Thermoelectric materials show the thermoelectric effect in a strong or convenient form. The thermoelectric effect refers to phenomena by which either a temperature difference creates an electric potential or an electric current creates a temperature difference. These phenomena are known more specifically as the Seebeck effect (creating a voltage from temperature difference), Peltier effect (driving heat flow with an electric current), and Thomson effect (reversible heating or cooling within a conductor when there is both an electric current and a temperature gradient). While all materials have a nonzero thermoelectric effect, in most materials it is too small to be useful. However, low-cost materials that have a sufficiently strong thermoelectric effect (and other required properties) are also considered for applications including power generation and refrigeration. The most commonly used thermoelectric material is based on bismuth telluride (Bi2Te3). Thermoelectric materials are used in thermoelectric systems for cooling or heating in niche applications, and are being studied as a way to regenerate electricity from waste heat. Research in the field is still driven by materials development, primarily in optimizing transport and thermoelectric properties.
Thermoelectric figure of merit The usefulness of a material in thermoelectric systems is determined by the device efficiency. This is determined by the material's electrical conductivity (σ), thermal conductivity (κ), and Seebeck coefficient (S), which change with temperature (T). The maximum efficiency of the energy conversion process (for both power generation and cooling) at a given temperature point in the material is determined by the thermoelectric materials figure of merit z T {\displaystyle zT} , given by z T = σ S 2 T κ . {\displaystyle zT={\sigma S^{2}T \over \kappa }.}
Device efficiency The efficiency of a thermoelectric device for electricity generation is given by η {\displaystyle \eta } , defined as η = energy provided to the load heat energy absorbed at hot junction . {\displaystyle \eta ={{\text{energy provided to the load}} \over {\text{heat energy absorbed at hot junction}}}.}
The maximum efficiency of a thermoelectric device is typically described in terms of its device figure of merit Z T {\displaystyle ZT} where the maximum device efficiency is approximately given by η m a x = T H − T C T H 1 + Z T ¯ − 1 1 + Z T ¯ + T C T H , {\displaystyle \eta _{\mathrm {max} }={T_{\rm {H}}-T_{\rm {C}} \over T_{\rm {H}}}{{\sqrt {1+Z{\bar {T}}}}-1 \over {\sqrt {1+Z{\bar {T}}}}+{T_{\rm {C}} \over T_{\rm {H}}}},} where T H {\displaystyle T_{\rm {H}}} is the fixed temperature at the hot junction, T C {\displaystyle T_{\rm {C}}} is the fixed temperature at the surface being cooled, and T ¯ {\displaystyle {\bar {T}}} is the mean of T H {\displaystyle T_{\rm {H}}} and T C {\displaystyle T_{\rm {C}}} . This maximum efficiency equation is exact when thermoelectric properties are temperature-independent. For a single thermoelectric leg the device efficiency can be calculated from the temperature dependent properties S, κ and σ and the heat and electric current flow through the material. In an actual thermoelectric device, two materials are used (typically one n-type and one p-type) with metal interconnects. The maximum efficiency η m a x {\displaystyle \eta _{\mathrm {max} }} is then calculated from the efficiency of both legs and the electrical and thermal losses from the interconnects and surroundings. Ignoring these losses and temperature dependencies in S, κ and σ, an inexact estimate for Z T {\displaystyle ZT} is given by Z T ¯ = ( S p − S n ) 2 T ¯ [ ( ρ n κ n ) 1 / 2 + ( ρ p κ p ) 1 / 2 ] 2 {\displaystyle Z{\bar {T}}={(S_{p}-S_{n})^{2}{\bar {T}} \over [(\rho _{n}\kappa _{n})^{1/2}+(\rho _{p}\kappa _{p})^{1/2}]^{2}}} where ρ {\displaystyle \rho } is the electrical resistivity, and the properties are averaged over the temperature range; the subscripts n and p denote properties related to the n- and p-type semiconducting thermoelectric materials, respectively. Only when n and p elements have the same and temperature independent properties ( S p = − S n {\displaystyle S_{p}=-S_{n}} ) does Z T ¯ = z T ¯ {\displaystyle Z{\bar {T}}=z{\bar {T}}} . Since thermoelectric devices are heat engines, their efficiency is limited by the Carnot efficiency T H − T C T H {\displaystyle {\frac {T_{\rm {H}}-T_{\rm {C}}}{T_{\rm {H}}}}} , the first factor in η m a x {\displaystyle \eta _{\mathrm {max} }} , while Z T {\displaystyle ZT} and z T {\displaystyle zT} determines the maximum reversibility of the thermodynamic process globally and locally, respectively. Regardless, the coefficient of performance of current commercial thermoelectric refrigerators ranges from 0.3 to 0.6, one-sixth the value of traditional vapor-compression refrigerators.
Power factor Often the thermoelectric power factor is reported for a thermoelectric material, given by P o w e r f a c t o r = σ S 2 [ W / m / K 2 ] {\displaystyle \mathrm {Power~factor} =\sigma S^{2}[W/m/K^{2}]} where S is the Seebeck coefficient, and σ is the electrical conductivity. Although it is often claimed that TE devices with materials with a higher power factor are able to 'generate' more energy (move more heat or extract more energy from that temperature difference) this is only true for a thermoelectric device with fixed geometry and unlimited heat source and cooling. If the geometry of the device is optimally designed for the specific application, the thermoelectric materials will operate at their peak efficiency which is determined by their z T {\displaystyle zT} not σ S 2 {\displaystyle \sigma S^{2}} .
Aspects of materials choice For good efficiency, materials with high electrical conductivity, low thermal conductivity and high Seebeck coefficient are needed.
Electron state density: metals vs semiconductors The band structure of semiconductors offers better thermoelectric effects than the band structure of metals. The Fermi energy is below the conduction band causing the state density to be asymmetric around the Fermi energy. Therefore, the average electron energy of the conduction band is higher than the Fermi energy, making the system conducive for charge motion into a lower energy state. By contrast, the Fermi energy lies in the conduction band in metals. This makes the state density symmetric about the Fermi energy so that the average conduction electron energy is close to the Fermi energy, reducing the forces pushing for charge transport. Therefore, semiconductors are ideal thermoelectric materials.
Conductivity In the efficiency equations above, thermal conductivity and electrical conductivity compete. The thermal conductivity κ in crystalline solids has mainly two components:
κ = κ electron + κ phonon According to the Wiedemann–Franz law, the higher the electrical conductivity, the higher κ electron becomes. Thus in metals the ratio of thermal to electrical conductivity is about fixed, as the electron part dominates. In semiconductors, the phonon part is important and cannot be neglected. It reduces the efficiency. For good efficiency a low ratio of κ phonon / κ electron is desired. Therefore, it is necessary to minimize κ phonon and keep the electrical conductivity high. Thus semiconductors should be highly doped. G. A. Slack proposed that in order to optimize the figure of merit, phonons, which are responsible for thermal conductivity must experience the material as a glass (experiencing a high degree of phonon scattering—lowering thermal conductivity) while electrons must experience it as a crystal (experiencing very little scattering—maintaining electrical conductivity): this concept is called phonon glass electron crystal. The figure of merit can be improved through the independent adjustment of these properties.
Quality factor
The maximum Z T ¯ {\displaystyle Z{\bar {T}}} of a material is given by the material's quality factor
B = 2 k B 2 ℏ 3 π N v C l m l ∗ Ξ 2 κ L T {\displaystyle B={\frac {2k_{\rm {B}}^{2}\hbar }{3\pi }}{\frac {N_{\rm {v}}C_{\rm {l}}}{m_{\rm {l}}^{*}\Xi ^{2}\kappa _{\rm {L}}}}T}
where k B {\displaystyle k_{\rm {B}}} is the Boltzmann constant, ℏ {\displaystyle \hbar } is the reduced Planck constant, N v {\displaystyle N_{\rm {v}}} is the number of degenerated valleys for the band, C l {\displaystyle C_{\rm {l}}} is the average longitudinal elastic moduli, m l ∗ {\displaystyle m_{\rm {l}}^{*}} is the inertial effective mass, Ξ {\displaystyle \Xi } is the deformation potential coefficient, κ L {\displaystyle \kappa _{\rm {L}}} is the lattice thermal conduction, and T {\displaystyle T} is temperature. The figure of merit, Z T ¯ {\displaystyle Z{\bar {T}}} , depends on doping concentration and temperature of the material of interest. The material quality factor B {\displaystyle B} is useful because it allows for an intrinsic comparison of possible efficiency between different materials. This relation shows that improving the electronic component N v m l ∗ Ξ 2 {\displaystyle {\frac {N_{\rm {v}}}{m_{\rm {l}}^{*}\Xi ^{2}}}} , which primarily affects the Seebeck coefficient, will increase the quality factor of a material. A large density of states can be created due to a large number of conducting bands ( N v {\displaystyle N_{\rm {v}}} ) or by flat bands giving a high band effective mass ( m b ∗ {\displaystyle m_{\rm {b}}^{*}} ). For isotropic materials m b ∗ = m l ∗ {\displaystyle m_{\rm {b}}^{*}=m_{\rm {l}}^{*}} . Therefore, it is desirable for thermoelectric materials to have high valley degeneracy in a very sharp band structure. Other complex features of the electronic structure are important. These can be partially quantified using an electronic fitness function.
Materials of interest Strategies to improve thermoelectric performances include both advanced bulk materials and the use of low-dimensional systems. Such approaches to reduce lattice thermal conductivity fall under three general material types: (1) Alloys: create point defects, vacancies, or rattling structures (heavy-ion species with large vibrational amplitudes contained within partially filled structural sites) to scatter phonons within the unit cell crystal; (2) Complex crystals: separate the phonon glass from the electron crystal using approaches similar to those for superconductors (the region responsible for electron transport should be an electron crystal of a high-mobility semiconductor, while the phonon glass should ideally house disordered structures and dopants without disrupting the electron crystal, analogous to the charge reservoir in high-Tc superconductors); (3) Multiphase nanocomposites: scatter phonons at the interfaces of nanostructured materials, be they mixed composites or thin film superlattices. Materials under consideration for thermoelectric device applications include:
Bismuth chalcogenides and their nanostructures Materials such as Bi2Te3 and Bi2Se3 comprise some of the best performing room temperature thermoelectrics with a temperature-independent figure-of-merit, ZT, between 0.8 and 1.0. Nanostructuring these materials to produce a layered superlattice structure of alternating Bi2Te3 and Sb2Te3 layers produces a device within which there is good electrical conductivity but perpendicular to which thermal conductivity is poor. The result is an enhanced ZT (approximately 2.4 at room temperature for p-type). Note that this high value of ZT has not been independently confirmed due to the complicated demands on the growth of such superlattices and device fabrication; however the material ZT values are consistent with the performance of hot-spot coolers made out of these materials and validated at Intel Labs. Bismuth telluride and its solid solutions are good thermoelectric materials at room temperature and therefore suitable for refrigeration applications around 300 K. The Czochralski method has been used to grow single crystalline bismuth telluride compounds. These compounds are usually obtained with directional solidification from melt or powder metallurgy processes. Materials produced with these methods have lower efficiency than single crystalline ones due to the random orientation of crystal grains, but their mechanical properties are superior and the sensitivity to structural defects and impurities is lower due to high optimal carrier concentration. The required carrier concentration is obtained by choosing a nonstoichiometric composition, which is achieved by introducing excess bismuth or tellurium atoms to primary melt or by dopant impurities. Some possible dopants are halogens and group IV and V atoms. Due to the small bandgap (0.16 eV) Bi2Te3 is partially degenerate and the corresponding Fermi-level should be close to the conduction band minimum at room temperature. The size of the band-gap means that Bi2Te3 has high intrinsic carrier concentration. Therefore, minority carrier conduction cannot be neglected for small stoichiometric deviations. Use of telluride compounds is limited by the toxicity and rarity of tellurium.
Lead tellurides Heremans et al. (2008) demonstrated that thallium-doped lead telluride alloy (PbTe) achieves a ZT of 1.5 at 773 K. Later, Snyder et al. (2011) reported ZT~1.4 at 750 K in sodium-doped PbTe, and ZT~1.8 at 850 K in sodium-doped PbTe1−xSex alloy. Snyder's group determined that both thallium and sodium alter the electronic structure of the crystal increasing electronic conductivity. They also claim that selenium increases electric conductivity and reduces thermal conductivity. In 2012 another team used lead telluride to convert waste heat to electricity, reaching a ZT of 2.2, which they claimed was the highest yet reported.
Inorganic clathrates Inorganic clathrates have the general formula AxByC46-y (type I) and AxByC136-y (type II), where B and C are group III and IV elements, respectively, which form the framework where "guest" A atoms (alkali or alkaline earth metal) are encapsulated in two different polyhedra facing each other. The differences between types I and II come from the number and size of voids present in their unit cells. Transport properties depend on the framework's properties, but tuning is possible by changing the "guest" atoms. The most direct approach to synthesize and optimize the thermoelectric properties of semiconducting type I clathrates is substitutional doping, where some framework atoms are replaced with dopant atoms. In addition, powder metallurgical and crystal growth techniques have been used in clathrate synthesis. The structural and chemical properties of clathrates enable the optimization of their transport properties as a function of stoichiometry. The structure of type II materials allows a partial filling of the polyhedra, enabling better tuning of the electrical properties and therefore better control of the doping level. Partially filled variants can be synthesized as semiconducting or even insulating. Blake et al. have predicted ZT~0.5 at room temperature and ZT~1.7 at 800 K for optimized compositions. Kuznetsov et al. measured electrical resistance and Seebeck coefficient for three different type I clathrates above room temperature and by estimating high temperature thermal conductivity from the published low temperature data they obtained ZT~0.7 at 700 K for Ba8Ga16Ge30 and ZT~0.87 at 870 K for Ba8Ga16Si30.
Compounds of Mg and group-14 element Mg2BIV (B14=Si, Ge, Sn) compounds and their solid solutions are good thermoelectric materials and their ZT values are comparable with those of established materials. The appropriate production methods are based on direct co-melting, but mechanical alloying has also been used. During synthesis, magnesium losses due to evaporation and segregation of components (especially for Mg2Sn) need to be taken into account. Directed crystallization methods can produce single crystals of Mg2Si, but they intrinsically have n-type conductivity, and doping, e.g. with Sn, Ga, Ag or Li, is required to produce p-type material which is required for an efficient thermoelectric device. Solid solutions and doped compounds have to be annealed in order to produce homogeneous samples – with the same properties throughout. At 800 K, Mg2Si0.55−xSn0.4Ge0.05Bix has been reported to have a figure of merit about 1.4, the highest ever reported for these compounds.
Skutterudite thermoelectrics Skutterudites have a chemical composition of LM4X12, where L is a rare-earth metal (optional component), M is a transition metal, and X is a metalloid, a group V element or a pnictogen such as phosphorus, antimony, or arsenic. These materials exhibit ZT>1.0 and can potentially be used in multistage thermoelectric devices. Unfilled, these materials contain voids, which can be filled with low-coordination ions (usually rare-earth elements) to reduce thermal conductivity by producing sources for lattice phonon scattering, without reducing electrical conductivity. It is also possible to reduce the thermal conductivity in skutterudite without filling these voids using a special architecture containing nano- and micro-pores. NASA is developing a Multi-Mission Radioisotope Thermoelectric Generator in which the thermocouples would be made of skutterudite, which can function with a smaller temperature difference than the current tellurium designs. This would mean that an otherwise similar RTG would generate 25% more power at the beginning of a mission and at least 50% more after seventeen years. NASA hopes to use the design on the next New Frontiers mission.
Oxide thermoelectrics Homologous oxide compounds (such as those of the form (SrTiO3)n(SrO)m—the Ruddlesden-Popper phase) have layered superlattice structures that make them promising candidates for use in high-temperature thermoelectric devices. These materials exhibit low thermal conductivity perpendicular to the layers while maintaining good electronic conductivity within the layers. Their ZT values can reach 2.4 for epitaxial SrTiO3 films, and the enhanced thermal stability of such oxides, as compared to conventional high-ZT bismuth compounds, makes them superior high-temperature thermoelectrics. Interest in oxides as thermoelectric materials was reawakened in 1997 when a relatively high thermoelectric power was reported for NaCo2O4. In addition to their thermal stability, other advantages of oxides are their low toxicity and high oxidation resistance. Simultaneously controlling both the electric and phonon systems may require nanostructured materials. Layered Ca3Co4O9 exhibited ZT values of 1.4–2.7 at 900 K. If the layers in a given material have the same stoichiometry, they will be stacked so that the same atoms will not be positioned on top of each other, impeding phonon conductivity perpendicular to the layers. Recently, oxide thermoelectrics have gained a lot of attention so that the range of promising phases increased drastically. Novel members of this family include ZnO, MnO2, and NbO2.
Cation-substituted copper sulfide thermoelectrics All variables mentioned are included in the equation for the dimensionless figure of merit, zT, which can be seen at the top of this page. The goal of any thermoelectric experiment is to make the power factor, S2 σ, larger while maintaining a small thermal conductivity. This is because electricity is produced through a temperature gradient, so materials that can equilibrate heat very quickly are not useful. The two compounds detailed below were found to exhibit high-performing thermoelectric properties, which can be evidenced by the reported figure of merit in either respective manuscript. Cuprokalininite (CuCr2S4) is a copper-dominant analogue of the mineral joegoldsteinite. It was recently found within metamorphic rocks in Slyudyanka, part of the South Baikal region of Russia, and researchers have determined that Sb-doped cuprokalininite (Cu1-xSbxCr2S4) shows promise in renewable technology. Doping is the act of intentionally adding an impurity, usually to modify the electrochemical characteristics of the seed material. The introduction of antimony enhances the power factor by bringing in extra electrons, which increases the Seebeck coefficient, S, and reduces the magnetic moment (how likely the particles are to align with a magnetic field); it also distorts the crystal structure, which lowers the thermal conductivity, κ. Khan et al. (2017) were able to discover the optimal amount of Sb content (x=0.3) in cuprokalininte in order to develop a device with a ZT value of 0.43. Bornite (Cu5FeS4) is a sulfide mineral named after an Austrian mineralogist, though it is much more common than the aforementioned cuprokalininite. This metal ore was found to demonstrate an improved thermoelectric performance after undergoing cation exchange with iron. Cation exchange is the process of surrounding a parent crystal with an electrolyte complex, so that the cations (positively charged ions) within the structure can be swapped out for those in solution without affecting the anion sublattice (negatively charged crystal network). What one is left with are crystals that possess a different composition, yet an identical framework. In this way, scientists are granted extreme morphological control and uniformity when generating complicated heterostructures. As to why it was thought to improve the ZT value, the mechanics of cation exchange often bring about crystallographic defects, which cause phonons (simply put, heat particles) to scatter. According to the Debye-Callaway formalism, a model used to determine the lattice thermal conductivity, κL, the highly anharmonic behavior due to phonon scattering results in a large thermal resistance. Therefore, a greater defect density decreases the lattice thermal conductivity, thereby making a larger figure of merit. In conclusion, Long et al. reported that greater Cu-deficiencies resulted in increases of up to 88% in the ZT value, with a maximum of 0.79. The composition of thermoelectric devices can dramatically vary depending on the temperature of the heat they must harvest; considering the fact that more than eighty percent of industry waste falls within a range of 373-575 K, chalcogenides and antimonides are better suited for thermoelectric conversion because they can utilize heat at lower temperatures. Not only is sulfur the cheapest and lightest chalcogenide, current surpluses may be causing threat to the environment since it is a byproduct of oil capture, so sulfur consumption could help mitigate future damage. As for the metal, copper is an ideal seed particle for any kind of substitution method because of its high mobility and variable oxidation state, for it can balance or complement the charge of more inflexible cations. Therefore, either the cuprokalininite or bornite minerals could prove ideal thermoelectric components.
Half-Heusler alloys Half-Heusler (HH) alloys have a great potential for high-temperature power generation applications. Examples of these alloys include NbFeSb, NbCoSn and VFeSb. They have a cubic MgAgAs-type structure formed by three interpenetrating face-centered-cubic (fcc) lattices. The ability to substitute any of these three sublattices opens the door for wide variety of compounds to be synthesized. Various atomic substitutions are employed to reduce the thermal conductivity and enhance the electrical conductivity. Previously, ZT could not peak more than 0.5 for p-type and 0.8 for n-type HH compound. However, in the past few years, researchers were able to achieve ZT≈1 for both n-type and p-type. Nano-sized grains is one of the approaches used to lower the thermal conductivity via grain boundaries- assisted phonon scattering. Another approach was to utilize the principles of nanocomposites, by which certain combination of metals were favored on others due to the atomic size difference. For instance, Hf and Ti is more effective than Hf and Zr, when reduction of thermal conductivity is of concern, since the atomic size difference between the former is larger than that of the latter.
Flexible Thermoelectric Materials
Electrically conducting organic materials
Conducting polymers are of significant interest for flexible thermoelectric development. They are flexible, lightweight, geometrically versatile, and can be processed at scale, an important component for commercialization. However, the structural disorder of these materials often inhibits the electrical conductivity much more than the thermal conductivity, limiting their use so far. Some of the most common conducting polymers investigated for flexible thermoelectrics include poly(3,4-ethylenedioxythiophene) (PEDOT), polyanilines (PANIs), polythiophenes, polyacetylenes, polypyrrole, and polycarbazole. P-type PEDOT:PSS (polystyrene sulfonate) and PEDOT-Tos (Tosylate) have been some of the most encouraging materials investigated. Organic, air-stable n-type thermoelectrics are often harder to synthesize because of their low electron affinity and likelihood of reacting with oxygen and water in the air. These materials often have a figure of merit that is still too low for commercial applications (~0.42 in PEDOT:PSS) due to the poor electrical conductivity.
Hybrid Composites Hybrid composite thermoelectrics involve blending the previously discussed electrically conducting organic materials or other composite materials with other conductive materials in an effort to improve transport properties. The conductive materials that are most commonly added include carbon nanotubes and graphene due to their conductivities and mechanical properties. It has been shown that carbon nanotubes can increase the tensile strength of the polymer composite they are blended with. However, they can also reduce the flexibility. Furthermore, future study into the orientation and alignment of these added materials will allow for improved performance. The percolation threshold of CNT's is often especially low, well below 10%, due to their high aspect ratio. A low percolation threshold is desirable for both cost and flexibility purposes. Reduced graphene oxide (rGO) as graphene-related material was also used to enhance figure of merit of thermoelectric materials. The addition of rather low amount of graphene or rGO around 1 wt% mainly strengthens the phonon scattering at grain boundaries of all these materials as well as increases the charge carrier concentration and mobility in chalcogenide-, skutterudite- and, particularly, metal oxide-based composites. However, significant growth of ZT after addition of graphene or rGO was observed mainly for composites based on thermoelectric materials with low initial ZT. When thermoelectric material is already nanostructured and possesses high electrical conductivity, such an addition does not enhance ZT significantly. Thus, graphene or rGO-additive works mainly as an optimizer of the intrinsic performance of thermoelectric materials. Hybrid thermoelectric composites also refer to polymer-inorganic thermoelectric composites. This is generally achieved through an inert polymer matrix that is host to thermoelectric filler material. The matrix is generally nonconductive so as to not short current as well as to let the thermoelectric material dominate electrical transport properties. One major benefit of this method is that the polymer matrix will generally be highly disordered and random on many different length scales, meaning that the composite material will can have a much lower thermal conductivity. The general procedure to synthesize these materials involves a solvent to dissolve the polymer and dispersion of the thermoelectric material throughout the mixture.
Silicon-germanium alloys Bulk Si exhibits a low ZT of ~0.01 because of its high thermal conductivity. However, ZT can be as high as 0.6 in silicon nanowires, which retain the high electrical conductivity of doped Si, but reduce the thermal conductivity due to elevated scattering of phonons on their extensive surfaces and low cross-section. Combining Si and Ge also allows to retain a high electrical conductivity of both components and reduce the thermal conductivity. The reduction originates from additional scattering due to very different lattice (phonon) properties of Si and Ge. As a result, Silicon-germanium alloys are currently the best thermoelectric materials around 1000 °C and are therefore used in some radioisotope thermoelectric generators (RTG) (notably the MHW-RTG and GPHS-RTG) and some other high^temperature applications, such as waste heat recovery. Usability of silicon-germanium alloys is limited by their high price and moderate ZT values (p-SiGe ~0.7 and n-SiGe ~1.0); however, ZT can be increased to 1–2 in SiGe nanostructures owing to the reduction in thermal conductivity.
Sodium cobaltate Experiments on crystals of sodium cobaltate, using X-ray and neutron scattering experiments carried out at the European Synchrotron Radiation Facility (ESRF) and the Institut Laue-Langevin (ILL) in Grenoble were able to suppress thermal conductivity by a factor of six compared to vacancy-free sodium cobaltate. The experiments agreed with corresponding density functional calculations. The technique involved large anharmonic displacements of Na0.8CoO2 contained within the crystals.
Amorphous materials In 2002, Nolas and Goldsmid have come up with a suggestion that systems with the phonon mean free path larger than the charge carrier mean free path can exhibit an enhanced thermoelectric efficiency. This can be realized in amorphous thermoelectrics and soon they became a focus of many studies. This ground-breaking idea was accomplished in Cu-Ge-Te, NbO2, In-Ga-Zn-O, Zr-Ni-Sn, Si-Au, and Ti-Pb-V-O amorphous systems. It should be mentioned that modelling of transport properties is challenging enough without breaking the long-range order so that design of amorphous thermoelectrics is at its infancy. Naturally, amorphous thermoelectrics give rise