The rising demand for energy supply, the elimination of greenhouse gas due to carbon-based energy sources, and the enhancement in the energy consumption efficiency have sparked significant research into alternative energy sources and energy harvesting technologies. One of the promising candidates is thermoelectricity, in which heat is transferred directly into electricity.^[1–3] Because of the distinct advantages of thermoelectric devices: no moving parts, long steady-state operation period, zero emission, precise temperature control and capable of function in extreme environment,^[4–6] the prospect of thermoelectric applications is promising, especially for power generation and refrigeration. For the power generation mode, energy is captured from waste, environmental, or mechanical sources, and converted into an exploitable form—electricity by thermoelectric devices.^[7–10] Thermoelectric materials are also able to generate power by using solar energy to create a temperature difference across thermoelectric materials.^[11,12] Nuclear reactors and radioisotope thermoelectric generators can be used as spacecraft propulsion and for power supply.^[13–16] For the refrigeration mode, micro thermoelectric cooling modules can be installed in the integrated circuit to tackle the heat-dissipation problem, and flexible thermoelectric materials can be equipped in the uniform of people working in the extreme environment to serve as the wearable climate control system.^[17]

The wide application of thermoelectric materials requires high energy conversion efficiency and the enhancement involves the simultaneous management of several parameters. First, Seebeck coefficient (S), the generated voltage over the applied temperature, is defined. Since thermoelectric materials involve charge carrier transport and heat flow, electrical conductivity (σ) and thermal conductivity (κ) should be taken into account. To ensure a high output power, both S and σ should be as large as possible. To maintain the temperature difference across the material, a low κ is preferred. Accordingly, the dimensionless figure-of-merit, zT has been defined to quantify the thermoelectric performance at a given temperature (T), namely zT = S²σTκ.^[1,18,19] The criteria of good thermoelectric materials are high power-factor (S²σ and low κ. S²σ can be enhanced by resonant state doping,^[1,20,21] minority carrier blocking,^[22] band convergence,^[23–27] reversible phase transition,^[28–30] and quantum confinement;^[31,32] and κ can be reduced by nanostructuring,^[33–39] hierarchical architecturing,^[40–42] producing dislocations,^[43–45] introducing stacking faults,^[46,47] and incorporating nanoprecipitates into the matrix.^[48–53]

Owing to the intensive theoretical studies and experimental demonstrations over the past decades, zT has been improved dramatically. Figures 1(a) and 1(b) plot the achieved state-of-the-art zT values for both n-type and p-type materials working over a wide temperature range. Bi₂Te₃, PbTe, and GeSi are the classical thermoelectric materials working near room-, mid-, and high-temperature, respectively.^[5,54] Through band alignment, Na-doped PbTe_1−xSe_x exhibited zT up to 1.8.^[23] In addition, nanostructuring successfully improved zT for GeSe to over 1.^[55] Moreover, SnTe, as an environmentally friendly lead-free thermoelectric candidate, exhibited zT over 1.2 through producing band convergence and introducing nanoprecipitates.^[56–61] The lead-free SnSe with earth-abundant elements has attracted wide attention due to the reported record-high zT of 2.6 along the b axis of the single crystal.^[28] Later on, Na-doping was employed to significantly enhance the mid-temperature zT for SnSe single crystal.^[62–66]

Fig. 1.

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Fig. 1. (color online) The state-of-the-art zT values for n-type (a) Bi2Te2.7Se0.3,[37] Mg2Sn0.75Ge0.25,[25] PbSe1−xBrx,[67] YbxCo4Sb12,[68] and GeSi;[69] p-type (b) Ge0.89Sb0.1In0.01,[47] Bi0.5Sb1.5Te3,[70] TePbTe0.85Se0.15,[23] Sn0.98Bi0.02Te-(HgTe)0.03,[60] FeNb0.8Ti0.2Sb,[71] AgSbTe1.85Se0.15,[46] and GeSi.[55] (c) Corresponding thermoelectric efficiency calculated using zTavg values of these summarized materials. (d) The schematic diagram of a multi-layer thermoelectric device assembled from materials working at high (HT), mid (MT), and room (RT) temperatures along the thermal gradient from the hot side to the cold side.

The efficiency (ϕ_TE) of a thermoelectric device as a function of zT is calculated by^[72,73]

In the above equations, Q_H is the net heat flow rate, W is the generated electric power, T_C is the cold side temperature, and T_H is the hot side temperature, respectively.

According to Eq. (1), the dependence of thermoelectric efficiency on average zT (zT_avg) for single-leg state-of-the-art thermoelectric materials is plotted in Fig. 1(c), in which the cold side temperature is set as 300 K, and the hot side temperature is the corresponding temperature for peak zT. The efficiency of thermoelectric materials for room-temperature power generation is lower than 10%, for mid-temperature applications, the peak efficiency could be ∼25%, and for high-temperature applications, the efficiency is 22%.

To allow a maximum energy harvesting efficiency from a heat source, a thermoelectric device can be assembled by triple layers of p–n-junction arrays in a tandem mode, as shown in Fig. 1(d). The first layer is high-temperature thermoelectric materials, while the second and third layers are respectively built from mid- and low-temperature candidates as regenerative cycles. So far, Bi₂Te₃ families are still the most promising room-temperature thermoelectric candidates. It is necessary to dedicate significant research into this classical thermoelectric category.

In this review, we provide an overview of the development of Bi₂Te₃-based thermoelectric materials, including the fundamentals on thermoelectric effects, current research progress, and new trends in Bi₂Te₃-based thermoelectric materials. Firstly, we study the fundamentals of thermoelectric effects and find that thermoelectric effects are substantially the re-distribution of electrons disturbed by temperature difference or extra potential and the attendant energy exchange between the free charge carriers and environment. Also, we derived the model of electronic transport coefficients from the Boltzmann equation (BTE). On this basis, we performed simulations of the effect of materials’ parameters on electronic transport coefficient. Secondly, we summarized the features of Bi₂Te₃-based thermoelectric materials and the correspondingly developed strategies for enhancing their thermoelectric performance. Finally, we quantitatively analyzed the reported data for Bi₂Te₃-based thermoelectric materials, which is believed to provide innovative directions for developing high-performance thermoelectric candidates in broader materials.

Thermoelectric effect includes Seebeck effect and Peltier effect.^[74] Seebeck effect originates from the charge current flow driven by the temperature difference. Reversibly, the charge current flow driven by extra applied voltage can generate temperature difference across the material, which is Peltier effect.^[75,76] In this regards, thermoelectric effect involves how temperature difference or extra voltage disturb the distribution of free charge carriers and the attendant energy exchange.^[77]

At equilibrium, the distribution of free charge carriers, for instance, electrons, follows the Fermi–Dirac function, i.e.

Figure 2(a) shows a single-leg thermoelectric device consisting of a channel (thermoelectric material) with two contacts. T_i, u_i, and are temperatures, chemical potentials, and Fermi–Dirac functions for the two contacts (i = 1 and 2 representing the left and right contacts), respectively. The competition between and , i.e., , accounts for the charge current flow through the channel. Without temperature or potential disturbances, (i.e., T₁ = T₂ and u₁ = u₂), . When T₁ < T₂ but u₁ = u₂ (namely, applying a temperature difference) the transition of f₁ from 0 to 1 occurs over a wider energy window than f₂ does, which means at an energy higher than the chemical potential, , otherwise . Electrons with energy higher than the chemical potential flow from the left contact to the right contact, while electrons with lower energy flow from the right contact to the left contact. Despite f₀, the other factor affecting the number of electrons at a certain energy is the density of states (DOS, g(E)), which describes the possible states of electrons at the energy level of E.^[80] In Fig. 2(a), the plotted g(E) corresponds to n-type semiconductors and increases with increasing energy level, indicative of more electron states at the higher energy level. Consequently, the net electron current flows from hot side to cold side, resulting in the hot side to be positive and the cold side to be negative. Thus, u₁ becomes lower than u₂, and the difference between u₁ and u₂ increases when more and more electrons accumulate on the code side. Note that negative electrode has a higher potential for electrons. Figure 2(b) describes the updated at equilibrium, and there is no net electron flow.

Fig. 2.

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	Fig. 2. (color online) Seebeck effect with charge current driven by the temperature difference for n-type thermoelectric materials: (a) the initial stage and (b) equilibrium. (c) Peltier effect with charge current driven by the voltage for n-type thermoelectric materials: (c) the initial stage and (d) equilibrium.

For the Peltier effect, the temperature difference is generated by charge current flow, which is driven by the external voltage. Figure 2(c) is the schematic illustrating the Peltier effect, in which an external voltage is applied to the two contacts, for example, left contact being negative and right contact being positive, i.e., u₁ < u₂ for electrons, leading to the electron current flows from left to right. For simplicity, the channel is regarded as an elastic resistor, in which the electrons current does not lose energy and energy exchange only occurs at the two contacts. For the right contact, the arrival electrons with a higher energy of E_e should release energy by an amount of Q_rel = E_e−u₂ per each electron. On the other hand, the provided electrons from the left contact should absorb energy to climb to the higher energy level of E_e and the required energy value is Q_abs = E_e−u₁ per each electron. Accordingly, the left contact is cooled down, resulting in T₁ > T₂. Therefore, varies, as shown in Fig. 2(d). Finally, there is no net electron flow at the equilibrium. Note that within the framework of elastic resistor, Q_rel−Q_abs = u₁−u₂, which is the potential difference provided by the external power; however, the practical thermoelectric materials are inelastic resistor because of the inelastic electron-electron and electron-nucleus collisions, which means electron current loses energy inside the thermoelectric materials in the form of heat, resulting in Q_rel−Q_abs = u₁−u₂, namely the input power is higher than the generated heat energy difference.

Based on above discussion, charge current flow results from the disturbance of Fermi–Dirac function, which can be motivated by the temperature difference and the external potential. Seebeck effect is the Fermi–Dirac function disturbed by the temperature difference. Working under the power generation mode, the cold side corresponds to the negative pole of n-type, while the hot side corresponds to the negative pole of p-type. Peltier effect is the energy exchange between the free electrons and the contacts when Fermi–Dirac function is disturbed by an external potential. Working under the refrigeration mode, the negative pole is cooled down for n-type, while positive pole is cooled down for p-type.

Based on above equations, we calculated the electronic transport coefficients as a function of η for Bi₂Te₃. Figure 3(a) shows the calculated σ as a function of η at 300 K with the inset illustrating the variation of η in the band structure. Note that we used E_g = 0.15 eV, and set the VB maximum as 0, which means the CB minimum is at 0.15 eV in energy. Therefore, at 300 K, η = −5.8 corresponding to the CB minimum. Moreover, considering the identical band effective mass for CB and VB, the middle point of band gap region is at η = ∼ −3. As a consequence, σ for n-type (left side of −3) and p-type (right side of −3) is identical, and the total σ (blue curve) is generally superimposed with the CB component (red curve) for n-type and VB component (green curve) for p-type, respectively. Furthermore, in the whole studied η range, σ increases with enlarging |η| for either n-type or p-type. The observed characteristics of symmetry (i.e., the calculated curve as a function of η is symmetrical relative to the middle of band gap region) and superimposition (i.e., the total value is respectively superimposed with the CB/VB component for n/p-type situation) also appear in the other calculated thermoelectric properties.

Fig. 3.

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	Fig. 3. (color online) Calculated (a) S, (b) σ, (c) S2σ, (d) L, (e) κe, and (f) κe as a function of η at 300 K with the blue curve representing the total values, the purple curve representing the CB component, green curve representing the VB component.

Figure 3(b) shows the calculated S as a function of η at 300 K. The characteristics of symmetry and superimposition are also observed in |S|. When −5.8 > η > 0, the total S is different from each component contributed by either CB or VB, which reveals n/p-type transition, i.e., the bipolar conduction. The peak value of |S| depends on the onset of bipolar conduction, and |S| decreases with increasing |η| for either n-type or p-type. Based on the calculated S and σ, the plots of S²σ as a function of η at 300 K were obtained, as shown in Fig. 3(c). Likewise, S²σ also shows symmetrical and superimposing characteristics. Because of the bipolar conduction, the positions of total S²σ peaks are slightly different from the CB/VB components. If the η corresponding to the peak of S²σ is defined as the optimized η (η^opt), η^opt for is 0.25 and −6.05 for p-type and n-type, respectively.

Figure 3(d) shows the plots of L as a function of η at 300 K. We can observe the superimposing and symmetrical features, and L increases with increasing |η| . Based on the calculated σ and L, we calculated κ_e, shown in Fig. 3(e), from which κ_e increases with increasing |η| . Figure 3(f) shows the calculated κ_bi. As can be seen, κ_bi is prominent in the band gap region and reaches the maximum value in the middle of band gap region. Moreover, κ_bi decreases with increasing |η|, because large |η| makes it more difficult to activate minor carriers.

Based on above discussions, S and σ are inversely related to η, resulting in a peak for S²σ. Bipolar conduction has further limited the maximum values of S for n/p-type materials, therefore, the possible maximum values for S²σ is even smaller by considering both CB and VB. In addition to the electrical energy, the charge carriers can also transport thermal energy in the form of κ_e and κ_bi, which are anticipated to reduce the ultimate zT.

Based on the Kane band model, we can see S is only related to η and β(=k_BT/E_g). Apart from η and β, n_H, and μ_H are determined by , , and E_def. Therefore, σ, κ_e, and κ_bi are also related to these parameters. Through band engineering, we can tune these parameters to tailor the electronic transport. Here, we quantitatively predict the effects of , E_def, and E_g on the electronic transport properties. Note that from the Kane model equations, all thermoelectric properties are direct as a function of η. Here, we want to examine the variations of these thermoelectric properties with n_H.

Figure 4(a) shows the determined η with n_H ranging from 10¹⁸ cm⁻³ to 10²¹ cm⁻³ for evenly selected seven values from 0.2m₀ to 2m₀. With increasing n_H, η monotonically increases, and with increasing , η decreases for a given n_H, which results in the E_f corresponding to high n_H still resides in the band gap region for large . Thus, larger would unfavorably lead to a strong bipolar conduction. Based on the determined η, figures 4(b)–4(d) show the effects of on n_H-dependent S, μ_H, and S²σ, respectively. With increasing n_H, both S and μ_H increase and then decrease. Moreover, we observed that the calculated variation of S and μ_H at low n_H is different from the monotonic decreasing trends in both S and μ_H with increasing n_H calculated by the single band model (refer to the bold green lines in Figs. 4(b) and 4(c)). The observed difference suggests that, at low n_H region (band gap region), both S and μ_H calculated by the two bands model are lower than those from single band model, and the reason is ascribed to the bipolar conduction. Moreover, with increasing , S increases, while μ_H decreases, and μ_H is more sensitive to the variation of . As a consequence, S²σ decreases with increasing , as shown in Fig. 4(d). In addition, optimal n_H ( ) corresponding to the peak S²σ shifts to a higher value with increasing .

Fig. 4.

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	Fig. 4. (color online) (a) Determined η with nH ranging from 1018 cm−3 to 1021 cm−3 for evenly selected seven values from 0.2m0 to 2m0. Correspondingly calculated (b) S, (c) μH, and (d) S2σ as a function of nH for different values. The bold green lines in panels (b) and (c) are calculated using single band model with for S and μH, respectively.

Figure 5 shows the effects of E_g on thermoelectric properties. Firstly, with increasing n_H from 10¹⁸ cm⁻³ to 10²¹ cm⁻³, the determined η for evenly selected seven E_g values from 0.1 eV to 0.5 eV is exhibited in Fig. 5(a). As can be seen, |η| tends to increases with increasing E_g for a given n_H. Figure 5(b) presents the plots of S as a function of n_H for different E_g values. Larger E_g produces larger S peak and shifts the peak of S to low n_H, which quantitatively verifies the effectiveness of E_g on suppressing bipolar conduction. The suppressed bipolar conduction due to large E_g is also demonstrated in the variation of μ_H (see Fig. 5(c)). Figure 5(d) shows the variations of S²σ with E_g, from which enlarging E_g can greatly enhance peak S²σ but does not change the significantly.

Fig. 5.

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	Fig. 5. (color online) (a) Determined η with nH ranging from 1018 cm−3 to 1021 cm−3 for evenly selected seven Eg values from 0.1 eV to 0.5 eV. Correspondingly calculated (b) S, (c) μH, and (d) S2σ as a function of nH for different Eg values.

Lastly, we studied the impacts of E_def on electronic transport coefficients. Because E_def characterizes the strength of phonon scattering on free charge carriers,^[93,94] we anticipate that E_def would not affect η and bipolar conduction. This has been confirmed by the determined η and the correspondingly calculated S, as shown in Figs. 6(a) and 6(b), respectively. However, small E_def can greatly increase μ_H (refer to Fig. 6(c)). As a consequence, small E_def leads to high S²σ, which can be seen from Fig. 6(d). Interestingly, E_def does not change .

Fig. 6.

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	Fig. 6. (color online) (a) Determined η with nH ranging from 1018 cm−3 to 1021 cm−3 for evenly selected seven Edef values from 5 eV to 20 eV. Correspondingly calculated (b) S, (c) μH, and (d) S2σ as a function of nH for different Edef values. The bold green lines in panels (b) and (c) are calculated using SKB model with Edef = 8 eV for S and μH, respectively.

It is well documented that bipolar conduction is detrimental to the thermoelectric performance by generating κ_bi and reducing S. Here, we emphasized the significance of suppressing bipolar conduction by enlarging E_g. Figures 7(a) and 7(b) show the calculated κ_bi and S as a function of n_H for evenly selected seven E_g values from 0.1 eV to 0.5 eV. Because bipolar conduction is more notable at high temperature, the calculation covers the results at 300 K, 400 K, and 500 K. As can be seen, at high temperature, κ_bi is large but S is small, and enlarging E_g can greatly reduce κ_bi but increases S.

Fig. 7.

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	Fig. 7. (color online) Calculated (a) κbi, and (b) S as a function of nH at 300 K, 400 K, and 500 K for evenly selected seven Eg values from 0.1 eV to 0.5 eV.

Based on above discussions, we can see that , E_g, and E_def can significantly affect S²σ, but only is able to change the . To determine , we calculated S²σ as functions of n_H and , shown in Fig. 8(a). Based on this, the values corresponding to different are plot as a white curve in Fig. 8(b), in which the background is the contour plot of S²σ as functions of n_H and . As can be seen, the variation of contour plot follows the white curve. To enhance thermoelectric performance, we want to ensure the experimental n_H value close to .

Fig. 8.

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	Fig. 8. (color online) (a) Calculated S2σ as functions of nH and , and (b) the corresponding contour map with the white curve indicating the -dependent .

Bi₂Te₃-based materials share the same rhombohedral crystal structure of the space group (see Fig. 9(a)). This category consists of five-atom layers arranged along the c axis, known as quintuple layers. The coupling is strong between two atomic layers, but is much weaker within one quintuple layer, predominantly of the van der Waals type. Lattice parameters and band gap (E_g) of these layered materials are shown in Table 1. The electronic band structures of Bi₂Te₃ are shown in Fig. 9(c) with the selected high symmetry k points shown in Fig. 9(b). As can be seen, both the highest valence band and lowest conduction band have six valleys. Besides these two bands, the second conduction and valence band with energy separations of 30 meV and 20 meV, respectively.^[95]

Fig. 9.

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	Fig. 9. (color online) (a) crystal structure, (b) first Brillouin zone, and (c) band structure. Reproduced from Ref. [96].

Table 1.

Table 1.

Table 1. Physical properties of N2M3(N: Bi, Sb; M: Te, Se).[97,98] . Bi2Te3 Bi2Se3 Sb2Te3 Structure hexagonal hexagonal hexagonal a/Å 4.38 4.14 4.26 c/Å 30.48 28.64 30.45 Unit layer/Å 10.16 9.55 10.15 Band gap/eV 0.15 0.3 0.22

Table 1. Physical properties of N2M3(N: Bi, Sb; M: Te, Se).[97,98] .

Pnictogen (Bi and Sb) and chalcogenides (Te and Se) materials have been preferably studied for room-temperature thermoelectric applications.^[70] These materials share the same rhombohedral crystal structure of the space group (see Fig. 9). This category consists of five-atom layers arranged along the c axis, known as quintuple layers. The coupling is strong between two atomic layers, but is much weaker within one quintuple layer, predominantly of the van der Waals type. Lattice parameters and band gap (E_g) of these layered materials are shown in Table 1.

Based on above discussions, Bi₂Te₃ families crystalize in layered structures and consist of heavy atoms, which can potentially ensure low κ. Moreover, the narrow E_g can secure a high σ, and the large band degeneracy is also beneficial to produce a high S²σ. Because of these advantages of Bi₂Te₃ for thermoelectric applications, great efforts have been dedicated to enhancing the thermoelectric efficiencies. Table 2 summarizes the reported thermoelectric properties for both n-type Bi₂Te₃ and p-type Sb₂Te₃ based thermoelectric materials. As can be seen, zT of 1.2 has been achieved in n-type Bi₂Te₃,^[99–102] and zT of 1.56 has been obtained in p-type Sb₂Te₃.^[103] The big difference between the n-type and the p-type materials is mainly due to the much lower S²σ in Bi₂Te₃, although the obtained lowest κ of n-type Bi₂Te₃ is even smaller than that of p-type Sb₂Te₃.

Table 2.

Table 2.

Table 2. Thermoelectric properties of the Bi2Te3-based materials prepared by different methods. . Material Type S2σ/10−4 W⋅m−1⋅K−2 κ (κl)/W⋅m−1⋅K−1 zT T/K Methoda) Nanostructuring Bi2Te3[104] n 11.9 0.46(0.25) 0.91 350 MSS+CP Bi0.5Sb1.5Te3[104] P 14.9 0.45(0.25) 1.2 363 MSS+CP Bi2Te2.7Se0.3[105] n 11 0.6 0.55 300 SG+SPS Bi2Te2.7Se0.3[106] n 11 0.6 0.54 300 SG+SPS Bi0.5Sb1.5Te3[38] p 28 0.7(0.4) 1.2 320 MSS+SPS Bi0.4Sb1.7Te3.0[107] p 9 0.35(0.16) 0.9 413 SG+SPS (Bi2Te3)0.85(Bi2Se3)0.15[108] n 12 0.68(0.45) 0.71 480 SG+SPS (Bi2Te3)0.8(Bi2Se3)0.2[109] n 9 0.53(0.38) 0.71 450 SG+SPS Bi0.5Sb1.5Te3[110] p 24 0.66(0.3) 1.13 360 MSS+SPS Bi2Te3[111] n 15.4 1.1 0.66 470 SG+HP Bi2Te3-Te[112] n 18.7 1.22(0.45) 0.6 390 SG+HP Bi2Te3[35] n 6.9 0.45(0.28) 0.62 400 SG+SPS Bi2Se3[113] n 4.4 0.42 0.35 400 LIE+HP Bi2Se3[114] n 4.7 0.41(0.3) 0.48 425 MSS+SPS S doped Sb2Te3[115] p 20.0 0.7(0.35) 0.95 423 MSS+CP Bulk materials Bi2Te3[116] p 20 0.78(0.36) 1.03 403 HPS Bi2Se3[117] n 6 0.97(0.4) 0.37 560 HPS Bi0.5Sb1.5Te3[70] p 44 1 1.4 373 BM+HP Bi0.5Sb1.5Te3[118] p 43 1 1.3 373 BMA+HP Bi2Te2.7Se0.3[119] n 26 1.08 1.04 400 BMA+HP Bi2Te3[102] n 33 1.1 1.2 425 BMA+HP Bi0.5Sb1.5Te3[120] p 38 0.85(0.48) 1.4 300 MA+HP Bi2Te2.79Se0.21[99] n 42 0.8(0.56) 1.2 357 HP Bi2Te2.3Se0.7[100] n 28 1.1(0.4) 1.2 445 MA+BM+HP Bi0.3Sb1.7Te3[100] p 1.3 380 MA+BM+HP Bi2Te2.925Se0.075[121] n 47 1.65(1.27) 0.85 (a–b) 293 THM Bi0.52Sb1.48Te3[103] p 35 0.65(0.25) 1.56 300 MS Cu0.01Bi2Te2.7Se0.3[122] n 31.2 1.1 1.06 373 BM+HP Bi2Te2.7Se0.3[101] n 53.8 1.87 1.18 410 BS Bi2(Te1−xSex)3-I(0.08%)[123] n 55 1.5(0.9) 1.1 340 ZM Bi2(Te0.5Se0.5)3-I 0.1%[123] n 25 1.42(0.45) 0.85 570 ZM a) The abbreviations used in the column of preparation method represent the following meanings: MSS = microwave solvothermal, CP = cold pressing, SG = solution grow, SPS = spark plasma sintering, HP = hot pressing, LIE = lithium ionic exfoliation, BMA = ball milling alloy, MA = melting alloy, HPS = high pressure synthesis, BS = Bridgman–Stockbarger, BM = ball milling, THM = travelling heater method, MS = melt spinning, Te-MS = Te-rich melt spinning, ZM = zone melting.

Table 2. Thermoelectric properties of the Bi2Te3-based materials prepared by different methods. .

Based on the summarized feature of Bi₂Te₃ families, some strategies have been developed to enhance the thermoelectric performance. In fact, these strategies are combined together to achieve a higher zT.

7.1. Suppressing bipolar conduction

As discussed in Section 4, increasing E_g is effective to suppress bipolar conduction. Forming ternary phases of Bi₂Te_3−xSe_x and Bi_xSb_2−xTe₃ can tune E_g. Figure 11(a) shows the E_g for Bi₂Te_3−xSe_x with different compositions. With increasing Se content, E_g for Bi₂Te_3−xSe_x increases until x = 1, and then decreases. The reason for the variation of E_g with Se content is due to the chemical bonding environment and the electronegativity difference. As demonstrated earlier, Bi₂Te₃ consists of quintuple layers, in which the atoms are arranged in the order of Te(1)–Bi–Te(2)–Bi–Te(1) with two types of differently bonded Te atoms.^[133] While chemical bonding between Bi–Te(2) is pure covalent, it is slightly ionic but still covalent in nature between Bi–Te(1), suggesting the bonding between Bi–Te(1) is stronger.^[134] To form Bi₂Te_3−xSe_x, Se atoms firstly substitute Te at Te(2) sites. When x < 1, Se further goes to Te(1) sites randomly. Owing to Se being more electronegative than Te (refer to Table 3),^[129] the chemical bonding of Bi–Se is stronger than Bi–Te(2), which enables electrons in Bi₂Te_3−xSe_x being more localized. It is understood that with increasing x from 0 to 1 in Bi₂Te_3−xSe_x, E_g increases. Thereafter, E_g tends to decrease with further increasing x < 1, because Se may weaken Bi–Te(1) bonding.

Fig. 11.

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	Fig. 11. (color online) Composition-dependent Eg of (a) Bi2Te3−xSex and (b) BixSb2−xTe3. Reproduced from Refs. [136] and [137].

For Bi_xSb_2−xTe₃ with an electronegativity of Bi slightly less than that of Sb, it is understood that with increasing Sb content, E_g increases, as depicted in Fig. 11.

Noteworthy, it is well documented that the optimal compositions corresponding to the peak zT values are Bi₂Te_2.7Se_0.3, and Bi_0.5Sb_1.5Te₃, in which E_g values are not the highest.^[135] To increase zT, we should simultaneously control the band structures (including E_g, , and E_f) and phonon scatterings. Among these strategies, enlarging E_g is still a critical factor in Bi₂Te_2.7Se_0.3, and Bi_0.5Sb_1.5Te₃ to achieve higher zT than their respective binary phases.

Moreover, reducing the size of nanostructures can also increase E_g due to the quantum confinement effect.^[138–140] For example, it has been confirmed that E_g of Bi₂Se₃ nanosheets with a thickness of 1 nm is ∼ 0.85 eV, much higher than that of 0.3 eV for the bulk counterpart.^[141] Consequently, reducing the thickness of Bi₂Se₃ nanosheets can enhance the thermoelectric performance. Experimentally, zT of Bi₂Se₃ nanosheets with 1 nm was enhanced to be over 0.3.

In respect of suppressing the bipolar conduction, we can also introduce potential barriers to resist the transport of minor carriers. Considering the band alignment between Bi₂Te₃ and Bi₂Se₃, potential barriers of 0.26 eV in the valence band and 0.11 eV in the conduction band of the n-type Bi₂Te₃/Bi₂Se₃ could be formed.^[142] In this scenario, the transport of excited minor carriers (holes) in the valance band could be resisted.^[76] Combined with the energy filtering effect on the major carriers in the conduction band, thermoelectric performance of the n-type Bi₂Te₃/Bi₂Se₃ was enhanced significantly.^[108] Moreover, increasing the carrier concentration to push E_f away from the band gap region can also be effective to suppress bipolar conduction, because the bipolar effect is the strongest in the band gap region (refer to Figs. 3(b) and 3(f)). In nanostructures prepared by solution or ball milling methods, more point defects would be formed, which results in higher carrier concertation.^[100] Therefore, we can observe that in these products, the peak zT generally occurs at relatively high temperature.^{[102,112,122,143,144]}

7.2. Point defect engineering

As mentioned previously, point defects unavoidably present in Bi₂Te₃ families, and significantly affect the thermoelectric properties. On one hand, the anion vacancies and antisite defects serve as donors and acceptors, respectively, to determine the carrier type and carrier concentration. On the other hand, point defects, leading to the mass fluctuations and lattice strains, can enhance the scattering of high-frequency phonons to reduce κ.^[131] In this regard, it is necessary to control the inherent vacancies and antisite defects by point defect engineering. The effective methods are mainly to form the ternary phases (i.e., n-type Bi₂Te_3−xSe_x and p-type Bi_xSb_2−xTe₃), and doping. In this section, we focus on the effect of point defects on electronic transport. Note that the smaller evaporation energy leads to the easier formation of vacancies, and the smaller differences of electronegativity and atomic size motivate the formation of antisite defects.^[145] From Table 3, the point defects strongly depend on the composition of Bi₂Te_3−xSe_x and Bi_xSb_2−xTe₃. Specifically, increasing Se content in Bi₂Te_3−xSe_x increases anion vacancies but decreases antisite defects, and increasing Bi content in Bi_xSb_2−xTe₃ can suppress antisite defects but does not notably affect the anion vacancies.

To clarify the effects of point defects on electronic transport, we summarized the reported data for these ternary phases. Figure 12 summarized n_H, μ_H, σ, and S at 300 K for the representative n-type Bi₂Te_3−xSe_x single crystal,^[146] single crystal doped with Ag (0.1%),^[146] hot pressing plus hot deformation (BM+HP+HD) processed sample,^[100] and ingot doped with I (0.08 wt%).^[123] From Fig. 12(a), with increasing Se content in Bi₂Te_3−xSe_x, n_H for the single crystals and the ingot gently increases, whereas n_H for the samples prepared by BM+HP+HD initially decreases and then increases. The general increasing trend of n_H with increasing Se content is ascribed to the increase in anion vacancies dominating over that of antisite defects. The decrease in n_H for the BM+HP+HD processed samples with low Se content is caused by the antisite defects exhibiting a stronger effect on carrier concentration over vacancies. From Fig. 12(b), μ_H for single crystals and ingot show intensive fluctuations, while that for BM+HP+HD processed samples stabilize at a plateau, which means the effects of point defects on μ_H also depends on the sample preparation methods. Because of the variation of n_H and μ_H caused by point defects, σ and S are modified, shown in Figs. 12(c) and 12(d), respectively. While σ generally increases with increasing Se content, S decreases. Based on the discussion in Section 4, large n_H means high η, resulting in high σ but low S. Moreover, in the pristine Bi₂Te_3−xSe_x single crystal with lower n_H (black data points), its S transfers from p-type to n-type with increasing Se content, suggesting the major carriers change from holes to electrons. This is because the Bi₂Te₃ single crystal is a nearly intrinsic p-type semiconductor, whereas substituting Te in the lattice of Bi₂Te₃ single crystal with Se atoms can increase anion vacancies contributing more electrons, which produces the transition from p-type to n-type.

Fig. 12.

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	Fig. 12. (color online) n-type Bi2Te3−xSex with (a) nH, (b) μH, (c) σ, and (d) S at 300 K as a function of Se content for single crystal,[146] single crystal doped with Ag (0.1%),[146] BM+HP+HD processed sample,[100] and ingot doped with I (0.08 wt%).[123]

Figure 13 presents the effect of Bi content on electronic transport properties for the typical p-type Bi_xSb_2−xTe₃ single crystals^[132] and BM+HP+HD processed analogs.^[100] With increasing Bi content, n_H increases, whereas μ_H generally decreases. As a consequence, σ increases, whereas S generally decreases.

Fig. 13.

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	Fig. 13. (color online) p-type BixSb2−xTe3 with (a) nH, (b) μH, (c) σ, and (d) S at 300 K as a function of Bi content for single crystal,[132] and BM+HP+HD processed sample.[100]

In addition, doping can also modify the point defects. S-doped Sb₂Te₃ can reduce the antisite defects to reduce the carrier concentration and diminish the impurity scattering on holes to enhance the carrier mobility.^[115] Another case is Cu-doped Bi₂Te_2.7Se_0.3, which can reduce the vacancies to enhance the carrier mobility.^[122] We also noted that hot deformation can reduce the anion vacancies to decrease n_H for the sintered polycrystalline samples. For example, n_H for Bi₂Te₃ was reduced to only 1.5 × 10¹⁹ cm⁻³ by hot deformation at 733 K, compared with that of 5.9 × 10¹⁹ cm⁻³ in the unprocessed counterpart, and as a consequence, S increased from −116 μV⋅K⁻¹ to −141 μV⋅K⁻¹.^[99,100]

7.3. Crystalline alignment

Compared with single crystal Bi₂Te₃, polycrystalline materials are promising to realize practical applications, which is due to (i) stronger mechanical strength^[147] and (ii) dense grain boundaries to reduce κ.^[37] Nevertheless, the strong anisotropic behavior of Bi₂Te₃ would worsen S²σ in polycrystalline materials. Therefore, crystalline alignment (i.e., enhancing the texture) is likely to enhance zT for polycrystalline samples.^[148] Hot deformation is widely used to enhance the texture of Bi₂Te₃ families.^[149] Figure 14 summarizes the cutting-edge thermoelectric performance of both n-type Bi₂Te_3−xSe_x and p-type Bi_xSb_2−xTe₃ benefiting from the hot deformation to enhance the texture of the sintered samples. For n-type ones, σ is enhanced significantly after hot deformation, while the enhancement of S caused by hot deformation is not so significant. Overall, S²σ for the n-type Bi₂Te_3−xSe_x is elevated dramatically after hot deformation, which leads to enhanced zT. For p-type Bi_xSb_2−xTe₃, hot deformation does not affect S²σ notably but can reduce κ to some extent. For this reason, zT of p-type candidates can also be enhanced. On this basis, hot deformation enhances zT for n-type Bi₂Te_3−xSe_x and p-type Bi_xSb_2−xTe₃ from different aspects: enhancing S²σ and reducing κ, respectively.

Fig. 14.

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	Fig. 14. (color online) The effects of hot deformation on reported (a) σ, (b) S, (c) κ, (d) κl (e) S2σ, and (f) zT for n-type Bi2Te2.7Se0.3,[119] Bi2Te3,[102] Bi2Te2.3Se0.7,[100] and p-type Bi0.5Sb1.5Te3,[120] Bi0.3Sb1.7Te3.[100]

7.4. Enhancing phonon scattering

Enhancing phonon scattering to reduce κ is also effective to enhance the final zT. Despite the point defect scattering and hot deformation, which can reduce κ (as discussed above), we will cover other strategies for reducing κ.

7.4.1. Nanostructuring

A variety of 1D, 2D, and 3D nanostructures of Bi₂Te₃ have been synthesized by the solution grow method, including nanowires,^[36,150] T-shaped Bi₂Te₃-Te heteronanojunctions,^[143] Te/Bi₂Te₃ nanostring-cluster hierarchical nanostructures,^[151–153] hexagonal nanoplates,^{[106,151,154]} Bi₂Se₃ ultrathin nanosheets,^{[113,114,133]} Bi₂Te₃/Bi₂Se₃ multishell nanoplates,^[109] and 3D nanoflowers.^[108,155] In the synthesis of nanostructures, surfactants are generally used to control the morphology. However, the residuals of surfactants are detrimental to the final thermoelectric performance. Therefore, it is necessary to remove the surfactants or employ the synthesis without any surfactant.

Because of the enhanced phonon scatterings in the nanostructures, κ is reduced. Figures 15(a) and 15(b) show the temperature-dependent κ and κ−κ_e for Bi_0.5Sb_1.5Te₃ nanoplates,^[38] Bi₂Te_2.7Se_0.3 nanoplates,^[38] Bi₂Se₃ ultrathin nanosheets,^[114] Bi₂Te₃/Bi₂Se₃ nanoflowers,^[108] and Bi₂Te₃ nanoplates,^[35] compared with the ingot.^[123] As can be seen, κ of nanostructures can be less than half of the ingot.

Fig. 15.

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	Fig. 15. (color online) (a) κ, and (b) κ−κe for Bi0.5Sb1.5Te3 nanoplates,[38] Bi2Te2.7Se0.3 nanoplates, Bi2Se3 ultrathin nanosheets,[114] Bi2Te3/Bi2Se3 nanoflowers,[108] and Bi2Te3 nanoplates,[35] compared with the ingot.[123]

7.4.2. Ball milling

Ball milling can reduce the grain size so as to enhance the grain boundary scattering on phonons. Ball milling generally includes two methods: grounding the ingot with final product phase to obtain fine powders and forming pure phase by high-energy mechanical allying. Both techniques of ball milling have been successfully used to enhance zT for Bi₂Te₃ families.^[156]

7.4.3. Melt spinning

Melt spinning (MS) can also significantly reduce κ. Figure 16 summarizes the thermoelectric performance of p-type Bi_0.5Sb_1.5Te₃ prepared by MS.^{[103,157,158]} As can be seen, MS can reduce κ by 34% compared with the corresponding ingot and lattice component (κ−κ_e) could be even lower.

Fig. 16.

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	Fig. 16. (color online) (a) κ, (b) κl, (c) S2σ, and (d) zT for Bi0.5Sb1.5Te3 ingot,[160] Xie MS,[103] Zheng MS,[157] and Ivanova MS.[158]

In the case of n-type ones, MS failed to effectively reduce κ. Ivanova et al. employed MS to prepare n-type Bi₂Te_2.7Se_0.3 alloys, but κ was not significantly reduced, which resulted in a zT similar to its ingot.^[159]

Because thermoelectric properties are correlated with each other, we must employ multi-strategies to enhance thermoelectric performance.^[161] Thermoelectric properties are related to the electronic band structure, charge carrier scattering, and phonon scattering. For a specific case with enhanced zT values, it is always due to the combination of multi-strategies to achieve the compromise in these parameters so as to realize a net increase in zT.

Based on above modeling studies, we will combine the results with the reported thermoelectric properties for Bi₂Te₃-based materials to understand the underlying reasons and provide extra hints for further enhancing their performance.

8.1. Underlying reasons for the anisotropy behavior of Bi₂Te₃ families

Crystallographically, the anisotropy behavior of Bi₂Te₃ families is caused by the layered structure. Here, we revealed the underlying fundamentals based on the reported data for single crystals. Figures 17(a) and 17(b) show the data points of S and μ_H versus n_H for n-type Bi₂Te_3−xSe_x single crystals, respectively.^[121] The curves are theoretical plots of S and μ_H as a function of n_H calculated with the determined for S versus n_H, and E_def for μ_H versus n_H. The bold lines correspond to the fitted average values of and E_def. Likewise, figures 17(c) and 17(d) present the analysis results for p-type Bi_xSb_3−xTe₃ single crystals.^[132] From Figs. 17(a) and 17(c), the data points of S versus n_H for both n-type and p-type generally locate near the bold lines, which suggests that the difference of along the ab plane and the c axis is small. From Figs. 17(b) and 17(d), the data points of μ_H versus n_H along the two directions locate near different calculated bold lines. Therefore, the E_def values are significantly different along the two directions, and most importantly, such difference in E_def values is even larger in n-type cases. Figures 17(e) and 17(f) show the data points of S²σ versus n_H and the corresponding theoretical curves for n-type and p-type ones, respectively. As can be seen, the S²σ along the ab plane is larger than that along the c axis, and such anisotropy is stronger for n-type materials.

Fig. 17.

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Fig. 17. (color online) (a) Data points of |S| versus nH compared with the calculated nH-dependent |S| curves, and (b) data points of μH versus nH compared with the calculated nH-dependent μH curves for n-type Bi2Te3−xSex single crystals.[121] (c) Data points of S versus nH compared with the calculated nH-dependent S curves and (d) data points of μH versus nH compared with the calculated nH-dependent μH curves for p-type BixSb3−xTe3 single crystals.[132] (e) and (f) Data points of S2σ versus nH compared with the calculated nH-dependent S2σ curves for n-type Bi2Te3−xSex single crystals[121] and p-type BixSb3−xTe3 single crystals,[132] respectively.

Based on above discussion, we concluded that the significantly different E_def along ab plane and c axis is responsible for the strong anisotropic σ, and the nearly identical leads to the similar S along different directions. In n-type case, the difference of E_def along the two perpendicular directions is larger than that of p-type ones, therefore, anisotropy in n-type is even stronger.

8.2. Understanding the enhanced performance of ternary phases

As discussed above, the enhancement in thermoelectric performance for ternary phases may be caused by the enlarged E_g and point defect engineering. Here, we studied the fundamental reasons for the achieved enhancement in S²σ for the reported n-type Bi₂Te_3−xSe_x. Figure 18(a) is the reported Se content-dependent data points of n_H for Bi₂Te_3−xSe_x ingots doped with I (wt 0.08%) (solid green data points),^[123] Bi₂Te_3−xSe_x processed by BM+HP+HD (hollow red data points),^[100] and Bi₂Te_3−xSe_x single crystals (hollow blue data points).^[121] Considering the reported n_H, S, and μ_H data, we determined η, , and E_def for all compositions using the Kane band model with CB and VB, shown in Figs. 18(b), 18(c), and 18(d), respectively. On this basis, we calculated the theoretical curves of μ_H and S as a function of n_H for each data point with the correspondingly determined , and E_def, exhibited in Figs. 18(e) and 18(f), respectively, in which the corresponding data points were also presented. The comparison of data points with the theoretical curves suggests that our determinations for and E_def are sufficiently precise because the data points locate on the relevant curves, and the values of and E_def strongly depend on the compositions and the material fabrication methods.

Fig. 18.

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Fig. 18. (color online) The Se content-dependent data points of (a) nH, (b) determined η, (c) determined , and (d) determined Edef. The nH-dependent data points of (e) μH, and (f) S compared with the theoretical curves of μH versus nH, and S versus nH calculated with the correspondingly determined Edef, and . In all figures, the solid green data points are from Bi2Te3−xSex ingots doped with I (wt 0.08%),[123] the hollow red data points are from Bi2Te3−xSex processed by BM+HP+HD,[100] and the hollow blue data points are from Bi2Te3−xSex single crystals.[121]

The combination of theoretical curves of μ_H versus n_H and S versus n_H enables to calculate the theoretical curves of S²σ versus n_H, shown in Fig. 19(a), in which the corresponding data points are also plotted. According to our discussion in Section 4, mainly depends on . To examine the relations between S²σ peak and n_H, figure 19(b) demonstrates the data points of determined and n_H for all studied materials, compared with the previously determined curve of versus from Fig. 8(b). As can be seen, when the data points are located closer to the grey curve in Fig. 19(b), it is more likely for the data points in Fig. 19(a) to approach the peaks of corresponding theoretical curves of S²σ versus n_H. However, the difference of S²σ values for different data points cannot be fully explained by the variation of , although small could lead to high S²σ. For instance, the green hexagon star with of ∼ 0.2m₀ shows S²σ of ∼ 7 × 10⁻⁴ W⋅m⁻¹⋅K⁻², which is much smaller than S²σ of ∼ 6 × 10⁻³ W⋅m⁻¹⋅K⁻² for the green round disk with of ∼ 1.7 m₀. Here, we cannot ascribe the enhanced S²σ to the decreased .

Fig. 19.

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Fig. 19. (color online) (a) Data points of nH dependent S2σ compared with the theoretical curves of S2σ versus nH calculated with correspondingly determined Edef, and . (b) Determined data points of nH-dependent with the grey curve indicating the as a function of . (c) Data points of λEdef-dependent S2σ compared with the theoretical curves of S2σ versus λEdef for compositions of Bi2Te3 (labeled with 1#), Bi2Te2.4Se0.6 (labeled with 2#) and Bi2Se3 (labeled with 3#) calculated with the corresponding ηopt. (d) Determined data points of λEdef versus η. In all figures, the solid green data points are from Bi2Te3−xSex ingots doped with I (wt 0.08%),[123] the hollow red data points are from Bi2Te3−xSex processed by BM+HP+HD,[100] and the hollow blue data points are from Bi2Te3−xSex single crystals.[121]

Therefore, we should develop new concepts to understand the enhancement in S²σ. As reported in our previous study,^[38] we defined the λE_def (with ), serving as the decoupling factor for S and σ, and we concluded that reducing λE_def is the key to enhance S²σ, provided that η has been sufficiently optimized. Figure 19(c) shows the data points of determined λE_def dependent S²σ, compared with the theoretical curves of S²σ versus λE_def in the range of 2 eV–6 eV. Note that theoretical curves of S²σ versus λE_def were calculated according to the optimal η (η^opt). Since η^opt is affected by the E_g,^[114] for each composition with different E_g, there is a unique theoretical curve of S²σ versus λE_def. Considering the small difference of these theoretical curves for various composition, in Fig. 19(c) we only plotted the representative ones for Bi₂Te₃ ingot, Bi₂Te_2.4Se_0.6 ingot, and Bi₂Se₃ ingot. Figure 19(d) presents the data points of λE_def against η, compared with the η^opt values, indicated by the vertical lines. As can be seen, small λE_def indeed results in large S²σ and narrowing the difference between the determined η and the corresponding η^opt in Fig. 19(d) allows the data point in Fig. 19(c) to approach the corresponding theoretical curve.

Also, we analyzed the p-type BM+HP+HD processed Bi_xSb_2−xTe₃^[100] and the single crystals.^[132] Figures 20(a)–20(d) show the n_H, determined η, , and E_def, respectively. On this basis, we calculated the curves of S and μ_H as a function of n_H over a wide range using the determined parameters, shown in Figs. 20(e) and 20(f), respectively.

Fig. 20.

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Fig. 20. (color online) (a) nH of different p-type BixSb2−xTe3. Determined (b) η, (c) , and (d) Edef. The nH-dependent data points of (e) μH, and (f) S compared with the theoretical curves of μH versus nH, and S versus nH calculated with the correspondingly determined Edef, and . In all figures, the solid purple data points correspond to BM+HP+HD processed samples,[100] and the hollowed data points correspond to single crystals.[132]

Figures 21(a) and 21(d) present the curves of S²σ as a function of n_H, and the determined versus n_H. We can observe that when the data point of versus n_H is close to the optimal curve of versus n_H in Fig. 21(b), the data point of S²σ versus n_H is close to the peak of the corresponding curve of S²σ as a function of n_H. But, although some data points are close to the peak of the corresponding curve of S²σ as a function of n_H, the S²σ could be lower than that for data points deviate from the peak position.

Fig. 21.

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Fig. 21. (color online) (a) Data points of nH-dependent S2σ compared with the theoretical curves of S2σ versus nH calculated with correspondingly determined Edef, and . (b) Determined data points of nH-dependent with the grey curve indicating the as a function of . (c) Data points of λEdef dependent S2σ compared with the theoretical curves of S2σ versus λEdef for compositions of Bi2Te3 (labeled with 1#), and Sb2Te3 (labeled with 2#) calculated with the corresponding ηopt. (d) Determined data points of λEdef versus η. In all figures, the solid purple data points correspond to BM+HP+HD processed samples,[100] and the hollowed data points correspond to single crystals.[132]

Figures 21(c) and 21(d) present the S²σ as a function of λE_def, and λE_def versus η, respectively. From which, we can fully understand the reason for enhanced S²σ.

In this progress report, we studied the physical fundamentals of thermoelectric effects. While Seebeck effect is the distribution of electrons disturbed by temperature difference, and Peltier effect is the energy exchange between free electrons and the surroundings. We also provided a detailed mathematical process of the derivation of electronic transport coefficients from BTE. On this basis, we performed simulation studies on the effects of materials parameters, , E_g, and E_def on these transport coefficients, which provides significant insights into the dependence of thermoelectric properties on materials. We summarized the features of Bi₂Te₃-based thermoelectric, and the correspondingly developed strategies for enhancing the thermoelectric performance. Specifically, owing to the narrow band gap, Bi₂Te₃ families tend to exhibit intensive bipolar conduction. To suppress bipolar conduction, enlarging band gap is required, which is normally achieved by forming ternary phases or doping. Moreover, minor charge carrier filtering can also be applied to suppress the bipolar conduction. Another feather of Bi₂Te₃ is the point defects, which can enhance the mid-frequency phonon scatterings and determine the carrier type as well as carrier concentration. Point defect engineering is widely employed to control the point defects. Finally, caused by the layered structures, Bi₂Te₃ shows anisotropic behavior in terms of the thermoelectric properties along the basal plane and the c axis, which is even stronger in the n-type ones. Therefore, we can observe the n-type S²σ is much lower than that of the p-type. Correspondingly, enhancing the texture of polycrystalline materials is anticipated to improve the thermoelectric performance. Moreover, to understand the strong anisotropic behavior and the reported enhanced thermoelectric performance, we re-analyzed the electronic transport properties of Bi₂Te₃-based thermoelectric materials. The strong anisotropy is found to be caused by the different E_def along the a–b basal and c axis. We further analyzed the achieved enhancement in Bi₂Te₃. Based on the modeling studies, we highlight the significance of λE_def in enhancing S²σ. Reducing λE_def is the key to enhance S²σ provided that η has been optimized, which is believed to enlighten the development of high-performance thermoelectric materials.