The fundamental challenge of high ZT thermoelectric material design stems from S, σ, and к. Through the strong correlation of carrier concentration n, the energy level can generally be adjusted by controlling the doping. Assuming that the dopant does not significantly change the scattering or band structure, the Seebeck coefficient can be derived from (Cutler et al., 1964): S = 8 π 2 k B 2 3 e h 2 m ∗ T ( π 3 n ) 2 / 3 (3)

Among them, k _B is Boltzmann’s constant, m* is the effective carrier mass, h is Planck’s constant, and n is the carrier concentration. In semiconductor thermoelectric materials, according to the Kane energy band theory, the Hall carrier concentration can be expressed as (Ioffe et al., 1959; Cutler et al., 1964): n H = 1 e R H = A − 1 N v ( 2 m b ∗ k B T ) 3 / 2 3 π 2 h 3 F 0 3 / 2 (4) where N _v is the degree of degeneration, ⁰ F ₀ is the Fermi integral function, which is the reduced Planck constant. Although the carrier concentration n has an inverse relationship with the Seebeck coefficient, the increase of n has a positive effect on the energy band degeneration and the increase of effective mass. Therefore, the current strategy of optimizing carrier concentration usually adopts the increasing carrier Concentration method to improve thermoelectric performance (Dashevsky et al., 2002; Kuznetsov et al., 2002; Pei et al., 2011).

The main strategy for optimizing the carrier concentration is doping, such as modulation doping, uniform doping, and gradient doping (Figure 3). Feng et al. (2020) systematically revealed the theoretical origin of high average ZT in GeTe-based alloys uniformly doped with Pb through theoretical simulations and experimental tests on GeTe-based alloys. On the one hand, the intrinsic high hole carrier density is reduced to a rough optimal range, and then the carrier density is fine-tuned by Pb doping. The lead-doped energy band convergence can maintain a higher power factor. On the other hand, lead causes a decrease in carrier density and can significantly reduce κ, and the combination of the two is almost the same. PF results in a maximum ZT at the corresponding carrier density, so that the average ZT is about 1.5 in the 300–773 K range and the peak ZT is about 2.0 at 573 K, indicating that Pb doping can be used over a wide temperature range (e.g., 300–800 K), rather than only for TE applications at higher temperatures (e.g., T > 600 K) (Feng et al., 2020). In the case of uniform doping, the carrier concentration is generally independent of temperature, so the best thermoelectric performance cannot be guaranteed in the entire temperature range. One way to deal with this problem is to use gradient doping. By integrating two or more different segments, a common method of preparing this graded material is the so-called spark plasma sintering or hot-pressed powder layer. Each powder layer has different carrier concentration (Dashevsky et al., 2002; Selimefendigil et al., 2021). Zhao et al. (2014c) take advantage of the low thermal conductivity of layered materials in the out-layer direction. The migration of carriers between layers is improved in the out-layer direction by adjusting the symmetry of the crystal structure, thereby promoting electron tunneling in the inter-layer direction. At 600–800 K, SnSe has a continuous phase transition process from low-symmetry Pnma (L-Pnma) phase to high-symmetry Pnma (H-Pnma) phase, and then to high-temperature high-symmetry Cmcm phase. In addition to temperature, introducing stress into SnSe crystals by doping/solid solution can also adjust the symmetry of the crystal structure, thereby optimizing the thermoelectric properties of the material, as shown in Figure 4 (Su et al., 2022).

However, with prolonged use, the initial carrier concentration gradient in the gradient material may decrease or disappear due to the homogenization effect induced by diffusion, thereby reducing the conversion efficiency. To solve this limitation, using the temperature dependence of the solubility of certain specific dopants (Yamini et al., 2013), a carrier concentration n is controlled only by temperature, and its gradient can be created in a single material. A well-known example is Cu, Ag, and excess Pb. They have negligible solubility in PbTe at room temperature but have high solubility at high temperatures (Bergum et al., 2011). Lidong Zhao et al. synthesized an n-type SnSe crystal with a two-dimensional layered structure using the temperature gradient method and bromine doping method. The electron doping promotes the hybridization of delocalized electrons and realizes the tunneling of electrons between the n-type SnSe layers. This “two-dimensional phonon/three-dimensional charge” transfer characteristic greatly improves the thermoelectric properties of n-type SnSe crystal materials, with a ZT as high as 2.8 (Chang et al., 2018). This temperature-dependent doping is reversible in the heating-cooling process and eliminates the diffusion problem of gradient doping, making it more suitable for practical applications. Polyatomic doping takes advantage of the synergistic effect to have a more significant change in carrier concentration (Zhu et al., 2002). Lixia Zhang et al. fabricated the Yb-filled CoSb₃ skutterudites with an ultra-high Yb filling fraction by melt-spinning methods, and they found a high ZT value of about 1.3 was achieved at 823 K for the nominal composition Yb_0.4Co₄Sb₁₂. An ultra-low lattice thermal conductivity approaching the glass limit was achieved due to the enhanced rattling effect from the ultra-high Yb filling fraction and extra phonon scattering from the ordered superstructures, nano-scale inhomogeneous Yb fillers, and high-density lattice strain caused by the ordered and modulated fillers (Ren et al., 2021). Shi et al. (2011) synthesized CoSb₃ with a variety of co-fillers such as Ba, La, and Yb. Finally, from single filling to double filling, and finally to multiple fillings to achieve continuous growth of ZT value, the maximum ZT at 850 K was increased to 1.7. Therefore, for thermoelectric material systems with different characteristics, it is particularly important to select a suitable doping method (the most current method is temperature-dependent doping) to optimize the carrier concentration in a broader temperature range.

The improvement of carrier mobility is mainly through introducing impurity atoms in the intrinsic atomic vacancies. In most cases, the increase of m* will lead to a decrease in carrier mobility, and it will reduce the conductivity (Ioffe et al., 1959): μ = e τ m ∗ (5) where τ is the relaxation time, so the improvement of carrier mobility also has a positive effect on the increase of ZT. Generally speaking, the smaller the electronegativity difference between the elements of the compound, the greater the mobility of the material, such as PbTe, Bi₂Se₃, etc. Lidong Zhao et al. further studied the effect of copper doping on n-type PbTe. The effective filling of Cu reduces the scattering of carriers in the gaps of Pb crystals, resulting in considerable carrier mobility and a high power factor (Xiao et al., 2017). The PbTe-2% Cu₂Te reaches a peak value of ZT ∼ 1.5 at 723 K, and the ZT _ave ∼ 1.0 of the n-type PbTe system achieves the highest value in history, as shown in Figure 5.

Studies have shown that to improve carrier mobility, three-dimensional modulation doping (mainly under low-temperature conditions) can effectively increase the ZT value of some important thermoelectric materials (Zebarjadi et al., 2011; Koirala et al., 2013; Pei et al., 2014). The modulated doped sample is a two-phase composite material composed of undoped and heavily doped. Undoped original samples have low carrier concentration but high carrier mobility, while uniformly doped and heavily doped samples have high carrier concentration but low carrier mobility. The Fermi level of undoped samples is usually in the middle of the energy gap, and the Fermi level of heavily doped samples goes deep into the conduction band (n-type doping) or valence band (p-type doping). With the energy imbalance between the undoped phase and the heavily doped phase, the carriers in the sample overflow from the heavily doped area to the undoped site, and this process enhances the carrier mobility (Valset et al., 2012).

In addition to modulating doping, the texture structure of the material can be used as another feasible way to improve carrier mobility, especially for some materials with anisotropic structures. In various heterostructures, the carrier mobility may only be higher in some specific crystal orientations (Zhao et al., 2014a). Li et al. (2018) proposed a method of high-efficiency thermoelectric materials that optimizes both electrical and heat transport performance. In (Bi, Sb)₂Te₃, the two-step sintering process with excess Te can increase mobility and reduce thermal conductivity at the same time. The two-step sintering process reduces the grain boundaries and defects that seriously hinder the transport of charge carriers, thereby increasing the mobility, and the maximum ZT of Bi_0.4Sb_1.6Te₃ can reach 1.3. Studies have shown that the two-step sintering technology is an effective method, which can control the existence and distribution of element inhomogeneity, so that the carrier transport and phonon transport have a special directionality. This has a specific guiding significance for other thermoelectric material systems with similar characteristics (Cha et al., 2019; Pan et al., 2019).

Introducing lattice point defects into the matrix lattice is an effective way to reduce the thermal conductivity of the lattice, as shown in Figure 8A. This is because phonons are more likely to be scattered by point defects rather than electrons, and thus have less impact on carrier mobility. Figures 8B–D show typical doping methods commonly used in thermoelectric materials research, namely single element doping, cross-substitution, and formation of lattice vacancies. In the case of single doping, the dopant can be the same valence as the main element, resulting in lattice disorder, or it can be heterovalent, so as to control the carrier concentration. However, this doping causes the system charge imbalance, which may hinder the reduction of к _L if done alone.

To improve the solubility of different elements, cross-substitution is generally used. Cross-substitution refers to the pair-to-pair substitution of one or more main elements from other groups in the periodic table, while keeping the total number of valence electrons unchanged (Tan et al., 2013; Tan et al., 2015b).

Yu et al. (2018a) designed thermoelectric materials by isoelectronic substitution of the atom Ta for the atom Nb. By using isoelectronic substitution of atoms with similar size and chemical properties but the large mass difference, the lattice thermal conductivity of the alloy was greatly suppressed, but good electrical properties were maintained. As a result, the ZT reaches a peak of 1.6 at a Ta content of 0.4. It shows that the point defects caused by the substitute atoms will change the thermal conductivity of the lattice (Yu et al., 2018a). It is worth noting that the cross-substitution not only greatly affects the transport of phonons, but may also change the electronic structure (mainly the band gap), providing other ways to adjust the thermoelectric properties of the matrix material. Because only when these two heterogeneous elements exist together in a specific ratio, the amount of them entering the matrix will be greater. We call this effect synergistic alloying. In the Pb_0.98Na_0.02Te-8% SrTe sample, the ZT value is 2.5 at 923 K, and the average ZT value is 1.67 in the range of 300–900 K. It is further proved that by optimizing the Na concentration, a ZT of 2.5 can be obtained at a lower temperature of about 800 K (Xu et al., 2020a). Alloying is currently the most widely used method to enhance the scattering of point defects, in Bi₂Te₃ (Hu et al., 2014; Chen et al., 2015), Pb(Te, Se) (Pei et al., 2011), GeTe (Chen et al., 2020) and Half-Heusler (HH) alloys (Xue et al., 2016; Shen et al., 2018; Yu et al., 2018b) have applications.

In addition to alloying, vacancies and interstitial atoms also belong to a relatively special point defect scattering mechanism (Xue et al., 2016). Jiaqing He introduced double-vacancy defects by doping BiI₃ (Xu et al., 2020b) to improve the thermoelectric performance of Sb₂Te₃(GeTe)₁₇. The maximum value of ZT is 2.2 at 723 K. There are nearly 20% intrinsic Nb vacancies in the HH alloy Nb_0.8CoSb, which makes the Nb_0.8CoSb alloy have a relatively low lattice thermal conductivity (Xia et al., 2018). The same phenomenon exists in thermoelectric materials such as Cu₂SnSe₄ (Li et al., 2016). Like vacancies, interstitial atoms can also be generated by a solid solution method, but only compounds with a larger cation-anion ratio are applicable. The cations of such compounds need to have a smaller radius to fit the interstitial sites. Taking the solid solution (SnTe)_1−x (Cu₂Te)_x as an example (Li et al., 2017; Zheng et al., 2017), its lattice thermal conductivity is as low as 0.5 W m⁻¹ K⁻¹, which is close to the minimum lattice thermal conductivity limit of SnTe (About 0.4 W m⁻¹ K⁻¹).

Dislocations are a typical line defect, especially in metal materials. Dislocations and strain fields will scatter mid-and high-frequency phonons, so dislocations can effectively reduce the free path of phonons (Figure 9A). Kim et al. (2015) reported that by forming a high-density dislocation array at the grain boundary by extrusion, the lattice thermal conductivity of the Bi_0.5Sb_1.5Te₃ material could be significantly reduced, which is a dense dislocation array pair. The result of phonon scattering. In addition, dislocations can also be introduced through the precipitation of the second phase, where dislocations can play a role in reconciling the lattice mismatch at the phase boundary (Hu et al., 2015).

In solid solution materials, due to the accumulation of vacancies, adjacent spaces collapse under external conditions to form vacancy dislocations. At the same time, vacancies will also spontaneously reduce energy. The released energy can promote dislocations to climb. The climbing motion of dislocations will increase the density of dislocations, and finally produce high-density and uniformly distributed dislocations in the crystal grain, thereby reducing к _L . In Mg₂Si_1−xSb_x materials (Xin et al., 2017), high-dose alloying of Sb has a large number of Mg vacancies, making the vacancy concentration much higher than the equilibrium vacancy density, and the excess Mg vacancies spontaneously aggregate to form dislocations, as shown in Figure 9B. In Mg₂Si_0.5Sb_0.5, the dislocation density is as high as 2.8 × 10¹⁶ m⁻². Besides, similar phenomena were also observed in the Na_yEu_0.03Pb_0.97−yTe system (Chen et al., 2017). Studies have shown that with the increase of Na doping, the main microscopic defects in the system gradually change from point defects to dislocations. Dislocation scattering reduces the lattice thermal conductivity of PbTe to below 0.4 W m⁻¹ K⁻¹.

Because atomic defects and dislocation defects can effectively scatter low- and mid-wavelength phonons, there are still some long-wavelength phonons that are not scattered and affect the thermal conductivity of the lattice. In polycrystalline materials, grain boundaries or phase boundaries can effectively scatter low-frequency phonons, and the scattering rate is inversely proportional to the grain size. Therefore, the effective method to effectively scatter long-wavelength phonons is to introduce micro-nano structures (Girard et al., 2010). The mechanism of action is shown in Figure 10A. In particular, nanostructures have been proven to be an effective method to enhance ZT by placing suitable nano-scale precipitates in the matrix to reduce к _L , such as AgPb_mSbTe_m+2 (Hsu et al., 2004), NaPb_xSbTe_2−x (Poudeu et al., 2006) and PbTe-Ag₂Te (Zhao et al., 2013a). In addition, p-type PbTe_1−xSe_x (Pei et al., 2011) and Tl-PbTe (Heremans et al., 2008) also have excellent thermoelectric properties, which come from the introduction of multiple valence bands and the density of states distortions in the valence band, respectively. Biswas et al. (2012), Liu et al. (2016), and others considered phonon scattering sources on all scales from the perspective of a layered approach, ranging from atomic-scale lattice disorder and nano-scale internal deposits to mesoscale crystals. The thermal conductivity of the crystal lattice is greatly reduced. Finally, the ZT of PbTe-SrTe is 2.2, and the ZT of Bi_0.88Ca_0.06Pb_0.06CuSeO is 1.5, which proves that the grain boundary scattering is important in reducing the thermal conductivity. Zhao et al. (2019) introduced the Ag₂Te phase into Cu₂Te. Due to multiple phase transitions, they show complex temperature dependence in the temperature range of 300–1000 K. As the Ag₂Te content increases, the interface scattering increases, and к _L decreases significantly (as shown in Figures 10B–D). At the same time, its highest ZT value reaches 1.8. It shows ultra-low lattice thermal conductivity at 900 K, and its value is about 0.3 W m⁻¹ K⁻¹ (Zhao et al., 2019).

Commonly used methods to enhance grain boundary scattering include ball milling (Li et al., 2015) and plasma sintering (Xie et al., 2018), etc., to obtain finer or smaller grains from coarser-grained crystal powders to increase the grain boundary area. Li et al. (2015) prepared nanostructured Na_0.02Pb_0.98Te samples with a grain size of 20–100 nm through high-energy ball milling and semi-solid powder processing. Through observation, they found that the interface between the particles can be clearly seen. The size (0.1–1 μm) of the pores, so there is stronger phonon scattering at the grain boundary, which reduces the lattice thermal conductivity к _L to 0.74 W m⁻¹ K⁻¹ at 623 K. Similarly, Yu et al. (2017) combined melt spinning, ball milling and spark plasma sintering processes to construct a microstructure containing a large number of 60° twin grain boundaries in the Bi_0.5Sb_1.5Te₃ liquid alloy. The bilateral grain boundaries not only increase the current load mobility, and its scattering effect on phonons greatly reduces the thermal conductivity, so that ZT = 1.42 at 348 K (Yu et al., 2017).

In addition to the above methods, the process of separating the micro-nano phases to form twin crystals and dislocation network structures can also increase the grain boundary area, thereby enhancing phonon scattering and reducing thermal conductivity (Kim et al., 2015). Gelbstein et al. (2013) separated the p-type Ge_0.87Pb_0.13Te into two phases of GeTe and PbTe through spark plasma sintering, thereby generating the characteristics of multiple interfaces, enhancing the phonon scattering at the crystal plane, and achieving a relatively highly stable TE Performance.

It can be seen that defects of different sizes prepared by doping in materials and related physical and chemical methods can effectively scatter phonons of different wavelengths and different free paths, thereby reducing the thermal conductivity of the lattice. Therefore, the changes in energy band and structure (mass ratio and degree of distortion) caused by the coordinated effect of point defect scattering, dislocation scattering, and interface scattering will enhance the scattering of phonons at different wavelength levels simultaneously (Li et al., 2018; Lee et al., 2019).

Resonance scattering is generally used in thermoelectric materials with special crystal structures, such as cage compounds (Christensen et al., 2008; Beekman and VanderGraaff, 2017), skutterudite (Duan et al., 2016), and some thermoelectric materials with topological insulation (Wei et al., 2016; Zeugner et al., 2019). By adding filler atoms, a strong local vibration close to the vibration frequency is generated, and a resonance spectrum of a specific frequency (shown in Figure 11) is introduced, thereby reducing the thermal conductivity.

Researchers fill CoSb₃ with S and Se as electronegative objects under equilibrium conditions. Because S and Se have unique localized “cluster vibrations,” a section can be introduced in the phonon spectrum. The optical branch with lower frequency is coupled with the acoustic branch, which significantly affects the lattice dynamics, greatly reduces the thermal conductivity of the lattice, and obtains S_0.26Co₄Sb_11.11Te_0.73 with ZT = 1.5 at 850 K (Zeugner et al., 2019). In recent years, research on topological insulating thermoelectric materials has gradually increased, and many studies have also shown that some of them have resonance scattering. Samanta et al. (2018) reported a layered structure of n-type BiSe (Se-Bi-Se-Bi-Se), the study found that the local vibration generated by the Bi layer can cause some low-energy optical branches to inhibit the propagation of the acoustic branches (i.e., photoacoustic coupling), and the sound wave branch with low cut-off frequency and strong anharmonic vibration Phonon interaction further reduces the thermal conductivity, and finally κ _L = 0.3 W m⁻¹ K⁻¹ at 300 K. Similarly, Wei et al. (2016), Christensen et al. (2008) predicted the minimum thermal conductivity of bismuth-based stacked structures with topological insulation and found that the NI layer has a strong influence on Bi₂TeI lattice dynamics and impedes phonon propagation, with low-frequency photo-phonon and phonon interactions arising from local vibrations of the NI layer causing a high degree of lattice anharmonicity and producing extremely low thermal conductivity. Moreover, Ying et al. (2017) studied the cause and physical mechanism of the intrinsic low thermal conductivity of α-MgAgSb thermoelectric materials and predicted a class of thermoelectric material systems with low thermal conductivity. The study found that α-MgAgSb has weak chemical bonds in addition to layering. In addition to the low sound velocity, the half-Heusler-like twisted lattice makes it form a Mg-Ag-Sb triple-center bond structure (Figures 12A,B). The Ag atoms in the Mg-Ag-Sb tri-center bond can move reciprocally in the direction of the arrow to a greater extent, forming a low-frequency optical branch in the phonon spectrum (Figure 12C). These low-frequency optical branches can generate resonance scattering and effectively reduce the thermal conductivity of the lattice (Ying et al., 2017). It can be seen from the above that the research on reducing thermal conductivity through resonance scattering is becoming more mature.

The lattice thermal conductivity is proportional to the speed of sound, so obtaining low sound speed performance often helps to improve the thermoelectric properties of the material. Materials with weak chemical bonds have a lower speed of sound, atoms have more space for movement near their equilibrium positions, and electron cloud distribution is more diffuse. In the phonon spectrum, weak chemical bonds often correspond to some low-frequency phonon models, which are easier to couple with the acoustic branch, thereby further reducing the contribution of the acoustic branch to the thermal conductivity.

SnSe is a typical simple thermoelectric material with weak chemical bonds and is very stable. SnSe has an orthogonal layer structure in the room temperature range. The Sn-Se bond in the bc direction is stronger and weaker in a direction. It is easy to cleave along the (100) plane and form a foldable projection in the b-axis direction. The structure contains a highly distorted SnSe₇ coordination polyhedron with three short Sn-Se bonds and four long Sn-Se bonds. Such a special structure makes it have strong non-resonance and high anisotropy, which essentially has ultra-low thermal conductivity. Lidong Zhao et al. prepared SnSe single crystal by the Briman method and found that the special crystal structure of SnSe (as shown in Figure 13A) made SnSe have a very low к _L , and the room temperature thermal conductivity of SnSe in the direction of the axis a was about 0.47 W m⁻¹ K⁻¹. With the increase of temperature, the thermal conductivity at 973 K decreased to about 0.23 W m⁻¹ K⁻¹ (as shown in Figures 13A, C), and a historic breakthrough was made at 923 K with a ZT of 2.6 along the b-axis (as shown in Figure 13B) (Zhao et al., 2014a). Subsequently, Zhao et al. (2014a) synthesized an n-type SnSe crystal with a two-dimensional layered structure with ZT up to 2.8 (Chang et al., 2018). Similarly, based on the low thermal conductivity of SnSe, Qin et al. (2020) introduced SnSe₂ as an extrinsic defect dopant to increase the carrier concentration to 6.55 × 10¹⁹ cm⁻³ while increasing the effective Mass and Seebeck coefficient, obtained an unusually high power factor at room temperature (about 5.4 × 10^–2 W m⁻¹ K⁻²), so that the maximum ZT value reached 2.2 and the average ZT value reached 1.7.

In addition to single crystals SnSe, polycrystalline SnSe has gradually been widely used in research due to its thermal conductivity comparable to that of single crystals SnSe. Although SnSe crystals have strong anisotropy, polycrystalline materials have more carrier migration than single crystals SnSe materials. The rate is much lower, and the conductivity is very low, but therefore, increasing the conductivity has become an important way to improve the thermoelectric properties of polycrystalline SnSe. Zhang et al. (2015) prepared n-type SnSe polycrystalline powder by using I doping and SnS solid solution, and processed it in a vacuum device, and found that the thermal conductivity of polycrystalline SnSe would decrease, approaching 0.30 W m⁻¹ K⁻¹ at 773 K, which makes ZT = 1 finally.

Perhaps because polycrystalline materials have many dislocations, vacancies, bond deformations, and other defects in the grain boundary during the powder metallurgy process, they are in a state of stress distortion, and the energy is high, which makes the material in an unstable state at high temperatures, resulting in relatively poor performance. There are many speculations about the reason for the low thermal conductivity of SnSe. For example, the spring-type crystal structure of SnSe has a great shock-absorbing and buffering effect on the transmission of phonons in it (Heremans, 2014). Therefore, the thermal conductivity of SnSe still needs further investigation and verification.

The resonance effect refers to the balance of external forces experienced by phonons during the transmission process. The sound wave transmits uniformly forward in the form of a parabola, which is similar to the transmission in a perfect lattice, but when the transmission of phonons is affected by external factors, it will deviate from the equilibrium position and cause non-resonance effects. The strength of anharmonicity is mainly related to the symmetry of chemical bonds and atomic equilibrium positions. During the vibration of an atom, the greater the deviation of its symmetry center, the stronger the asymmetry. Materials with lone pairs of electrons are often due to the uneven distribution of the electron cloud, the crystal structure will be deformed to a certain extent, and the asymmetry is significantly enhanced, which is beneficial to obtain strong anharmonicity.

Because there are two isolated electrons in the outermost layer of the Sb nucleus. The two lone electrons in the outermost layer of the nucleus will make the transmission of phonons unbalanced, resulting in non-resonance effects, resulting in Sb compounds with low heat transport properties. In the same way, compounds with Bi atoms belonging to the same group as Sb atoms should also have anharmonic effects. Therefore, the common thermoelectric materials with intrinsic low thermal conductivity of this kind are AgSbSe₂, BiCuSeO, and so on. The room temperature thermal conductivity of AgSbSe₂ is 0.48 W m⁻¹ K⁻¹ (Nielsen et al., 2013), which is lower than most thermoelectric materials at room temperature. In recent years, some people have introduced AgSbSe₂ into GeTe to prepare (GeTe)₈₀ (AgSbSe₂)₂₀. The introduction of hierarchical nano/mesoporous structure inside the material causes large-scale scattering of phonons, which reduces the lattice thermal conductivity к _L to 0.4 W m⁻¹ K⁻¹ at 300–700 K, which is close to the thermal conductivity of GeTe. The theoretical limit of the rate finally makes its ZT _max reach 1.9 at 660 K (Samanta et al., 2017). Later, Gao et al. (2018) used the method of mechanical alloying and rapid hot pressing to manufacture Ca doped AgSbSe₂ with the layered structure. Ca doping further optimized the carrier concentration and caused the point defect scattering of phonons, and obtained the ultra-low lattice thermal conductivity of 0.27 W m⁻¹ K⁻¹ at 673 K, thus increasing the ZT peak value to 1.2.

Since BiCuSeO was reported in 2010 (Zhao et al., 2010), BiCuSeO is considered to be one of the most promising oxygen-containing thermoelectric materials due to its special natural superlattice structure and corresponding ultra-low thermal conductivity. Later, researchers found that in BiCuSeO, modulating doping to increase carrier mobility can greatly improve thermoelectric performance. Modulating the heterostructure of the doped sample makes the carriers preferentially transport in the low carrier concentration region, which increases the carrier mobility by 2 times while maintaining the carrier concentration similar to the uniformly doped sample. The synergistic effect of the increased conductivity and the basically constant Seebeck coefficient results in a wide range of high power factors, about 5–10 × 10^–2 W cm⁻¹ K⁻². The combination of ultra-high power factor and extremely low thermal conductivity (about 0.25 W m⁻¹ K⁻¹) enables BiCuSeO to obtain a high ZT ≈ 1.4 at 923 K (Pei et al., 2014) ^.

Later, with the widespread acceptance of simulation calculations, Saha (2015) used first-principles density functional theory calculations to propose the atomic displacement map of the lowest frequency optical mode of BiCuSeO, and systematically studied the correlation of BiCuSeO (such as dielectric and Anharmonic) characteristics, and compared with LaCuSeO of the same structure, it is found that the reason for the ultra-low thermal conductivity κ of BiCuSeO is that the Bi atom exhibits a significant displacement during the action, which indicates that it has a higher anharmonic effect. Furthermore, the calculated out-of-plane thermal conductivity of BiCuSeO is approximately twice that of the in-plane thermal conductivity, which indicates that BiCuSeO has a greater anisotropy of heat flow between in-plane and out-of-plane.

In solid, C _v = 3N _k B, while in liquid, most transverse vibration waves cannot be transmitted, C _v decreases to 2–2.5N _k B, and N _k is the total atomic number. Therefore, materials with liquid properties often have relatively low thermal conductivity due to their small heat capacity. Ionic conductors introduce some ions with “liquid” characteristics into solid materials to form an ionic liquid-like semiconductor, thus reducing the lattice thermal conductivity to a level lower than that of glass, which can not only reduce the mean free path of phonons but also eliminate lattice vibration. Cu_2−xSe compounds belong to this class of ion-electron composite conductors with special structures with two-phase structures at room temperature (transition from low-temperature α phase to high-temperature β phase at 400 K). The lattice network structure of Cu_2−xSe face-centred cubic Se atoms provides a good electrical transport pathway for the randomly distributed free movement of Cu ions in the interstitial positions, which enhances the scattered lattice phonons while reducing some lattice vibrational modes, so that the lattice heat capacity of the material decreases with increasing temperature and ultimately low thermal conductivity properties can be obtained.

Skomorokhov et al. (2006) experimentally found the local migration of Cu atoms in Cu₂Se. Later, Liu et al. (2012) found that the abnormal “liquid-like” behavior of copper ions around the crystalline sublattice of Se in Cu_2−xSe (Figure 3 shows the simple Face-centered cubic structure of Se atoms in the High-temperature β phase) leads to essentially very low lattice thermal conductivity (0.4–0.6 W m⁻¹ K⁻¹), thus achieving high ZT = 1.5 (T = 1,000 K) in this originally simple semiconductor. This unusual combination of properties resulted in ideal thermoelectric materials. The results show that exploring the network structure with electron conduction sublattices surrounded by liquid ions can provide new strategies and directions for High-efficiency thermoelectric materials.

Subsequently, Zhong et al. (2014) generated highly aligned wafers in the bulk Cu_1.94Al_0.02Se by the direct current hot pressing process according to the alternating arrangement of single disordered layers of Se ions and double disordered layers of Cu ions. The superionic mechanism in Cu_1.94Al_0.02Se was further enhanced by the enhancement of Cu ions and high crystal orientation. Finally, ZT = 2.62 was obtained at 756°C (Zhong et al., 2014). This study also provides a reliable way to use the superior mechanism. In the research process of Cu_2−xSe, the high fluidity of copper ions causes problems such as thermal stability during the preparation of Cu_2−xSe, which prevents the development of Cu_2−XSe. Therefore, it is also necessary to consider how to control such problems in the research process.

Heat capacity C _v is the important factor influencing the thermal conductivity and is proportional to the lattice thermal conductivity, based on the debye model for the heat capacity, the acoustic wave is the main source of contribution to the thermal conductivity, the assumption in a polyatomic system, the total number of the original cell of N, every cell in the atomic number is n, total system degrees of freedom to 3 nN, among them, the acoustic branch has 3N, optical 3(n−1)N, by the equipartition principle, the contribution of the acoustic branch heat capacity as the C/n, optical to C(n−1)/n (Toberer et al., 2011). Therefore, the total heat capacity remains unchanged. The more atoms in the primary cell, the less contribution of acoustic branches to the total heat capacity is, and the more conducive to obtaining low lattice thermal conductivity, which means that the thermoelectric materials with heavy molecular weight have certain advantages to obtain excellent thermoelectric properties. This has been demonstrated in many thermoelectric materials with complex crystal structures.

Zintl phase Yb₁₄MnSb₁₁ is a typical macromolecular mass material with a relative molecular weight of 3,783.088 g/mol, and its crystal structure is shown in Figure 14C (Wang Y. et al., 2018). Brown et al. (2006) found that electronic and thermal properties could be potentially modulated by doping at different locations in the A₁₄MPn₁₁ class of structures. Doped at cationic metal site A, the carrier concentration and phonon disordered scattering can be adjusted. Doped at cationic metal site A, the carrier concentration and phonon disordered scattering can be adjusted. Doping at a metal site M can adjust the electronic parameters, and for the first time by preparing Zintl phase Yb₁₄MnSb₁₁ to obtain the thermoelectric performance of the stability at high temperature, the thermal conductivity in about 0.7–0.9 W m⁻¹ K⁻¹ (400–1,300 K), the Seebeck coefficient reaches the maximum value of 185 μV/K at 1,275 K, and the ZT value reaches one at 1,223 K, which provides new guidance for the study of Zintl phase Yb₁₄MnSb₁₁.

Then, Cox et al. (2009) began to conduct Al doping on the metal sites of Yb₁₄Mn_1−xAl_xSb₁₁ structure to regulate electronic parameters. Studies have shown that within a certain range of heat capacity (300–1,100 K), as the aluminum content increases, the unit cell volume increases, and the bond distance changes less than 2%, which means that the increase in cell volume is related to the decrease in the deformation of the tetrahedron with the increase in Al content. When the ZT peak appears at 1,223 K, it deviates from the measurement range, indicating that the lattice thermal conductivity here is extremely low (about 0.3–0.4 W m⁻¹ K⁻¹), as shown in Figure 14A. Subsequently, Uvarov et al. (2012) improved Seebeck’s coefficient and reduced thermal conductivity by replacing Yb²⁺ with equivalent Ca²⁺ in Yb₁₄MnSb₁₁, thus increasing ZT and obtaining higher thermoelectric performance. Therefore, it can be seen that the thermoelectric materials with similar heavy molecular weight can be adjusted at different sites to obtain low lattice thermal conductivity and stable thermoelectric properties with great exploration value.

It is well known that the main factors affecting the thermal conductivity of materials are heat capacity, sound velocity, and phonon relaxation time. The complex crystal structure not only reduces the contribution of the acoustic branches to the total heat capacity, but also reduces the group velocity of the acoustic branches.

Due to its complex crystal structure, Ag₉TlTe₅ has a heavy molecular mass, and the number of atoms in a single cell is 298. Meanwhile, the low elastic modulus indicates that the chemical bond of the material is weak. The thermal conductivity of Ag₉TlTe₅ remains about 0.25 W m⁻¹ K⁻¹ from room temperature to 650 K (Kurosaki et al., 2005), which makes the ZT of the material reach 1.25 at 673 K. The ternary alkali metal-bismuth-chalcogenides exhibit extremely low thermal conductivity due to their more complex crystal structure, such as β-K₂Bi₈Se₁₃ (Figure 15A), CsBi₄Te₆ (Figure 15B), etc. The low symmetry monoclinic crystal structure of β-K₂Bi₈Se₁₃ makes it highly anisotropic. β-K₂Bi₈Se₁₃ was first proposed by Meng et al. (2003), and its thermal conductivity is as low as 1.28 W m⁻¹ K⁻¹. Afterwards, Kyratsi et al. (2011)prepared crystalline/amorphous β-K₂Bi₈Se₁₃ nanocomposites by ball milling the melt-synthesized polycrystalline β-K₂Bi₈Se₁₃ under an inert atmosphere. It was found that with the time of ball milling, the nanocrystalline phase gradually formed, the carrier concentration gradually decreased, the Seebeck coefficient gradually increased, and the thermal conductivity gradually decreased from the initial 1.28–0.3 W m⁻¹ K⁻¹, which greatly improved the thermoelectric properties of β-K₂Bi₈Se₁₃, and provided a new and reliable idea for the follow-up research. In addition, there are many materials with complex crystal structures, such as Bicuseo (Figure 15C) and Yb₁₄Mn_1-xAl_xSb₁₁ mentioned above, all of which are more or less affected by their structures. Therefore, given the many materials yet to be investigated, there is certainly much work ahead and promise for developing TE materials.