Thermoelectric materials

Thermoelectric materials [1][2] 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.[3] Research in the field is still
driven by materials development, primarily in optimizing transport and thermoelectric properties.[4]

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[1][5][6]

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[7]
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.[8][9][10] 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
by[1][5]

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.[11]

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 .[12]

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.[13]

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.[13] 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[14] 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 (detailed theory on semiconductors)

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.[15]

The material quality factor is useful because it allows for an intrinsic comparison of possible efficiency
between different materials.[16] 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.[17] Other complex
features of the electronic structure are important. These can be partially quantified using an electronic
fitness function.[18]

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;[19] (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[20]); (3) Multiphase nanocomposites: scatter phonons at the
interfaces of nanostructured materials,[21] 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.[22]
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).[23] 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.[24]

Lead tellurides
Heremans et al. (2008) demonstrated that thallium-doped lead telluride alloy (PbTe) achieves a ZT of 1.5
at 773 K.[25] Later, Snyder et al. (2011) reported ZT~1.4 at 750 K in sodium-doped PbTe,[26] and ZT~1.8
at 850 K in sodium-doped PbTe1−xSex alloy.[27] 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.[28][29]

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.[30][31][32]

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.[33][34] 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.[35][36] Partially filled variants can be synthesized as semiconducting or even insulating.[37]

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.[38]

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.[39] 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.[40]

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.[41]

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.[42] It is also possible to reduce the thermal conductivity in skutterudite
without filling these voids using a special architecture containing nano- and micro-pores.[43]

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.[44]

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.[45] 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.[46]

Interest in oxides as thermoelectric materials was reawakened in 1997 when a relatively high
thermoelectric power was reported for NaCo2O4.[47][46] 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.[46] 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.[45] 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,[46]
MnO2,[48] and NbO2.[49][50]

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.[51] 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.[52] 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.[52]

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 undering cation exchange with iron.[53] 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).[54] 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.[55] 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.[56] 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.[57]

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.[58] 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.[52] 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.[59]
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.[59] Nano-sized
grains is one of the approaches used to lower the thermal conductivity via grain boundaries- assisted
phonon scattering.[60] Other 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.[61]

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.[62] 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.[63] Generation of electricity by grabbing
both sides of a flexible PEDOT:PSS
thermoelectric device
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.[64] Furthermore, future study into the PEDOT:PSS-based model
orientation and alignment of these added materials will allow for embedded into a glove to generate
electricity by body heat
improved performance.[65] The percolation threshold of CNT’s is
often especially low, well below 10%, due to their high aspect
ratio.[66] 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.[67] 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.[68]

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.[69]

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.[70] 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 (~0.7); however, ZT can be increased to 1–2 in SiGe nanostructures owing
to the reduction in thermal conductivity.[71]

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.[72][73]

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.[74]
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,[75] NbO2,[76] In-Ga-Zn-O,[77] Zr-Ni-Sn,[78] Si-
Au,[79] and Ti-Pb-V-O[80] 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.[81]

Nanomaterials and superlattices

In addition to nanostructured Bi2Te3/Sb2Te3 superlattice thin films, other nanostructured materials,
including silicon nanowires,[69] nanotubes and quantum dots 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).[82]

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.[69]

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.[83]

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.[84]

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
Graphene is known for its high electrical conductivity and Seebeck coefficient at room
temperature.[85][86] However, from thermoelectric perspective, its thermal conductivity is notably high,
which in turn limits its ZT.[87] Several approaches were suggested to reduce the thermal conductivity of
graphene without altering much its electrical conductivity. These include, but not limited to, the
following:

Doping with carbon isotopes to form isotopic heterojunction such as that of 12C and 13C.
Those isotopes possess different phonon frequency mismatch, which leads to the scattering
of the heat carriers (phonons). This approach has been shown to affect neither the power
factor nor the electrical conductivity.[88]
Wrinkles and cracks in the graphene structure were shown to contribute to the reduction in
the thermal conductivity. Reported values of thermal conductivity of suspended graphene of
size 3.8 μm show a wide spread from 1500 to 5000 W/(m·K). A recent study attributed that
to the microstructural defects present in graphene, such as wrinkles and cracks, which can
drop the thermal conductivity by 27%.[89] These defects help scatter phonons.
Introduction of defects with techniques such as oxygen plasma treatment. A more systemic
way of introducing defects in graphene structure is done through O2 plasma treatment.
Ultimately, the graphene sample will contain prescribed-holes spaced and numbered
according to the plasma intensity. People were able to improve ZT of graphene from 1 to a
value of 2.6 when the defect density is raised from 0.04 to 2.5 (this number is an index of
defect density and usually understood when compared to the corresponding value of the un-
treated graphene, 0.04 in our case). Nevertheless, this technique would lower the electrical
conductivity as well, which can be kept unchanged if the plasma processing parameters are
optimized.[85]
Functionalization of graphene by oxygen. The thermal behavior of graphene oxide has not
been investigated extensively as compared to its counterpart; graphene. However, it was
shown theoretically by Density Functional Theory (DFT) model that adding oxygen into the
lattice of graphene reduces a lot its thermal conductivity due to phonon scattering effect.
Scattering of phonons result from both acoustic mismatch and reduced symmetry in
 graphene structure after doping with oxygen. The reduction of thermal conductivity can
easily exceed 50% with this approach.[86]

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.[23]

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.[71][70]

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.[90]

Superlattice 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.[23]

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.[71][70]

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.[71][70]

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.[91]

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[23] are consistent with
the reported ZT~2.4 of superlattice materials at 300 K.[92]

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.[93]

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.[94]

Tin selenide
In 2014, researchers at Northwestern University discovered that tin selenide (SnSe) has a ZT of 2.6 along
the b axis of the unit cell.[95][96] This was the highest value reported to date. This was 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, much lower than previously reported values of 0.5 W·m−1·K−1
and greater.[97] This material also exhibited a ZT of 2.3 ± 0.3 along the c-axis and 0.8 ± 0.2 along the a-
axis. These results were obtained at a temperature of 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. Power factor, conductivity, and thermal conductivity all reach their optimal values at or
above 750 K, and appear to plateau at higher temperatures. However, other groups have not been able to
reproduce the reported bulk thermal conductivity data.[98]

Although it exists at room temperature in an orthorhombic

structure with space group Pnma, SnSe undergoes a transition to a
structure with higher symmetry, space group Cmcm, at higher
temperatures.[99] 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.[97]

One impediment to further development of SnSe is that it has a

relatively low carrier concentration: approximately 1017 cm−3. SnSe performance metrics[97]
Compounding this issue is the fact that SnSe has been reported to
have low doping efficiency.[100]

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.

In 2021 the researchers announced a polycrystalline form of SnSe that was at once less brittle and
featured a ZT of 3.1.[101]

Anderson localization
Anderson localization is a quantum mechanical phenomenom where charge carriers in a random potential
are trapped in place (i.e. they are in localized states as opposed to being in scattering states if they could
move freely).[102] This localization prevents the charge carriers from moving, which inhibits their
contribution to the thermal conductivity of a material, but because it also lowers the electrical
conductivity, it was thought to reduce ZT and be detrimental for thermoelectric materials.[103][104] In
2019, it was proposed that by localizing only the minority charge carriers in a doped semiconductor (i.e.
holes in an n-doped semiconductor or electrons in a p-doped semiconductor), Anderson localization could
increase ZT. The heat conductivity associated with movement of the minority charge carriers would be
reduced while electrical conductivity of the majority charge carrier would be unaffected.[105]

In 2020, researchers at Kyung Hee University demonstrated the use of Anderson localization in an n-type
semiconductor to improve the thermoelectric properties of a material. They embedded nanoparticles of
silver telluride (Ag2Te) in a lead telluride (PbTe) matrix. Ag2Te undergoes a phase transition around 407
K. Below this temperature, both holes and electrons are localized at the Ag2Te nanoparticles, while after
the transition, holes are still localized, but electrons can move freely in the material. The researchers were
able to increase ZT from 1.5 to above 2.0 using this method.[106]

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,
particle size, and composition.[107] In crystal growth techniques dopants are often mixed with melt, but
diffusion from gaseous phase can also be used.[108] 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.

3D Printing
Significant improvement on 3D printing skills has made it possible for thermoelectric components to be
prepared via 3D printing. Thermoelectric products are made from special materials that absorb heat and
create electricity. The requirement of fitting complex geometries in tightly constrained spaces makes 3D
printing the ideal manufacturing technique.[109] There are several benefits to the use of additive
manufacturing in thermoelectric material production. Additive manufacturing allows for innovation in the
design of these materials, facilitating intricate geometries that would not otherwise be possible by
conventional manufacturing processes. It reduces the amount of wasted material during production and
allows for faster production turnaround times by eliminating the need for tooling and prototype
fabrication, which can be time-consuming and expensive.[110]

There are several major additive manufacturing technologies that have emerged as feasible methods for
the production of thermoelectric materials, including continuous inkjet printing, dispenser printing, screen
printing, stereolithography, and selective laser sintering. Each method has its own challenges and
limitations, especially related to the material class and form that can be used. For example, selective laser
sintering (SLS) can be used with metal and ceramic powders, stereolithography (SLA) must be used with
curable resins containing solid particle dispersions of the thermoelectric material of choice, and inkjet
printing must use inks which are usually synthesized by dispersing inorganic powders to organic solvent
or making a suspension.[111][112]
The motivation for producing thermoelectrics by means of additive manufacturing is due to a desire to
improve the properties of these materials, namely increasing their thermoelectric figure of merit ZT, and
thereby improving their energy conversion efficiency.[113] Research has been done proving the efficacy
and investigating the material properties of thermoelectric materials produced via additive manufacturing.
An extrusion-based additive manufacturing method was used to successfully print bismuth telluride
(Bi2Te3) with various geometries. This method utilized an all-inorganic viscoelastic ink synthesized using
Sb2Te2 chalcogenidometallate ions as binders for Bi2Te3-based particles. The results of this method
showed homogenous thermoelectric properties throughout the material and a thermoelectric figure of
merit ZT of 0.9 for p-type samples and 0.6 for n-type samples. The Seebeck coefficient of this material
was also found to increase with increasing temperature up to around 200 °C.[114]

Groundbreaking research has also been done towards the use of selective laser sintering (SLS) for the
production of thermoelectric materials. Loose Bi2Te3 powders have been printed via SLS without the use
of pre- or post-processing of the material, pre-forming of a substrate, or use of binder materials. The
printed samples achieved 88% relative density (compared to a relative density of 92% in conventionally
manufactured Bi2Te3). Scanning Electron Microscopy (SEM) imaging results showed adequate fusion
between layers of deposited materials. Though pores existed within the melted region, this is a general
existing issue with parts made by SLS, occurring as a result of gas bubbles that get trapped in the melted
material during its rapid solidification. X-ray diffraction results showed that the crystal structure of the
material was intact after laser melting.

The Seebeck coefficient, figure of merit ZT, electrical and thermal conductivity, specific heat, and
thermal diffusivity of the samples were also investigated, at high temperatures up to 500 °C. Of particular
interest is the ZT of these Bi2Te3 samples, which were found to decrease with increasing temperatures up
to around 300 °C, increase slightly at temperatures between 300-400 °C, and then increase sharply
without further increase in temperature. The highest achieved ZT value (for an n-type sample) was about
0.11.

The bulk thermoelectric material properties of samples produced using SLS had comparable
thermoelectric and electrical properties to thermoelectric materials produced using conventional
manufacturing methods. This the first time the SLS method of thermoelectric material production has
been used successfully.[113]

Mechanical Properties
Thermoelectric materials are commonly used in thermoelectric generators to convert the thermal energy
into electricity. Thermoelectric generators have the advantage of no moving parts and do not require any
chemical reaction for energy conversion, which make them stand out from other sustainable energy
resources such as wind turbine and solar cells; Nevertheless, the mechanical performance of
thermoelectric generators may decay over time due to plastic, fatigue and creep deformation as a result of
being subjected to complex and time-varying thermomechanical stresses.

Thermomechanical Stresses in Thermoelectric Devices[115]

Geometrical Effects
In their research, Al-Merbati et al.[116] found that the stress levels around the leg corners of
thermoelectric devices were high and generally increased closer to the hot side. However, switching to a
trapezoidal leg geometry reduced thermal stresses. Erturun et al.[117] compared various leg geometries
and discovered that rectangular prism and cylindrical legs experienced the highest stresses. Studies have
also shown that using thinner and longer legs can significantly relieve stress.[118][119][120][121] Tachibana
and Fang [122] estimated the relationship between thermal stress, temperature difference, coefficient of
thermal expansion, and module dimensions. They found that the thermal stress was proportional to
, where L, α, ΔT and h are module thickness, Coefficients of Thermal Expansion(CTE),
temperature difference and leg height, respectively.

Effect of Boundary Conditions

Clin et al.[123] conducted finite-element analysis to replicate thermal stresses in a thermoelectric module
and concluded that the thermal stresses were dependent on the mechanical boundary conditions on the
module and on CTE mismatch between various components. The corners of the legs exhibited maximum
stresses. In a separate investigation, Turenne et al.[124] examined the distribution of stress in large
freestanding thermoelectric modules and those rigidly fixed between two surfaces for thermal exchange.
Although boundary conditions significantly altered the stress distribution, the authors deduced that
external compressive loading on the TE module resulted in the creation of global compressive stresses.

Effect of Thermal Fatigue

Thermoelectric materials commonly contain different types of defects, such as dislocations, vacancies,
secondary phases and antisite defects. These defects can affect thermoelectric performance by evolving
under service conditions. In 2019, Yun Zheng et al.[125] studied thermal fatigue of -based
materials and they proposed that their fatigue behavior can be reduced via boosting the fracture toughness
by introducing pores, microcracks or inclusion with the inextricable trade-off with fracture strength.

Effect of Thermal Shocks

Thermoelectric materials can undergo thermal shock loading through service temperature spikes,
soldering and metallizing processes. The thermoelectric leg can be coated with metals to form the
required diffusion barrier (Metallizing) and dipping the metallized leg in a molten alloy bath (Soldering)
for connecting the leg to the interconnect. In a study conducted by Pelletier et al.[126] thermoelectric disks
were quenched for the purpose of thermal shock experiments. They realized that quenching in a hot
medium helped disks' surface to produce compressive stresses in contrary to the core, which developed
tensile stress. Anisotropic materials and thin disks were reported to develop greater maximum stresses.
They also observed fracturing of specimens during quenching process in a soldering bath from room
temperature.

Effect of Tensile Stresses

Thermal stresses have been quantified and extensively studied in thermoelectric modules throughout the
years but von Mises stresses are commonly reported. The von Mises stress defines a constraint on plastic
yielding without having any information of the stress nature.
For instance, in a study by Sakamoto et al.[127] the mechanical stability of a -based structure was
investigated that could utilize thermoelectric legs at an angle with elecftrical interconnects and substrates.
Maximum tensile strength stresses were calculated and compared to the ultimate tensile streength of
different materials. This approach might be misleading for brittle materials (such as ceramics) as they do
not possess a defined tensile strength.

Thermal Mismatch Stresses

In 2018, Chen et al.[128] investigated the cracking failure of Cu pillar bump that was caused by
electromigration under thermoelectric coupling load. They showed that under thermoelectric coupling
load, will experience severe joule heat and current density that can be accumulate thermoemechanical
stress and miscrostructure evolution. They also pointed out that the difference in CTE between materials
in the flip chip package causes thermal mismatch stress which can later develop the cavities to expand
along cathode into cracks. Also, it is worth noting that they mentioned thermal-electrical coupling can
cause electromigration, microcracks and delamination due to temperature and stress concentration that
can fail Cu pillar bumps.

Phase-Transformation Stresses
Phase transformation can occur in thermoelectric materials as well as many other energy materials. As
pointed out by Al Malki et al.,[129] phase transformation can lead to a total plastic strain when internal
mismatch stresses are biased with shear stress. The alpha phase of transforms to a body centered
cubic phase. Liang et al. [130] showed that a crack was observed when heating through 407 K through this
phase transformation.

Creep Deformation
Creep deformation is a time-dependent mechanism where strain accumulates as amaterial is subjected to
external or internal stressesat a high homologous temperature in excess ofT/Tm= 0.5(whereTmis the
melting point in K).[129] This phenomenon can emerge in thermoelectric devices after operating for a
long time (i.e. months to years). A coarse-grained or monocrystalline structures have been shown to be
desirable as creep-resistant materials.[131]

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).[132]

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.[82]
Today, Peltier coolers are only used in niche applications, especially small scale, where efficiency is not
important.[132]

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, until
recently no known thermoelectrics had a ZT>3.[133] In 2019, researchers reported a material with
approximated ZT between 5 and 6.[134][135]

As of 2010, thermoelectric generators serve application niches where efficiency and cost are less
important than reliability, light weight, and small size.[136] [137]

Internal combustion engines capture 20–25% of the energy released during fuel combustion.[136] [138]
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.)[139] 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.[136][138]

Cogeneration power plants use the heat produced during electricity generation for alternative purposes;
being this more profitable in industries with high amounts of waste energy.[136]

Thermoelectrics may find applications in such systems or in solar thermal energy generation.[136] [140]

See also
Batteryless radio
Pyroelectric effect
Thermionic converter

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Bibliography
Rowe, D.M. (2018) [2006]. Thermoelectrics Handbook: Macro to Nano. CRC Press.
ISBN 978-1-4200-3890-3.

External links
TE Modules Application Tips and Hints (http://www.rmtltd.ru/tec_app_tips.htm) Archived (htt
ps://web.archive.org/web/20100323091501/http://www.rmtltd.ru/tec_app_tips.htm) 2010-03-
23 at the Wayback Machine
The Seebeck Coefficient (http://www.electronics-cooling.com/2006/11/the-seebeck-coefficie
nt/)
Materials for Thermoelectric Devices (4th chapter of Martin Wagner dissertation) (http://ww
w.iue.tuwien.ac.at/phd/mwagner/node48.html)
 New material breaks world record for turning heat into electricity (https://phys.org/news/2019
-11-material-world-electricity.html)

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