# Thermoelectric materials

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This article is about materials that are used or could be used to exploit the thermoelectric effect in practical applications. For the definition of the thermoelectric effect and its underlying physics, see thermoelectric effect.

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 potential creates a temperature difference. These phenomena are known more specifically as the Seebeck effect (converting temperature to current), Peltier effect (converting current to temperature), and Thomson effect (conductor heating/cooling). 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) could be used in applications including power generation and refrigeration. A commonly used thermoelectric material in such applications is bismuth telluride (Bi
2
Te
3
).

Thermoelectric materials are used in thermoelectric systems for cooling or heating in niche applications,[1] and are being studied as a way to regenerate electricity from waste heat.[2]

## Materials selection criteria

The usefulness of a material in thermoelectric systems is determined by the two factors device efficiency and power factor. These are determined by the material's electrical conductivity, thermal conductivity, Seebeck coefficient and behavior under changing temperatures.

### Device efficiency

The efficiency of a thermoelectric device for electricity generation is given by ${\displaystyle \eta }$, defined as

${\displaystyle \eta ={{\text{energy provided to the load}} \over {\text{heat energy absorbed at hot junction}}}.}$

The ability of a given material to efficiently produce thermoelectric power is related to its dimensionless figure of merit given by:

${\displaystyle ZT={\sigma S^{2}T \over \lambda }}$,

which depends on the Seebeck coefficient S, thermal conductivity λ, electrical conductivity σ, and temperature T.

In an actual thermoelectric device, two materials are used. The maximum efficiency ${\displaystyle \eta _{\mathrm {max} }}$ is then given by

${\displaystyle \eta _{\mathrm {max} }={T_{H}-T_{C} \over T_{H}}{{\sqrt {1+Z{\bar {T}}}}-1 \over {\sqrt {1+Z{\bar {T}}}}+{T_{C} \over T_{H}}},}$

where ${\displaystyle T_{H}}$ is the temperature at the hot junction and ${\displaystyle T_{C}}$ is the temperature at the surface being cooled. ${\displaystyle Z{\bar {T}}}$ is the modified dimensionless figure of merit, which takes into consideration the thermoelectric capacity of both thermoelectric materials being used in the device and, after geometrical optimization regarding the legs sections,[3] is defined as

${\displaystyle Z{\bar {T}}={(S_{p}-S_{n})^{2}{\bar {T}} \over [(\rho _{n}\kappa _{n})^{1/2}+(\rho _{p}\kappa _{p})^{1/2}]^{2}}}$

where ${\displaystyle \rho }$ is the electrical resistivity, ${\displaystyle {\bar {T}}}$ is the average temperature between the hot and cold surfaces and the subscripts n and p denote properties related to the n- and p-type semiconducting thermoelectric materials, respectively. Since thermoelectric devices are heat engines, their efficiency is limited by the Carnot efficiency, hence the ${\displaystyle T_{H}}$ and ${\displaystyle T_{C}}$ terms in ${\displaystyle \eta _{\mathrm {max} }}$. 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.[4]

### Power factor

In order to determine the usefulness of a material in a thermoelectric generator or a thermoelectric cooler the power factor is calculated by its Seebeck coefficient and its electrical conductivity under a given temperature difference:

${\displaystyle \mathrm {Power~factor} =\sigma S^{2}.}$

where S is the Seebeck coefficient, and σ is the electrical conductivity.

Materials with a high power factor are able to 'generate' more energy (move more heat or extract more energy from that temperature difference) in a space-constrained application, but are not necessarily more efficient in generating this energy.

### Aspects of materials choice

For good efficiency, materials with high electrical conductivity, low thermal conductivity and high Seebeck coefficient are needed.

#### 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.[5] Due to the small Seebeck coefficient metals have a very limited performance and the main materials of interest are Semiconductors.

#### Conductivity

In the efficiency equations above, thermal conductivity and electrical conductivity compete.

The thermal conductivity κ 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.[5] 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 can not 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[6] 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). The figure of merit can be improved through the independent adjustment of these properties.

#### Quality Factor (detailed theory on semiconductors)

The maximum ${\displaystyle Z{\bar {T}}}$ of a material is given by the material's Quality Factor:

${\displaystyle B={\frac {2k_{B}^{2}\hbar }{3\pi }}{\frac {N_{v}C_{l}}{m_{l}^{*}\Xi ^{2}\kappa _{L}}}T}$

where ${\displaystyle k_{B}}$ is the Boltzmann constant, ${\displaystyle \hbar }$ is the reduced Planck constant, ${\displaystyle N_{v}}$ is the number of degenerated valleys for the band, ${\displaystyle C_{l}}$ is the average longitudinal elastic moduli, ${\displaystyle m_{l}^{*}}$ is the inertial effective mass, ${\displaystyle \Xi }$ is the deformation potential coefficient, ${\displaystyle \kappa _{L}}$ is the lattice thermal conduction, and ${\displaystyle T}$ is temperature. The figure of merit, ${\displaystyle Z{\bar {T}}}$, depends on doping concentration and temperature of the material of interest.[7] The material Quality Factor: ${\displaystyle B}$ is useful because it allows for an intrinsic comparisons of possible efficiency between different materials.[8] This relation shows that improving the electronic component ${\displaystyle {\frac {N_{v}}{m_{l}^{*}\Xi ^{2}}}}$, 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 (${\displaystyle N_{v}}$) or by flat bands giving a high band effective mass (${\displaystyle m_{b}^{*}}$). For isotropic materials ${\displaystyle m_{b}^{*}=m_{l}^{*}}$. Therefore, it is desirable for thermoelectric materials to have high valley degeneracy in a very sharp band structure.[9]

## Materials of interest

Strategies to improve thermoelectrics 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;[10] (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[11]); (3) Multiphase nanocomposites: scatter phonons at the interfaces of nanostructured materials,[12] be they mixed composites or thin film superlattices.

Materials under consideration for thermoelectric device applications include:

### Bismuth chalcogenides and their nanostructures

Materials such as Bi
2
Te
3
and Bi
2
Se
3
comprise some of the best performing room temperature thermoelectrics with a temperature-independent figure-of-merit, ZT, between 0.8 and 1.0.[13] Nanostructuring these materials to produce a layered superlattice structure of alternating Bi
2
Te
3
and Sb
2
Te
3
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).[14] 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.[15]

### Lead telluride

In 2008 Joseph Heremans and his colleagues demonstrated that thallium-doped lead telluride alloy (PbTe) achieves a ZT of 1.5 at 773 K.[16] Later, Snyder and his colleagues reported ZT~1.4 at 750 K in sodium-doped PbTe,[17] and ZT~1.8 at 850 K in sodium-doped PbTe1-xSex alloy.[18] Snyder’s group determined that both thallium and sodium alter the electronic structure of the crystal increasing electric conductivity. They also claim that selenium increases electric conductivity and reduces thermal conductivity.

In 2012 another team used lead telluride to convert 15 to 20 percent of waste heat to electricity, reaching a ZT of 2.2, which they claimed was the highest yet reported.[19][20]

### 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.[21][22]

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.[23]

### Magnesium group IV compounds

Mg2BIV (BIV=Si, Ge, Sn) compounds and their solid solutions are good thermoelectric materials and their ZT values are comparable with those of established materials. Due to a lack of systematic studies about their thermoelectric properties, however, the suitability of these materials and in particular their quasi-ternary solutions, for thermoelectric energy conversion remains in question. 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 crystalline material. Solid solutions and doped compounds have to be annealed in order to produce homogeneous samples - with the same properties throughout. At 800 K Mg2Si1-xSnx has been reported to have a figure of merit about 0.9.[24]

### Silicides

Higher silicides display ZT levels with current materials. They are mechanically and chemically strong and therefore can often be used in harsh environments without protection. Possible fabrication methods include Czochralski and floating zone for single crystals and hot pressing and sintering for polycrystalline.[25]

### Skutterudite thermoelectrics

Recently, skutterudite materials have sparked the interest of researchers in search of new thermoelectrics.[26] These structures are of the form (Co,Ni,Fe)(P,Sb,As)
3
and are cubic with space group Im3. Unfilled, these materials contain voids into which low-coordination ions (usually rare earth elements) can be inserted in order to alter thermal conductivity by producing sources for lattice phonon scattering and decrease thermal conductivity due to the lattice without reducing electrical conductivity.[27] Such qualities make these materials exhibit PGEC behavior.

Skutterudites have the chemical formula LM4X12, where L is a rare earth metal, M a transition metal and X a metalloid, a group V element or pnictogen whose properties lie between those of a metal and nonmetal such as phosphorus, antimony, or arsenic. These materials could be potential in multistage thermoelectric devices as it has been shown that they have ZT>1.0, but their properties are not well known.[28]

### Oxide thermoelectrics

Their layered superlattice structure gives homologous oxide compounds (such as those of the form (SrTiO
3
)n(SrO)
m
—the Ruddleson-Popper phase) potential in high-temperature thermoelectric devices.[29] These materials exhibit low thermal conductivity perpendicular to the layers while maintaining electrical conductivity within the layers. ZT is relatively low (~0.34 at 1,000K),[30] but their enhanced thermal stability, as compared to conventional high-ZT bismuth compounds, makes them superior for use in high-temperature applications.[31]

Interest in oxides as thermoelectric materials was reawakened in 1997 when NaxCoO2 was found to exhibit good thermoelectric behavior. In addition to their thermal stability, other advantages of oxides are their nontoxicity and high oxidation resistance. Simultaneously controlling both the electric and phonon systems may require nanostructured materials. Some layered oxide materials are thought to have ZT~2.7 at 900 K.[citation needed] 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.[29] 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,[32][33] MnO2,[34][35] and NbO2,[36][37] to name but a few.

### Half Heusler alloys

Half Heusler alloys have potential for high temperature power generation applications especially as n-type material. These alloys have three components that originate from different element groups or combinations of elements. Two of the groups are composed of transition metals and the third group consists of metals and metalloids. Currently only n-type material is usable in thermoelectrics but some sources claim that they have achieved ZT~1.5 at 700 K, but according to other sources only ZT~0.5 at 700 K has been achieved. They state that primary reason for this difference is the disagreement between thermal conductivities measured by different groups. These alloys are relatively cheap and also have a high power factor.[38]

### Electrically conducting organic materials

Some electrically conducting organic materials may have a higher figure of merit than existing inorganic materials. Seebeck coefficient can be even millivolts per Kelvin but electrical conductivity is usually low, resulting in small ZT values. Quasi-one-dimensional organic crystals are formed from linear chains or stacks of molecules that are packed into a 3D crystal. Under certain conditions some Q1D organic crystals may have ZT~20 at room temperature for both p- and n-type materials. This has been credited to an unspecified interference between two main electron-phonon interactions leading to the formation of narrow strip of states in the conduction band with a significantly reduced scattering rate as the mechanism compensate each other, yielding high ZT.[39]

### Silicon-germanium

Silicon-germanium alloys are currently the best thermoelectric materials around 1000 ℃ 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 price and mid-range ZT (~0.7).

### 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 Na
0.8
CoO
2
contained within the crystals.[40][41]

### 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.[42] 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,[43] NbO2,[44] In-Ga-Zn-O,[45] Zr-Ni-Sn,[46] Si-Au,[47] and Ti-Pb-V-O[48] 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 to extensive phonon scattering, which is still a challenge for crystalline thermoelectrics. A bright future is expected for these materials.

### Functionally graded materials

Functionally graded materials make it possible to improve the conversion efficiency of existing thermoelectrics. These materials have a non-uniform carrier concentration distribution and in some cases also solid solution composition. In power generation applications the temperature difference can be several hundred degrees and therefore devices made from homogeneous materials have some part that operates at the temperature where ZT is substantially lower than its maximum value. This problem can be solved by using materials whose transport properties vary along their length thus enabling substantial improvements to the operating efficiency over large temperature differences. This is possible with functionally graded materials as they have a variable carrier concentration along the length of the material, which is optimized for operations over specific temperature range.[49]

### Nanomaterials and superlattices

In addition to nanostructured Bi
2
Te
3
/Sb
2
Te
3
superlattice thin films, other nanomaterials show potential in improving thermoelectric properties.

#### PbTe/PbSeTe quantum dot superlattice

Another example of a superlattice involves a PbTe/PbSeTe quantum dot superlattices provides an enhanced ZT (approximately 1.5 at room temperature) that was higher than the bulk ZT value for either PbTe or PbSeTe (approximately 0.5).[50]

#### Nanocrystal stability and thermal conductivity

Not all nanocrystalline materials are stable, because the crystal size can grow at high temperatures, ruining the materials' desired characteristics.

Nanocrystalline materials have many interfaces between crystals, which Physics of SASER scatter phonons so the thermal conductivity is reduced. Phonons are confined to the grain, if their mean free path is larger than the material grain size.

Measured lattice thermal conductivity in nanowires is known to depend on roughness, the method of synthesis and properties of the source material.[51]

#### Nanocrystalline transition metal silicides

Nanocrystalline transition metal silicides are a promising material group for thermoelectric applications, because they fulfill several criteria that are demanded from the commercial applications point of view. In some nanocrystalline transition metal silicides the power factor is higher than in the corresponding polycrystalline material but the lack of reliable data on thermal conductivity prevents the evaluation of their thermoelectric efficiency.[52]

#### Nanostructured skutterudites

Skutterudites, a cobalt arsenide mineral with variable amounts of nickel and iron, can be produced artificially, and are candidates for better thermoelectric materials.

One advantage of nanostructured skutterudites over normal skutterudites is their reduced thermal conductivity, caused by grain boundary scattering. ZT values of ~0.65 and > 0.4 have been achieved with CoSb3 based samples; the former values were 2.0 for Ni and 0.75 for Te-doped material at 680 K and latter for Au-composite at T > 700 K.[53]

Even greater performance improvements can be achieved by using composites and by controlling the grain size, the compaction conditions of polycrystalline samples and the carrier concentration.

#### Graphene

Due to the unique nature of graphene, it is possible to develop a thermoelectric device based on it with an extremely high Seebeck coefficient.

One theoretical study suggests that the Seebeck coefficient might achieve a value of 30 mV/K at room temperature and ZT for their proposed device would be approximately 20.[54]

#### Superlattices and roughness

Superlattices - nano structured thermocouples, are considered a good candidate for better thermoelectric device manufacturing, with materials that can be used in manufacturing this structure.

Their production is expensive for general-use due to fabrication processes based on expensive thin-film growth methods. However, since the amount of thin-film materials required for device fabrication with superlattices, is so much less than thin-film materials in bulk thermoelectric materials (almost by a factor of 1/10,000) the long-term cost advantage is indeed favorable.

This is particularly true given the limited availability of tellurium causing competing solar applications for thermoelectric coupling systems to rise.

Superlattice structures also allow the independent manipulation of transport parameters by adjusting the structure itself, enabling research for better understanding of the thermoelectric phenomena in nanoscale, and studying the phonon-blocking electron-transmitting structures - explaining the changes in electric field and conductivity due to the material's nano-structure.[14]

Many strategies exist to decrease the superlattice thermal conductivity that are based on engineering of phonon transport. The thermal conductivity along the film plane and wire axis can be reduced by creating diffuse interface scattering and by reducing the interface separation distance, both which are caused by interface roughness.

Interface roughness can naturally occur or may be artificially induced.

In nature, roughness is caused by the mixing of atoms of foreign elements. Artificial roughness can be created using various structure types, such as quantum dot interfaces and thin-films on step-covered substrates.[55]

##### Problems in superlattices

Reduced electrical conductivity:
Reduced phonon-scattering interface structures often also exhibit a decrease in electrical conductivity.

The thermal conductivity in the cross-plane direction of the lattice is usually very low, but depending on the type of superlattice, the thermoelectric coefficient may increase because of changes to the band structure.

Low thermal conductivity in superlattices is usually due to strong interface scattering of phonons. Minibands are caused by the lack of quantum confinement within a well. The mini-band structure depends on the superlattice period so that with a very short period (~1 nm) the band structure approaches the alloy limit and with a long period (≥ ~60 nm) minibands become so close to each other that they can be approximated with a continuum.[56]

Superlatice structure countermeasures:
Counter measures can be taken which practically eliminate the problem of decreased electrical conductivity in a reduced phonon-scattering interface. These measures include the proper choice of superlattice structure, taking advantage of mini-band conduction across superlattices, and avoiding quantum-confinement. It has been shown that because electrons and phonons have different wavelengths, it is possible to engineer the structure in such a way that phonons are scattered more diffusely at the interface than electrons.[14]

Phonon confinement countermeasures:
Another approach to overcome the decrease in electrical conductivity in reduced phonon-scattering structures is to increase phonon reflectivity and therefore decrease the thermal conductivity perpendicular to the interfaces.

This can be achieved by increasing the mismatch between the materials in adjacent layers, including density, group velocity, specific heat, and the phonon-spectrum.

Interface roughness causes diffuse phonon scattering, which either increases or decreases the phonon reflectivity at the interfaces. A mismatch between bulk dispersion relations confines phonons, and the confinement becomes more favorable as the difference in dispersion increases.

The amount of confinement is currently unknown as only some models and experimental data exist. As with a previous method, the effects on the electrical conductivity have to be considered.[55]

Attempts to Localize long wavelength phonons by aperiodic superlattices or composite superlattices with different periodicities have been made. In addition, defects, especially dislocations, can be used to reduce thermal conductivity in low dimensional systems.[55]

Parasitic heat:
Parasitic heat conduction in the barrier layers could cause significant performance loss. It has been proposed but not tested that this can be overcome by choosing a certain correct distance between the quantum wells.

The Seebeck coefficient can change its sign in superlattice nanowires due to the existence of minigaps as Fermi energy varies. This indicates that superlattices can be tailored to exhibit n or p-type behavior by using the same dopants as those that are used for corresponding bulk materials by carefully controlling Fermi energy or the dopant concentration. With nanowire arrays, it is possible to exploit semimetal-semiconductor transition due to the quantum confinement and use materials that normally would not be good thermoelectric materials in bulk form. Such elements are for example bismuth. The Seebeck effect could also be used to determine the carrier concentration and Fermi energy in nanowires.[57]

In quantum dot thermoelectrics, unconventional or nonband transport behavior (e.g. tunneling or hopping) is necessary to utilize their special electronic band structure in the transport direction. It is possible to achieve ZT>2 at elevated temperatures with quantum dot superlattices, but they are almost always unsuitable for mass production.

However, in superlattices, where quantum-effects are not involved, with film thickness of only a few micrometers (µm) to about 15 µm, Bi2Te3/Sb2Te3 superlattice material has been made into high-performance microcoolers and other devices. The performance of hot-spot coolers[14] are consistent with the reported ZT~2.4 of superlattice materials at 300 K.[58]

Nanocomposites are promising material class for bulk thermoelectric devices, but several challenges have to be overcome to make them suitable for practical applications. It is not well understood why the improved thermoelectric properties appear only in certain materials with specific fabrication processes.[59]

SrTe nanocrystals can be embedded in a bulk PbTe matrix so that rocksalt lattices of both materials are completely aligned (endotaxy) with optimal molar concentration for SrTe only 2%. This can cause strong phonon scattering but would not affect charge transport. In such case, ZT~1.7 can be achieved at 815 K for p-type material.[60]

### Tin selenide

In 2014 a research group discovered that tin selenide (SnSe) has a ZT of 2.6 along the b axis of the unit cell.[61][62] This is the highest value reported to date. This high ZT figure of merit has been attributed to an extremely low thermal conductivity found in the SnSe lattice. Specifically, SnSe demonstrated a lattice thermal conductivity of 0.23 W·m−1·K−1, which is much lower than previously reported values of 0.5 W·m−1·K−1 and greater.[63] This SnSe material also exhibited a ZT of 2.3±0.3 along the c-axis and 0.8±0.2 along the a-axis. These excellent figures of merit were obtained by researchers working at elevated temperatures, specifically 923 K (650 °C). As shown by the figures below, SnSe performance metrics were found to significantly improve at higher temperatures; this is due to a structural change that is discussed below. Power factor, conductivity, and thermal conductivity all reach their optimal values at or above 750 K, and appear to plateau at higher temperatures.

SnSe Performance Metrics[63]

Although it exists at room temperature in an orthorhombic structure with space group Pnma, SnSe has been shown to undergo a transition to a structure with higher symmetry, space group Cmcm, at higher temperatures.[64] This structure consists of Sn-Se planes that are stacked upwards in the a-direction, which accounts for the poor performance out-of-plane (along a-axis). Upon transitioning to the Cmcm structure, SnSe maintains its low thermal conductivity but exhibits higher carrier mobilities, leading to its excellent ZT value.[63]

One particular impediment to further development of SnSe is that it has a relatively low carrier concentration: approximately 1017 cm−3. Further compounding this issue is the fact that SnSe has been reported to have low doping efficiency.[65]

However, such single crystalline materials suffer from inability to make useful devices due to their brittleness as well as narrow range of temperatures, where ZT is reported to be high. Further, polycrystalline materials made out of these compounds by several investigators have not confirmed the high ZT of these materials.

## Production methods

Production methods for these materials can be divided into powder and crystal growth based techniques. Powder based techniques offer excellent ability to control and maintain desired carrier distribution. In crystal growth techniques dopants are often mixed with melt, but diffusion from gaseous phase can also be used. In the zone melting techniques disks of different materials are stacked on top of others and then materials are mixed with each other when a traveling heater causes melting. In powder techniques, either different powders are mixed with a varying ratio before melting or they are in different layers as a stack before pressing and melting.

There are applications, such as cooling of electronic circuits, where thin films are required. Therefore, thermoelectric materials can also be synthesized using physical vapor deposition techniques. Another reason to utilize these methods is to design these phases and provide guidance for bulk applications.

## Applications

### Refrigeration

Thermoelectric materials can be used as refrigerators, called "thermoelectric coolers", or "Peltier coolers" after the Peltier effect that controls their operation. As a refrigeration technology, Peltier cooling is far less common than vapor-compression refrigeration. The main advantages of a Peltier cooler (compared to a vapor-compression refrigerator) are its lack of moving parts or refrigerant, and its small size and flexible shape (form factor).

The main disadvantage of Peltier coolers is low efficiency. It is estimated that materials with ZT>3 (about 20–30% Carnot efficiency) would be required to replace traditional coolers in most applications.[50] Today, Peltier coolers are only used in niche applications, especially small scale, where efficiency is not important.

### Power generation

Thermoelectric efficiency depends on the figure of merit, ZT. There is no theoretical upper limit to ZT, and as ZT approaches infinity, the thermoelectric efficiency approaches the Carnot limit. However, no known thermoelectrics have a ZT>3.[66] As of 2010, thermoelectric generators serve application niches where efficiency and cost are less important than reliability, light weight, and small size.[67]

Internal combustion engines capture 20–25% of the energy released during fuel combustion.[68] Increasing the conversion rate can increase mileage and provide more electricity for on-board controls and creature comforts (stability controls, telematics, navigation systems, electronic braking, etc.)[69] It may be possible to shift energy draw from the engine (in certain cases) to the electrical load in the car, e.g. electrical power steering or electrical coolant pump operation.[68]

Cogeneration power plants use the heat produced during electricity generation for alternative purposes. Thermoelectrics may find applications in such systems or in solar thermal energy generation.[70]

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