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Thermoelectrics: Material Candidates and Structures I – Chalcogenides and Silicon-Germanium Alloys

  • N. M. Ravindra
  • Bhakti Jariwala
  • Asahel Bañobre
  • Aniket Maske
Chapter
  • 526 Downloads
Part of the SpringerBriefs in Materials book series (BRIEFSMATERIALS)

Abstract

Bismuth telluride, Bi2Te3, state-of-the-art material, is a well-established and effective thermoelectric material from V–VI group of materials. The Peltier effect (thermal cooling) has been observed in p-Bi2Te3 coupled with n-type samples and has been commercialized since the early 1960s. Tremendous amount of research has been reported on these materials from single crystal form to polycrystalline form and from 3D to nanodimensions to quantum confinement.

Keywords

Bi 2Te 3 Seebeck coefficientSeebeck Coefficient Electrical conductivityElectrical Conductivity Power factorPower Factor dopingDoping 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

5.1 Chalcogenides

5.1.1 Bismuth Telluride/Antimony Telluride

Bismuth telluride, Bi2Te3 , state-of-the-art material, is a well-established and effective thermoelectric material from V–VI group of materials. The Peltier effect (thermal cooling) has been observed in p-Bi2Te3 coupled with n-type samples and has been commercialized since the early 1960s. Tremendous amount of research has been reported on these materials from single crystal form to polycrystalline form and from 3D to nanodimensions to quantum confinement.

The atomic arrangement in A2B3 (A = Bi,Sb; B = Se,Te,S) compounds can be described as in Fig. 5.1. Here, the Bi and Te atoms are arranged by following the sequence of Te(1)-Bi-Te(2)-Bi-Te(1). Such a sequence is continuously repeated in parallel layers and single sequence known as quintuple. Here, the superscript for Te refers to various types of bonding with bismuth. The Te(1)-Bi and Bi-Te(2) are bonded by strong covalent-ionic bond, whereas a weak van der Waals force is responsible for bonding between Te(1) and Te(1) atoms. Due to this weak bonding between two successive quintuples, this compound has layered structure, and the crystal can easily cleavage along this direction, i.e., normal to the c-direction. There are a number of factors which contribute to making these materials the best thermoelectric material category among all other TE materials. These compounds are highly anisotropic in nature with high electrical conductivity with improved thermopower, good Seebeck coefficient, and lower thermal conductivity in the perpendicular direction compared to parallel to c-direction.
Fig. 5.1

Layered crystal structures of Bi2Te3 atom: (a) bulk unit cell ; (b) free standing slab with thickness of one quintuple layer (QL). (Source: Zahid and Lake [1]); (c) The first Brillouin zone for the rhombohedral cell along with symmetry axes and k points (d) position of dopant atom in the crystal structure. (Source: Huang and Kaviany [2])

Thermoelectric performance of chalcogenide-based thermoelectric materials can be improved by various approaches, such as enhancing electronic transport properties ; tuning the carrier conduction, via doping, alloying, and band structure engineering; or lowering the phonon conductivity through reduction in the dimension of the structure. Recently, the latter approach has been adopted by researchers to improve the thermoelectric (TE) efficiency of Bi2Te3 (Sb2Te3)-based materials by reducing one or more dimensions such as nanowires or thin films with simultaneous control over the transport properties and good optimization of the carrier selection. In nanostructured materials, grain boundary scattering plays an important role to suppress the phonon thermal conductivity, while the electronic thermal conductivity can be tuned efficiently by carrier concentration with the benefits in electrical conductivity. In one such instance, p-type bismuth telluride has been shown to have an improved Figure of Merit ZT = 1·41 at 300 K [3] in bulk crystals and ZT = 1·80 at 316 K [4] in nanodimensions, respectively. Apparently, the maximum Figure of Merit, ZT = 1.1 at 300 K [3], for n-type bismuth telluride, has been reported in bulk.

Synthesis techniques influence the material microstructure which in turn controls the transport properties along with the semiconducting properties through defect mechanism either intrinsically or extrinsically. Generally, melt growth techniques are utilized (Bridgman and zone melting) for the growth of single crystals [5]. Polycrystalline samples, in nanodimensions, can be prepared either chemically through electroplating [6, 7, 8] and aerogel method [9] or mechanically by processes such as ball milling, hot pressing, exfoliation [10], top-up [11], bottom-up wet chemical synthesis [12], etc. and be further subjected to annealing treatment for improved ZT. The maximum ZT = 1.3, for polycrystalline Bi0.3Sb1.7Te3 at 380 K, has been reported by a top-down hot deformed method by suppression of intrinsic conduction at elevated temperatures [13]. Here, the hot deformed method induces multi-scale microstructures and enhances textures and donor-like effects that contribute to improved electrical transport properties , whereas multiple phonon scattering centers, including local nanostructures that are induced by dynamic recrystallization and high-density lattice defects, significantly reduce the lattice thermal conductivity . All these effects combine to result in improved ZT over the room temperature to 500 K temperature range [13]. During the last decade, nanowire superlattices of Bi2Te3 [7], Bi/Sb [6, 14], Bi2Te3/Te [8], Bi2Te3/Sb [15], and Bi2Te3/(Bi0.3Sb0.7)2Te3 [16] multilayered nanowire arrays have been reported to be grown by the simple and efficient pulsed electrodeposition technique in a single ethanol bath. The inherent defect mechanisms, generally observed in such types of compounds, have been explained in the literature by utilizing experimental approaches [17]. Here, the existence of point defects can be found in the form of either vacancies or antisite defects or both. For example, Bi2Se3 often shows n-type conductivity due to donor-like defects VSe1 and SeBi (Fig. 5.2a), and it is difficult to be tuned into p-type via compensation doping [18, 19, 20, 21, 22]. Certainly, the compound formation is due to their lowest formation energies which in turn depend on the growth conditions [23, 24]. This will lead to an intrinsic n-type doping as has been observed experimentally. In the extreme Bi-rich condition, the acceptor-like defect BiSe1 will be preferred and the resulting doping will be p-type. Sb2Te3 shows SbTe1 antisite defects reflecting p-type tendency in general with the lowest formation energy in most ranges of growth conditions, especially in the Sb-rich condition [25, 26]. As the growth atmosphere evolves to be extremely Te-rich, the antimony vacancy VSb becomes the most energetically stable. It should be noted that both SbTe1 and VSb are acceptor-like defects; Sb2Te3 is thus always intrinsic p-type [23, 25, 26]. For Bi2Te3 , antisite defects, BiTe1 and TeBi, are more preferred; Bi2Te3 is reported to be either n-type due to donor-like TeBi in Te-rich condition [21, 27, 28] or p-type [29] through acceptor-like BiTe1 in Bi-rich condition, depending on the growth method and the environment. There is also reported work on the coexistence of n and p-type conduction in Bi2Te3 . Generally, the carrier type varies with the chemical potentials, and its correlation with formation energy is shown in Fig. 5.2.
Fig. 5.2

The formation energy (H) as a function of anion chemical potential for all possible intrinsic defects in (a) Bi2Se3 , (b) Bi2Te3 , and (c) Sb2Te3 . VBi, VSb, VSe, and VTe represent bismuth vacancy, antimony vacancy, selenium vacancy, and tellurium vacancy, respectively, while BiSe, BiTe, SbTe, SeBi, and TeBi are antisite defects. 1 and 2 are labeled to distinguish Se (Te) in different layers. X rich (X for Bi, Sb, Se, or Te) indicates the extreme growth condition. Vertically dotted lines highlight the boundary of carrier types. (Source: Zhang et al. [17]; Color figure online)

Bismuth (antimony) telluride -based compounds are anisotropic in nature; for example, the electrical and thermal conductivities are higher along planes parallel to the cleavage than perpendicular to them. This has been reported experimentally in terms of the electrical conductivity, Hall mobility, and Seebeck coefficient measurements for Bridgman-grown Bi2Te3 single crystals [30]. However, it must be noted that the stoichiometric compounds of Bi2Te3 were grown by the zone melting technique successfully during the first reports in the literature. Under the conserved stoichiometric condition, in p-Bi2Te3 , obtained in the presence of excess of Bi atoms, the excess Bi atoms appear to act as acceptor impurities leading to p-type conduction, by producing corresponding vacancies on some of the Te sites. Bismuth telluride has been the most studied material among all the thermoelectric compounds due to its high mean atomic weight, relatively low melting temperature of 585 °C and low lattice conductivity. The increase in electrical resistivity has been observed by Nassary et al. [30], in the temperature range of 163–666 K, for all the three regions, extrinsic, transition, and intrinsic, for both the longitudinal and transverse directions of Bi2Te3 layers. Transport parameters such as carrier concentration, in the extrinsic region, increases slowly with increasing temperature, though it increases rapidly with temperature in the intrinsic region. The Hall mobility values, obtained in the parallel and perpendicular direction, are 182.03 cm2 V−1 s−1 and 44.89 cm2 V−1 s−1, respectively; a higher value of mobility in the parallel direction clearly indicates the anisotropic nature of Bi2Te3 ; the corresponding hole concentration is 2.64 × 1017 cm−3 at room temperature. Also, the maximum value of Seebeck coefficient (477.69 μVK−1) is reported in the parallel direction than that along the perpendicular direction at room temperature.

In thermoelectrics, the most utilized approach is alloying or doping, in which intentionally doped anion/cation plays a role in the optimization of transport parameters, such as carrier concentration, carrier mobility, carrier effective mass, and Fermi level. Bulk samples of n-type Bi2Te2.7Se0.3, with significant lower thermal conductivity of 1.06 Wm−1 K−1 and a lattice contribution of 0.7 Wm−1 K−1, have been reported by Yan et al. [31]. The randomness of small grains reflects in lowering the power factor and is not observed in enhancement of ZT. The electrical conductivity can be increased through subjecting the samples to hot press method. In the case of Se doping, the electrical conductivity of the BiTeSe system decreases with increasing Se content up to x = 0.21 [32]. Basically, Se can increase the defect content in the base material and enhance the carrier scattering effects/phonon scattering [33]. Recently, Zahid et al. [1] reported a theoretical maximum value of ZT = 7.5 and twofold improvement in Seebeck coefficient for bulk samples at room temperature. Experimentally, for thin 2D films of Bi2Te3 , for the thickness of 1QL (quintuple layer), Goyal et al. [34] have achieved in-plane thermal conductivity value of 0.7 W/mK and cross plane thermal conductivity value of 0.14 W/mK for the stacked exfoliating Bi2Te3 films up to thickness of 0.5 mm with the value of Seebeck coefficient in the range of 231–247 μVK−1. A comparatively good Seebeck coefficient of 255 μVK−1 and a power factor of 20.5 × 10−4 WK−2 m−1 were obtained for Bi2Te3 thin films deposited by close space vapor transport (CSVT) method at a substrate temperature of 350 °C [35].

The transport properties of Bi2Te3-Sb2Te3 alloy system, formed by zone melting, has been investigated [36]. Here, the increase in Bi2Te3 content led to a substitution of the Sb atoms in Sb2Te3, leading to a decrease in hole concentration and thus resulted in a decrease in σ and an increment in the Seebeck coefficient. The ultimate maximum Figure of Merit, Z = 2.7 × 10−3 K−1, was obtained at about 300 K for the composition: 25%Bi2Te3–75%Sb2Te3 with 3 wt% excess of Te. Principally, the antisite defect structure, created by Bi2Te3 content in the Sb2Te3 structure, affects the hole concentration and electrical conductivity and, in turn, the Seebeck coefficient.

Bulk single crystals exhibit high thermal conductivities and have limited applications in thermoelectrics. One can overcome such a disadvantage in polycrystalline materials. In the case of polycrystalline materials, the microstructure plays an important role and influences the transport properties, as experimentally analyzed by Zhang et al. [37]. They have observed higher carrier concentration in hot-pressed samples compared to zone-melted crystals (one of the widely adopted techniques to grow single crystals) mainly due to the grain boundary scattering of electrons in hot-pressed samples. Despite the high carrier concentration, the Seebeck coefficient value has been lowered due to scattering mechanism. The thermopower values are 2.09 × 10−4 Wm−1 K−2 and 16.59 × 104 Wm−1 K−2 for hot press samples and single crystals, respectively. One can conclude that phonon transport is greatly affected by the grain boundary scattering mechanism and lowers the thermal conductivity which further diminishes the electronic properties. Therefore, it can be suggested that the optimization of both chemical composition and microstructure is required for maximizing the ZT values in polycrystalline samples. Another successful effort has been reported by Xiaohua et al. [38], utilizing grain boundary engineering in polycrystalline p-type Bi2Te3 system via an alkali metal salt hydrothermal nano-coating treatment approach. The thermal conductivity has been reduced up to 38% compared to the bulk sample. Here, alkali metal salt coating of amorphous layer on Bi2Te3 grains introduces an elastic mismatch at the grain boundary , resulting in increased phonon scattering and, consequently, a reduction in the lattice thermal conductivity. This also acts as a charge reservoir for tuning the electronic properties.

In addition to their applications in thermoelectrics, bismuth- and antimony-based chalcogenides exhibit topological insulating surface states and time-reversal symmetry breaking [39, 40], which make them essential candidates for applications in spintronics [41] and superconductors [42]. Research scientists have enormous interest in three-dimensional (3D) topological insulators (TIs) with both metallic surface states and insulating bulk states [43] and the experimental evidence of proximity-induced high-Tc superconductivity [11] in Bi2Se3 and Bi2Te3 . The three-dimensional strong topological insulators (TI), with realistically large (a few hundred meV) bulk gap and simple surface electronic structures, have been observed, both theoretically and experimentally, for the first time in such compounds. Topological insulators have insulating bulk states and gapless conducting surface states [18, 19, 28, 44, 45, 46, 47, 48, 49]. Basically, research efforts are in progress to achieve magnetization in these compounds, in the form of dilute magnetic semiconductors (DMS), by doping them with magnetic ions. The introduction of ferromagnetism, due to doping of such magnetic atoms, 3D transition metal (TM) elements, V, Cr, Mn, and Fe, in general, will break the time-reversal symmetry [50]. This intricate interplay between topological order and ferromagnetism has inspired several proposals and new ideas to realize exotic quantum phenomena such as the magnetoelectric effect [40] and quantum anomalous Hall effect (QAHE) [51, 52, 53, 54, 55, 56, 57]. The probability of incorporation of transition metal atoms into Bi2Se3 , Bi2Te3, and Sb2Te3 , as well as by utilizing defect mechanisms , either at a substitution site or at an interstitial site or coexistence of substitutional and interstitial sites, has been elaborated by Zhang et al. [17] in detail. They have explained such phenomena in terms of the formation energies for the individually incorporated TM atoms, as a function of chemical potential, as shown in Fig. 5.3. Here, the formation energy is dependent on the size of the transition metal, that is being doped, in each of the compounds [58]. The formation energies in Bi2Se3 [59] and Sb2Te3 [60, 61] have been found to be negative upon V and Cr [40, 62, 63] doping, indicating the most favorable and spontaneous doping and is positive for Mn [42, 64, 65, 66] and Fe [67, 68] doping, suggesting the doping needed, for the entire range of chemical potentials except for Mn in Bi2Se3 which requires an extremely Se-rich atmosphere. Moreover, considering point defects , substitution is a more preferable mechanism in Fe-doped Bi2Se3 where Fe substitutes Bi in Bi2Se3 , which is further independent of the variation in growth conditions. However, this is not the case for Cu doping; interstitial site is dominant in Cu-doped Bi2Se3, along with the possibility of interstitial sites between different layers (intercalated sites) and interstitial sites on the same layer [69]. The details of the electronic structure and magnetization of these TE compounds have been thoroughly described in the literature [17].
Fig. 5.3

(Color online) Calculated formation energies of the most stable configurations of single V-, Cr-, Mn-, and Fe (impurities)-doped (a) Bi2Se3 , (b) Bi2Te3 , and (c) Sb2Te3 as a function of the host element chemical potentials. (Source: Zhang et al. [17]; Color figure online)

Some of the important results that have been reported on the thermoelectric properties of Bi2Te3 -based materials are summarized in Fig. 5.4; the related transport parameters are presented in Table 5.1.
Fig. 5.4

Comparison of (a) Figure of Merit (ZT); (b) Seebeck coefficient (S) as a function of temperature for undoped and doped Bi2Te3 . (Source: Jariwala and Nuggehalli [70])

Table 5.1

Transport parameters of Bi2Te3 at various temperatures (K)

Compound

σ (μΩm)

S (μVK−1)

κ (Wm−1 K1)

ZT

Growth method

p-(Bi0.25Sb0.75)2Te3 [3]

~9.5 (308)

~225 (308)

1.21 (308)

1.41

Crystal-Bridgman

n-Bi2(Te0.94Se0.06)3 [3]

~10 (308)

~240 (308)

1.26 (308)

1.13

Crystal-Bridgman

p-Bi0.4Sb1.6Te3 [4]

   

1.8 (316)

Nanocomposite

n-(Bi2Te3)0.24(Sb2Te3)0.76 [71]

~1 (300)

~215 (300)

1.50 (300)

1.14(350)

Crystal-zone melt

5.1.2 Lead Telluride

PbTe is a narrow bandgap chalcogenide semiconductor . It has octahedral coordination with rock-salt structure (Fig. 5.5), and its lattice dynamics manifests a high degree of anharmonicity [72]. PbTe and their alloys have been of great interest because of their fundamental electronic properties and their practical applications such as in infrared detectors, light-emitting devices, infrared lasers, thermophotovoltaics, and thermoelectrics [74, 75, 76]. Generally, PbTe is found as a p-type semiconductor [77] although n-type conduction due to the excess of Pb in PbTe has also been reported [78].
Fig. 5.5

(a) Conventional cell of PbTe showing simple cubic structure. Yellow and gray beads are Te and Pb, respectively. (Source: Kim and Kaviany [72]) (b) Supercell model of RPb31Te32 where R is either a vacancy or an impurity atom. Small beads are for Pb and Te, large beads are for R. (c) Brillouin zone image [73]: low and high degeneracy hole pockets centered at the L point and along the Σ-line, respectively, represented in orange and blue colors. Here, total 4 full number of valleys are available along with the 12 valley degeneracy of Σ-band. (Source: Pei et al. [73])

The high symmetry crystal structure of PbTe has significant valley degeneracy in both valence and conduction bands that play supporting role for the convergence of many valleys if the Fermi surface forms isolated pockets at low symmetry points. It means that bands may be regarded as effectively converged when their energy separation is small compared with kBT, significantly increasing the valley degeneracy even when the bands do not exactly degenerate [73]. Such a situation is easily possible in low-dimensional systems and attracts scientists to perform research in this direction [79]. As seen in Fig. 5.5c, the valence band extremum in PbTe occurs at the L point in the Brillouin zone (valley degeneracy, 4) [80, 81] with second valence band along the Σ-line, just below the first valence band at the L band (valley degeneracy, 12) [80].

In this case of the binary compound, PbTe, recent trend has significantly focused on its alloys, known as TAGS (Te/Sb/Ge/Ag) – i.e., alloys of AgSbTe2 and GeTe with SnTe and PbSe; these alloys represent the best thermoelectric materials based on PbTe so far. The maximum Figure of Merit reported is ZT ~ 1.8 at 850 K in sodium-doped PbTe1−xSex alloys [76]. Regardless of the effort of improving the Figure of Merit, the thermally induced topological transitions in PbTe/CdTe heterostructures, from 2D epilayer to quasi 1D percolation phase and to 0D quantum dots, have been derived by parameter-free geometrical model as well as demonstrated experimentally [82]. In the case of n-PbTe [83] quantum dots, the measured data indicate that the electrical conductivity, Seebeck coefficient, and power factor depend on the carrier concentration and the electrical conductivity increases with carrier concentration; the magnitude of the Seebeck coefficient decreases, and the power factor displays a broad maximum around a level of n ~ 4–5 × 1018 cm−3. At lower carrier concentrations, all three scattering mechanisms are important, while phonon deformation potential scattering, through both acoustic and optical phonons, dominates at higher carrier concentrations. This is accompanied by decrease in the electrical conductivity, and the Seebeck coefficient increases with temperature. All the experimental results have been seen to be in good accord with those that are obtained by simulations. Seebeck coefficient is found to be slightly higher for p-PbTe than for n-PbTe. The impact of nanostructuring is almost identical for both n- and p-type PbTe/PbSe nanodot superlattice (NDSL) structures . Mobility of charge carriers in the PbTe/PbSe NDSL system is 25–35% lower compared to the homogeneous PbTe, but the Seebeck coefficient is essentially the same for both the nanodot superlattice suggesting that the scattering rate has increased. The measured transport parameters have been reported as follows: electrical conductivity is ~1000 Ω−1cm−1(in-plane) at 300 K for carrier concentration, n = 4.73 × 1018 cm−3, and Seebeck coefficient is ~425 μVK−1 at 550 K for carrier concentration, p = 8.85 × 1018 cm−3, in n-PbTe/PbSe and p-PbTe/PbSe nanodot superlattice structures, respectively [83].

Further, the enhancement in the thermoelectric performance has been reported through nanocomposite effect for AgPbmSbTem+2 alloys [84]. Quantum wells of PbTe/Pb1−xEuxTe and PbSe0.98Te0.02/PbTe superlattices [85] and novel quaternary compounds, AgSbPb2n−2Te2n (n = 9, 10) [84] and Na1−xPbmSbyTem+2 [86], have attracted considerable attention because of their low thermal conductivity and large thermoelectric Figure of Merit. Most of the above systems have stoichiometry closer to the parent compound PbTe. Moreover, solvothermal synthesized PbTe/SnTe hybrid nanocrystals have been reported recently [87] with the advantages of the freedom of tuning the shape, size, and chemical composition with ligand-free nanocrystal as well as mass production. The increment in electrical conductivity is by 15 orders of magnitude compared to as-grown samples by spark plasma sintering (SPS) method, one of the most utilized techniques so far. The second most adopted technique is powder metallurgy, and transport properties have been reported for n- and p-type PbTe and Pb1−xSnxTe compounds [88]. The spin-orbit coupling has been studied experimentally in n-PbTe quantum wells, grown by molecular beam epitaxy on (111) plane BaF2 substrates by Peres et al. [89]. Vatanparast et al. [90] have reported nanostructures of PbTe synthesized by a less known technique, called sonochemical method. The impact of growth methods on the electronic transport properties of Cr-doped PbTe crystals, grown by two different growth methods, directional crystallization of melt and vapor-liquid-solid (VLS) technique, has been described in the literature [91]. The Hall effect and electrical conductivity measurements showed that the crystals that are obtained by directional crystallization of the melt exhibit n-type conductivity with electron concentration of 1.22 × 1018 cm−3, while crystals, prepared by vapor-liquid-solid technique, exhibit p-type conductivity with electron concentration of 6.58 × 1018 cm−3, respectively. The electrical resistivity shows a typical metallic behavior with more than an order magnitude increase with a positive temperature coefficient. Generally, the charge carrier concentration in lead telluride and its solid solutions is comparatively high due to the existence of vacancies and interstitials in the crystal lattice.

It is well-known that the transport properties of semiconductors are dominated by doping of impurity atom or by vacancy in the binary or ternary compound depending on either Pb or Te atom replaced by a donor or acceptor like impurity or a vacancy. There are a number of atoms that are possible for substitution of Pb such as Cu, Cd, Hg, Ga, Sn, Zn, In, Tl, Sb, Bi, or As and S, Se, or I for Te substitution. However, in order to reduce the lattice thermal conductivity , the useful thermoelectric materials are usually ternary or even quaternary alloys of the type Pb1−xSnxTe1−ySey [92], Pb1−xSnx1−yInyTe [93], or similar mixtures of group IV and group VI elements. PbTe samples, containing nanometer-sized (40 nm) precipitates of Pb metal , prepared by quenching and subsequent anneal, show enhancement in the Seebeck coefficient in both n-and p-type samples [94]. An enhancement in Seebeck coefficient is attributed to scattering mechanism by nanoprecipitates which is of the same magnitude as observed in PbTe-based quantum-dot superlattices. However, this reduces the carrier mobility by a factor of ~3.

Modeling and simulation of the thermoelectric properties for p-PbTe has been reported in the high-temperature range using Ab Initio Molecular Dynamics (AIMD) with wave-based density functional theory (DFT) [72]. ZT has been calculated from DFT and MD/Green-Kubo calculations, and similar trends have been obtained by analytical model predictions (temperature-dependent effective mass) and wave-based DFT which is also in good agreement with the experimental results [95]. Tian et al. [96] have reported that the contributions from phonon conduction mechanisms to lattice thermal conductivity are particularly important. They estimate the impact of nanostructuring and alloying on further reducing the lattice thermal conductivity for PbSe, PbTe, and PbTe1−xSex by density functional perturbation theory (DFPT) calculations. Their results show that the optical phonons are important not only because they directly comprise of the lattice thermal conductivity but also because they provide strong scattering channels for acoustic phonons, which is crucial for the low thermal conductivity. On the other hand, alloying and nanostructures are relatively effective ways to reduce the lattice thermal conductivity if the size of the nanostructure is ∼10 nm or less. Similar simulations have been performed by considering mode-dependent phonon (normal and Umklapp) scattering rates. The lowering of the thermal conductivity in PbTe is due to the scattering of the longitudinal acoustic phonons [97]. Optical properties of PbTe, PbSe, and heavily doped p-type PbSe, with maximum Figure of Merit, ZT ~ 2 at 1000 K, were simulated by first-principles calculations as well as by empirical models [98, 99, 100, 101]. Wrasse et al. [102] have also reported results for PbSe and PbTe nanowires by similar simulations. Electronic properties are strongly correlated to in-plane stoichiometry, quantum confinement, and spin-orbit (SO) interactions, whereas stability depends on the nanowire diameter. The bandgap could be indirect or direct depending, totally, on the in-plane stoichiometry indicating that there is an electronic compensation mechanism between quantum confinement effects and SO interactions, resulting in an almost diameter-independent bandgap [103]. In IV–VI semiconductors , the group III impurities, such as indium, thallium, and gallium, have been known to exhibit anomalous behavior [104, 105]. For example, PbTe, doped with group III impurities, can act as either donor or acceptor depending on the specific composition of the semiconductor. The pinning of the Fermi energy and mixed-valence behavior has also been observed in this system. The upper localized band moves toward the valence band and overlaps with the top of the valence band. Because of the strong hybridized nature of both the upper and lower localized bands, photoexcitation to the conduction band from these states can lead to strong electronic and lattice relaxation. Indeed, group III impurities possess two kinds of valence states in solids, trivalent and monovalent, whereas divalent impurity states act as excited states. Ab initio density functional calculations, using a periodic supercell model, have been performed to determine localized states, induced by group III impurities, in PbTe [106, 107, 108, 109]. In the case of In, two “localized” bands of states appear, one below the valence band minimum and the other above the valence band maximum, which are deep defect states that are associated with the In impurity. Here, the valence band loses one state per impurity and leads to the pinning of the Fermi energy in the bandgap. Further, the position of defect levels of cationic and anionic substitutional impurities in the density of states , near the top of the valence band and the bottom of the conduction band, for RPb2n−1Te2n and MPb2nTe2n−1 [106] (where R is vacancy or monovalent, divalent, or trivalent atom of different valence and M is vacancy, S, Se, or I), gets significantly modified for most of these defects. The transport properties of PbTe, in the presence of impurities, may not always be interpreted by simple carrier doping concepts. Hong et al. [110] have studied the defect states that are associated with different substitutional impurities and native defects in pure PbTe(001) films. In the supercell models, the bulk to subsurface to surface layer transition is accompanied by the formation of localized bands by hyper-deep defect states, such as Ga-, In-, and Tl-doped PbTe films which are similar to those in bulk PbTe. These localized bands get narrower and move toward the bottom of the valence band and exhibit a crossover from 3D to 2D band structure due to the change in the impurity-impurity interaction along the z direction. The deep defect states, in the first and the second layers, tend to be shifted upward toward the conduction band bottom compared to that in the third layer. The defect states that are associated with various monovalent (Ag, Na, and K), divalent (Cd and Zn), and other trivalent (Sb and Bi) impurities and Pb and Te vacancies also get modified with transition from the bulk to thin films and from one layer to another [110].

Experimentally, Heremans et al. [111] reported maximum ZT for Tl-doped PbTe. For these films, they obtain the following: maximum ZT ~ 1.5 for Tl0.02Pb0.98Te at 773 K, an increase in carrier concentration, lowering of the Seebeck coefficient and electrical resistivity, and ambipolar thermal conduction at high temperature. Indeed, increase in carrier density more than compensates for decrease in mobility by Tl doping, which in turn is responsible for maximum ZT. Recently, the same group of authors also reported their studies on Al (monovalent impurity)-doped n-type PbTe. Here, Al behaves as a normal donor in PbTe, whose energy level lies deep in the conduction band and leads to a maximum electron concentration of 4 × 1019 cm−3 [103]. The effects of K and K-Na substitution for Pb atoms in Pb1−xNaxTe and Pb0.9875−xK0.0125NaxTe have been reported, experimentally, by Androulakis et al. [112]. Basically, resonant states emerge in the valence band that may enhance the thermoelectric power, but K-Na codoping does not form resonance states; they just control the energy difference of the maxima of the two primary valence subbands in PbTe. This leads to enhanced interband interaction with rising temperature and a significant rise in the thermoelectric Figure of Merit ZT ~ 1.3 at 700 K in K-Na-codoped Pb0.9815K0.0125Na0.006Te [112]. Jaworski et al. [113] have elucidated, theoretically and experimentally, that antimony acts as an amphoteric dopant in PbTe. Their band structure calculations show that Sb acts as a donor by substituting for Pb and acceptor on the Te site, with limited solubility of Sb on the Te site in Pb-rich PbTe, giving rise to a large excess density of states (DOS) . Experimentally, Te-rich Pb1−xSbxTe samples are n-type with maximum n ~ 9 × 1018 cm−3 at 500 K for Pb0.9975Sb0.0025Te; Pb-rich PbSbxTe1−x samples are p-type with maximum p ~ 4.9 × 1019 cm−3 at 300 K for PbSb0.01Te0.99, with enhanced Seebeck coefficient throughout the temperature range. The thermal conductivity is found to increase in Pb1−xSbxTe with increasing x due to increased electronic thermal conductivity; similar trend has been found in PbSbxTe1−x in the temperature range of 300–800 K.

Thermoelectric performance enhancement through nanocomposite effects has been reported for undoped and Ag-doped PbTe [114] and AgPbmSbTem+2  + x vol% SiC (x ≤ 2 vol%) nanoparticles [115], fabricated by densification procedure and mechanical alloying including spark plasma sintering . The unique temperature dependence of the resistivity and carrier mobility for these PbTe nanocomposites suggests that grain boundary potential barrier scattering is the dominant scattering mechanism in which carrier trapping in the grain boundaries forms energy barriers that impede the conduction of carriers between grains, essentially filtering charge carriers with energy less than the barrier height. These nanocomposites, therefore, demonstrate an enhanced Seebeck coefficient as compared to single-crystal or polycrystalline PbTe at similar carrier concentrations [114]. In the case of AgPbmSbTem+2  + x vol% SiC nanocomposite , the thermal conductivity reduction is due to phonon scattering by small amount of 30 nm SiC dispersions. This is due to the energy filtering effect being unavailable due to mismatch at the interface of SiC and the matrix. The maximum Figure of Merit, ZT ~ 1.54 at 723 K, was obtained in the AgPb20SbTe20 matrix composite containing 1 vol% SiC nanoparticles [115]. Recently, the nanoscale topological transitions from 2D to 0D have been reported experimentally in epitaxial PbTe/CdTe heterostructures by Groiss et al. [82]. An overview of the thermoelectric properties of some of the PbTe-based materials is presented in Fig. 5.6 and Table 5.2.
Fig. 5.6

Overview of (a) Figure of Merit (ZT), (b) Seebeck coefficient (S), (c) thermal conductivity (k), and lattice thermal conductivity (kl) as a function of temperature for conventional optimized n- and p-type PbTe. Here, filled symbols show total thermal conductivity, and unfilled symbols show lattice thermal conductivity of corresponding material. (Source: Jariwala and Nuggehalli [70])

Table 5.2

Thermoelectric properties of PbTe-based alloys at respective temperatures (K)

Materials

S (μV/K)

κ (Wm−1 K−1)

κlat (Wm−1 K−1)

ZT (T)

AgPb20SbTe20 + 1% SiC [115]

−230 (700)

0.7 (700)

 

1.5 (720)

PbI2-doped PbTe [116]

−300 (650)

1.3 (650)

0.9 (650)

1.35 (650)

Na0.007Pb0.993Se [117]

200 (800)

1.3 (800)

0.65 (800)

1.2 (850)

Na0.95Pb20SbTe22 [86]

350 (650)

1 (650)

1.7 (650)

PbSe [100]a

230 (1000)

2 (1000)

Pb0.96Mn0.04Te [118]

250 (700)

1.25 (700)

0.68 (700)

1.5 (750)

2% Na-doped (PbTe)0.86(PbSe)0.07(PbS)0.07 [119]

260 (800)

1.25 (800)

0.6 (800)

2.0(800)

aSimulation

5.2 Silicon-Germanium System

Most of the power generation based on thermoelectric devices is contributed from SiGe. This is mainly due to its compatibility, easy to be engineered, and, most importantly, its integration with complementary metal oxide silicon (CMOS) circuits. SiGe-based thermoelectrics operate in the temperature range of 600–1000 °C, with a Figure of Merit of 1.3 for n-type [120] and 0.95 for p-type [121] around 900 °C, respectively.

While Chap.  4 has presented a detailed discussion of SiGe-based thermoelectrics, a brief discussion of the topic is presented here.

SiGe has a cubic lattice structure known as the diamond lattice structure, and the unit cell is actually two interpenetrating fcc lattices separated by a/4 along each axis of the cell, represented by Fig. 5.7, along with the four nearest neighbor atoms bonding the Si lattice. The lattice constant of SiGe can be approximated using a simple linear interpolation from the lattice constant of Si and Ge, 5.43 Å and 5.66 Å, respectively, as a function of composition.
Fig. 5.7

The unit cell and diamond lattice structure for SiGe. (Sources: Streetman and Banerjee [122] and Ref. [123])

As described in the earlier sections, the microstructure has a significant influence on the thermal conductivity, especially in nanocrystalline structures. Regardless of just alloying, the reduction in dimension strongly decreases the mean free path of low frequency phonons; this leads to the maximum reduction in thermal conductivity. The dependency of the thermal conductivity on temperature, grain size L, and misorientation angle have been analyzed in SiGe alloys using molecular dynamics simulations [124]. The thermal conductivity varies with grain size as L1/4 which is further influenced by disorder scattering, in contrast to phonon transport mechanism that is mainly governed by boundary scattering in non-alloyed systems, whereas temperature and angle misorientation are less affected.

As one can observe in Fig. 5.8a and b, the figures show the finite size effects as well as the grain arrangement influence on κ, which is in agreement with the previous work of Ju and Liang [125]. The variation in κ with temperature, for specific grain size, is shown in Fig. 5.8c. The enhancement in thermoelectric performance of nanoscale Ge/SiGe heterostructure materials grown on Si substrates by low-energy plasma-enhanced chemical vapor deposition (LEPECVD), producing quantum wells and quantum dots, has been reported in the literature. The authors have reported the transport parameters as well as the Figure of Merit as a function of quantum well width. The electrical conductivity, thermal conductivity, Seebeck coefficient, power factor, and Figure of Merit have been investigated. In these studies, as the quantum well width is reduced, there is a sudden transition to a reduced electrical conductivity for samples with a larger amount of Si in the barriers which can be attributed to an increase in interface roughness scattering [126], although it is higher compared to the bulk ~33,300 S/m [127]. Due to this, the electrical conductivity and the Seebeck coefficient have been found to be sensitive to the dislocation density in this regime due to the local variations in the high threading dislocation density for each sample [128]. The presence of high dislocation density positively affects the Seebeck coefficient; an increase in the value up to a significant extent along with the enhancement by larger asymmetry across the chemical potential has been reported. The maximum Seebeck coefficient values have been reported in the range of 236.0 ± 3.5 and 279.5 ± 1.2 μV/K. Similar results have been obtained in the case of power factor, approximately six times larger than that of bulk thin film Ge for a comparable doping density [127]. In the thermal conductivity measurements, lower thermal conductivities have been observed for narrower quantum wells which is anticipated as diffuse phonon scattering should increase as the quantum well width is reduced, whereas high thermal conductivity is obtained for larger Si content due to the interface roughness scattering resulting in lowering the diffuse phonon scattering [129, 130].
Fig. 5.8

The thermal conductivity behavior as a function of (a) grain arrangement. (b) The average grain size and (c) temperature, for nanocrystalline Si0.8Ge0.2 obtained by EMD (equilibrium molecular dynamics) simulations. (Source: Abs da Cruz et al. [124])

Thermoelectric devices can also be fabricated successfully by utilizing the simplest 2D films. An efficient silicon germanium thermoelectric film has been deposited by electrophoresis deposition with large carrier mobility which in turn yields higher power factor [131]. The SEM micrographs, in Fig. 5.9, show excellent film uniformity and denseness. Figure 5.9a is the top view of the as-deposited film. Figure 5.9b represents the cross sections of the heat-treated samples of Si0.8Ge0.2 layers with thickness of approximately 160 nm on Si substrate.
Fig. 5.9

SEM images of Si0.8Ge0.2. (a) Top view of the as-deposited film and (b) cross sections of two pressed and heat-treated films, with 23 and 160 μm thicknesses, respectively, on Si substrate. (Source: Nozariasbmarz et al. [131])

Due to the ability to improve the Figure of Merit by modulation doping, it is a powerful and efficient way to increase the power factor. This technique is widely used in the fabrication of thin film semiconductors including nanocomposites (Si80Ge20)70(Si100B5)30 [132]. Basically, in modulation doping, the carrier mobility has to be increased significantly which consequently increases the electrical conductivity, but it also leads to an increase in the electronic component of the thermal conductivity and results in no improvement in ZT. Such an increase in the electronic part of the thermal conductivity is inevitable because charge carriers are also heat carriers. Therefore, one could lower the thermal conductivity through its lattice component, especially in nanostructured materials, and it eventually enhances the value of the Figure of Merit; maximum ZT of 1.3 ± 0.1 at 900 °C has been reported so far in the literature [132]. Similar results have been observed in 3D bulk nanocomposites; power factor of p-type Si86Ge14B1.5 and uniform n-type Si84Ge16P0.6 sample was improved by 40% and 20% using the modulation-doping approach in (Si80Ge20)0.7(Si100B5)0.3 and (Si80Ge20)0.8(Si100P3)0.2, respectively [133].

A thermoelectric generator , based on nanoscale-heterostructured, Ge-rich Ge/SiGe/Si superlattices, has been grown by low-energy plasma-enhanced chemical vapor deposition [134] technique. This method is accurate for the fabrication of multiple quantum well stacks in the sense that uniform composition and layer thickness, both vertically and laterally, with strain-balanced and lattice-matched features, have been obtained. Here, the authors report two advantages: the enhancement in the density of states near the Fermi level due to the low-dimensional structures as well as phonon scattering (at the interface roughness and ionized impurities) at heterointerfaces. The variation in carrier mobility, sheet density, and electrical conductivity is represented in Fig. 5.10. Maximum mobility has been observed in the region of 30 K (Fig. 5.10a). Mobility decreases with decreasing temperature, indicating ionized impurity scattering, and it further decreases in the region of ~100 K by following the function μ ∞ T−2, which is typical of optical phonon scattering [135]. Figure 5.10b shows the Hall sheet density per quantum well (QW). Here, the 1 and 3 QW structures show some increase in the density per QW with temperature compared to 10 and 50 QW structures, due to the fact that the structures of the fewer QWs are more sensitive to the potentials at the surface of the sample or at the interface between the MQW stack. The increased ionization of dopants in the barriers between the QWs results in the absolute change in density in 50 QW samples. The conductivity of carriers, as a function of their mobility, has been presented in Fig. 5.10c. The peak at around 1400 cm2 V−1 s−1 is due to the conduction within the QWs themselves, while the peak at lower mobility is assigned to parallel to bulk-like conduction within the doped barriers [134].
Fig. 5.10

At high temperatures (>100 K), (a) the Hall mobility (left, measured up to 1 T) decreases with a μ ∝ T−2 behavior typical of optical phonon scattering . Maximum mobilities are generally reached in the region of 30 K, and the mobility then decreases with decreasing temperature, indicating ionized impurity scattering. (b) The Hall sheet density per QW (right) is about 1.2 × 1012 cm−2 for the 10 and 50 QW structures, but the 1 and 3 QW structures show some increase in density with temperature as dopants are ionized. (c) Mobility spectra at 300 K generally indicate two peaks, corresponding to transport within the QWs and within the doped SiGe layers. The QWs are represented by the peaks at higher mobility, in the region of 1500 cm2 V−1 s−1. (Source: Chrastina et al. [134])

In Fig. 5.11, the temperature dependence of the Figure of Merit of SiGe is compared with those of Bi2Te3 and PbTe. As can be seen in this figure, the thermoelectric performance of Si-Ge is generally less sensitive to temperature, and its value of Z is considerably low compared to Bi2Te3 and PbTe.
Fig. 5.11

A diagram of Figure of Merit trend as a function of temperature for Bi2Te3 , PbTe, and SiGe. (Source: https://thermal.ferrotec.com/technology/thermoelectric-referenceguide/thermalref02/)

References

  1. 1.
    F. Zahid, R. Lake, Appl. Phys. Lett. 97(21), 212102 (2010)CrossRefGoogle Scholar
  2. 2.
    B.-L. Huang, M. Kaviany, Phys. Rev. B 77, 125209 (2008)CrossRefGoogle Scholar
  3. 3.
    O. Yamashita, S. Tomiyoshi, K. Makita, J. Appl. Phys. 93, 368–374 (2003)CrossRefGoogle Scholar
  4. 4.
    S. Fan, J. Zhao, J. Guo, Q. Yan, J. Ma, H.H. Hng, Appl. Phys. Lett. 96, 182104 (2010)CrossRefGoogle Scholar
  5. 5.
    K.A. Kokh, S.V. Makarenko, V.A. Golyashov, O.A. Shegai, O.E. Tereshchenko, CrystEngComm 16, 581–584 (2014)CrossRefGoogle Scholar
  6. 6.
    X. Dou, G. Li, H. Lei, Nano Lett. 8, 1286–1290 (2008)CrossRefGoogle Scholar
  7. 7.
    F. Xiao, B. Yoo, K.H. Lee, N.V. Myung, J. Am. Chem. Soc. 129, 10068–10069 (2007)CrossRefGoogle Scholar
  8. 8.
    W. Wang, X. Lu, T. Zhang, G. Zhang, W. Jiang, X. Li, J. Am. Chem. Soc. 129, 6702–6703 (2007)CrossRefGoogle Scholar
  9. 9.
    S. Ganguly, C. Zhou, D. Morelli, J. Sakamoto, S.L. Brock, J. Phys. Chem. C 116, 17431–17439 (2012)CrossRefGoogle Scholar
  10. 10.
    P. Puneet, R. Podila, M. Karakaya, S. Zhu, J. He, T.M. Tritt, M.S. Dresselhaus, A.M. Rao, Sci. Rep. 3, 3212 (2013)CrossRefGoogle Scholar
  11. 11.
    P. Zareapour, A. Hayat, S.Y.F. Zhao, M. Kreshchuk, A. Jain, D.C. Kwok, N. Lee, S.-W. Cheong, Z. Xu, A. Yang, G.D. Gu, S. Jia, R.J. Cava, K.S. Burch, Nat. Commun. 3, 1056 (2012)CrossRefGoogle Scholar
  12. 12.
    R.J. Mehta, Y. Zhang, C. Karthik, B. Singh, R.W. Siegel, T. Borca-Tasciuc, G. Ramanath, Nat. Mater. 11, 233–240 (2012)CrossRefGoogle Scholar
  13. 13.
    L.-P. Hu, T.-J. Zhu, Y.-G. Wang, H.-H. Xie, Z.-J. Xu, X.-B. Zhao, NPG Asia Mater. 6, e88 (2014)CrossRefGoogle Scholar
  14. 14.
    F.H. Xue, G.T. Fei, B. Wu, P. Cui, L.D. Zhang, J. Am. Chem. Soc. 127, 15348–15349 (2005)CrossRefGoogle Scholar
  15. 15.
    W. Wang, G. Zhang, X. Li, J. Phys. Chem. C 112, 15190–15194 (2008)CrossRefGoogle Scholar
  16. 16.
    B. Yoo, F. Xiao, K.N. Bozhilov, J. Herman, M.A. Ryan, N.V. Myung, Adv. Mater. 19, 296–299 (2007)CrossRefGoogle Scholar
  17. 17.
    J.-M. Zhang, W. Ming, Z. Huang, G.-B. Liu, X. Kou, Y. Fan, K.L. Wang, Y. Yao, Phys. Rev. B 88, 235131 (2013)CrossRefGoogle Scholar
  18. 18.
    Y. Xia, D. Qian, D. Hsieh, L. Wray, A. Pal, H. Lin, A. Bansil, D. Grauer, Y.S. Hor, R.J. Cava, M.Z. Hasan, Nat. Phys. 5, 398–402 (2009)CrossRefGoogle Scholar
  19. 19.
    D. Hsieh, Y. Xia, D. Qian, L. Wray, J.H. Dil, F. Meier, J. Osterwalder, L. Patthey, J.G. Checkelsky, N.P. Ong, A.V. Fedorov, H. Lin, A. Bansil, D. Grauer, Y.S. Hor, R.J. Cava, M.Z. Hasan, Nature 460, 1101–1105 (2009)CrossRefGoogle Scholar
  20. 20.
    Y.S. Hor, A. Richardella, P. Roushan, Y. Xia, J.G. Checkelsky, A. Yazdani, M.Z. Hasan, N.P. Ong, R.J. Cava, Phys. Rev. B 79, 195208 (2009)CrossRefGoogle Scholar
  21. 21.
    S. Urazhdin, D. Bilc, S.D. Mahanti, S.H. Tessmer, T. Kyratsi, M.G. Kanatzidis, Phys. Rev. B 69, 085313 (2004)CrossRefGoogle Scholar
  22. 22.
    Z. Wang, T. Lin, P. Wei, X. Liu, R. Dumas, K. Liu, J. Shi, Appl. Phys. Lett. 97, 042112 (2010)CrossRefGoogle Scholar
  23. 23.
    D. West, Y.Y. Sun, H. Wang, J. Bang, S.B. Zhang, Phys. Rev. B 86, 121201 (2012)CrossRefGoogle Scholar
  24. 24.
    L. Xue, P. Zhou, C.X. Zhang, C.Y. He, G.L. Hao, L.Z. Sun, J.X. Zhong, AIP Adv. 3, 052105 (2013)CrossRefGoogle Scholar
  25. 25.
    I.V. Gasenkova, L.D. Ivanova, Y.V. Granatkina, Inorg. Mater. 37, 1112–1117 (2001)CrossRefGoogle Scholar
  26. 26.
    Y. Jiang, Y.Y. Sun, M. Chen, Y. Wang, Z. Li, C. Song, K. He, L. Wang, X. Chen, Q.-K. Xue, X. Ma, S.B. Zhang, Phys. Rev. Lett. 108, 066809 (2012)CrossRefGoogle Scholar
  27. 27.
    B.Y. Yoo, C.K. Huang, J.R. Lim, J. Herman, M.A. Ryan, J.P. Fleurial, N.V. Myung, Electrochim. Acta 50, 4371–4377 (2005)CrossRefGoogle Scholar
  28. 28.
    Y.L. Chen, J.G. Analytis, J.-H. Chu, Z.K. Liu, S.-K. Mo, X.L. Qi, H.J. Zhang, D.H. Lu, X. Dai, Z. Fang, S.C. Zhang, I.R. Fisher, Z. Hussain, Z.-X. Shen, Science 325, 178–181 (2009)CrossRefGoogle Scholar
  29. 29.
    J. Lee, S. Farhangfar, J. Lee, L. Cagnon, R. Scholz, U. Gösele, K. Nielsch, Nanotechnology 19, 365701 (2008)CrossRefGoogle Scholar
  30. 30.
    M.M. Nassary, H.T. Shaban, M.S. El-Sadek, Mater. Chem. Phys. 113, 385–388 (2009)CrossRefGoogle Scholar
  31. 31.
    X. Yan, B. Poudel, Y. Ma, W.S. Liu, G. Joshi, H. Wang, Y. Lan, D. Wang, G. Chen, Z.F. Ren, Nano Lett. 10, 3373–3378 (2010)CrossRefGoogle Scholar
  32. 32.
    A. Soni, Z. Yanyuan, Y. Ligen, M.K.K. Aik, M.S. Dresselhaus, Q. Xiong, Nano Lett. 12, 1203–1209 (2012)CrossRefGoogle Scholar
  33. 33.
    X. Cai, X.A. Fan, Z. Rong, F. Yang, Z. Gan, G. Li, J. Phys. D. Appl. Phys. 47, 115101 (2014)CrossRefGoogle Scholar
  34. 34.
    V. Goyal, D. Teweldebrhan, A.A. Balandin, Appl. Phys. Lett. 97, 133117 (2010)CrossRefGoogle Scholar
  35. 35.
    O. Vigil-Galán, F. Cruz-Gandarilla, J. Fandiño, F. Roy, J. Sastré-Hernández, G. Contreras-Puente, Semicond. Sci. Technol. 24, 025025 (2009)CrossRefGoogle Scholar
  36. 36.
    G. Kavei, M. Karami, Bull. Mater. Sci. 29, 659–663 (2006)Google Scholar
  37. 37.
    T. Zhang, J.M. Chen, J. Jiang, Y.L. Li, W. Li, G.J. Xu, J. Electron. Mater. 40, 1107–1110 (2011)CrossRefGoogle Scholar
  38. 38.
    X. Ji, J. He, Z. Su, N. Gothard, T.M. Tritt, J. Appl. Phys. 104, 034907 (2008)CrossRefGoogle Scholar
  39. 39.
    Y. Okada, C. Dhital, W. Zhou, E.D. Huemiller, H. Lin, S. Basak, A. Bansil, Y.B. Huang, H. Ding, Z. Wang, S.D. Wilson, V. Madhavan, Phys. Rev. Lett. 106, 206805 (2011)CrossRefGoogle Scholar
  40. 40.
    M. Liu, J. Zhang, C.-Z. Chang, Z. Zhang, X. Feng, K. Li, K. He, L.-L. Wang, X. Chen, X. Dai, Z. Fang, Q.-K. Xue, X. Ma, Y. Wang, Phys. Rev. Lett. 108, 036805 (2012)CrossRefGoogle Scholar
  41. 41.
    J.W.G. Bos, M. Lee, E. Morosan, H.W. Zandbergen, W.L. Lee, N.P. Ong, R.J. Cava, Phys. Rev. B 74, 184429 (2006)CrossRefGoogle Scholar
  42. 42.
    Y.S. Hor, P. Roushan, H. Beidenkopf, J. Seo, D. Qu, J.G. Checkelsky, L.A. Wray, D. Hsieh, Y. Xia, S.Y. Xu, D. Qian, M.Z. Hasan, N.P. Ong, A. Yazdani, R.J. Cava, Phys. Rev. B 81, 195203 (2010)CrossRefGoogle Scholar
  43. 43.
    I. Vobornik, U. Manju, J. Fujii, F. Borgatti, P. Torelli, D. Krizmancic, Y.S. Hor, R.J. Cava, G. Panaccione, Nano Lett. 11, 4079–4082 (2011)CrossRefGoogle Scholar
  44. 44.
    B.A. Bernevig, S.-C. Zhang, Phys. Rev. Lett. 96, 106802 (2006)CrossRefGoogle Scholar
  45. 45.
    J.E. Moore, L. Balents, Phys. Rev. B 75, 121306 (2007)CrossRefGoogle Scholar
  46. 46.
    L. Fu, C.L. Kane, E.J. Mele, Phys. Rev. Lett. 98, 106803 (2007)CrossRefGoogle Scholar
  47. 47.
    H. Zhang, C.-X. Liu, X.-L. Qi, X. Dai, Z. Fang, S.-C. Zhang, Nat. Phys. 5, 438–442 (2009)CrossRefGoogle Scholar
  48. 48.
    M.Z. Hasan, C.L. Kane, Rev. Mod. Phys. 82, 3045–3067 (2010)CrossRefGoogle Scholar
  49. 49.
    X.-L. Qi, S.-C. Zhang, Rev. Mod. Phys. 83, 1057–1110 (2011)CrossRefGoogle Scholar
  50. 50.
    Y.H. Choi, N.H. Jo, K.J. Lee, J.B. Yoon, C.Y. You, M.H. Jung, J. Appl. Phys. 109, 07E312 (2011)CrossRefGoogle Scholar
  51. 51.
    I. Garate, M. Franz, Phys. Rev. Lett. 104, 146802 (2010)CrossRefGoogle Scholar
  52. 52.
    R. Yu, W. Zhang, H.-J. Zhang, S.-C. Zhang, X. Dai, Z. Fang, Science 329, 61–64 (2010)CrossRefGoogle Scholar
  53. 53.
    H. Jin, J. Im, A.J. Freeman, Phys. Rev. B 84, 134408 (2011)CrossRefGoogle Scholar
  54. 54.
    L.A. Wray, S.-Y. Xu, Y. Xia, D. Hsieh, A.V. Fedorov, Y.S. Hor, R.J. Cava, A. Bansil, H. Lin, M.Z. Hasan, Nat. Phys. 7, 32–37 (2011)CrossRefGoogle Scholar
  55. 55.
    J. Zhang, C.-Z. Chang, P. Tang, Z. Zhang, X. Feng, K. Li, L.-L. Wang, X. Chen, C. Liu, W. Duan, K. He, Q.-K. Xue, X. Ma, Y. Wang, Science 339, 1582–1586 (2013)CrossRefGoogle Scholar
  56. 56.
    H.-J. Kim, K.-S. Kim, J.F. Wang, V.A. Kulbachinskii, K. Ogawa, M. Sasaki, A. Ohnishi, M. Kitaura, Y.Y. Wu, L. Li, I. Yamamoto, J. Azuma, M. Kamada, V. Dobrosavljević, Phys. Rev. Lett. 110, 136601 (2013)CrossRefGoogle Scholar
  57. 57.
    M. Lang, L. He, X. Kou, P. Upadhyaya, Y. Fan, H. Chu, Y. Jiang, J.H. Bardarson, W. Jiang, E.S. Choi, Y. Wang, N.-C. Yeh, J. Moore, K.L. Wang, Nano Lett. 13, 48–53 (2012)CrossRefGoogle Scholar
  58. 58.
    J.-M. Zhang, W. Zhu, Y. Zhang, D. Xiao, Y. Yao, Phys. Rev. Lett. 109, 266405 (2012)CrossRefGoogle Scholar
  59. 59.
    P.P.J. Haazen, J.-B. Laloë, T.J. Nummy, H.J.M. Swagten, P. Jarillo-Herrero, D. Heiman, J.S. Moodera, Appl. Phys. Lett. 100, 082404 (2012)CrossRefGoogle Scholar
  60. 60.
    J.S. Dyck, P. Hájek, P. Lošt’ák, C. Uher, Phys. Rev. B 65, 115212 (2002)CrossRefGoogle Scholar
  61. 61.
    Z. Zhou, Y.-J. Chien, C. Uher, Phys. Rev. B 74, 224418 (2006)CrossRefGoogle Scholar
  62. 62.
    X.F. Kou, W.J. Jiang, M.R. Lang, F.X. Xiu, L. He, Y. Wang, Y. Wang, X.X. Yu, A.V. Fedorov, P. Zhang, K.L. Wang, J. Appl. Phys. 112, 063912 (2012)CrossRefGoogle Scholar
  63. 63.
    J.S. Dyck, Č. Drašar, P. Lošt’ák, C. Uher, Phys. Rev. B 71, 115214 (2005)CrossRefGoogle Scholar
  64. 64.
    J. Choi, H.-W. Lee, B.-S. Kim, S. Choi, J. Choi, J.H. Song, S. Cho, J. Appl. Phys. 97, 10D324 (2005)CrossRefGoogle Scholar
  65. 65.
    J. Choi, S. Choi, J. Choi, Y. Park, H.-M. Park, H.-W. Lee, B.-C. Woo, S. Cho, Phys. Status Solidi B 241, 1541–1544 (2004)CrossRefGoogle Scholar
  66. 66.
    C. Niu, Y. Dai, M. Guo, W. Wei, Y. Ma, B. Huang, Appl. Phys. Lett. 98, 252502 (2011)CrossRefGoogle Scholar
  67. 67.
    V.A. Kulbachinskii, A.Y. Kaminskii, K. Kindo, Y. Narumi, K. Suga, P. Lostak, P. Svanda, Phys. B Condens. Matter 311, 292–297 (2002)CrossRefGoogle Scholar
  68. 68.
    Z. Salman, E. Pomjakushina, V. Pomjakushin, A. Kanigel, K. Chashka, K. Conder, E. Morenzoni, T. Prokscha, K. Sedlak, A. Suter, arXiv preprint arXiv:1203.4850 (2012)Google Scholar
  69. 69.
    Y.-L. Wang, Y. Xu, Y.-P. Jiang, J.-W. Liu, C.-Z. Chang, M. Chen, Z. Li, C.-L. Song, L.-L. Wang, K. He, X. Chen, W.-H. Duan, Q.-K. Xue, X.-C. Ma, Phys. Rev. B 84, 075335 (2011)CrossRefGoogle Scholar
  70. 70.
    B. Jariwala, N.M. Ravindra, Process, property and performance of chalcogenide-based thermoelectric materials. Nanomater. Energy 3(3), 68–81 (2014)CrossRefGoogle Scholar
  71. 71.
    J. Jiang, L. Chen, S. Bai, Q. Yao, Q. Wang, J. Cryst. Growth 277, 258–263 (2005)CrossRefGoogle Scholar
  72. 72.
    H. Kim, M. Kaviany, Phys. Rev. B 86, 1–12 (2012)Google Scholar
  73. 73.
    Y. Pei, X. Shi, A. LaLonde, H. Wang, L. Chen, G.J. Snyder, Nature 473, 66–69 (2011)CrossRefGoogle Scholar
  74. 74.
    N.K. Dutta, G.P. Agrawal, Semiconductor Lasers (Van Nostrand Reinhold, New York, 1993), p. 547Google Scholar
  75. 75.
    Z.H. Dughaish, Phys. B Condens. Matter 322, 205–223 (2002)CrossRefGoogle Scholar
  76. 76.
    D.S. Trimmer, E.A. Skrabek, Handbook of Thermoelectrics (CRC Press, Boca Raton, 1995)Google Scholar
  77. 77.
    W.W. Scanlon, Phys. Rev. 126, 509–513 (1962)CrossRefGoogle Scholar
  78. 78.
    R.F. Brebrick, J. Electron. Mater. 6, 659–692 (1977)CrossRefGoogle Scholar
  79. 79.
    M.S. Dresselhaus, G. Chen, M.Y. Tang, R.G. Yang, H. Lee, D.Z. Wang, Z.F. Ren, J.P. Fleurial, P. Gogna, Adv. Mater. 19, 1043–1053 (2007)CrossRefGoogle Scholar
  80. 80.
    I.U.I. Ravich, Semiconducting Lead Chalcogenides (Springer US, New York, 2012)Google Scholar
  81. 81.
    D. Khokhlov, Lead Chalcogenides: Physics and Applications (Taylor & Francis, London, 2002)Google Scholar
  82. 82.
    H. Groiss, I. Daruka, K. Koike, M. Yano, G. Hesser, G. Springholz, N. Zakharov, P. Werner, F. Schäffler, APL Mater. 2, 012105 (2014)CrossRefGoogle Scholar
  83. 83.
    C.J. Vineis, T.C. Harman, S.D. Calawa, M.P. Walsh, R.E. Reeder, R. Singh, A. Shakouri, Phys. Rev. B 77, 235202 (2008)CrossRefGoogle Scholar
  84. 84.
    K.F. Hsu, S. Loo, F. Guo, W. Chen, J.S. Dyck, C. Uher, T. Hogan, E.K. Polychroniadis, M.G. Kanatzidis, Science 303, 818–821 (2004)CrossRefGoogle Scholar
  85. 85.
    T.C. Harman, P.J. Taylor, M.P. Walsh, B.E. LaForge, Science 297, 2229–2232 (2002)CrossRefGoogle Scholar
  86. 86.
    P.F.P. Poudeu, J. D’Angelo, A.D. Downey, J.L. Short, T.P. Hogan, M.G. Kanatzidis, Angew. Chem. 118, 3919–3923 (2006)CrossRefGoogle Scholar
  87. 87.
    W. Jiang, Z.-L. Yang, D. Weng, J.-W. Wang, Y.-F. Lu, M.-J. Zhang, Z.-Z. Yang, Chin. Chem. Lett. 25(6), 849–853 (2014)Google Scholar
  88. 88.
    Y. Gelbstein, Z. Dashevsky, M.P. Dariel, Phys. B Condens. Matter 391, 256–265 (2007)CrossRefGoogle Scholar
  89. 89.
    M.L. Peres, H.S. Monteiro, V.A. Chitta, S. de Castro, U.A. Mengui, P.H.O. Rappl, N.F. Oliveira, E. Abramof, D.K. Maude, J. Appl. Phys. 115, 1–6 (2014)CrossRefGoogle Scholar
  90. 90.
    M. Vatanparast, M. Ranjbar, M. Ramezani, S.M. Hosseinpour-Mashkani, M. Mousavi-Kamazani, Superlattice. Microst. 65, 365–374 (2014)CrossRefGoogle Scholar
  91. 91.
    J. Trajic, N. Romcevic, M. Romcevic, D. Stojanovic, L.I. Ryabova, D.R. Khokhlov, J. Alloys Compd. 602, 300–305 (2014)CrossRefGoogle Scholar
  92. 92.
    J. Bland, M.F. Thomas, T.M. Tkachenka, Hyperfine Interact. 131, 61–65 (2000)CrossRefGoogle Scholar
  93. 93.
    V. Jovovic, S.J. Thiagarajan, J.P. Heremans, T. Komissarova, D. Khokhlov, A. Nicorici, J. Appl. Phys. 103, 1–7 (2008)CrossRefGoogle Scholar
  94. 94.
    J.P. Heremans, C.M. Thrush, D.T. Morelli, J. Appl. Phys. 98, 1–6 (2005)CrossRefGoogle Scholar
  95. 95.
    Y. Pei, N.A. Heinz, A. LaLonde, G.J. Snyder, Energy Environ. Sci. 4, 3640–3645 (2011)CrossRefGoogle Scholar
  96. 96.
    Z. Tian, J. Garg, K. Esfarjani, T. Shiga, J. Shiomi, G. Chen, Phys. Rev. B 85, 1–7 (2012)CrossRefGoogle Scholar
  97. 97.
    T. Shiga, J. Shiomi, J. Ma, O. Delaire, T. Radzynski, A. Lusakowski, K. Esfarjani, G. Chen, Phys. Rev. B 85, 155203 (2012)CrossRefGoogle Scholar
  98. 98.
    D.J. Singh, Phys. Rev. B 81, 1–6 (2010)Google Scholar
  99. 99.
    C.E. Ekuma, D.J. Singh, J. Moreno, M. Jarrell, Phys. Rev. B 85, 1–7 (2012)CrossRefGoogle Scholar
  100. 100.
    D. Parker, D.J. Singh, Phys. Rev. B 82, 1–5 (2010)CrossRefGoogle Scholar
  101. 101.
    Y. Zhang, X. Ke, C. Chen, J. Yang, P.R.C. Kent, Phys. Rev. B 80, 1–12 (2009)Google Scholar
  102. 102.
    E.O. Wrasse, R.J. Baierle, T.M. Schmidt, A. Fazzio, Phys. Rev. B 84, 1–6 (2011)CrossRefGoogle Scholar
  103. 103.
    C.M. Jaworski, J.P. Heremans, Phys. Rev. B 85, 033204 (2012)CrossRefGoogle Scholar
  104. 104.
    L.I. Ryabova, D.R. Khokhlov, J. Exp. Theor. Phys. Lett. 80, 133–139 (2004)CrossRefGoogle Scholar
  105. 105.
    S. Ahmad, K. Hoang, S.D. Mahanti, Phys. Rev. Lett. 96, 1–4 (2006)Google Scholar
  106. 106.
    S. Ahmad, S.D. Mahanti, K. Hoang, M.G. Kanatzidis, Phys. Rev. B 74, 155205 (2006)CrossRefGoogle Scholar
  107. 107.
    K. Hoang, S.D. Mahanti, Phys. Rev. B 78, 1–8 (2008)CrossRefGoogle Scholar
  108. 108.
    K. Hoang, S.D. Mahanti, M.G. Kanatzidis, Phys. Rev. B 81, 1–15 (2010)Google Scholar
  109. 109.
    S. Ahmad, S.D. Mahanti, Phys. Rev. B 81, 1–11 (2010)CrossRefGoogle Scholar
  110. 110.
    K. Hoang, S.D. Mahanti, P. Jena, Phys. Rev. B 76, 1–18 (2007)CrossRefGoogle Scholar
  111. 111.
    J.P. Heremans, V. Jovovic, E.S. Toberer, A. Saramat, K. Kurosaki, A. Charoenphakdee, S. Yamanaka, G.J. Snyder, Science 321, 554–557 (2008)CrossRefGoogle Scholar
  112. 112.
    J. Androulakis, I. Todorov, D.-Y. Chung, S. Ballikaya, G. Wang, C. Uher, M. Kanatzidis, Phys. Rev. B 82, 1–8 (2010)CrossRefGoogle Scholar
  113. 113.
    C.M. Jaworski, J. Tobola, E.M. Levin, K. Schmidt-Rohr, J.P. Heremans, Phys. Rev. B 80, 1–10 (2009)Google Scholar
  114. 114.
    J. Martin, L. Wang, L. Chen, G.S. Nolas, Phys. Rev. B 79, 1–5 (2009)Google Scholar
  115. 115.
    Z.-Y. Li, J.-F. Li, W.-Y. Zhao, Q. Tan, T.-R. Wei, C.-F. Wu, Z.-B. Xing, Appl. Phys. Lett. 104, 1–5 (2014)Google Scholar
  116. 116.
    P.K. Rawat, B. Paul, P. Banerji, ACS Appl. Mater. Interfaces 6, 3995–4004 (2014)CrossRefGoogle Scholar
  117. 117.
    H. Wang, Y. Pei, A.D. LaLonde, G.J. Snyder, Adv. Mater. 23, 1366–1370 (2011)CrossRefGoogle Scholar
  118. 118.
    Y. Pei, H. Wang, Z.M. Gibbs, A.D. LaLonde, G.J. Snyder, NPG Asia Mater. 4, 28 (2012)CrossRefGoogle Scholar
  119. 119.
    R.J. Korkosz, T.C. Chasapis, S.-H. Lo, J.W. Doak, Y.J. Kim, C.-I. Wu, E. Hatzikraniotis, T.P. Hogan, D.N. Seidman, C. Wolverton, V.P. Dravid, M.G. Kanatzidis, J. Am. Chem. Soc. 136, 3225–3237 (2014)CrossRefGoogle Scholar
  120. 120.
    X.W. Wang, H. Lee, Y.C. Lan, G.H. Zhu, G. Joshi, D.Z. Wang, J. Yang, A.J. Muto, M.Y. Tang, J. Klatsky, S. Song, M.S. Dresselhaus, G. Chen, Z.F. Ren, Appl. Phys. Lett. 93, 193121 (2008)CrossRefGoogle Scholar
  121. 121.
    G. Joshi, H. Lee, Y. Lan, X. Wang, G. Zhu, D. Wang, R.W. Gould, D.C. Cuff, M.Y. Tang, M.S. Dresselhaus, G. Chen, Z. Ren, Nano Lett. 8, 4670–4674 (2008)CrossRefGoogle Scholar
  122. 122.
    B.G. Streetman, S. Banerjee, Solid State Electronic Devices (Pearson Prentice Hall, Upper Saddle River, NJ, 2006)Google Scholar
  123. 123.
  124. 124.
    C. Abs da Cruz, N.A. Katcho, N. Mingo, R.G.A. Veiga, J. Appl. Phys. 114, 164310 (2013)CrossRefGoogle Scholar
  125. 125.
    S. Ju, X. Liang, J. Appl. Phys. 112, 064305 (2012)CrossRefGoogle Scholar
  126. 126.
    B. Laikhtman, R.A. Kiehl, Phys. Rev. B 47, 10515–10527 (1993)CrossRefGoogle Scholar
  127. 127.
    W.L.C. Hui, J.P. Corra, J. Appl. Phys. 38, 3477–3478 (1967)CrossRefGoogle Scholar
  128. 128.
    J.R. Watling, D.J. Paul, J. Appl. Phys. 110, 114508 (2011)CrossRefGoogle Scholar
  129. 129.
    G. Chen, M. Neagu, Appl. Phys. Lett. 71, 2761–2763 (1997)CrossRefGoogle Scholar
  130. 130.
    G. Chen, J. Heat Transf. 119, 220–229 (1997)CrossRefGoogle Scholar
  131. 131.
    A. Nozariasbmarz, A. Tahmasbi Rad, Z. Zamanipour, J.S. Krasinski, L. Tayebi, D. Vashaee, Scr. Mater. 69, 549–552 (2013)CrossRefGoogle Scholar
  132. 132.
    B. Yu, M. Zebarjadi, H. Wang, K. Lukas, H. Wang, D. Wang, C. Opeil, M. Dresselhaus, G. Chen, Z. Ren, Nano Lett. 12, 2077–2082 (2012)CrossRefGoogle Scholar
  133. 133.
    M. Zebarjadi, G. Joshi, G. Zhu, B. Yu, A. Minnich, Y. Lan, X. Wang, M. Dresselhaus, Z. Ren, G. Chen, Nano Lett. 11, 2225–2230 (2011)CrossRefGoogle Scholar
  134. 134.
    D. Chrastina, S. Cecchi, J.P. Hague, J. Frigerio, A. Samarelli, L. Ferre-Llin, D.J. Paul, E. Müller, T. Etzelstorfer, J. Stangl, G. Isella, Thin Solid Films 543, 153–156 (2013)CrossRefGoogle Scholar
  135. 135.
    S. Madhavi, V. Venkataraman, Y.H. Xie, J. Appl. Phys. 89, 2497–2499 (2001)CrossRefGoogle Scholar

Copyright information

© The Author(s), under exclusive licence to Springer International Publishing AG, part of Springer Nature 2019

Authors and Affiliations

  • N. M. Ravindra
    • 1
  • Bhakti Jariwala
    • 2
  • Asahel Bañobre
    • 3
  • Aniket Maske
    • 3
  1. 1.Department of PhysicsNew Jersey Institute of TechnologyNewarkUSA
  2. 2.New Jersey Institute of TechnologyNewarkUSA
  3. 3.Interdisciplinary Program in Materials Science & Engineering New Jersey Institute of TechnologyNewarkUSA

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