Odyssey of thermoelectric materials: foundation of the complex structure

Growing energy crises and pollution are the major issues of the modern world. The thermoelectric concept seems to be the promising solution to deal with these problems, because of the ability of thermoelectric materials to convert waste heat into electricity without adding more pollution to the atmosphere. The development of thermoelectric materials (TE) is driven by fundamental interest and their potential applications. To replace the conventional techniques, the figure of merit (zT) of the thermoelectric materials should be higher than 2 for power generation and greater than 3 for cooling. Recently, there have been significant advances in enhancing the figure of merit of thermoelectric materials and also to find new materials for the thermoelectric purpose. Low thermal conductivity is the key for a promising thermoelectric material that can be achieved through the complex structures. This review provides insights into the recent advancements in improving the efficiency of thermoelectric systems, complex nature of thermoelectric materials, with a concise introduction to preparative approaches for thermoelectric (TE) materials.


Introduction
Due to the increasing global energy crises, the hazardous impact on the environment and the limited supply of fossil fuels, the need for some alternative energy source is significant. The thermoelectric materials have come to rescue the world from the growing energy crisis. The waste heat coming out of motor vehicles and other electrical appliances can be put to good use by generating electricity from it without adding more pollution to the atmosphere which is only possible with the help of thermoelectric materials. Thermoelectric materials have a wide range of applications ranging from small-scale production of electricity to their use in missiles and spacecraft. Thermoelectric (TE) phenomenon involves three essential effects: Seebeck effect, Peltier effect and Thomson effect. Seebeck effect is the direct conversion of heat into electricity (power generation), and Peltier effect is just its opposite (cooling). For both the results, a junction needs to be formed between n-type and p-type semiconductors. Thomson effect, on the other hand, requires only one conductor carrying DC which when subjected to temperature gradient gives the absorption or evolution of heat. TE devices have the advantage over other conventional devices because of no moving parts, noise-free and exceptional service reliability. A TE module for both power generation and cooling is made of electrically connected thermocouples which include p-type and n-type semiconductors. For power generation, the thermocouples are connected thermally in parallel and electrically in series.
The efficiency of TE materials is governed by its dimensionless figure of merit zT=S 2 σT/K which depends on both electrical and thermal properties of the materials. S is the Seebeck coefficient which is given by the ratio of voltage output to the temperature gradient (V/ΔT), σ is the electrical conductivity, and K is the thermal conductivity (K=K e +K l ; electronic and lattice thermal conductivity). The quantity S 2 σ is called the power factor and is associated with the electric transport.
The thermodynamic efficiency of power generation is given by [39,40] h = D + - T c is the temperature of cold side, T h is the temperature of hot side, zT is the figure of merit, and ΔT/T h is the Carnot efficiency. Thus large zT and substantial difference between T c and T h is the key to increase thermodynamic efficiency η. Enhancing zT of any material requires the increment of σ and reduction of K simultaneously which contradicts with Weidmann-Franz law. According to Weidmann-Franz law, the ratio of σ to K remains constant which implies that these two quantities cannot be simultaneously increased and decreased respectively [41]. In order to enhance zT, some special strategies have to be employed to reduce K and increase σ simultaneously. Searching for the materials that can be better thermoelectrics, it is found that degenerate semiconductors can be the potential thermoelectric materials as is clear from figure 1. For degenerate semiconductors, S is given by [42]  K B is the Boltzmann constant, e is electron charge, h is Plank constant, m * is the effective mass of charge carriers. It is clear that S increases with the decrease in carrier concentration n. Electrical conductivity on the other hand is given by σ=neμ; where μ is the mobility of charge carriers. To increase the power factor, it is necessary to decouple Seebeck coefficient and electrical conductivity because these two quantities depend on n in opposite manners. Also as total thermal conductivity K is the sum of electronic thermal conductivity K e and lattice thermal conductivity K l , both these parts of thermal conductivity are to be looked at separately. K e is given by LσT=LneμT where L is Lorentz number [41]. Ke is directly proportional to the number of charge carriers n, and hence it becomes challenging to reduce this part of thermal conductivity. Lattice thermal conductivity K l is given by K l = 1 3 Cv vl [43], where Cv is the specific heat per unit volume, v is the speed of sound, l is phonon mean free path (mfp) and has very little dependence on n. Therefore to reduce thermal conductivity, strategies are to be made mainly to reduce K l . Altering C v and v is very difficult because these quantities are constant in case of solids. So, the primary focus is to minimize mfp of phonons and that too of long wavelength phonons because heat is mainly carried by the long wavelength phonons [44,45]. The mfp of phonons can be reduced by phonon scattering that can be induced by various approaches such as doping (also increases the carrier concentration) [40,46], nanostructuring [45,47], introducing fluid like characteristics in solid crystals [48][49][50] and by introducing rattling ions in cage like structures [51][52][53]. The phonon scattering mechanism can be understood from figure 2.
2. Ways to optimize thermoelectric properties 2.1. Phonon glass electron crystal (PGEC) and complex structures The reduction in lattice thermal conductivity by scattering of phonons and not affecting the transport of electrons can be achieved in the materials favouring Phonon-Glass Electron-Crystal (PGEC) concept as is proposed by Slack [55]. Heat is mainly carried by a wide range of phonons with varying mean free paths [56]. Figure 1. This diagram shows the relation between zT and other parameters like electrical conductivity σ, Seebeck coefficient S, thermopower σ 2 s, electronic thermal conductivity K e , lattice thermal conductivity K l and total thermal conductivity K.
Glasses have the lowest thermal conductivities because in glasses, thermal conductivity can be considered as the random walk of energy through the lattice and not by the transport of phonons [43] while the crystalline materials favour electrical conductivity. PGEC behaviour in thermoelectric materials can be achieved by alloying. Alloying with isoelectronic elements (elements having same electronic configuration) increases the disorder and helps in the scattering of phonon on the sites and preserves the crystalline electronic structure. Complex crystal structures show better PGEC behaviour. Complexity may be due to disorder in the unit cells or due to the complex unit cell. More complex structures have less lattice thermal conductivity. The reduction in thermal conductivity through disorder in the unit cell is large in the species like clathrates [51] and skutterudites [52,53]. CsBi 4 Te 6 (which is the complicated alternative of Bi 2 Te 3 ) has low lattice thermal conductivity of 1.1 Wm −1 k −1 due to complex unit cell and hence has improved zT of 0.8 below room temperature [57,58]. A very low thermal conductivity of 0.42 to 0.20 Wm −1 k −1 in the temperature range 300 to 837 K in K 2 Bi 8 Se 13 is due to its large unit cell and complex anisotropic structure which accounts for its high zT of 1.3 at 873 K [59]. Recently, a new semiconductor Cs 4 Cu 3 Bi 9 S 17 is found to have a low thermal conductivity of 0.71 Wm −1 k −1 at room temperature and decreases to 0.46 Wm −1 k −1 at 773 K [60]. With such a small thermal conductivity, this material can be a promising thermoelectric material. The low thermal conductivity is due to its complex 3D structure consisting of interconnected Bi 2 Te 3 and CdI 3 type fragments [60].

Phonon-phonon interaction and anharmonicity
Phonon-phonon interaction is the primary process for reducing the mean free path of phonons and inducing phonon scattering at high temperatures. There are two types of phonon-phonon interactions: a normal operation in which the total momentum is conserved and Umklapp process in which the whole momentum is not conserved. To attain low thermal conductivity, all the phonon scattering processes must be employed. Umklapp process is the dominating scattering process at high temperatures and at such temperatures lattice thermal conductivity takes the form [61] Where M denotes average mass per atom, V is the average atomic volume, θ D is the Debye temperature, and γ is the GrÜneisen parameter which is the measure of anharmonicity of lattice vibrations and is given by γ= a r .
Large γ is the condition for small K l and is observed in materials with large thermal expansion coefficient, isothermal bulk modulus and having low density. Also, significant anharmonicity (sizeable nonlinear dependence of restoring force on the atomic displacement) is the key for large γ which is generated by weak bonding and heavy elements. Large anharmonicities are observed in complex crystal structures with large primitive cells and thus lowering K l .

Reduction of specific heat C v
Lattice thermal conductivity is proportional to specific heat C v which can be reduced in materials containing liquid like ions like in ionic conductors. Ionic conductors comprise molten sublattice (apart from the solid sublattice) in which atoms can move freely throughout. Specific heat C v in solid materials can be reduced to the liquid limit by introducing the unique structural characteristics of ionic conductors thereby increasing complexity in the crystal. This concept is called the Phonon-Liquid Electron-Crystal (PLEC) which is used to explain the low thermal conductivity and high thermoelectric performance of Cu based thermoelectric materials [48][49][50]. PLEC is discussed in detail in section 3.3.

Effective mass and band engineering
Carrier mobility μ is inversely proportional to the band effective mass * m band of the charge carriers [62]. Seebeck coefficient, on the other hand, is directly proportional to the density of states effective mass * m DOS [40,42] [63]. Moreover, * m band and * m DOS act in opposite manners when it comes to enhance zT because large * m band (for flat bands) lowers the carrier mobility which in turn reduces electrical conductivity while large * m DOS increases power factor. Thus, low * m band is required to increase the thermoelectric performance of materials. Such an effect of band effective mass * m band on the electrical properties is observed by the doping of n-type PbTe [64, 65, 65a] as is shown in figure 3.
The maximum zT of the thermoelectric material is determined by its quality factor given by [46,63,66,67], which can have greater value for considerable band degeneracy N v , low lattice thermal conductivity, small band effective mass * m band and small deformation potential coefficient Ξ. A low deformation potential coefficientΞis required for the weak scattering of charge carriers dominated by acoustic phonons [68][69][70] which enables high carrier mobility without affecting the Seebeck coefficient.
In case of the system with two valence bands having the Seebeck coefficient and conductivity of S 1 , σ 1 and S 2 , σ 2 respectively, the total Seebeck coefficient is given by S=(σ 1 S 1 +σ 2 S 2 )/(σ 1 +σ 2) and the overall conductivity is given by σ=σ 1 +σ 2 . As is already mentioned that with the increase in the number of carriers (n), conductivity increases and the Seebeck coefficient decreases. The total Seebeck coefficient is closer to the smaller value of S for the two bands. To maintain the large value of total Seebeck coefficient S, the two bands need to be aligned so that the Seebeck coefficient S is same in the two bands while the total conductivity is higher than the specific conductivity of either of the bands.
Complex or multi-band systems show greater band degeneracy as compared to single-band systems. Lead chalcogenides and their alloys are the examples of complex band systems consisting of two bands in which apart from principal valence band L there exists another secondary valence band ∑ [68,69] as is shown in figure 4 (a). Band convergence or overlapping of light valence band L and heavy valence band ∑ can increase the band degeneracy in lead chalcogenides which can be achieved by higher doping concentration. The position of L and ∑ bands is the function of temperature. L band lowers its position with the increase in temperature keeping the position of ∑ band almost constant [69,71] resulting in the convergence of these bands as is shown in figure 4 (a). By converging L and ∑ bands, N v of these two bands add up to increase the total band degeneracy and hence increasing B which leads to the increment in zT as is shown in figure 4 (c). Apart from band convergence, the high degeneracy of ∑ band also significantly improves the quality factor [71]. Band convergence can also be achieved in specific materials by increasing the crystal symmetry of the materials towards a more cubic arrangement [72]. In some cases, resonant levels are formed by the dopants merged with the valence band which increase the Seebeck coefficient S especially at room temperature leading to the improvement in thermoelectric properties [73,74] as is shown in figure 4 (b). The electron resonant states strongly scatter the charge carriers and hence reduce the electronic mobility thereby reducing electrical conductivity. To benefit from the resonant states, the Seebeck coefficient must be so increased to overpower the damage done by the reduction of electrical conductivity.

Nano-tailoring
Thermoelectric performance can be enhanced significantly by the nanostructuring of thermoelectric materials. Nanostructures like nanowires, nanotubes, nanoforks, quantum wells, quantum dots, and superlattices show improved power factor and reduced thermal conductivity than their bulk counterparts. Nanostructuring can increase the thermoelectric performance by taking into account the two approaches. One is by strengthening the DOS near Fermi level via quantum confinement, improving the power factor [77][78][79]. Other approach is by the efficient scattering of phonons at grain boundaries because of their large mfp than electrons, hence decreasing the lattice thermal conductivity [44,45,47]. In case of nanostructured thermoelectric materials, lattice thermal conductivity is mainly reduced by the phonon-electron scattering mechanism which promotes the scattering of long wavelength heat-carrying phonons. To achieve the peak zT, nanostructured thermoelectric materials require high doping concentration. At the grain boundaries, low energy minority carriers are scattered more strongly than the high energy majority charge carriers resulting in the more moderate bipolar transition [80,81]. Due to this effect, nanostructured thermoelectrics show higher Seebeck coefficient than their bulk counterparts at similar doping concentrations.
In case of 1D thermoelectric materials (nanowires), quantum confinement greatly enhances the thermoelectric performance as compared to their 2D variants [82,83]. Nanotubes show lower thermal conductivity than nanowires due to the additional phonon scattering on inner and outer surfaces [82,84,85]. In case of rough wires, the phonon drag can result in the increment of thermopower which in turn enhances the thermoelectric performance [86]. Nanocomposites show better thermoelectric properties because of their low lattice thermal conductivity due to scattering of phonons at the interfaces between neighbouring nanoparticles, and power factor is also larger than the constituent phases [87]. In case of the thermoelectrics with nanoinclusions, Seebeck coefficient S can be increased by energy filtering [54,88].
Combining all the above discussed mechanisms, there has been a significant reduction in lattice thermal conductivity of thermoelectric materials since the last decade. Recently developed thermoelectric nanocomposites, copper based thermoelectric materials and tin chalcogenides show significantly low lattice thermal conductivity apart from complex material systems as is clear from figure 5.
The groups of thermoelectric materials to be discussed in this review article are summarized in table 1.

Caged compounds
The compounds with caged structures are better in showing the Phonon-Glass Electron-Crystal behaviour which focuses on conserving the electrical properties and reducing the lattice thermal conductivity. The typical caged compounds include Skutterudites and Clathrates. Both the families of caged compound possess cubic structure which favours good electronic transport. These compounds contain large voids in their framework. When these voids are filled with guest atoms, these act as independent oscillators. Due to the large size of the voids, these oscillators vibrate with the more substantial amplitudes than the atomic displacement of the structural atoms. This effect is called as rattling effect and due to this effect, the resonant modes of low frequency are formed. These resonant modes act as the traps for low-frequency phonons and hence decrease the lattice thermal conductivity. It is also believed that the resonant modes formed are high-frequency modes which actively interfere with the low-frequency phonon modes thereby diminishing the lattice thermal conductivity. The rattlers not only reduce the lattice thermal conductivity but also improve electrical conductivity due to their electro-positivity.

Skutterudites
These are the minerals with general formula TX 3 where T is the transition metal mainly Co, Rh or Ir and X is a pnictogen (group 15 element) primarily P, As or Sb. The structure of skutterudites is cubic with the space group Im3 which was first described by Oftedal in 1928. The binary skutterudite is filled by electropositive element A (rare-earth [91,92], alkaline-earth [77,93] or alkali metals [92,94]) to form the ternary skutterudite A 2 T 8 X 24 which can also be described as the half of the unit cell AT 4 X 12 . The crystal structure of skutterudites is shown in figure 6(a). Skutterudites based on CoSb 3 are most studied because of the high mobility, low electrical resistivity, high atomic masses and good Seebeck coefficients [95,96]. Despite having high power factor, CoSb 3 cannot achieve high zT due to its high lattice thermal conductivity [97,98]. The lattice thermal conductivity is significantly reduced by filling the structural voids with appropriate filler elements. Filled antimonides have the smallest lattice thermal conductivity because of the more significant cage and due to these larger cages, the amplitude of vibration of a filled atom is stronger which in turn actively interferes with the acoustic phonons [99]. In case of CoSb 3 based skutterudites whether the atom or ion can serve as a filler or not, depends on the  electronegativity difference between the filler and the Sb atom of the framework. Thermodynamically most stable filled skutterudites are the ones in which the electronegativity difference falls in the range >0.8 [100,101]. zT of CoSb 3 is enhanced from 0.5 for unfilled to 1.2 for partially filled CoSb 3 due to the reduction in lattice thermal conductivity and improved electrical conductivity [77,102]. The lattice thermal conductivity is reduced in filled skutterudites by the formation of Einstein-like vibrational modes arising due to the weak bonding between fillers and Sb atoms of skutterudite framework, thereby scattering the normal phonon modes of the structure having similar energies [77,103]. The vibrational frequencies depend on the type of fillers in the cages and it was found that the rare-earth metals possess weakest vibrational frequencies followed by the alkalineearth metals which yield medium frequencies and the highest vibrational frequencies are maintained by alkali metals [104]. By introducing filler atoms in the cages, lattice thermal conductivity is reduced and this reduction can further be increased by adding two or more filler atoms of different vibrational frequencies which will help in the significant increase of zT like in multi filled skutterudites Ba 0.08 La 0.05 Yb 0.04 Co 4 Sb 12 with the enhanced zT of 1.7 at 577°C [105]. Recently it was found that zT is improved in p-type skutterudites due to coherency strain fields arising from spinodal decomposition [107]. The lattice thermal conductivity is reduced due to phonon scattering through coherency strain field keeping the electrical conductivity unchanged. The Seebeck coefficient is increased due to increase in the density of states near Fermi level which is expected to happen because the coherency strain field is in the state of tension. Due to this, the enhanced zT of 1.2 is obtained for multi-filled p-type La 0.8 Ti 0.1 Ga 0.1 Fe 3 CoSb 12 [107]. The lattice thermal conductivity is also reduced by the nano-inclusion in skutterudites forming skutterudite nanocomposites. This is another efficient way to enhance zT of skutterudites. Zong et al reported that in skutterudite/graphene nanocomposite, the lattice thermal conductivity is reduced due to increase in the grain boundaries [108]. zT of 1.5 was observed in n-type Yb y Co 4 Sb 12, and zT of 1.06 was found in p-type Ce y Fe 3 CoSb 12 by introducing multilayer graphene into grain boundaries of these skutterudites [108]. zT of 1.0 was achieved in In 0.04 Co 4 Sb 12 -(InSb) 0.05 nanocomposite at 575 K which is highest for cobalt skutterudites at T575 K containing single filler of In because of the reduced thermal conductivity and high electrical conductivity as compared to pristine Co 4 Sb 12 [109]. Lattice thermal conductivity is reduced due to high phonon scattering at the InSb nano-inclusions, and electrical conductivity is increased due to the high mobility of InSb [109]. Khan et al reported a porous architecture of skutterudites containing nano-to micro-sized, irregularly shaped and randomly oriented phonons to scatter a broad spectrum of phonons without employing the conventional rattling structure hence the zT of 1.6 was obtained in the nano-micro porous architecture Co 23.4 Sb 69.1 Si 1.5 Te 6 alloy which is highest reported for any unfilled skutterudite [106]. Methods of preparation and peak zT of skutterudites is summarized in table 2.

Clathrates
Clathrate structure consists an open framework with voids similar to skutterudites filled by some guest fillers which act as rattlers and help in reducing lattice thermal conductivity [53]. Clathrates contain Al, Si, Ga, Ge, Sn, etc, atoms which are tetrahedrally coordinated with cages of different sizes. These cages are large polyhedrons having at least 12 faces and 20 vertices, hence making clathrates a unique class of compounds. The atoms are situated in the vertices of these polyhedra. There are various types of clathrates such as clathrate-I, clathrate-II, clathrate-III, clathrate-VII, clathrate-VIII, clathrate-XI and twisted clathrates out of which, only clathrate-I to clathrate-VII are true clathrates. The clathrates are classified according to the shape and number of cages. Clathrate-I and clathrate-II are the main types of clathrates having the crystal structures as shown in figures 7(a), (b). Clathrate-I consist of two polyhedra packed in a cubic arrangement and majority of these clathrates have the space group Pm3n. The clathrate-I structure is most accomplished for anionic and cationic clathrates and is represented by the formula U 2 V 6 E 46 ; U and V being filler atoms encapsulated in two different polyhedrons E 20 and E 24 while E represents the elements Al, Si, Ga, Ge, Sn, etc. The rattling of fillers occurs in the cages similar to skutterudites due to which phonons are strongly scattered resulting in low thermal conductivity. The filler atoms have the strongest vibration amplitudes in the cage E 24 [110]. In case of clathrate-II, the largest clathrate forming polyhedra (having 28 vertices and 16 faces) along with the smallest polyhedra are present in the crystal structure. Clathrate-II have the space group Fd3m and this structure is most realized in anionic clathrates. Clathrate-II structure contains 16 small and 8 large polyhedra which can be filled by same or different type of guest atoms and have the generalized formula M X E 136 . M represents the guest atoms which can be of more than one type (like Na, K, Rb, Cs, Ba, Sr, Ca, Cl, Br, I, Eu, P, Te, Li, Mg), X can have the values between 0 to 24 and E represents Si, Ge, Sn, Al, Ga etc. X=0 means no guest atom is present in the cage which is the unique property of the clathrate-II structure. This type of clathrate structure also allows partial filling of polyhedra, unlike Clathrate-I structure which favors only complete filling. Due to the partial filling, the electrical properties of clathrate-II can be readily adjusted [111]. Method of preparation and peak zT of clathrates is summarized in table 3.

Binary chalcogenides
Binary chalcogenides like bismuth telluride, bismuth selenide, antimony telluride and their alloys have the reputation of being the efficient thermoelectric materials at room temperature and are widely used for thermoelectric refrigeration. In the moderate temperature range of heat source, these materials can also be used in thermoelectric generators. Out of all the binary chalcogenides, Bi 2 Te 3 and its alloys are mostly used for thermoelectric applications because of their efficiency over other binary chalcogenides. The crystal system of Bi 2 Te 3 possesses layered hexagonal structure consisting of the quintuple layers of mostly covalently bonded Te(1)-Bi-Te(2)-Bi-Te(1) layer with adjacent layers connected by weak van der Waals bonds [77,82] as is shown   [21] in figure 8 (a). Hence the intra-layer interactions are much stronger than inter-layer interactions. The electrical and thermal conductivities of bismuth telluride alloys are of anisotropic nature. Along the cleavage planes, lattice thermal conductivity is 1.5 Wm −1 K −1 which is twice that of the lattice thermal conductivity in the perpendicular direction [112,113] and resistivity along the cleavage plane is less than the resistivity along perpendicular direction by a factor of 3-4 at room temperature [77]. In Bi 2 Te 3 , the minority charge carriers cannot be completely neglected because the energy gap of Bi 2 Te 3 is only 5KT at 27°C and hence the minority carriers make a large contribution to thermal conductivity because of the bipolar effect [114]. Moreover, the thermoelectric coefficients of minority and majority carriers are of opposite signs. This results in the reduction of Seebeck coefficient and hence for this reason, the minority carriers are unacceptable. Doping can minimize the effects of minority carriers in Bi 2 Te 3 but the electronic thermal conductivity is also going to increase with the increase in doping concentration. Moreover, Bi 2 Te 3 based alloys possess the excellent electronic transport properties despite being anisotropic because of the multi-valley nature of the band structure. On the other hand, tellurium is regarded as the high performance elemental thermoelectric due to the presence of the original band nestification which enables a large number of effective band valley degeneracy [115], which might be the possible reason for excellent thermoelectric performance of Bi 2 Te 3 based thermoelectric materials. Ball milling and sintering techniques are commonly employed to produce Bi 2 Te 3 based alloys with high efficiency. But during this process, oxygen inclusion takes place in the lattice, which results in the degradation of thermoelectric properties. To overcome this problem, Seo et al carried out annealing in hydrogen atmosphere to remove the dissolved oxygen due to which the hole concentration is increased thereby increasing the electrical conductivity  [117]. The enhancement in ZT is based on the principle that the optimal sintering temperature coincided with the temperature at which the maximum Seebeck coefficient begins to degrade whereas the optimal sintering pressure coincided with the pressure at which the ratio of electrical conductivity to the total thermal conductivity reached the maximum value [117]. . Excess Te enabled liquid phase sintering in spark plasma sintering process reduces the lattice and bipolar contribution to the thermal conductivity without affecting the power factor and hence resulting in the increment in zT value [117b]. Nanoinclusion in bulk materials also helps to scatter phonons and decrease the lattice thermal conductivity. Jiang et al reported the nano-inclusion of n-type ZnO in p-and n-type Bi 2 Te 3 [119]. ZnO is an intrinsic n-type semiconductor with low thermal conductivity. In case of n-type Bi 2 Te 3 , ZnO reduces carrier concentration, and hence resistivity is increased. In case of p-type Bi 1.5 Sb 0.5 Te 3 , the lattice and total thermal conductivity is decreased and due to the decrease in thermal conductivity, zT reached the value of 1.3 [119]. Li et al reported that the thermoelectric nanocomposite of Bi 0.4 Sb 1.6 Te 3 incorporated with graphene nanosheets reached the zT value of 1.29 at 300 K and 1.54 at 440 K [118]. These values were obtained in Bi 0.4 Sb 1.6 Te 3 incorporated with only 0.3 vol% and 0.4 vol% graphene nanosheets. The Seebeck coefficient S increases with increase in temperature and after reaching a maximum value, it decreases with further increase in temperature. This behavior is due to the thermal excitation of minority carriers at high temperature. S also decreases with increase in the graphene nanosheet content [118]. Li et al reported zT of 0.55 in Bi 2 Te 3 /GQDs (GQDs: Graphene Quantum Dots) hybrid nanosheets at 425 K [120]. This value of Bi 2 Te 3 /GQDs-20 nm is the higher than that of Bi 2 Te 3 without hybrid nanostructures. Tang et al reported that highest power factor of the MoS 2 /Bi 2 Te 3 nanocomposite of 18.3 μWcm −1 which is about 30% higher than that of the pristine Bi 2 Te 3 sample at 319 K achieved from a nanocomposite sample containing 6 wt% MoS 2 [121]. The MoS 2 /Bi 2 Te 3 composite sample has more compact microstructure than the pristine Bi 2 Te 3 bulk sample. At a given temperature, the electrical conductivity of the composite increases first and then decreases as the MoS 2 content increases. This increase in electrical conductivity is due to more compact microstructure and well-grown grains. Out of all the MoS 2 /Bi 2 Te 3 nanocomposites, the nanocomposite in which the amount of added MoS 2 nanosheets is 17 wt% has the electrical conductivity lower than pristine Bi 2 Te 3 . It is because the MoS 2 grains form percolation networks in this sample which significantly lowers the electrical conductivity [121].
zT can also be increased up to 2-3 times in Bi 2 Te 3 -Sb 2 Te 3 superlattices [122][123][124] and also in Bi 2 Te 3 nanowires and nanoribbons [125]. Nano-particles based Bi 2 Se 1.2 Te 1.8 thin films have the highest reported ZT of 2.75 [126]. Hong et al reported ZT of 1.23 in n-type Bi 2 Te 2.7 Se 0.3 nanoplates at 480 K synthesized via microwave assisted surfactant free solvothermal method [22]. Peak ZT and method of preparation of binary chalcogenides is summarized in table 4.

Copper-based thermoelectrics
Copper-based compounds are considered efficient thermoelectric materials and because of the abundance of copper in nature these have attracted considerable interests in thermoelectric applications [127]. The thermal conductivity of copper-based materials is low because of the liquid like behavior of copper ions. The heat conductivity of crystalline materials is usually very high because of the long mean free path of phonons in the periodic structure. The lattice heat conductivity can be reduced by introducing the scattering centres in the crystal structure as is already discussed. Due to this, lattice thermal conductivity is reduced to the glass limit only. The lattice thermal conductivity can be reduced below the glass limit by eliminating some of the vibrational modes entirely which are responsible for the propagation of heat in crystalline solids. Transverse and shear vibrations are responsible for heat propagation in case of solid glass, but shear vibrations are not present in liquids [128,129]. So by introducing fluid like behavior of some ionic conductors, the lattice thermal conductivity can be reduced below the glass limit. This concept is referred to as the phonon-liquid electroncrystal (PLEC) and can be considered as the extension of the concept phonon-glass electron-crystal (PGEC). Also, the lattice thermal conductivity of solids is proportional to the specific heat as is mentioned earlier. Specific heat in the solid glass is usually constant and in liquids is less than that of solids. By introducing the liquid-like behaviour in solids, the specific heat is reduced from 3NK B to 2-2.5NK B because the propagation of most transverse vibrational modes is hindered in liquids which in turn reduces the lattice thermal conductivity [128][129][130] as is shown in figure 9(d). For a typical PLEC thermoelectric Cu 2−x Se, the value of specific heat falls in the range between that of solid and a liquid because of the partial liquid behaviour due to the presence of liquid like copper ions which also gives the extra boost to scatter the lattice phonons to disrupt the further heat propagation [50,131]. The crystal structure of Cu 2 Se is shown in figure 9(a). Copper-based thermoelectric are classified in various material systems termed as diamond-like compounds, superionic conductors, tetrahedrites, and oxyselenides. Copper-based diamond-like compounds are composed of tetrahedrally coordinated constituent elements which can be a ternary like Cu 2 SnSe 3 or a quarternary like Cu 2 ZnSn 0.9 In 0.1 Se 4 . Cu 2 SnSe 3 is a typical ternary copper based diamond-like compound, and its Indium doped variant is reported to have zT of 1.14 at 850 K [132]. The quarternary copper based diamond-like compound Cu 2 ZnSn 0.9 In 0.1 Se 4 has zT of 0.95 at 850 K [133]. Most of the diamond-like compounds possess a large band gap and hence were not considered for the thermoelectric performance because usually, the efficient thermoelectric materials have narrow band gap [134]. But high zT of 0.95 in Cu 2 ZnSn 0.9 In 0.1 Se 4 despite having large band gap opened a window to search for and such high zT is due to the presence of multiple degenerate valence bands which influence the transport of electrons significantly. Moreover, a significant anharmonicity is brought up in the crystal structure due to Ag doping which further reduces the lattice thermal conductivity [136]. Superionic conductors are solids having ionic conductivities as high as found in molten salts [130]. Copperbased superionic compounds can be binary like Cu 2 Se and ternary like CuCrSe 2 . Cu 2 Se consists of two different sub-lattices inside its crystal structure [50]. The Se atoms form a rigid sub-lattice favoring the electronic transport, and the copper sub-lattice exhibits liquid-like character which is responsible for the reduction of lattice thermal conductivity and thereby an increase in zT upto 1.5 was reported at 1000 K [50]. The zT value of 2.1 was reported in Cu 2 Se at 973 K prepared via ball milling method followed by spark plasma sintering and such high zT is due to the record low thermal conductivity of 0.34 W/m −1 k −1 . Such low thermal conductivity is because of the enhancement in scattering of phonons of wide range of wavelengths by different kinds of defects generated during ball milling process [137]. Zhu et al reported zT of 1.9 in Cu 2 S 0.5 Te 0.5 which is attributed to the formation of nanostructures in the crystal structures [138]. Enhancement in zT of Cu 2−x Se and its composites are reported by the inclusion of Cu 2 S nanosheets in Cu 2−x Se matrix [139]. This enhancement is due to the simultaneous improvement of Seebeck coefficient because of the external strain induced by Cu 2 S nanoinclusion in Cu 2−x Se matrix and decline of the total thermal conductivity by suppressing both electronic and lattice thermal conductivities. For the composite structure with 10 wt% nanoinclusion of Cu 2 S, the gain in Seebeck coefficient and the decline in thermal conductivity is largely resulting in the higher zT value of 0.90 at 773 K [139]. This composite material is a promising material in the mid-temperature range energy harvesting applications. Tetrahedrite is a natural mineral having the base composition Cu 12 Sb 4 S 13 having low thermal conductivity mainly due to the unique crystal structure. The maximum zT reported in Cu1 2 Sb 4 S 13 tetrahedrite system so far is around 1 at 700 K [140,141].
The oxyselenide BiCuSeO is a copper-based oxide system which has gained considerable attention in recent years because it is considered a promising p-type thermoelectric material. The crystal structure of BiCuSeO is shown in figure 10(a). Pristine BiCuSeO has very low electrical conductivity of around 5×10 2 s m −1 at 300 K [142]. To increase the electrical conductivity, BiCuSeO is doped with various elements at Bi-sites. In doped samples, the electrical conductivities were enhanced up to two orders of magnitude as compared to pristine BiCuSeO thereby improving zT in doped samples. zT of 1.4 was reported in Ba-doped BiCuSeO at 923 K [143]. Lan et al reported the ultrafast and low-cost fabrication of BiCuSeO in less than 20 min through self-propagating high-temperature synthesis combined with spark plasma sintering method [144]. They also reported high zT up to 0.70 in Bi 0.85 Na 0.15 CuSeO at 873 K which is about 100% higher than pristine BiCuSeO [144]. Das et al reported ZT of 1.09 in parent BiCuSeO which is higher than its Sn doped variant Bi 0.96 Sn 0.04 CuSeO [23]. This is due to the presence of thermally conducting SnO 2 secondary phase in the doped sample because of which the overall thermal conductivity increases and thereby decreasing zT [23]. Method of preparation and peak zT values of Cu-based thermoelectric is summarized in table 5.

Lead chalcogenides
Lead chalcogenides like (PbTe, PbSe, and PbS) and their derivatives are among the most promising thermoelectric materials in the mid-temperature range. The band gaps of PbTe, PbSe and PbS are 0.29, 0.27 and 0.37 eV respectively. Among these lead chalcogenides, PbTe is considered the best candidate for thermoelectric applications. The crystal structure of PbTe is shown in figure 11 (a). PbTe based thermoelectric materials are the efficient thermoelectric materials in the temperature range of 500-900 K [76,145] which is because of its twovalence band structure. A first light hole L band and a secondary lower-lying heavy hole ∑ band are present having the energy difference of 0.15-0.20 eV [68] as is shown in figure 11 (b). PbTe is being used as thermoelectric material since 1960's, and back then its figure of merit was believed to be 0.8 [76]. But according to recent studies, it is found that the intrinsic figure of merit of both n-and p-type PbTe materials is 1.4 [145]. PbTe has low thermal conductivity which may be due to many factors. In case of PbTe, the Umklapp process in  phonon scattering is the dominating process above 300 K which can be concluded because of the low speed of sound due to the harmonic lattice vibrations and relatively high anharmonicity. High anharmonicity is the key to large Gruneisen parameter. PbTe has weak bonding and contains heavy atoms which also result in large Gruneisen parameter. This large anharmonicity results in low lattice thermal conductivity which has already been discussed. The thermoelectric figure of merit of lead chalcogenides is continuously being increased by using different concepts of band engineering (band convergence [146,147], bands alignment [148,149], resonant levels [150,151], etc) and microstructure formation on all scale hierarchical architectures [148,149,152]. P-type PbTe 0.8 Se 0.2 shows a perfect example of band structure engineering to increase the band valley degeneracy where the small and controlled manipulation of band energies is allowed by alloying and the peak zT of 1.8 was observed [75]. Recently, zT of 2.2 was reported in PbTe bulk materials by multifunctional alloying [24]. PbTe 0.8 Se 0.2 was taken as a base matrix because of its large zT of 1.  [24]. Tan et al reported the high figure of merit up to 2.5 in PbTe-SrTe system [153]. Hole doped PbTe was heavily alloyed with SrTe beyond its thermodynamic solubility limit of <1 mol% which was predicted by previous studies using non-equilibrium processing. Such heavy alloying of SrTe produces an efficient thermoelectric material because the performance-enhancing mechanisms like valence band convergence and an increase in the point defect phonon scattering work simultaneously in this material. As a result, the figure of merit as high as 2.5 is obtained in Na-doped PbTe-8%SrTe at 923 K [153]. It is also reported that the average values of Na-doped PbTe-SrTe can be increased by the addition of small amount of Mn [154]. Alloying of PbTe-SrTe with MnTe can greatly alter the band structure of PbTe-SrTe, enlarging the band gap and increasing the band degeneracy. Alloying with MnTe also introduces low angle grain boundaries and reduces the lattice thermal conductivity by dislocation scattering. As a result of these effects, zT of 1.98 was observed [154]. In another study, Bi is doped in PbTe nanocubes to develop high-performance n-type PbTe based thermoelectric material [25]. The electronic transport properties of as-sintered PbTe nanocubes are improved by Bi addition and lattice thermal conductivity is reduced which is lower than its bulk counterparts. Such low thermal conductivity is due to the enhanced phonon scattering by high-density grain boundaries and dislocations. Hence the peak zT of 1.35 at 675 K is observed for n-type Pb 0.99 Bi 0.01 Te which is the highest reported in n-type PbTe based thermoelectric materials [25]. Ginting et al reported high zT of 2.3 in (PbTe) 0.95−x (PbSe) x (PbS) 0.05 for x=0.20 at 800 K [155].
With the increase in Se concentration, the energy band gap between conduction and valence L-band was decreased, and the energy difference between L-and ∑-bands was increased, and this band convergence enhances the power factor. Also, the PbS nanoscale precipitation in the matrix results in the reduction of lattice thermal conductivity. These two factors are responsible for such a huge ZT of (PbTe) 0.95−x (PbSe) x (PbS) 0.05 [155]. Now there is growing interest in tellurium free materials because of the growing expense and rarity of tellurium. PbSe can be considered as an alternative for PbTe but with lower performance because of its lower band gap at low temperatures [156]. But Parker and Singh reported that the figure of merit of heavily doped PbSe might reach up to 2 at the temperatures near 1000 K [157]. Wang et al reported zT>1.2 at 850 K for Na doped polycrystalline P-type PbSe samples [158]. Such high ZT is due to the sufficiently low thermal conductivity in PbSe particularly at high temperatures, which is mainly due to large Gruneisen parameter γ and smaller lattice parameter [158]. Qian et al reported that by introducing the mesostructures, the lattice thermal conductivity is reduced in n-type PbSe-PbS system and hence the increased zT value of 1.3 to 1.5 is observed at 923 K [26]. The development and large-scale applications of lead chalcogenides are restrained because of possible hazardous effects of lead present in these thermoelectric materials. Table 6 summarizes the methods of preparation and peak zT of lead chalcogenides.

Lead-free tin chalcogenides
Tin chalcogenides like SnSe, SnTe, and SnTe have emerged as the most promising thermoelectric materials in the last few years. The zT value of 2.6 was reported in p-type SnSe single crystals in 2014 which attracted great interest in the thermoelectric properties of tin chalcogenides [90]. Among these tin chalcogenides, SnTe has rock salt crystal structure with isotropic crystal properties while as SnSe and SnS have layered orthorhombic crystal structure and their thermoelectric properties are anisotropic which is mainly reflected in the thermal and electronic properties [159]. SnSe is a very stable compound containing abundant earth elements. The crystal structure of SnSe is shown in figures 12(a)- (d). It exhibits an intrinsically ultra-low thermal conductivity because of its complex, layered structure [90]. At the room, temperature SnSe exhibits the space group Pnma, and at the higher temperature, there is a transition from Pnma phase to Cmcm space group [90,160]. SnSe is known for its semiconducting properties having various applications like in solar cells and phase-change memory alloys [159,161,162]. Due to high resistivity and low zT value of 0.15, SnSe compound did not get any attention as a thermoelectric material in the past years [163,164]. But according to the recent investigation, ultra-high zT of 2.6 was found along b axis, 2.3 along the c axis and 0.8 along a axis at 923 K for SnSe single crystals that is for the high-temperature Cmcm phase [90] as shown in figure 12 (e). The difference in ZT along the three crystallographic axes is because the electrical conductivities along b and c axes are somewhat similar and higher than the electrical conductivity along a axis which is because of the higher carrier mobility along b and c directions [90]. The lattice thermal conductivity is significantly reduced in the high-temperature range, being lowest along a axis possibly because of the high anharmonicity while the Seebeck coefficient shows isotropic behavior [90]. Duong et al reported zT of 2.2 along b axis 733 K for Bi-doped SnSe single crystals [27]. The addition of Bi increases the carrier concentration which has a significant influence on the thermoelectric properties. Even by having such a massive figure of merit, the application of SnSe compound is substantially limited because of the lower thermoelectric properties of low-temperature Pnma phase [27]. Peng et al reported that acceptor doping in SnSe single crystals increases the carrier concentration and enhances zT in the Pnma phase. Na doped SnSe single crystals have average zT of 1.17 in the temperature range 300K-800K and the peak zT value exceeds 2 at 800 K along b axis in case of Sn 0.97 Na 0.03 Se [28]. By Na doping, the Fermi level is shifted, the valence band edge is flattened, and the number of carrier pockets is increased which has the positive effect on the electronic transport properties of Na-doped SnSe single crystals [28]. Due to the more inferior mechanical properties of single crystals as compared to the polycrystalline materials, their use in the thermoelectric applications is hindered. But the problem with polycrystalline materials is that they don't yield high zT values because of lower carrier mobility as compared to single crystals. Polycrystalline samples have lower thermal conductivity due to the presence of grain boundaries which scatter the phonons but also reducing the carrier mobility, and hence electrical conductivity is reduced [165]. The zT of undoped polycrystalline SnSe is reported to have the value 0.5 which is much lower than the undoped SnSe single crystals [166]. Various efforts have been made to enhance zT of polycrystalline SnSe for the use in thermoelectric applications. Fu et al reported zT as high as 0.92 at 873 K in p-type polycrystalline SnSe, and this enhancement is credited to the highly textured structure of SnSe crystals which is responsible for the increase in electrical conductivity. By introducing the grain boundaries, the peak zT value of 1.05 was obtained [167]. Chere et al reported the enhancement of zT in polycrystalline SnSe by Na doping [29]. The addition of Na increases the carrier concentration in polycrystalline SnSe which enhances the electrical conductivity and also because of the intrinsically low thermal conductivity, zT value as high as 0.8 at 773 K is obtained [29]. Zhang et al also reported zT of 0.8 in Iodine doped polycrystalline SnSe at 773 K and zT further attained to the value of 1 at 773 K by alloying the sample with 10at% SnS [168]. Tang et al demonstrated the simultaneous increment of power factor and the significant reduction in thermal conductivity in phase-separated Sn 1−x Pb x Se samples [30]. The electrical conductivity and power factor are improved by the introduction of PbSe phase in SnSe compound. The lattice thermal conductivity is reduced because of the nanoscale precipitates and mesoscale grains in all-scale architecture structures. These two factors get the credit for the high zT of 1.7 at 873 K in polycrystalline (SnSe+1% PbSe) samples [30].
SnTe is a highly degenerate p-type semiconductor but is considered a poor thermoelectric material. SnTe has high electrical conductivity but has very low zT of 0.5 at 900 K because of extremely low Seebeck coefficient and high thermal conductivity [159]. With the help of band structure engineering and nanostructure engineering, SnTe has the strong ability to become an efficient thermoelectric material [169][170][171]. In doping in SnTe creates resonant levels inside the valence band because of which the Seebeck coefficient around room temperature is enhanced [172]. The band structure engineering combined with nanostructure engineering leads to the maximum zT of 1.1 in In-doped SnTe [173]. Zhao et al reported zT of 0.9 at 823 K for Bi-doped Sn 0.97 Bi 0.03 Te because of the improved electrical transport properties and reduced thermal conductivity [174]. Doping resulted in the tuning of Fermi level and hence enhancing the electrical transport properties. zT is further increased by alloying with SrTe which created strained endotaxial nanostructures as phonon scattering centres to further reduce lattice thermal conductivity. The peak zT value of 1.2 at 823 K and the average zT value of 0.7 in the temperature range 300-823 K were obtained for Sn 0.97 Bi 0.03 Te-3%SrTe [174]. Doping of SnTe with Gd resulted in the drastic reduction of lattice thermal for Sn 0.94 Gd 0.6 Te, attributed to the formation of nanoprecipitates which strongly scatter phonons by mass fluctuation between a second phase and the matrix coupled with mesoscale scattering via grain boundaries [31]. The Seebeck coefficient is increased by the decrease in the carrier concentration due to further doping of Sn 0.96 Gd 0.06 Te with Ag. zT value of 1.1 at 823 K was obtained for Sn 0.96 Gd 0.06 Te containing 11at% Ag [31]. SnCd 0.03 Te possesses zT of 0.96 at 823 K, and this increment is due to the valence band engineering [31a] as is shown in figure 13(a). SnCd 0.03 Te entoxially nanostructured with CdS

Oxide thermoelectric
Oxides have gained interest as thermoelectric materials in recent years but were neglected in the past because of low electrical conductivity and high thermal conductivity because the constituents of oxides are usually light elements [175]. The oxide thermoelectrics have various advantages like high thermal stability, high chemical stability in the oxidizing atmosphere, non-toxic nature and easy fabrication methods [176]. Among the p-type oxides, cobaltites like NaCo 2 O 4 , Ca 3 Co 4 O 9 and Bi 2 Sr 3 Co 2 O 9 [175,176] are the promising thermoelectric materials, showing a positive temperature dependence of electrical conductivity in the high-temperature range due to Jahn-Teller polarons [177,178]. Out of these oxides, Ca 3 Co 4 O 9 is the most promising candidate for the use in thermoelectric applications because of the highly volatile character of Na and Bi in NaCo 2 O 4 and Bi 2 Sr 3 Co 2 O 9 respectively [179,180]. These oxides have anisotropic thermoelectric properties with the in-plane electrical resistivity less than that of the out-of-plane resistivity [175]. NaCo 2 O 4 single crystals have highly conducting CoO 2 block layer (CdI 2 -type) which is an incomplete layer containing randomly oriented and highly disordered Na + ions resulting in low lattice thermal conductivity [77,181]. The misfit layered single crystals of Ca 3 Co 4 O 9 show the better block-layer concept which is composed of two layers: the conducting layers of CoO 2 (CdI 2 -type) which sandwich the rock salt-type Ca 2 CoO 3 layer [182] as is shown in figure 14 (a). The low thermal conductivity occurs because phonons get scattered at the interfaces of these two sublattices having different b parameters [181]. Electronic correlations and spin entropy can explain the enhanced thermopower in these oxides [180,181]. zT of 0.74 was observed in Tb doped polycrystalline Ca 3 Ca 4 O 9 at 800 K which is the highest reported value for p-type oxides [32].
For n-type thermoelectric oxides, SrTiO 3 , CaMnO 3 , and ZnO based oxides have attracted a lot of attention. SrTiO 3 -based oxides exhibit perovskite structures having a very high melting point of 2080°C. These oxides are the promising n-type thermoelectrics because of the excellent electronic transport properties and greater stability at higher temperatures. zT of 0.33 at 900 K was reported by wang et al for Nb-doped SrTiO 3 ceramics doped with the surface modification of nanosized TiO 2 powder due to which the ratio of electrical to thermal conductivity is significantly increased without having much impact on the Seebeck coefficient [184]. zT of 0.41 at 973 K was reported in La-doped SrTiO 3 by Lu et al [183]. A record high zT>0.6 at 1000-1100 K was observed in La-Nb-doped SrTiO 3 nanopowders [33]. Such high zT is due to the increase in carrier concentration and electrical conductivity by La and Nb doping. The thermal conductivity, on the other hand, is reduced through complex microstructures [33]. Gd/W double substitution in polycrystalline calcium magnetite Ca 0.99 Gd 0.01 Mn 0.99 W 0.01 O 3 resulted in the zT of 0.12 at 700°C [185]. Due to Gd/W substitution, the electrical conductivity increases and thermal conductivity decreases [185]. zT of Ca 0.96 Dy 0.02 Yb 0.02 MnO 3 reached the value of 0.27at 800°C as a result of the improved electrical properties by Dy and Yb co-doping and the reduced lattice thermal conductivity [186]. ZnO is reported to have zT of 0.44 at 1000 K due to low lattice thermal conductivity which is the result of enhanced phonon scattering by Al-induced grain refinement and the presence of ZnAl 2 O 4 nanoprecipitates [187]. Method of preparation and peak zT of oxide thermoelectrics is summarized in table 8.

SiGe alloys
SiGe alloys are the promising thermoelectric materials used in RTGs and other high-temperature applications. SiGe has the band gap of 0.9 eV which is the reason for its significant Seebeck coefficient and low thermal conductivity at higher temperatures. SiGe alloys have potentially useful electronic properties because of their cubic structure [188,189] and by only reducing the lattice thermal conductivity their thermoelectric properties can be optimized. The reduction in the thermal conductivity was reported by the addition of silicide nanoinclusions to SiGe alloy as compared to the single-phase SiGe alloy [190]. The power factor is maintained or increased by these nano-inclusions and by the reduction of thermal conductivity, zT value reached to 1.3 in Si 0. 88 Ge 0.12 -Mg 2 Si nanocomposite at 950°C [190]. Peak zT of 0.73 was obtained in Boron-doped Si 80 Ge 20 with SiO 2 nano-inclusions due to the reduction in thermal conductivity and high values of Seebeck coefficient [191].
Ahmad et al reported the enhanced zT value of 1.81 in the P-type SiGe alloys by the incorporation of metallic Yttrium silicide nanoparticles [89]. The thermal conductivity is reduced by YSi 2 nano-inclusions due to the  formation of coherent states with SiGe matrix and also due to the reduction of grain size [89]. The temperature dependence of zT for various SiGe nanocomposites is shown in figure 15. 3.8. Mg 2 X (X=Si, Ge, and Sn) Mg 2 X compounds are the efficient thermoelectric materials in mid-temperature range and have the composition of non-toxic, inexpensive and earth-abundant elements [77]. Superior thermoelectric properties are exhibited in p-type Mg 2 X compounds originating from large density of states effective mass due to the large valley degeneracy of valence bands. Also like SiGe alloys, Mg 2 X compounds have cubic structure as is shown in figure 16(a) and thus have good electronic properties. So to optimise the thermoelectric properties, main focus is the reduction of thermal conductivity. Due to the low lattice thermal conductivity, zT value of 1.1 was observed in p-type Mg 2 Sn at 800 K [192] which is more than Mg 2 Si(0.8) and Mg 2 Ge(1). The low lattice thermal conductivity is due to low velocity of optical modes caused by the large mass density [192]. zT reached the value of 0.46 in Mg2Si microstructure via Yb and Bi doping because Yb doping lowers the thermal conductivity and Bi doping adjusts the electronic transport properties [193]. zT of 1.4 was obtained in Mg 2 Sn 0.73 Bi 0.02 Ge 0.25 at 673 K which shows that the charge donors are much more effective at Sn-site than Mg site [34]. Li et al reported HPHT synthesized Mg 2 Si 0.995 Sb 0.005 with zT up to 0.62 at 800 K [194]. Due to high pressure and temperature, the electrical conductivity increased while changing the Seebeck coefficient slightly resulting in the significant increase in power factor [194]. Iida et al reported that the thermal conductivity is reduced by the addition of small amount of Ge and this reduced thermal conductivity combined with the increased carrier concentration resulted in zT of 0.47 for Mg 2 Si 0. 94 Ge 0.05 Sb 0.005 [35]. Table 9 summarizes the peak zT and method of preparation of Mg 2 X compounds.

Half-Heusler alloys
The general formula of half-Heusler alloys is XYZ, X being a noble or a transition metal, or a rare-earth element, Y being a noble or a transition metal and Z being the main group element. Half-Heusler compounds of the composition XNiSn and XCoSb (X=Ti, Zr or Hf) are the excellent candidates for thermoelectric applications because the half-Heusler structure (cubic structure) as is shown in figure 17(a) allows better electronic transport properties and also have an inexpensive elemental composition with low toxicity. The problem in employing half-Heusler alloys in thermoelectric applications lies in their high thermal conductivity and to optimise their thermoelectric properties, main focus is the reduction of the thermal conductivity rather than the increment of the electrical transport properties. The isoelectronic alloying in half-Heusler compounds XNiSn and XCoSb (X=Ti, Zr or Hf) reduces lattice thermal conductivity to the large extent but the electrical transport properties also get degraded. Recently zT of 0.83 at 923 K was reported in Hf 0.25 Zr 0.75 NiSn 0.985 Sb 0.015 which is 67% more than that of the undoped sample [36]. Sb is found to be an effective dopant for n-type ZrNiSn half-Heusler alloys which effectively increases the carrier concentration and also reduces thermal conductivity [36]. Chen et al reported high zT of 1.3 in n-typeHf 0.65 Zr 0.25 Ti 0.15 NiSn 0.995 Sb 0.005 /nano-ZrO 2 composition at 850 K [195]. Such high zT resulted from Figure 15. Temperature dependence of zT for recently developed efficient SiGe alloy thermoelectric [190,191,89]. the elemental substitution of Ti in (Hf, Zr) sites and simultaneous embedment of ZrO 2 nanoparticles in (Hf, Zr)NiSn matrix. Due to Ti substitution, phonon scattering is enhanced which reduces lattice thermal conductivity. On the other hand, ZrO 2 nanoparticles act as potential barriers for carrier scattering that enhances the thermopower [195]. Among the prospective half-Heusler alloys are also p-type FeNbSb and α-MgAgSb based materials [196,197]. The excellent thermoelectric performance was reported in Ti-doped FeNbSb and zT of 1.1 achieved in the composition FeNb 0.8 Ti 0.2 Sb at 1100 K which is twice that of ZrCoSb [196]. Lattice thermal conductivity is reduced due to the presence of high Ti content, and the electrical properties are optimized via band engineering [196]. Fu et al reported the enhanced thermoelectric   [34] properties in Hf doped FeNbSb heavy band half-Heusler compound [37]. Hf doping at Nb sites induces more point defect scattering because of the larger mass and radius difference between Hf and Nb atoms. The heavy element Hf dopants optimize the electrical properties and suppress the thermal conductivity and hence zT value reached 1.5 for FeNb 0.88 Hf 0.12 Sb and FeNb 0.86 Hf 0.12 Sb at 1200 K [37]. Highly pure α-MgAgSb is a promising thermoelectric material because of the intrinsically low thermal conductivity which can further be reduced by point defect scattering through doping. zT of 1.1 was achieved in α-MgAgSb 0.99 In 0.1 at 525 K because of the enhancement of carrier concentration by In doping [38]. Methods of preparation and peak zT of half-Heusler alloys is summarized in table 10.  The comparison of zT versus temperature of some efficient thermoelectric materials belonging to different groups is shown in figure 18.

Conclusion
The constant high demand for energy, thermal management, and increasing pollution are the major issues of the world. Thermoelectric concept ties a knot between these major problems and can solve these problems simultaneously. The basic concepts are related to various challenges to find the suitable materials for thermoelectricity. These materials should follow phonon-glass electron-crystal behavior. Attaining phononglass electron-crystal behavior by decoupling electrical and thermal transport properties of materials has haunted researchers for many years. The discovery of materials with complex unit cells like the complex variants of chalcogenides and disordered large unit cells like skutterudites and clathrates have managed to decouple these properties. Band engineering strategies in materials like lead chalcogenides have demonstrated highly efficient thermoelectric materials. By reducing the specific heat in case of thermoelectrics with liquid-like behavior, the increased performance can be guaranteed. Nanostructure engineering also has the reputation of delivering efficient thermoelectric materials. The development of nanocomposite materials provides a new route to develop efficient thermoelectric materials because of their ability to scatter phonons randomly. The efficiency of bulk materials can be improved to a large extent with the inclusion of nanocomposites. This review insights the complex structures and have highlighted the strategies to increase zT of TE materials. The recent advances in the field of thermoelectricity have also been discussed. Still, a lot of work has to be done to deliver the thermoelectric materials with superior efficiency so that the energy crisis and pollution could be eliminated. It is anticipated that the further progress in TE materials with improved zT values and device fabrication shall lead to practical applications in the future so that living in the cleaner and greener world would be possible.