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 ().

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 , given by

Device efficiency The efficiency of a thermoelectric device for electricity generation is given by , defined as

The maximum efficiency of a thermoelectric device is typically described in terms of its device figure of merit where the maximum device efficiency is approximately given by where is the fixed temperature at the hot junction, is the fixed temperature at the surface being cooled, and is the mean of and . 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 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 is given byIoffe, A.F. (1960) Physics of semiconductors, Academic Press Inc., New York where 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 () does .

Since thermoelectric devices are heat engines, their efficiency is limited by the Carnot efficiency , the first factor in , while and 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 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 not .

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.Timothy D. Sands (2005), Designing Nanocomposite 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. SlackSlack GA., in 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 of a material is given by the material's quality factor

where is the Boltzmann constant, is the reduced Planck constant, is the number of degenerated valleys for the band, is the average longitudinal elastic moduli, is the inertial effective mass, is the deformation potential coefficient, is the lattice thermal conduction, and is temperature. The figure of merit, , depends on doping concentration and temperature of the material of interest.

The material quality factor is useful because it allows for an intrinsic comparison of possible efficiency between different materials. This relation shows that improving the electronic component , 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 () or by flat bands giving a high band effective mass (). For isotropic materials . 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;Bhandari, C. M. in (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 and 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 and 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