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Abstract Manipulating thermal properties of materials can be interpreted as the control of how vibrations of atoms (known as phonons) scatter in a crystal lattice. Compared to a perfect crystal, crystalline solids with defects are expected to have shorter phonon mean free paths caused by point defect scattering, leading to lower lattice thermal conductivities than those without defects. While this is true in many cases, alloying can increase the phonon mean free path in the Cd‐doped AgSnSbSe3 system to increase the lattice thermal conductivity from 0.65 to 1.05 W m−1 K−1 by replacing 18% of the Sb sites with Cd. It is found that the presence of lone pair electrons leads to the off‐centering of cations from the centrosymmetric position of a cubic lattice. X‐ray pair distribution function analysis reveals that this structural distortion is relieved when the electronic configuration of the dopant element cannot produce lone pair electrons. Furthermore, a decrease in the Grüneisen parameter with doping is experimentally confirmed, establishing a relationship between the stereochemical activity of lone pair electrons and the lattice anharmonicity. The observed “harmonic” behavior with doping suggests that lone pair electrons must be preserved to effectively suppress phonon transport in these systems.

Abstract Half‐Heusler compounds with semiconducting behavior have been developed as high‐performance thermoelectric materials for power generation. Many half‐Heusler compounds also exhibit metallic behavior without a bandgap and thus inferior thermoelectric performance. Here, taking metallic half‐Heusler MgNiSb as an example, a bandgap opening strategy is proposed by introducing the d–d orbital interactions, which enables the opening of the bandgap and the improvement of the thermoelectric performance. The width of the bandgap can be engineered by tuning the strength of the d–d orbital interactions. The conduction type and the carrier density can also be modulated in the Mg1‐xTixNiSb system. Both improved n‐type and p‐type thermoelectric properties are realized, which are much higher than that of the metallic MgNiSb. The proposed bandgap opening strategy can be employed to design and develop new half‐Heusler semiconductors for functional and energy applications.

Additive manufacturing of lattices with ∼600 μm diameter struts is achieved via extrusion printing of an ink containing prealloyed powder of the half-Heusler alloy Nb1-xCoSb, followed by debinding and vacuum sintering to a relative density of ∼70–80%. The ink can also be poured and cast into square blocks, which, after debinding and sintering, achieve a similar relative density. Sintering in a Sb-rich atmosphere reduces Sb sublimation and decomposition of the half-Heusler phase. This is reflected in electrical conductivity values, for ink-cast specimens, similar to those of a sample created by vacuum hot-pressing of dry powders (1080 S/cm at 298 K). However, a lower Seebeck coefficient for the ink-cast specimens (92 vs. 150 µV/K for a hot-pressed sample) leads to a reduced figure of merit (zTmax = 0.10±0.015 vs. 0.26±0.04 at 873 K for a hot-pressed sample), where secondary phases, NbSb2 and CoSb3 were observed; these might be minimized, or even eliminated, via further optimization of the sintering conditions.

Lillianite materials usually have low thermoelectric efficiency due to the inherently inferior electrical properties. Here, the authors evaluate thermoelectric performances in Pb7Bi4Se13 based lillianites enabled by convergence of nested conduction bands.

Band convergence is a strategy to enhance a material’s thermoelectric performance, as it increases the charge carrier concentration for a given Fermi level. Here, the authors find that the benefit of band convergence can be negated by interband scattering depending on the manner in which bands converge.

n‐Type Mg3Sb2‐Mg3Bi2 alloys are some of the most promising thermoelectric materials in the low–mid temperature range. While discovered relatively recently, these materials have garnered intense attention, and numerous papers from the international thermoelectric community have been published in a relatively short period of time. As with all materials, detailed insights into the underlying mechanisms that contribute to these alloys’ distinguished thermoelectric properties are important for future researchers to push the performance of this material to new heights. Herein, experimental studies on the role defects, synthesis conditions, electronic band structure, and microstructure along with future prospects arecompiled to establish a guide for fully exploiting the potential of this material system. Considering the limited number of n‐type thermoelectric materials with this performance for low‐grade heat recovery and cooling technologies, further development of the Mg3Sb2‐Mg3Bi2 alloys is an important step toward commercial applications of thermoelectric materials, including cooling technologies and waste heat recovery applications.

Upon uniaxial compressive loading at 500 °C (T/Tm = 0.67, where Tm is the absolute melting point), the n-type Skutterudite alloy Yb0.3Co4Sb12 deforms plastically by creep via a power-law, with a stress exponent ∼3 consistent with dislocation viscous glide. An activation energy of 171 kJ/mol is measured over the temperature range of 500–587 °C (T/Tm = 0.67–0.75) at a stress of 30 MPa. Yb0.3Co4Sb12 is ductile at 500 °C, exhibiting a compressive strain of 25% when subjected to stresses ranging from 22 to 90 MPa for up to 28 days. Among the thermoelectric materials tested so far for creep, Yb0.3Co4Sb12 exhibits a creep resistance intermediate between low-melting (Bi2Te3, TAGS-85) and high-melting thermoelectrics (Mg2Si and ZrNiSn). A relatively modest drop in the figure of merit zT, from 0.67 to 0.52, is displayed by Yb0.3Co4Sb12 after accumulating 3.7% compressive creep strain at 500 °C, mostly due to a drop in electrical conductivity.

Alloys of Bi2Te3 and Sb2Te3 are the best performing p-type thermoelectrics near room temperature and have been the subject of extensive engineering efforts. Dramatic improvement is achieved by introducing defects that effectively scatter phonons and reduce thermal conductivity. Unfortunately, outstanding results are often difficult to reproduce as the process variables involved are difficult to control or possibly unknown. Here, a reproducible and controllable method of fabricating porous Bi0.5Sb1.5Te3+x is presented. While effective medium theory (EMT) predicts no benefit, improvements in the thermoelectric quality factor, B (which determines the maximum zT of a materials), were as high as 45% parallel to the pressing direction for a sample of roughly 20% porosity. The study of microstructural evolution with increasing porosity is facilitated by a combination of Scanning/Transmission Electron Microscopy (S/TEM) and Electron Backscattered Diffraction (EBSD). This study reveals a statistically significant shift in the distribution of grain boundaries favoring lower energy twins, which coincides with an increase in the presence of stepped twin boundaries. This work demonstrates the potential benefits of careful grain boundary engineering and the need for further detailed studies of the dependence of thermal and electrical transport on grain boundary structure and orientation in these alloys.

Phonon transport across an interface is of fundamental importance to applications ranging from electronic and optical devices to thermoelectric materials. The phonon scattering by an interface can dramatically suppress the thermal transport, which can benefit thermoelectric applications but create problems for the thermal management of electronic/optical devices. In this aspect, existing molecular dynamics simulations on phonon transport across various interfaces are often based on estimates of atomic structures and are seldom compared with measurements on real interfaces. In this work, planar Si/Ge heterojunctions formed by film-wafer bonding are measured for the interfacial thermal resistance (RK) that is further compared with predictions from existing simulations and analytical models. The twist angle between a 70-nm-thick Si film and a Ge wafer is varied to check the influence of the crystal misorientation. Detailed transmission electron microscopy studies are carried out to better understand the interfacial atomic structure. It is found that the alloyed interfacial layer with mixed Si and Ge atoms dominates the measured thermal resistance (RK). Some oxygen impurities may also help to increase RK due to the formation of glassy structures. Following this, RK reduction should be focused on how to minimize the interdiffusion of Si and Ge atoms during the formation of a Si/Ge heterojunction. Keywords: Thermal boundary resistance, Si/Ge heterojunction, Film-wafer bonding, Phonon

Abstract Half‐Heusler (hH) compounds are promising candidates for inexpensive, low‐toxicity thermoelectric materials. It is well known that engineering electronic bands with high valley degeneracy is an effective approach for enhancing the performance of thermoelectric materials, and there are several routes for achieving high valley degeneracy in hH systems. For instance, there are multiple locations in the first Brillouin zone where the valence band maximum can be found (at the Γ‐, L‐, or W‐point), and there are two competing low‐lying conduction bands at the X‐point, where the conduction band minimum is located. By converging the multiple valence band and conduction band extrema, the valley degeneracy, and hence, performance of these materials can be improved. Here, group theoretical and tight‐binding approaches, in addition to first‐principles density functional theory calculations, are used to study the chemical origins of various band extrema in both the n‐type and p‐type compounds, with particular focus on ZrNiSn and NbFeSb. Specifically, the importance of avoided crossings is explained. The results of this work can be used to better understand and develop design strategies for engineering better performing hH thermoelectrics.

Atomic vibrations, in the form of phonons, are foundational in describing the thermal behavior of materials. The possible frequencies of phonons in materials are governed by the complex bonding between atoms, which is physically represented by a spring-mass model that can account for interactions (spring forces) between the atoms (masses). The lowest-order, harmonic, approximation only considers linear forces between atoms and is thought incapable of explaining phenomena like thermal expansion and thermal conductivity, which are attributed to nonlinear, anharmonic, interactions. Here, we show that the kinetic energy of atoms in a solid produces a pressure much like the kinetic energy of atoms in a gas does. This vibrational or phonon pressure naturally increases with temperature, as it does in a gas and therefore results in a thermal expansion. Because thermal expansion thermodynamically defines a Grüneisen parameter γ, which is a typical metric of anharmonicity, we show that even a harmonic solid will necessarily have some anharmonicity. A consequence of this phonon pressure model is a harmonic estimation of the Grüneisen parameter as γ≈3/23−4x2/1+2x2, where x=vt/vl is the ratio of the transverse and longitudinal speeds of sound. We demonstrate the immediate utility of this model by developing a high-throughput harmonic estimate of lattice thermal conductivity that is comparable to other state-of-the-art estimations. By linking harmonic and anharmonic properties explicitly, this study provokes new ideas about the fundamental nature of anharmonicity, while also providing a basis for new material engineering design metrics.

As the featured material of the superionic thermoelectric (TE) material family, copper-chalcogenide Cu2-xSe is attracting growing research interest for its excellent TE performance derived from the satisfactory power factor and the ultra-low thermal conductivity induced by the superionic effect. Various efforts have been made and proved to be effective to further enhance the TE performance for Cu2-xSe. However, this material is still far from the application stage, which is mainly due to concerns regarding control of the properties and the costly complex fabrication technology. Here we report a scalable pathway to achieve high-performance and tunable Cu2-xSe, utilizing conventional sintering technology and copper (Cu)-vacancy engineering with an effective mass model. The figure of merit zT is a competitive value of 1.0 at 800 K for the optimized binary Cu2-xSe, based on the precise modeling prediction and Cu-vacancy engineering. The changes in TE properties of Cu2-xSe under heating-cooling cycle tests are also revealed. Our work offers the referable method along with the decent parent material for further enhancement of TE performance, paving a possible route for the application and industrialization of Cu2-xSe TE materials. Keywords: Thermoelectric, Copper selenide, Copper-vacancy engineering, Effective mass model

The optimization of thermoelectric materials for use in various applications, such as spacecraft power generation, waste heat recovery, and Peltier coolers, requires a careful optimization of material properties. This can be achieved via defect engineering in which defects are purposefully added to a material to produce desired properties. In this tutorial, we discuss a defect engineering strategy called phase-boundary mapping. While many compound thermoelectric semiconductors are often called “line compounds” due to their appearance as a line on a binary phase diagram, in reality, due to the laws of thermodynamics, all phases have a finite phase width. The edges of this phase space define the chemical potential of the material. By making small compositional changes across this phase space, appreciable differences in thermoelectric properties are observed due to this change in the chemical potential. Additionally, the phase equilibria of a thermoelectric material impacts alloying and dopability that further impacts material properties. Phase-boundary mapping is a strategy that allows us to explore the limits of a material and ultimately reproducibly optimize thermoelectric performance by considering the effects of off-stoichiometry on chemical potential, and thus defect energies and material properties. This technique can be applied in the optimization of numerous thermoelectric materials as well as extended to other semiconductors with properties controlled by defects.

Mixed ionic–electronic conductors are limited by material decomposition. Here the authors reveal the mechanism for atom migration and deposition in Cu2–δ (S,Se) materials based on a critical chemical potential difference and propose electronically conducting, ion-blocking interfaces to enhance stability.

Thermoelectric semiconductors based on CoSb3 hold the best promise for recovering industrial or automotive waste heat because of their high efficiency and relatively abundant, lead-free constituent elements. However, higher efficiency is needed before thermoelectrics reach economic viability for widespread use. In this study, n-type InxCeyCo4Sb12+z skutterudites with high thermoelectric performance are produced by combining several phonon scattering mechanisms in a panoscopic synthesis. Using melt spinning followed by spark plasma sintering (MS-SPS), bulk InxCeyCo4Sb12+z alloys are formed with grain boundaries decorated with nano-phase of InSb. The skutterudite matrix has grains on a scale of 100–200 nm and the InSb nano-phase with a typical size of 5–15 nm is evenly dispersed at the grain boundaries of the skutterudite matrix. Coupled with the presence of defects on the Sb sublattice, this multi-scale nanometer structure is exceptionally effective in scattering phonons and, therefore, InxCeyCo4Sb12/InSb nano-composites have very low lattice thermal conductivity and high zT values reaching in excess of 1.5 at 800 K.

Electronic materials: In search of the right mass A simple method for determining a material’s thermoelectric properties is developed by researchers in the United States and Belgium. Jeffrey Snyder from Northwestern University and his co-workers’ model could simplify the search for materials that efficiently generate electricity from waste heat. Even though the environment of an electron in a solid is very complex, the way an electron moves through a solid’s lattice of atoms can be treated as if it is moving in free space. However, because of the influence of its environment an effective mass, not its true mass, is used to model the movement of electrons and that material’s properties. But this effective-mass can be defined in several ways depending on which material property is being modeled. Snyder et al. determine that the ratio of two different effective masses, as computed from different electronic properties, could be a good method to identify novel thermoelectric materials and can be associated with the “complexity” of the electronic structure.

Alloying bismuth telluride with antimony telluride and bismuth selenide for p- and n-type materials, respectively, improves the thermoelectric quality factor for use in room temperature modules. As the electronic and thermal transports can vary substantially, the alloy composition is a key engineering parameter. The n-type Bi2Te3-xSex alloy lags its p-type counterpart in thermoelectric performance and does not lend itself as readily to simple transport modeling which complicates engineering. Combining literature data with recent results across the entire alloy composition range, the complex electronic structure dynamics and trends in lattice thermal conductivity are explored. Spin-orbit interaction plays a critical role in determining the position and degeneracy of the various conduction band minima. This behavior is incorporated into a two-band effective mass model to estimate the transport parameters in each band. An alloy scattering model is utilized to demonstrate how phonon scattering behaves differently on either side of the intermediate ordered compound Bi2Te2Se due to chalcogen site occupancy preference. The parametrization of the electronic and thermal transports presented can be used in future optimization efforts.

Most crystalline materials follow the guidelines of T−1 temperature-dependent lattice thermal conductivity (κL) at elevated temperatures. Here, we observe a weak temperature dependence of κL in Mg3Sb2, T−0.48 from theory and T−0.57 from measurements, based on a comprehensive study combining ab initio molecular dynamics calculations and experimental measurements on single crystal Mg3Sb2. These results can be understood in terms of the so-called “phonon renormalization” effects due to the strong temperature dependence of the interatomic force constants (IFCs). The increasing temperature leads to the frequency upshifting for those low-frequency phonons dominating heat transport, and more importantly, the phonon-phonon interactions are weakened. In-depth analysis reveals that the phenomenon is closely related to the temperature-induced asymmetric movements of Mg atoms within MgSb4 tetrahedron. With increasing temperature, these Mg atoms tend to locate at the areas with relatively low force in the force profile, leading to reduced effective 3rd-order IFCs. The locally asymmetrical atomic movements at elevated temperatures can be further treated as an indicator of temperature-induced variations of IFCs and thus relatively strong phonon renormalization. The present work sheds light on the fundamental origins of anomalous temperature dependence of κL in thermoelectrics.

Half-Heusler materials are strong candidates for thermoelectric applications due to their high weighted mobilities and power factors, which is known to be correlated to valley degeneracy in the electronic band structure. However, there are over 50 known semiconducting half-Heusler phases, and it is not clear how the chemical composition affects the electronic structure. While all the n-type electronic structures have their conduction band minimum at either the Γ- or X-point, there is more diversity in the p-type electronic structures, and the valence band maximum can be at either the Γ-, L-, or W-point. Here, we use high throughput computation and machine learning to compare the valence bands of known half-Heusler compounds and discover new chemical guidelines for promoting the highly degenerate W-point to the valence band maximum. We do this by constructing an “orbital phase diagram” to cluster the variety of electronic structures expressed by these phases into groups, based on the atomic orbitals that contribute most to their valence bands. Then, with the aid of machine learning, we develop new chemical rules that predict the location of the valence band maximum in each of the phases. These rules can be used to engineer band structures with band convergence and high valley degeneracy.

Abstract Accurate determination of the intrinsic electronic structure of thermoelectric materials is a prerequisite for utilizing an electronic band engineering strategy to improve their thermoelectric performance. Herein, with high‐resolution angle‐resolved photoemission spectroscopy (ARPES), the intrinsic electronic structure of the 3D half‐Heusler thermoelectric material ZrNiSn is revealed. An unexpectedly large intrinsic bandgap is directly observed by ARPES and is further confirmed by electrical and optical measurements and first‐principles calculations. Moreover, a large anisotropic conduction band with an anisotropic factor of 6 is identified by ARPES and attributed to be one of the most important reasons leading to the high thermoelectric performance of ZrNiSn. These successful findings rely on the grown high‐quality single crystals, which have fewer Ni interstitial defects and negligible in‐gap states on the electronic structure. This work demonstrates a realistic paradigm to investigate the electronic structure of 3D solid materials by using ARPES and provides new insights into the intrinsic electronic structure of the half‐Heusler system benefiting further optimization of thermoelectric performance.

In thermoelectric materials, dislocations at grain boundaries can be used to scatter midfrequency phonons. Here, Chenet al. use vacancy engineering and thermal annealing to generate dislocations homogeneously within the crystalline grains and obtain good figures of merit for PbSe-based thermoelectrics.

The thin film metallic glass (TFMG) is an effective diffusion barrier layer for PbTe-based thermoelectric (TE) modules. Reaction couples structured with Cu/TFMG/PbTe are prepared via sputter-deposition and are annealed at 673 K for 8-96 h. The transmission line method is adopted for the assessment of electrical contact resistivity upon the PbTe/TFMG, and the value remains in the range of 3.3-2.5 × 10−9 (Ω m2). The titanium-based TFMG remains amorphous upon annealing at 673 K for 48 h and effectively blocks the inter-diffusion by not having grain-boundaries, which only allows the bulk diffusion between the metal electrode and the TE substrate.

The thermoelectric performance of Mg3+xSb1.5Bi0.49Te0.01 was improved by reducing the amount of excess Mg (x = 0.01-0.2). A 20% reduction in effective lattice thermal conductivity at 600 K was observed by decreasing the nominal x from 0.2 to 0.01 in Mg3+xSb1.5Bi0.49Te0.01, leading to a 20% improvement in the figure-of-merit zT. Since materials with different amounts of Mg have similar electronic properties, the enhancement is attributed primarily to the reduction in thermal conductivity. It is known that excess Mg is required to make n-type Mg3+xSb1.5Bi0.49Te0.01; however, too much excess Mg in the material increases the thermal conductivity and is therefore detrimental for the overall thermoelectric performance of the material.

Fifty years ago, the optimization of thermoelectric devices was analyzed by considering the relation between optimal performances and local entropy production. Entropy is produced by the irreversible processes in thermoelectric devices. If these processes could be eliminated, entropy production would be reduced to zero, and the limiting Carnot efficiency or coefficient of performance would be obtained. In the present review, we start with some fundamental thermodynamic considerations relevant for thermoelectrics. Based on a historical overview, we reconsider the interrelation between optimal performances and local entropy production by using the compatibility approach together with the thermodynamic arguments. Using the relative current density and the thermoelectric potential, we show that minimum entropy production can be obtained when the thermoelectric potential is a specific, optimal value.

The electrical resistivity curves for binary phase compounds of p-type lead chalcogenide (PbTe)(0.9−x)(PbSe)0.1(PbS)x, (x = 0.15, 0.2, 0.25), which contain PbS-rich secondary phases, show different behaviour on heating and cooling between 500-700 K. This is contrast to single phase compounds which exhibit similar behaviour on heating and cooling. We correlate these anomalies in the electrical resistivities of multiphase compounds to the variation in phase composition at high temperatures. The inhomogeneous distribution of dopants between the matrix and secondary phase is found to be crucial in the electronic transport properties of the multiphase compounds. These results can lead to further advances in designing composite Pb-chalcogenides with high thermoelectric performance.

In analyzing zT improvements due to lattice thermal conductivity (κL) reduction, electrical conductivity (σ) and total thermal conductivity (κTotal) are often used to estimate the electronic component of the thermal conductivity (κE) and in turn κL from κL = ∼ κTotal − LσT. The Wiedemann-Franz law, κE = LσT, where L is Lorenz number, is widely used to estimate κE from σ measurements. It is a common practice to treat L as a universal factor with 2.44 × 10−8 WΩK−2 (degenerate limit). However, significant deviations from the degenerate limit (approximately 40% or more for Kane bands) are known to occur for non-degenerate semiconductors where L converges to 1.5 × 10−8 WΩK−2 for acoustic phonon scattering. The decrease in L is correlated with an increase in thermopower (absolute value of Seebeck coefficient (S)). Thus, a first order correction to the degenerate limit of L can be based on the measured thermopower, |S|, independent of temperature or doping. We propose the equation: L = 1 . 5 + exp − | S | 116 (where L is in 10−8 WΩK−2 and S in μV/K) as a satisfactory approximation for L. This equation is accurate within 5% for single parabolic band/acoustic phonon scattering assumption and within 20% for PbSe, PbS, PbTe, Si0.8Ge0.2 where more complexity is introduced, such as non-parabolic Kane bands, multiple bands, and/or alternate scattering mechanisms. The use of this equation for L rather than a constant value (when detailed band structure and scattering mechanism is not known) will significantly improve the estimation of lattice thermal conductivity.

While thermoelectric materials can be used for solid state cooling, waste heat recovery, and solar electricity generation, low values of the thermoelectric figure of merit, zT, have led to an efficiency too low for widespread use. Thermoelectric effects are characterized by the Seebeck coefficient or thermopower, which is related to the entropy associated with charge transport. For example, coupling spin entropy with the presence of charge carriers has enabled the enhancement of zT in cobalt oxides. We demonstrate that the coupling of a continuous phase transition to carrier transport in Cu2Se over a broad (360–410 K) temperature range results in a dramatic peak in thermopower, an increase in phonon and electron scattering, and a corresponding doubling of zT (to 0.7 at 406 K), and a similar but larger increase over a wider temperature range in the zT of Cu1.97Ag.03Se (almost 1.0 at 400 K). The use of structural entropy for enhanced thermopower could lead to new engineering approaches for thermoelectric materials with high zT and new green applications for thermoelectrics.

The tuning of carrier concentration through chemical doping is very important for the optimization of thermoelectric materials. Traditionally, a rigid band model is used to understand and guide doping in such semiconductors, but it is not clear whether such an approximation is valid. This letter focuses on the changes in the electronic density of states (DOS) near the valence band maximum for different p-type dopants (Na, K, Tl, or vacancy on Pb site) maintaining the high symmetry of the NaCl structure. Na- and K-doped, and vacancy-introduced PbTe show a clear rigid-band like change in DOS unlike that concluded from supercell based calculations.