility. Introducing a disorder to suppress the thermal conductivity usually leads to decrease of charge carriers' mobility. This is the reason of slow progress in the development of efficient thermoelectrics.

The unique characteristics of an electronic band structure of Mg2X compounds make possible to explore the combination of two approaches to optimize the thermoelectric performance of such materials: the band structure engineering and the alloying [2, 5]. The combination allows to simultaneously maximize electronic parameters, characterized by power factor *S*<sup>2</sup> *σ*, and to minimize lattice thermal conductivity, yielding high values of parameter *Z*.

In this chapter, we summarize the present state of the knowledge on the crystal and electronic structure of Mg2X compounds and their alloys, and review experimental data on thermoelectric properties of compounds.
