Nanostructural thermoelectric materials and their performance

Abstract

In this review, an attempt was made to introduce the traditional concepts and materials in thermoelectric application and the recent development in searching high-performance thermoelectric materials. Due to the use of nanostructural engineering, thermoelectric materials with a high figure of merit are designed, leading to their blooming application in the energy field. One dimensional nanotubes and nanoribbons, two-dimensional planner structures, nanocomposites, and heterostructures were summarized. In addition, the state-of-the-art theoretical calculation in the prediction of thermoelectric materials was also reviewed, including the molecular dynamics (MD), Boltzmann transport equation, and non-equilibrium Green’s function. The combination of experimental fabrication and first-principles prediction significantly promotes the discovery of new promising candidates in the thermoelectric field.

Keywords

nanostructural / low-dimensional / thermoelectric material / figure of merit / first-principles

Introduction

Due to their ability of directly converting waste heat into electricity and vice versa, thermoelectric materials [¹–⁶] have attracted a lot of attention in recent years. It has been considered as one of the effective ways to resolve the severe energy problem using thermoelectric materials. Compared with other methods such as lithium ion batteries, solar cells, and supercapacitor, it possesses the advantages of having no moving components, no leakage, and being environmentally friendly [⁷,⁸].Generally, the energy conversion efficiency is adopted to evaluate the conversion performance. As is known, the Carnot coefficient h_C is considered as the highest reversible energy conversion efficiency under certain circumstances, which is defined as

(1){\eta }_{\mathrm{C}}={\displaystyle \frac{\mathrm{\Delta }T}{T_{\mathrm{h}}}}={\displaystyle \frac{T_{\mathrm{h}}-T_{\mathrm{c}}}{T_{\mathrm{h}}}},

where DT = T_h−T_c denotes the temperature gradient between the heat and cold terminals, which are defined as T_h and T_c, respectively. As in the thermoelectric field, the energy generation efficiency of thermoelectric material, h_TE, can be expressed as

(2){\eta }_{\mathrm{TE}}={\displaystyle \frac{\mathrm{\Delta }T}{T_{\mathrm{h}}}}\cdot {\displaystyle \frac{\sqrt{\mathrm{1}+ZT}-\mathrm{1}}{\sqrt{\mathrm{1}+ZT}+T_{\mathrm{c}}/T_{\mathrm{h}}}},

where ZT is the so-called thermoelectric figure of merit, which is determined by the intrinsic properties of a certain material. As is known from Eq. (2), in order to obtain a high energy generation efficiency (i.e. to approach the Carnot coefficient), ZT should be large enough, ideally exceeding 3 or even 4, as shown in Fig. 1.

The thermoelectric figure of merit [⁹,¹⁰] is defined according to

(3)ZT={\displaystyle \frac{\sigma S^{\mathrm{2}}T}{\kappa }},

(4)\kappa ={\kappa }_{\mathrm{el}}+{\kappa }_{\mathrm{ph}},

where s, S, and k are the electrical conductivity, Seebeck coefficient, and thermal conductivity, respectively. The thermal conductivity can be contributed by both electrons and phonons, denoted as k_el and k_ph, respectively [¹¹].

As shown in the definition of ZT, it would require a high electrical conductivity and Seebeck coefficient as well as a low thermal conductivity to obtain high-performance thermoelectric materials. However, these transport coefficients are inter-related. It is difficult to alter one parameter without significantly affecting the other transport coefficients. For example, as the carrier concentration increases, both electrical conductivity and thermal conductivity increase but the opposite is true of the Seebeck coefficient, as shown in Fig. 2.

Due to the inter-relationship among thermoelectric factors, ZT has been around for many years during the last century. Two strategies to design high-performance thermoelectric materials are proposed. The first one is the framework of phonon-glass electron-crystal (PGEC), in which glass-like thermal properties and crystal-like electrical properties are required in one system [¹²] and only small progress has been made. The other strategy, as pointed out by Hicks and Dressalhaus [¹³,¹⁴], is nanostructural engineering, in which the quantum confinement can weaken the inter-relationship among the transport coefficients and many progresses have been made.

Enhancing thermoelectric performance using nanostructural engineering

Tables 1 and 2 summarize the ZT obtained in experimental samples in recent years based on Bi₂Te₃ (working temperature usually at 200–500 K) and IV–VI family (working temperature usually at 600–900 K), respectively. Using nanostructural engineering, the highest ZT of these families can even exceed 2, as illustrated in Fig. 3. For instances, in the work of Venkatasubramanian et al. [¹⁵], a figure of merit of 2.4 can be observed in p-type Bi₂Te₃/Sb₂Te₃ at 300 K.

Nanostructured engineering can enhance the thermoelectric performance by lowering the thermal conductivity. The reason comes from the stronger phonon scattering induced by the increasing nano-surfaces and interfaces in nano-size samples. It should be mentioned that the effect of nanostructures on reducing thermal conductivity is significant at low temperatures. At a high temperature range, the contribution of short wave phonons to the lattice thermal conductivity will be dominant and therefore point defects will have much stronger effects on the lattice thermal conductivity than nanostructures.

Nanograin/interface effect

Both Boukai et al. [⁶⁸] and Hochbaum et al. [⁶⁹] investigated the efficient thermoelectric performance of silicon nanowires by varying the nanowire size and their studies indicated that the improved efficiency originates from phonon effects (a three-dimensional to one-dimensional crossover of the phonons participating in phonon drag). Poudel et al. [²⁵] observed a ZT of 1.4 at 373 K in the p-type nanocrystalline BiSbTe bulk alloy and found that the improvement results from the low thermal conductivity were caused by grain boundaries and defects. Miao et al. [⁷⁰] concluded that the hollow structure of titanate nanotubes was responsible for the ultralow thermal conductivity, which greatly enhanced their thermoelectric properties. Li et al. [⁷¹] synthesized SnTe particles with controlled sizes from micro-scale to nano-scale and found that the ZT of the specimen using 165-nm-sized nano-particles was about 2.3 times that of the SnTe bulk samples due to the enhanced phonon scattering. Yang et al. [⁷²] found that the lattice thermal conductivity of nanoscale three dimensional Si phononic crystals was decreased by 500 times compared with that of porous Si, which led to a 26 times increase in ZT. He et al. [⁷³] showed that YbAl₃ from the nanometer to mesoscopic scales can effectively scatter phonons and remarkably decrease the lattice thermal conductivity, which produced a 74% increase in ZT.

Nano particles/inclusions effect

Zhao et al. [⁷⁴] achieved dual control of phonon- and electron-transport properties by embedding nanoparticles of a soft magnetic material in a thermoelectric matrix and thereby improved the thermoelectric performance of the resulting nanocomposites. Pei el al. [⁷⁵] found that PbTe with nanoscale Ag₂Te precipitates and La doping had a low lattice thermal conductivity. In the work of Johnsen et al. [⁵⁸], the nanostructuring in (PbS)_1–x(PbTe)_x samples led to substantial decreases in lattice thermal conductivity relative to pristine PbS. Gahtori et al. [⁷⁶] reported a ZT of 2.1 at 973 K in Cu₂Se with different nanoscale dimensional defect features, in which the low thermal conductivity origined from the enhanced low-to-high wavelength phonon scattering by different kinds of defects. Ahmad et al. [⁷⁷] reported a ZT of 1.81 at 1100 K in p-type SiGe alloys since YSi₂ nanoinclusions formed coherent interfaces with SiGe matrix and facilitated reduction in the grainsize of SiGe, which greatly reduced the thermal conductivity.

In addition, many other researchers conducted a lot of research in reducing the thermal conductivity in the systems of grapheme [⁶³,⁷⁸], carbon nanotubes [⁶¹,⁷⁹], graphynenanoribbons [⁸⁰,⁸¹], PbTe family [³⁷,⁶⁴,⁸²,⁸³], and Bi₂Te₃ nanowires [⁵¹].

The electrical properties can be tuned as well to enhance the thermoelectric properties. The electrical conductivity can usually be increased by enhancing the electron mobility or altering the electronic structures. Nanostructuring can enhance the density of states near Fermi level via quantum confinement, and therefore, increase the thermopower, which provides a way to decouple the thermopower and electrical conductivity [⁸⁴]. For example, Ginting et al. [⁸⁵] synthesized composites with nano-inclusions of n-type (PbTe_0.93−xSe_0.07Cl_x)_0.93(PbS)_0.07 while the composites with nano-inclusions enhanced the Seebeck coefficient in a dilute Cl^- doped compound and led to a ZT of 1.52 at 700 K.

Theoretical calculation in low-dimensional thermoelectric materials

In recent years, the research into thermoelectric materials has achieved a great success in the combination of theoretical calculations [⁸⁶]. Based on the start-of-the-art density functional theory, several computational methods have been employed in the prediction of high-performance thermoelectric materials and exploration of the enhancement mechanism. In the heat transport field, there are typically three kinds of methods which are used to study the thermal properties. This section will concentrate on the theoretical method of thermal transport properties using the molecular dynamics (MD) [⁸⁷,⁸⁸], Boltzmann transport equation [⁸⁹–⁹¹], and non-equilibrium Green’s function method [⁹²–⁹⁴], respectively. Generally, these methods adopt the potential data from the first-principles density functional theory.

Theoretical methods

Molecular dynamics

Based on Newton’s laws of motion, MD can be used in the study of heat transport. Equilibrium MD adopts the Green-Kubo formula to calculate the thermal conductivity, as shown below.

(5){\mathit{\kappa }}_{\alpha \beta }={\displaystyle \frac{\mathrm{1}}{V{k}_{\mathrm{B}}{T}^{\mathrm{2}}}}{\displaystyle \underset{\mathrm{0}}{\overset{\infty }{\int }}\langle {\mathit{J}}_{\alpha }\left(t\right)\cdot {\mathit{J}}_{\beta }\left(t\right)\rangle }\mathrm{d}t,

where κ_αβ, V, k_B, and T are the thermal conductivity tensor, volume, Boltzmann constant, and absolute temperature, respectively. J_α and J_β are the heat flow along the α and β direction, respectively.

Non-equilibrium MD obtains the thermal conductivity of the system according to Fourier’s law. By introducing a gradient of temperature or heat flow density into the system, the heat flow can be calculated as

(6){\mathit{J}}_{\alpha }=-{\displaystyle \sum _{\beta }\frac{\partial T}{\partial x_{\beta }}}.

Boltzmann transport equation

The phonon (lattice) thermal conductivity can be calculated by employing the phonon Boltzmann transport equation with relaxation time approximation (RTA) according to the following formula.

(7){\mathit{\kappa }}_{\mathrm{ph},\alpha \beta }={\displaystyle \frac{\mathrm{1}}{V}}{\displaystyle \sum _{\lambda }{C}_{\mathrm{ph},\lambda }{\mathit{\nu }}_{\lambda \alpha }}{\mathit{\nu }}_{\lambda \beta }{\tau }_{\lambda \alpha },

where α and β denote the components of the second-order tensor k_ph. In addition, C_l, ν, and t denote the phonon mode volumetric specific heat, group velocity, and phonon lifetime, respectively [⁸³].

The RTA phonon lifetime can be computed according to the Matthiessen rule where phonon-phonon scattering (t^ph), isotope scattering (t^iso), and boundary scattering (t^b) are fully taken into consideration [⁸⁹].

(8){\displaystyle \frac{\mathrm{1}}{{\tau }_{\lambda }}}={\displaystyle \frac{\mathrm{1}}{{\tau }_{\lambda }^{\mathrm{ph}}}}+{\displaystyle \frac{\mathrm{1}}{{\tau }_{\lambda }^{\mathrm{iso}}}}+{\displaystyle \frac{\mathrm{1}}{{\tau }_{\lambda }^{\mathrm{b}}}}.

The electronic transport coefficients can be computed based on the Boltzmann transport equation. The Seebeck coefficient S and electrical conductivity s can be calculated by

(9)S={\displaystyle \frac{e{k}_{\mathrm{B}}}{\sigma }}{\displaystyle \int \mathrm{d}\epsilon \left(-{\displaystyle \frac{\partial f_{\mathrm{0}}}{\partial \epsilon }}\right)}\Xi \left(\epsilon \right){\displaystyle \frac{\epsilon -\mu }{k_{\mathrm{B}}T}},

(10)\sigma =e^{\mathrm{2}}{\displaystyle \int \mathrm{d}\epsilon \left(-{\displaystyle \frac{\partial f_{\mathrm{0}}}{\partial \epsilon }}\right)}\Xi \left(\epsilon \right),

where \Xi \left(\epsilon \right)={\displaystyle \sum _k{\mathit{\nu }}_k{\mathit{\nu }}_k{\tau }_k} denotes the transport distribution; m, ε, e, and k_B are the chemical potential, electron energy, unit charge, and Boltzmann constant, respectively. In addition, f₀ is the Fermi distribution function, ν is the group velocity, and t is the relaxation time at the k state [⁹⁵,⁹⁶].

Non-equilibrium Green’s function

When the transport scale is smaller than the mean free path (MFP), the ballistic regime is valid. In such a condition, the non-equilibrium Green’s function method can be effectively used in the study of transport properties. Generally, a typical model of the NEGF can be described as the “left lead-conductor-right lead” (LCR) configuration, as demonstrated in Fig. 4. The conductor can be set to be exactly the same as the leads (in the case of perfect crystal) or totally different from the leads (in the case of interface).

To investigate the thermoelectric properties, both electronic and phononic transport should be studied. For ballistic electronic transport, the retarded Green’s function of the central conductor is

(11){\mathit{G}}^{\mathrm{r}}={\left[E{\mathit{S}}_{\mathrm{C}}-{\mathit{H}}_{\mathrm{C}}-{\mathit{\Sigma }}_{\mathrm{L}}^{\mathrm{r}}-{\mathit{\Sigma }}_{\mathrm{R}}^{\mathrm{r}}\right]}^{-\mathrm{1}},

where E, H_C, and S_C are the electron energy, Hamiltonian and overlap matrix, respectively; and the self-energy term S^r can be obtained as

(12){\mathit{\Sigma }}_{\mathrm{L}}^{\mathrm{r}}={\mathit{H}}_{\mathrm{LC}}^{†}{\mathit{g}}_{\mathrm{L}}^{\mathrm{r}}{\mathit{H}}_{\mathrm{LC}},\hspace{0.17em}\hspace{0.17em}{\mathit{\Sigma }}_{\mathrm{R}}^{\mathrm{r}}={\mathit{H}}_{\mathrm{CR}}{\mathit{g}}_{\mathrm{R}}^{\mathrm{r}}{\mathit{H}}_{\mathrm{CR}}^{†},

where g^r is the retarded surface Green’s function from semi-infinite lead. Besides, H^LC (H^CR) denotes the Hamiltonian matrix between the left (right) leads and the central conductor. The electronic transmittance matrix T(E), which is significant in electronic transport, can be obtained by

(13){\mathit{\Gamma }}_{\beta }=i\left({\mathit{\Sigma }}_{\beta }^{\mathrm{r}}-{\mathit{\Sigma }}_{\beta }^{\mathrm{a}}\right),\hspace{0.17em}\hspace{0.17em}\beta =\mathrm{L,}\hspace{0.17em}R,

(14)\mathit{T}\left(E\right)=T\mathrm{r}\left({\mathit{G}}^{\mathrm{r}}{\mathit{\Gamma }}_{\mathrm{L}}{\mathit{G}}^{\mathrm{a}}{\mathit{\Gamma }}_{\mathrm{R}}\right),\hspace{0.17em}{\mathit{G}}^{\mathrm{a}}={\left({\mathit{G}}^{\mathrm{r}}\right)}^{†}.

For convenience, Lorenz functions L_n are introduced to calculate the thermoelectric factors

(15)L_n\left(\mu ,T\right)={\displaystyle \frac{\mathrm{2}}{h}}{\displaystyle \int \mathrm{d}E\mathit{T}\left(E\right)}\times {\left(E-\mu \right)}^n\times \left[-{\displaystyle \frac{\partial f\left(E,\mu ,T\right)}{\partial E}}\right],

(16)f\left(E,\mu ,T\right)={\displaystyle \frac{\mathrm{1}}{{\mathrm{e}}^{\frac{E-\mu }{k_{\mathrm{B}}T}}+\mathrm{1}}},

where f(E, m, T) is the Fermi-Dirac distribution function and m, T, and h are the chemical potential, absolute temperature, and Planck constant, respectively. According to Eqs. (17)–(19), the electronic conductance s, Seebeck coefficient S, and the electronic thermal conductance k_el, can be derived, respectively.

(17)\sigma =q^{\mathrm{2}}{L}_{\mathrm{0}},

(18)S={\displaystyle \frac{\mathrm{1}}{qT}}\times {\displaystyle \frac{L_{\mathrm{1}}}{L_{\mathrm{0}}}},

(19){\kappa }_{\mathrm{el}}={\displaystyle \frac{\mathrm{1}}{T}}\times \left(L_{\mathrm{2}}-{\displaystyle \frac{L_{\mathrm{1}}^{\mathrm{2}}}{L_{\mathrm{0}}}}\right).

To obtain the ZT, the phononic thermal conductance has to be calculated, which can be determined from the phonon transport part. The calculation of phonon transmittance is similar to that of the electron transmittance in the electronic transport part which has been described above. By replacing the Hamiltonian matrix and electron energy E with the interatomic force constant (F_C) matrix and phonon frequency ω, the phonon transmittance T(ω) can be calculated as

(20){\mathit{G}}^{\mathrm{r}}={\left[{\left(\omega +\mathrm{i}\eta \right)}^{\mathrm{2}}-{\mathit{F}}_{\mathrm{C}}-{\mathit{\Sigma }}_{\mathrm{L}}^{\mathrm{r}}-{\mathit{\Sigma }}_{\mathrm{R}}^{\mathrm{r}}\right]}^{-\mathrm{1}},

(21)\mathit{T}\left(\omega \right)=T\mathrm{r}\left({\mathit{G}}^{\mathrm{r}}{\mathit{\Gamma }}_{\mathrm{L}}{\mathit{G}}^{\mathrm{a}}{\mathit{\Gamma }}_{\mathrm{R}}\right).

After that, the phononic thermal conductance k_ph can be calculated by

(22){\kappa }_{\mathrm{ph}}\left(T\right)={\displaystyle \frac{\hslash }{\mathrm{2}\mathrm{\pi }}}{\displaystyle {\mathrm{\int }}_{\mathrm{0}}^{\infty }{\rm T}\mathit{T}\left(\omega \right)\omega {\displaystyle \frac{\partial g(\omega ,T)}{\partial T}}\mathrm{d}\omega },

(23)g\left(\omega ,T\right)={\displaystyle \frac{\mathrm{1}}{{\mathrm{e}}^{\frac{\hslash \omega }{k_{\mathrm{B}}T}}-\mathrm{1}}},

where g(w, T) is the Bose-Einstein distribution function, while \hslashand k_B denote the reduced Planck constant and Boltzmann constant, respectively.

Ballistic thermoelectric transport

In the past few years, the research group in Guangdong Engineering Technology Research Centre for Advanced Thermal Control Material and System Integration in Sun Yat-sen University has paid a lot of attention to the theoretical study of ballistic thermoelectric transport by using the density functional theory and non-equilibrium Green’s function method. The emphasis has been laid on the two-dimensional systems including graphyne, transition metal dichalcogenides (TMDs) and the VA group family.

Graphyne

Shortly after the discovery of graphene, graphyne, another member of the carbon family, attracted researchers’ attention. In Ref. [⁹⁷], the thermoelectric transport properties of graphyne nanotubes were investigated by using the non-equilibrium Green’s function method, as implemented in the density functional based tight binding framework. Figure 5 shows the previous study with regard to the thermoelectric properties of new emerging two-dimensional materials. Figure 5(a) reveals that both the band gap and thermoelectric figure of merit ZT of graphyne nanotubes show a damped oscillation as the tube diameter increases. In addition, by introducing hydrogenation, the thermoelectric performance is reduced. The thermoelectric performance of graphyne nanotubes is much better than that of graphene according to the theoretical calculation.

TMDs

Of all newly proposed two-dimensional materials, TMDs are believed to possess the lowest thermal conductivity. Therefore, these TMDs families were studied as new thermoelectric materials in Ref. [⁹³]. Four kinds of monolayer TMDs (MoS₂, MoSe₂, WS₂, WSe₂) were investigated. It was discovered that the monolayer WSe₂ harbored the highest thermoelectric figure of merit (ZT = 0.91) at room temperature. The nanotubes that scrolled from these monolayer TMDs were also investigated as a comparison. A degeneration in thermoelectric performance was observed from monolayers to nanotubes, as shown in Fig. 5(b).Following this research, in Ref. [⁹⁸] the thermoelectric properties of WSe₂ nanoribbons were studies since monolayer WSe₂ was found to exhibit the most excellent thermoelectric performance. The ZT of WSe₂ nanoribbons was higher than that of monolayer WSe₂ in both armchair and zigzag ribbons. The highest value of 2.2 could be observed in armchair WSe₂ nanoribbons, as depicted in Fig. 5(c).

VA group family

In the framework of 2D systems, the buckled and puckered systems which consist of the VA elements (denoted as arsenene, antimonene and bismuthene) were also studied. The first-principles calculation indicated that buckled antimonene harbored a thermoelectric figure of merit ZT of 2.15 at room temperature. The ZT could even be enhanced to 2.9 at a3% biaxial tensile strain. This is probably the highest value that has ever been reported in pristine 2D materials, as can be seen from Fig. 5(d). The enhancement mainly results from both tuning the electronic structures and reducing the thermal conductance [⁹⁴].

Low-dimensional thermoelectric materials

As pointed out in Section 2, nanostructural engineering is now acting as an effective strategy to enhance the thermoelectric performance [⁹⁹,¹⁰⁰]. Lots of low-dimensional materials have been adopted and studied. Here, the item of low dimensional means the size of the shape or crystal structure. These families can be summarized according to the diverse dimensionality, as are introduced in the following subsections. It should be mentioned that low-dimensional materials are difficult to fabricate precisely due to the high requirement in nanoscale samples. Therefore, many of these results have not yet been realized in experiments. However, the theoretical calculation can provide a valuable guidance to the future research and as the development of nanostructuring technology proceeds, nanoscale materials with atomic accuracy may be prepared.

One-dimensional nanotubes and nanoribbons

Much research based on the one-dimensional nanoribbons and nanotubes has been conducted. As is known, the thermoelectric application of graphene has been hampered due to its zero bandgap in the electronic structure. Considerable research has been carried out to open the bandgap of graphene, such as grapheme nanoribbons and nanotubes [¹⁰¹]. Sevinçli et al. [⁶³,¹⁰²] showed that by geometrical structuring and isotope cluster engineering, the thermal conductance of grapheme nanoribbons could be reduced by 98.8% and the thermoelectric figure of merit could be as high as 3.25 at 800 K. Chang et al. [¹⁰³] studied the grapheme nanoribbons perforated with an array of nanopores which exhibited a high ZT of ~5 at room temperature. Yeo et al. [¹⁰⁴] studied the thermoelectric performance of strained grapheme nanoribbons and discovered that the tensile strain increased the ZT value of certain armchair grapheme nanoribbons.

More research focusing on the thermoelectric performance of other family are presented, such as the experimental study in carbon nanotubes [¹⁰⁵,¹⁰⁶], silicon nanowire [⁶⁸,⁶⁹], titanate nanotubes [⁷⁰], Bi₂Te₃ nanowires [⁵¹,¹⁰⁷] and the theoretical study in carbon nanotubes [⁷⁹,⁹²,¹⁰⁶,¹⁰⁸], InSe nanotubes [¹⁰⁹], phosphorene nanoribbons [⁹⁶], graphyene nanoribbons and nanotubes [⁸⁰,⁹⁷], and transition metal dichalcogenide nanoribbons and nanotubes [⁹³,⁹⁵,⁹⁸].

Two-dimensional mono- and few-layers materials

As for two-dimensional systems, much work has been devoted to the study of TMDs. Huang et al. [¹¹⁰,¹¹¹], Chen et al. [⁹³] and Tahir and Schwingenschlögl [¹¹²] studied the monolayer TMDs and found that the monolayer TMDs exhibited a great potential in thermoelectric performance. Huang et al. [¹¹¹] and Wickramaratne et al. [¹¹³] studied the layer dependence of few-layer TMDs and discovered that thermal conductance per thickness approached bulk as the thickness increased. In the work of Lee et al. [¹¹⁴], layer mixing was predicted to be a promising way of improving the thermoelectric properties. Bhattacharyya et al. [¹¹⁵] and Guo [¹¹⁶] studied the stain effect on the thermoelectric performance of TMDs. They observed that the electronic structures of the TMDs family were sensitive to the applied strain and the thermoelectric figure of merit could be tuned by the strain level.

Many theoretical workers also devoted their effort to the design of high-performance two-dimensional thermoelectric candidates. Table 3 summarizes the calculated figure of merit for many new emerging two-dimensional materials. It can be seen that the TMDs and the VA group families are both promising candidates for thermoelectric application.

Nanocomposites and heterostructures

Nanocomposites and heterostructures are also adopted as candidates of thermoelectric materials. Zhang et al. [⁶¹] fabricated the Bi₂Te₃-Te micro-nanoheterostructure and discovered a ZT of ~0.4 at room temperature for such samples, with an enhancement of 40% compared to those without nanoscale heterostructures. Carrete et al. [¹²²] theoretically investigated the thermoelectric transport properties of hybrid thiophene/SiGe superlattices and found that the ZT was twice as those in bulk SiGe. Savelli et al. [¹²³] fabricated the Ti-based silicide quantum dot superlattices by reduced-pressure chemical vapor deposition and observed a trifold increase in the power factor compared with SiGe thin films. Duan et al. [¹²⁴] observed that the thermoelectric performance of graphene could be significantly enhanced in graphene/hBNvdW device. Yin et al. prepared the M_g2Si_1−xSn_x/SiC nano-composites and obtained a ZT of 1.2 at 750 K owing to the introduction of SiC nano-additives. In the work of Luo et al. [¹²⁵], ZnX acted as a nanoscalehetero structure barrier blocking in CuInTe₂, which led to an enhanced Seebeck coefficient and reduced thermal conductivity, with a ZT of 1.52. Yin et al. [¹²⁶] prepared Mg₂Si_1−xSn_x/SiC nano-composites with a maximum ZT value of ~1.20 at 750 K.

Perspective on the design of high-performance thermoelectric materials

With the advancement of nanotstructural technology, the fabrication of nanoscale thermoelectric materials is feasible. In this review, the importance of nanostructural engineering in the design of high-performance thermoelectric materialsis mainly emphasized. High ZT materials can be achieved in nanoscale family due to the quantum confinement effect.

The theoretical prediction regarding nanostructural systems has been conducted in recent years, and time will tell whether these systems exhibit excellent performance in experimental testing. Promising thermoelectric candidates may be discovered in the systems which possess heavy elements. Another suggestion for the design of high-performance thermoelectric materials would be the lowering of the dimensionality. For instance, preparing the half-Heusler alloys in nanoscale films or composites with nanoparticle additives might be an effective way to achieve this goal. In addition, research into thermoelectric materials regarding spin needs our attention. The spin Seebeck effect may provide a new opportunity in this field. Moreover, lots of topological insulators are found to be excellent thermoelectric candidates and the mechanism is still unclear.

The fast development in state-of-the-art first-principles method in the study of electron and phonon transport has also provided another strategy regarding material design. It is believed that by combining the non-equilibrium Green’s function (adopted in nanoscale systems) and the Boltzmann transport equation (adopted in mesoscale systems), one may effectively predict the properties of newly proposed thermoelectric materials. That would significantly enhance the explosive growth in excellent thermoelectric candidates. The blooming research into thermoele-ctric materials will significantly enhance their application in the energy field, which may act as an effective way to resolve the global energy crisis.

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