The attractive capability of thermoelectric (TE) materials in actualizing the conversion between temperature gradient and electrical power makes them strong candidates for waste-heat recovery as well as solid-state refrigeration ^[1][2][3][1,2,3]. The practical and widespread application of TE technology strongly relies on the development of high-performance TE materials, where the TE performance of materials is evaluated by a dimensionless figure of merit, zT = α²σT/κ. The TE parameters α and σ are the Seebeck coefficient and electrical conductivity which, respectively, constitute the power factor, PF = α²σ, used to evaluate electrical conductivity characteristics. Parameter T is the Kelvin thermodynamic temperature, while κ refers to the total thermal conductivity, which is composed of two major contributions from the charge carriers (κ_E) and the lattice (κ_L), respectively. From a computational perspective, the most ideal high-performance TE material should have a large α, high σ as well as a low κ value. What cannot be avoided is the strong coupling between thermoelectric parameters regarding carrier concentration, such as when a high σ means low α and a high κ_E, limiting the improvement of zT ^[4][5][6][4,5,6]. In order to achieve high zT in traditional or emerging TE materials, various methods and approaches have been adopted to reduce the correlation between thermal and electrical properties ^[7][8][9][7,8,9], including defect engineering, size effects, alloying effect and high-entropy engineering, etc. In addition to achieving high performance, the exploration of alternative materials consists of earth-abundant and eco-friendly components to meet the sake of clean and environmental protection is also considered as one of the most popular approaches in TE field ^{[10][11][12][13]}[10,11,12,13]. In recent years, diverse bulk TE materials have been widely researched, including liquid-like Cu₂(S, Se, Te), silver-based chalcogenides, Sn(Te, S, Se), half-heuslers, etc. ^[14][15][16][14,15,16].

As an environmentally friendly and promising TE material without precious elements, the performance advantages of copper-based diamond-like TE compounds lie in their high Seebeck coefficient and low thermal conductivity ^{[17][18][19][20][21]}[17,18,19,20,21]. Typical compounds include: Cu₃SbSe₄, with a high zT of 0.89 at 650 K [19]; Cu₂SnSe₃, with α of ~250 μV·K⁻¹ in the temperature range of 300–700 K [22]; and CuInTe₂, with a κ_L value as low as 0.3 W·m⁻¹·K⁻¹ [23], etc. Copper-based diamond-like TE compounds are a type of material that conforms to the concept of “phonon-glass electron-crystal” (PGEC) [17] materials, and their crystal structures are usually composed of two sublattices ^[23][24][25][23,24,25], in which one sublattice constitutes a conductive network, while the other acts as a thermal barrier and is sometimes also known as a charge reservoir. In 2011, Skoug et al. [24] summarized the significance of lone-pair electrons in the Cu-Sb-Se diamond-like system and demonstrated that the low intrinsic κ_L in compounds came from the interaction of lone-pair electrons with neighboring atoms. Moreover, Skoug et al. [25] also confirmed that the dominant Cu-Se network controlled the electric transport while the Sn orbitals only compensated the system for electrons. Several diamond-like crystal structures evolved from thecubic zincblende structure. Simultaneously, a series of advanced CBDL compounds have been discovered since 2009, most of which have presented outstanding TE properties. The timeline of maximum zTs and the temperature dependence of zTs for selected CBDL compounds. Taking the typical diamond-like compounds of Cu(In, Ga)Te₂, Cu₃SbSe₄, and Cu₂SnSe₃ as examples, long-term efforts have shown that they all apparently have superior TE transport properties with high zTs that exceed one. For instance, Liu et al. [23] devised a pseudocubic crystal structure in CuInTe₂ compounds; thus the highest zT of 1.24 was obtained in Ag-doped CuInTe₂ compounds. A peak zT of 1.14 was attained in a Cu₂Sn_0.90In_0.10Se₃ compound at 850 K by replacing Sn sites with In. It is also worth noting that a high average zT (zT_ave) value is desirable for overall TE conversion efficiency. For instance, a high zT_max of 1.67 at 873 K, and a zT_ave of 0.73, were realized in Cu_0.7Ag_0.3Ga_0.4In_0.6Te₂ [26]. In the latest research of Zhou’s group ^[27][28][27,28], record-high zT_ave values of 0.73 and 0.77 were achieved in Cu₃SbSe₄–based and Cu₃SbS₄–based materials, respectively, which were also comparable to other state-of-the-art TE compounds. Hence one can see that CBDL compounds are expected to become environmentally friendly candidates for TE applications and to achieve excellent performances.

2. Copper-Based Diamond-like Thermoelectric Compounds

Copper-based diamond-like compounds (CBDL) compounds contain a large number of family members, which include ternary I–III–VI₂ chalcopyrites, I₃–V–VI₄ stannites, I₂–IV–VI₃ stannites, quaternary I₂–II–IV–VI₄ compounds, and even large-cell Cu10B2C4D13 tetrahedrites and Cu₂₆P₂Q₆S₃₂ colusites. The TE properties of selected typical CBDL compounds including zT_ave, zT_max, α²σ, κ_L, and carrier concentration (n) at room temperature. Among CBDL compounds, CuGaTe₂ and CuInTe₂ are typical Cu–III–VI₂ (III = In, Ga; VI = Se, S, Te) chalcopyrites structural compounds which have exhibited excellent thermoelectric properties at higher temperatures. In 2012, Plirdpring et al. [29] achieved a record zT of 1.4 in CuGaTe₂ compound at 950 K, which indicated that it was a potential material in the field of TE applications. Comparatively, it was found that CuInTe₂ possessed a high zT of 1.18 at 850 K [20]. A large number of studies were conducted to optimize the TE transport behaviors of chalcopyrite-based materials in the following years. Through defect engineering, Pei’s team obtained a maximum zT of 1.0 at 750 K in the Ag-doped CuGaTe₂ compound ^[30][40] and identified that vacancy scattering was an active approach to improve TE transport behaviors ^[31][80]. Zhang et al. [26] synthesized a quinary alloy compound Cu_0.7Ag_0.3Ga_0.4In_0.6Te₂ with a complex nanosized strain domain structure, which presented excellent TE properties with a peak zT of 1.64 at 873 K and an average zT (zT_ave) of 0.73. Through compositing TiO₂ nanofibers, Yang et al. ^[32][36] achieved a maximum zT of 1.47 at 823 K in a CuInTe₂–based TE compound. Moreover, Chen et al. [23] obtained a maximum zT of 1.24 in the Cu_0.75Ag_0.2InTe₂ compound. The above shows that Cu(In, Ga)Te₂ diamond-like TE materials have a higher zTs, comparable to other advanced thermoelectric materials such as PbTe ^{[33][34][35][36]}[81,82,83,84] and SnTe ^[37][38][39][85,86,87]. In addition, a natural chalcopyrite mineral, CuFeS₂ ^{[40][41][42][43]}[52,53,54,55], was also recognized as an advanced CBDL thermoelectric material. It is noteworthy that the CuFeS₂ compound is a rare typical n-type TE compound among CBDL thermoelectric materials ^[44][45][88,89]. Cu₃–V–VI₄ (V = Sb, P, As; VI = Se, S, Te) compounds with a tetragonal diamond-like crystal structure can be approximately regarded as the superposition of four equivalent zincblendes, wherein Cu₃SbSe₄ is considered as a promising TE candidate owing to its narrow band gap of ~0.3 eV ^{[19][27][46][47]}[19,27,47,90]. For improving the TE performance of Cu₃SbSe₄–based materials, Li et al. ^[48][45] coordinately regulated electrical and thermal transport behaviors through the incorporation of Sn-doping and AgSb_0.98Ge_0.02Se₂ inclusion, and the highest zT of 1.23 was eventually achieved at 675 K. Bo et al. ^[47][90] successfully applied the concept of configuration entropy to optimize the TE performance of Cu₃SbSe₄, and the zT increased by about four times, compared to the initial phase, with the increase of entropy. In their latest report, Zhou’s group [27] attained a superior average power factor (PF_ave) of 19 µW·cm⁻¹·K⁻² in 300–723 K by using a small amount of foreign Al atoms as “stabilizers” to supply the high hole concentration, with almost no effect on carrier mobility. Consequently, combined with the reduced κ, a record-high zT of 1.4 and a zT_ave of 0.72 were obtained within the Cu₃SbSe₄–based compounds. A new unconventional doping process that can coordinate the TE properties of materials was also presented. Apart from Cu₃SbSe₄, Cu₃SbS₄ is also a promising Cu₃–V–VI₄–type of TE material ^[28][49][50][28,50,51], and it has been demonstrated that its PF_ave can reach up to 16.1 µW·cm⁻¹·K⁻² and the zT_ave up to 0.77 between 400 and 773 K via its optimization [28]. Different from Cu–III–VI₂ and Cu₃–V–VI₄ compounds, ternary Cu₂–IV–VI₃ (IV = Sn, Ge, Pb; VI = Se, Te, S) compounds crystallize in more distorted structures that are far from tetragonal. Cu₂SnSe₃ is a kind of CBDL compound with diverse structural phases, which has been found and synthesized successfully, including in cubic, tetragonal, orthogonal, and monoclinic phases involving three variants [22]. Hu et al. ^[51][62] improved the TE transport behaviors of Cu₂SnSe₃ by enhancing the crystal symmetry of it via Mg-doping and intensifying the phonon scattering through the introduction of dislocations and nanoprecipitates. Similarly, Ming et al. ^[52][65] obtained a peak zT of 1.51 at 858 K in the Cu₂Sn_0.82In_0.18Se_2.7S_0.3 compound through regulating the band structure and introducing multi-scale defects. In addition, a record-high zT of 1.61 was obtained at 848 K by Qin et al. ^[53][66] by constructing the intrinsic point defects, including high-dense stacking faults and endo-grown nanoneedles, to obstruct mid- as well as low-frequency phonons in Cu₂SnSe₃ compounds. Except for Cu₂SnSe₃, Cu₅A₂B₇ (A = Si, Ge, Sn; B = S, Se, Te), with a centrosymmetric space group C2/m, is also a kind of distorted CBDL compound which has been considered to possess a non-centrosymmetric cubic structure, with the phase crystallized as C-centered ^[54][55][56][91,92,93]. An undesirable characteristic of Cu₅A₂B₇ compounds is that they represent metal-like behaviors, such as the carrier concentration and κ of Cu₅Sn₂Te₇ at 300 K are 1.39×10²¹ cm⁻³ and 15.1 W·m⁻¹·K⁻¹, respectively ^[55][92]. Simultaneously, zinc atoms have been proven to be effective dopants for strengthening the semiconductor properties of Cu₅Sn₂Te₇ compounds; Sturm et al. ^[56][93] introduced a zinc dopant into Cu₅Sn₂Se₇ and Cu₅Sn₂Te₇ compounds, which also supports this conclusion. Especially noteworthy is that the effect of zinc doping is not optimal, and the TE performance of the compound still needs further improvement. Quaternary Cu₂–II–IV–VI₄ (II = Co, Mn, Hg, Mg, Zn, Cd, Fe; IV = Sn, Ge; VI = Se, S, Te) compounds with more complex tetragonal structures have also been widely studied. The distinguishing features of quaternary CBDL compounds are they possess a wider bandgap and a relatively lower carrier mobility compared with the ternary CBDL compounds ^{[57][58][59][60][61][62][63][64][65]}[68,70,76,94,95,96,97,98,99]. Taking the orthorhombic enargite-type Cu₂MnGeS₄ as an example ^[61][95], the bandgap of it is ~1.0 eV in the initial phase while it only converts to 0.9 eV in the Cu_2.5Mn_0.5GeS₄ by adjusting the ratio of Mn and Cu atoms. The large-cell Cu₁₀B₂C₄D₁₃ ^{[66][67][68][69]}[100,101,102,103]  (B = Ag, Cu; C = Co, Ni, Zn, Cu, Mn, Fe, Hg, Cd; Q = Sb, Bi, As; Q = Se, S) tetrahedrites have even more complex crystal structures. The featured“PGEC” framework is also displayed in the Cu₁₂Sb₄S₁₃ tetrahedrite, where the electric transmission is controlled by a CuS₄ network and the thermal transmission is governed by a cavity polyhedral consisting of CuS₃ and SbS₃ groups ^[66][100]. In 2013, Lu et al. ^[68][102] achieved an enhanced zT of 0.95 at 720 K in Cu₁₂Sb₄S₁₃ utilizing Zn-doping. Moreover, Li et al. ^[69][103] attained a high zT of 1.15 at 723 K in a porous Cu₁₂Sb₄S₁₃–based material; a segmented single-leg device based on the material was successfully fabricated which realized a high conversion efficiency of 6% when the ΔT reached up to 419 K. Cu₂₆P₂Q₆S₃₂ ^{[70][71][72][73][74]}[104,105,106,107,108](P = V, Ta, Nb, W, Mo; Q = Ge, Sn, As, Sb) colusites are other large-cell examples, which possess 66 atoms in a crystal cell while the tetrahedrites possess 58 atoms. Therefore, the common characteristic of both is their inherent low κ derived from high structural inhomogeneity ^[74][75][108,109]. For instance, Guilmeau’s group ^[71][105] obtained the lowest κ of 0.4 W·m⁻¹·K⁻¹ at 300 K in the Cu₂₆V₂Sn₆S₃₂ colusite, which was attributed to the structural complexity of colusite and mass fluctuations among the Cu, V and Sn atoms. In 2018, they further elucidated the potential mechanism related to the fountainhead of intrinsically low κ for a colusite along with the influence of antisite defects and S-vacancies on carrier concentration ^[71][72][105,106].