Thermoelectrics pp 69-89 | Cite as
Thermoelectrics: Material Candidates and Structures I – Chalcogenides and Silicon-Germanium Alloys
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Abstract
Bismuth telluride, Bi_{2}Te_{3}, 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-Bi_{2}Te_{3} 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 dopingDoping5.1 Chalcogenides
5.1.1 Bismuth Telluride/Antimony Telluride
Bismuth telluride, Bi_{2}Te_{3} , 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-Bi_{2}Te_{3} 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.
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 Bi_{2}Te_{3} (Sb_{2}Te_{3})-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.
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 Bi_{2}Te_{3} single crystals [30]. However, it must be noted that the stoichiometric compounds of Bi_{2}Te_{3} were grown by the zone melting technique successfully during the first reports in the literature. Under the conserved stoichiometric condition, in p-Bi_{2}Te_{3} , 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 Bi_{2}Te_{3} 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 cm^{2} V^{−1} s^{−1} and 44.89 cm^{2} V^{−1} s^{−1}, respectively; a higher value of mobility in the parallel direction clearly indicates the anisotropic nature of Bi_{2}Te_{3} ; the corresponding hole concentration is 2.64 × 10^{17} 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 Bi_{2}Te_{2.7}Se_{0.3}, 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 Bi_{2}Te_{3} , 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 Bi_{2}Te_{3} 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 Bi_{2}Te_{3} thin films deposited by close space vapor transport (CSVT) method at a substrate temperature of 350 °C [35].
The transport properties of Bi_{2}Te_{3}-Sb_{2}Te_{3} alloy system, formed by zone melting, has been investigated [36]. Here, the increase in Bi_{2}Te_{3} content led to a substitution of the Sb atoms in Sb_{2}Te_{3}, 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%Bi_{2}Te_{3}–75%Sb_{2}Te_{3} with 3 wt% excess of Te. Principally, the antisite defect structure, created by Bi_{2}Te_{3} content in the Sb_{2}Te_{3} 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 × 10^{4} 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 Bi_{2}Te_{3} 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 Bi_{2}Te_{3} 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.
Transport parameters of Bi_{2}Te_{3} at various temperatures (K)
Compound | σ (μΩm) | S (μVK^{−1}) | κ (Wm^{−1} K^{1}) | ZT | Growth method |
---|---|---|---|---|---|
p-(Bi_{0.25}Sb_{0.75})_{2}Te_{3} [3] | ~9.5 (308) | ~225 (308) | 1.21 (308) | 1.41 | Crystal-Bridgman |
n-Bi_{2}(Te_{0.94}Se_{0.06})_{3} [3] | ~10 (308) | ~240 (308) | 1.26 (308) | 1.13 | Crystal-Bridgman |
p-Bi_{0.4}Sb_{1.6}Te_{3} [4] | 1.8 (316) | Nanocomposite | |||
n-(Bi_{2}Te_{3})_{0.24}(Sb_{2}Te_{3})_{0.76} [71] | ~1 (300) | ~215 (300) | 1.50 (300) | 1.14(350) | Crystal-zone melt |
5.1.2 Lead Telluride
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 k_{B}T, 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 AgSbTe_{2} 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 PbTe_{1−x}Se_{x} 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 × 10^{18} 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^{−1}cm^{−1}(in-plane) at 300 K for carrier concentration, n = 4.73 × 10^{18} cm^{−3}, and Seebeck coefficient is ~425 μVK^{−1} at 550 K for carrier concentration, p = 8.85 × 10^{18} 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 AgPb_{m}SbTe_{m+2} alloys [84]. Quantum wells of PbTe/Pb_{1−x}Eu_{x}Te and PbSe_{0.98}Te_{0.02}/PbTe superlattices [85] and novel quaternary compounds, AgSbPb_{2n−2}Te_{2n} (n = 9, 10) [84] and Na_{1−x}Pb_{m}Sb_{y}Te_{m+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 Pb_{1−x}Sn_{x}Te compounds [88]. The spin-orbit coupling has been studied experimentally in n-PbTe quantum wells, grown by molecular beam epitaxy on (111) plane BaF_{2} 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 × 10^{18} cm^{−3}, while crystals, prepared by vapor-liquid-solid technique, exhibit p-type conductivity with electron concentration of 6.58 × 10^{18} 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 Pb_{1−x}Sn_{x}Te_{1−y}Se_{y} [92], Pb_{1−x}Sn_{x1−y}In_{y}Te [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 PbTe_{1−x}Se_{x} 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 RPb_{2n−1}Te_{2n} and MPb_{2n}Te_{2n−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 Tl_{0.02}Pb_{0.98}Te 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 × 10^{19} cm^{−3} [103]. The effects of K and K-Na substitution for Pb atoms in Pb_{1−x}Na_{x}Te and Pb_{0.9875−x}K_{0.0125}Na_{x}Te 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 Pb_{0.9815}K_{0.0125}Na_{0.006}Te [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 Pb_{1−x}Sb_{x}Te samples are n-type with maximum n ~ 9 × 10^{18} cm^{−3} at 500 K for Pb_{0.9975}Sb_{0.0025}Te; Pb-rich PbSb_{x}Te_{1−x} samples are p-type with maximum p ~ 4.9 × 10^{19} cm^{−3} at 300 K for PbSb_{0.01}Te_{0.99}, with enhanced Seebeck coefficient throughout the temperature range. The thermal conductivity is found to increase in Pb_{1−x}Sb_{x}Te with increasing x due to increased electronic thermal conductivity; similar trend has been found in PbSb_{x}Te_{1−x} in the temperature range of 300–800 K.
Thermoelectric properties of PbTe-based alloys at respective temperatures (K)
Materials | S (μV/K) | κ (Wm^{−1} K^{−1}) | κ_{lat} (Wm^{−1} K^{−1}) | ZT (T) |
---|---|---|---|---|
AgPb_{20}SbTe_{20} + 1% SiC [115] | −230 (700) | 0.7 (700) | 1.5 (720) | |
PbI_{2}-doped PbTe [116] | −300 (650) | 1.3 (650) | 0.9 (650) | 1.35 (650) |
Na_{0.007}Pb_{0.993}Se [117] | 200 (800) | 1.3 (800) | 0.65 (800) | 1.2 (850) |
Na_{0.95}Pb_{20}SbTe_{22} [86] | 350 (650) | 1 (650) | – | 1.7 (650) |
PbSe [100]^{a} | 230 (1000) | – | – | 2 (1000) |
Pb_{0.96}Mn_{0.04}Te [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) |
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.
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 L^{1/4} 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.
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 (Si_{80}Ge_{20})_{70}(Si_{100}B_{5})_{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 Si_{86}Ge_{14}B_{1.5} and uniform n-type Si_{84}Ge_{16}P_{0.6} sample was improved by 40% and 20% using the modulation-doping approach in (Si_{80}Ge_{20})_{0.7}(Si_{100}B_{5})_{0.3} and (Si_{80}Ge_{20})_{0.8}(Si_{100}P_{3})_{0.2}, respectively [133].
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