Realizing the Ultralow Lattice Thermal Conductivity of Cu3SbSe4 Compound via Sulfur Alloying Effect

Cu3SbSe4 is a potential p-type thermoelectric material, distinguished by its earth-abundant, inexpensive, innocuous, and environmentally friendly components. Nonetheless, the thermoelectric performance is poor and remains subpar. Herein, the electrical and thermal transport properties of Cu3SbSe4 were synergistically optimized by S alloying. Firstly, S alloying widened the band gap, effectively alleviating the bipolar effect. Additionally, the substitution of S in the lattice significantly increased the carrier effective mass, leading to a large Seebeck coefficient of ~730 μVK−1. Moreover, S alloying yielded point defect and Umklapp scattering to significantly depress the lattice thermal conductivity, and thus brought about an ultralow κlat ~0.50 Wm−1K−1 at 673 K in the solid solution. Consequently, multiple effects induced by S alloying enhanced the thermoelectric performance of the Cu3SbSe4-Cu3SbS4 solid solution, resulting in a maximum ZT value of ~0.72 at 673 K for the Cu3SbSe2.8S1.2 sample, which was ~44% higher than that of pristine Cu3SbSe4. This work offers direction on improving the comprehensive TE in solid solutions via elemental alloying.

Copper-based chalcogenides have garnered significant attention because of their relatively favorable electrical transport and low thermal transport properties [22][23][24][25].In addition, thermoelectric minerals like germanites, colusites, tetrahedrites, and other materials also have rather high ZT values [26][27][28].Among them, the Cu 3 SbSe 4 compound is a p-type semiconductor, featuring a narrow band gap of ~0.29 eV [29,30].More importantly, its components are earth-abundant, inexpensive, non-toxic, and environmentally friendly [31,32].However, its high κ and low σ, stemming from low carrier concentration and mobility, present challenges that hinder its practical use.Extensive efforts have been implemented to enhance the TE performance of Cu 3 SbSe 4 , including elemental doping [33][34][35][36][37], band engineering [38][39][40], and nanostructure modification [41,42].These approaches have potential in improving the carrier concentration of (n), S, or κ lat , and thus leading to an appealing figure of merit.Although high n can enhance σ, it has a negative impact on S and result in an increase in κ ele .The TE performance of Cu 3 SbSe 4 falls significantly short of that of Cu-based chalcogenides due to these two inherent issues.On one side, the narrow energy band gap of ~0.29 eV leads to bipolar diffusion, causing deterioration in electrical properties [29,30].On the other side, the high thermal conductivity (κ lat ) inherently arises from its composition comprising lightweight elements and a diamond-like structure [25].In other words, optimizing carrier concentration alone proves challenging in further enhancing the TE performance.
The formation of a solid solution via elemental alloying is an effective strategy for depressing the κ lat and thereby enhancing the TE performance.For example, Skoug et al. demonstrated that the substitution of Ge on Sn sites can lead to the formation of Cu 2 Sn 1−x Ge x Se 3 solid solutions, synergically optimizing the TE properties [43].Jacob et al. reported that a high ZT max value of ~0.42 was obtained in the Cu 2 Ge(S 1−x Se x ) 3 system via Se alloying [44].Wang et al. enhanced the TE properties of Cu 2 Ge(Se 1−x Te x ) 3 by incorporating Te on the Se site, resulting in a ZT max of ~0.55, which was 62% higher than that of the matrix [45].The afore-mentioned research give us an idea that the Cu 3 Sb(Se 1−x S x ) 4 solid solution is an effectively strategy for enhancing the thermoelectric performance of the Cu 3 SbSe 4 compound via S alloying.Moreover, the development of TE materials with more cost-efficient constituent elements is of significant importance for large-scale practical applications.
Herein, we present the synthesis and thermoelectric characterization of the Cu 3 Sb(Se 1−x S x ) 4 solid solutions with x covering the whole range from 0 to 1.The results demonstrate that the Cu 3 SbSe 4 -Cu 3 SbS 4 solid solutions exhibit an extremely high Seebeck coefficient and ultralow thermal conductivity.Firstly, S alloying can widen the band gap, alleviating the bipolar effect.Additionally, S substitution in the lattice can significantly increase the carrier effective mass, leading to a remarkably high Seebeck coefficient of ~730 µVK −1 .Moreover, the κ lat can be significantly depressed owing to point defect scattering and Umklapp scattering, thus obtaining a minimum κ lat of ~0.50 Wm −1 K −1 .Consequently, the multiple effects of S alloying boost the TE performance of the Cu 3 SbSe 4 -Cu 3 SbS 4 solid solution, and a maximum ZT value of ~0.72 at 673 K is obtained for the Cu 3 SbSe 2.8 S 1.2 sample.

Synthesis
The Cu 3 Sb(Se 1−x S x ) 4 solid solutions with varying S content (x = 0, 0.1, 0.2, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8, and 1) were synthesized by vacuum melting and plasma-activated sintering (Ed-PAS III, Elenix Ltd., Zama, Japan).Concretely, the synthesis was divided into two steps.The first step was to synthesize the primary powders.Firstly, the starting materials, consisting of high-purity components (Cu: 99.99 wt.%; Sb: 99.99 wt.%; Se: 99.999 wt.%; S: 99.99 wt.%) corresponding to the nominal composition of Cu 3 Sb(Se 1−x S x ) 4 (x = 0-1), were carefully sealed in the quartz tube under high vacuum conditions (<10 −3 Pa).Afterwards, the sealed tubes were incrementally heated to 1173 K with a controlled rate of 20 K/h and maintained at 1173 K for a duration of 12 h.Following a holding period, the tubes were cooled down with a relatively low rate of 10 K/h until reaching 773 K, and finally the samples were quenched into water.Subsequently, the acquired quenched ingots underwent direct annealing at 573 K for a period of 48 h to facilitate the uniformity of chemical compositions.After this step, the obtained ingots were finely pulverized using an agate mortar to produce uniform powders.The second step was to synthesize the target samples.The resultant powders were then introduced into a graphite die of Ø12.7 mm in diameter and treated using the PAS technique at 673 K for a duration of 5 min while applying an axial pressure of 50 MPa.In detail, the sintering temperature reached to 523 K after an activation time of 10 s under the activation voltage of 20 V and the activation current of 300 A, and then the current was manually adjusted to increase by a rate of 1.5 K/s to reach the desired sintering temperature of 673 K after 225 s; the temperature was then held for 300 s.Ultimately, the samples were furnace-cooled to room temperature.

Characterization
The X-ray diffraction (XRD) patterns for the Cu 3 Sb(Se 1−x S x ) 4 (x = 0-1) solid solutions were conducted using a Bruker D8 advance instrument, which was equipped with Cu Kα radiation (λ = 1.5418Å).Lattice parameters were refined using the Rietveld method, employing the HighScore Plus computer program for analysis.The morphologies and compositions of the afore-mentioned solid solutions were performed by a Nova NanoSEM450 (FESEM) and a JEM-2010F (HRTEM), equipped with a detector of energy-dispersive X-ray spectroscopy (EDS).

Thermoelectric Property Measurements
The as-sintered cylinders were processed into bars of 10 mm × 2 mm × 2 mm and disks of Ø12.7 mm × 2 mm.The bars were used for concurrently measuring σ and S by the commercial measuring system (LINSEIS, LSR-3) under a helium atmosphere, spanning a temperature range from room temperature to 673 K. Thermal conductivity was calculated using the equation of κ = DC p ρ. Herein, the D, C p , and ρ stand for the thermal diffusivity, specific heat, and density, respectively.The disks were used for simultaneously measuring D and C p by utilizing a Laser Flash apparatus of Netzsch (LFA-457) under a static argon atmosphere.The ρ of the Cu 3 Sb(Se 1−x S x ) 4 (x = 0-1) solid solutions were conducted using Archimedes' methods.The relative densities, in relation to the theoretical density of 5.86 g cm −3 , have been provided in Table S1.The n (carrier concentration) and µ (carrier mobility) of the afore-mentioned solid solutions at 300 K were performed using the Hall effect system (LAKE SHORE, 7707 A) according to the van der Pauw method under a magnetic field strength of 0.68 T.

Crystal Structure
The crystal structures and phase compositions for the Cu 3 Sb(Se 1−x S x ) 4 (x = 0-1) samples were performed by XRD. Figure 1a shows the crystal structure of tetragonal Cu 3 SbSe 4 , with blue, gray, and green atoms representing Cu, Sb, and Se, respectively.As displayed in Figure 1b, the major diffraction peaks of the pristine sample (x = 0) are fully indexed to the zinc-blende-based tetragonal structure (I-42m space group) of Cu 3 SbSe 4 (JCPDS No. 85-0003) without any detectable impurities [29].With increasing S content (0 < x < 1), a continuous shift of the (112) diffraction peak towards higher angles can be seen (Figure 1c), demonstrating that S atoms replace Se at the Se site to form Cu 3 Sb(Se 1−x S x ) 4 solid solutions.The shift in the diffraction peak can be ascribed to the smaller radius of S 2− (1.84 Å) in comparison to Se 2− (1.98 Å) [46].For x = 1, the XRD peaks match the pattern of Cu 3 SbS 4 (JCPDS No. 35-0581) [47].
The Rietveld refinement profiles of the Cu 3 Sb(Se 1−x S x ) 4 (x = 0.3) samples based on the famatinite crystal structure are shown in Figure 1d.The data of the final agreement factors (R p , R wp , and R exp ) of Cu 3 Sb(Se 1−x S x ) 4 (x = 0-1) samples are listed in Table S2.The lattice parameter exhibits a linear decrease with increasing S concentration, and closely follows the expected Vegard's law relationship [48] (Figure 1e), indicating the formation of Cu 3 SbSe 4 -Cu 3 SbS 4 solid solutions.

Microstructure
The morphologies and chemical compositions of the Cu3Sb(Se1−xSx)4 (x = 0.3) sample were characterized by a SEM equipped with an EDS detector (Figure 2).As presented in Figure 2a,b, the SEM images of fracture surfaces (x = 0.3) indicated that they were isotropic materials.The nanopores (marked by the blue dotted circles) were observed on the fracture surface due to the Se/S volatilization of the synthesis process of the sample (Figure 2a), which can contribute to blocking the transport of mid-wavelength phonons [47].To investigate the composition of the sample, we observed its polished surface (Figure 2c).According to the EDS elemental mapping (Figure 2d-h), the four constituent elements were uniformly distributed with no distinct micro-sized aggregations.This was combined with a back-scattered electron (BSE) image and elemental ratios (%), where Cu, Sb, Se, and S were present in proportions of 40.07:12.68:31.26:15.59(as depicted in Figure S1), which demonstrated the formation of the Cu3SbSe4-Cu3SbS4 (x = 0.3) solid solution.

Microstructure
The morphologies and chemical compositions of the Cu 3 Sb(Se 1−x S x ) 4 (x = 0.3) sample were characterized by a SEM equipped with an EDS detector (Figure 2).As presented in Figure 2a,b, the SEM images of fracture surfaces (x = 0.3) indicated that they were isotropic materials.The nanopores (marked by the blue dotted circles) were observed on the fracture surface due to the Se/S volatilization of the synthesis process of the sample (Figure 2a), which can contribute to blocking the transport of mid-wavelength phonons [47].To investigate the composition of the sample, we observed its polished surface (Figure 2c).According to the EDS elemental mapping (Figure 2d-h), the four constituent elements were uniformly distributed with no distinct micro-sized aggregations.This was combined with a back-scattered electron (BSE) image and elemental ratios (%), where Cu, Sb, Se, and S were present in proportions of 40.07:12.68:31.26:15.59(as depicted in Figure S1), which demonstrated the formation of the Cu 3 SbSe 4 -Cu 3 SbS 4 (x = 0.3) solid solution.
The morphologies and compositions of Cu 3 Sb(Se 1−x S x ) 4 (x = 0.3) were further investigated at nanoscale using high-resolution TEM (HRTEM) (Figure 3).The TEM images demonstrated that many nanophases were distributed in the sample, and elemental mapping taking over the entire region revealed that the four constituent elements (Cu, Sb, Se, and S) were uniformly dispersed within the Cu 3 SbSe 4 -Cu 3 SbS 4 solid solution (Figures 3a and S2).As presented in Figure 3b, the grain boundary (indicated by blue dot lines) could be clearly observed in the sample.Meanwhile, as shown in Figure 3b,c, the crossed fringes, with interplanar spacing of 3.26 Å and 1.99 Å corresponded to the (112) and (204) planes of Cu 3 SbSe 4 , respectively [49].Additionally, the SAED pattern taken from the Figure 3c   The morphologies and compositions of Cu3Sb(Se1−xSx)4 (x = 0.3) were further investigated at nanoscale using high-resolution TEM (HRTEM) (Figure 3).The TEM images demonstrated that many nanophases were distributed in the sample, and elemental mapping taking over the entire region revealed that the four constituent elements (Cu, Sb, Se, and S) were uniformly dispersed within the Cu3SbSe4-Cu3SbS4 solid solution (Figures 3a  and S2).As presented in Figure 3b, the grain boundary (indicated by blue dot lines) could be clearly observed in the sample.Meanwhile, as shown in Figure 3b,c, the crossed fringes, with interplanar spacing of 3.26 Å and 1.99 Å corresponded to the (112) and (204) planes of Cu3SbSe4, respectively [49].Additionally, the SAED pattern taken from the Figure 3c along the [110] zone axis is displayed in Figure 3d.The ordered diffraction spots can be indexed to the (002), (11

Charge Transport Properties
To explore the effects of S alloying on the TE properties of the Cu3Sb(Se1−xSx)4 (x = 0-1) solid solutions, the charge transport properties were conducted.The temperature dependence of electrical conductivity (σ) of the Cu3Sb(Se1−xSx)4 (x = 0-1) solid solutions is displayed in Figure 4a.The pristine Cu3SbSe4 exhibited a monotonous increase in σ with rising temperature, demonstrating characteristic behavior of a non-degenerate semicon-

Charge Transport Properties
To explore the effects of S alloying on the TE properties of the Cu 3 Sb(Se 1−x S x ) 4 (x = 0-1) solid solutions, the charge transport properties were conducted.The temperature dependence of electrical conductivity (σ) of the Cu 3 Sb(Se 1−x S x ) 4 (x = 0-1) solid solutions is displayed in Figure 4a.The pristine Cu 3 SbSe 4 exhibited a monotonous increase in σ with rising temperature, demonstrating characteristic behavior of a non-degenerate semiconductor.For the x > 0.2 samples, the samples showed a transition from non-degenerate semiconductors to a partially degenerate regime [51].The σ exhibited an initial decrease followed by an increase, with the minimum value occurring at ~473 K, indicating its association with bipolar conduction [38,52].The σ of S alloying samples increased with the S contents until x = 0.3, after which it started to decrease with a higher S content.Notably, the σ improved from ~4.6 S/cm of pristine Cu 3 SbSe 4 to ~42 S/cm of x = 0.3 solid solution at room temperature, arising from the augmented carrier concentration (Table S1).It is worth noting that the solid solutions with high S content (x > 0.5) had lower σ compared to the pristine Cu 3 SbSe 4 , which was ascribed to the reduced n (carrier concentration) and diminished µ (carrier mobility).Furthermore, due to the intensified lattice vibration at elevated temperatures, the solid solutions exhibited lower σ than the pristine sample at high temperatures, indicating that the intensified lattice vibration in the solid solutions at elevated temperatures hindered the carrier migration [40,53].Notably, the S value of the samples exhibited an initial ascent followed by a subsequent descent as the temperature rose, ultimately reaching its zenith at ~473 K.This be-  Notably, the S value of the samples exhibited an initial ascent followed by a subsequent descent as the temperature rose, ultimately reaching its zenith at ~473 K.This behavior can be attributed to the influence of the bipolar effect [54].The maximum S of ~730 µVK −1 was obtained from the x = 0.6 solid solution.We calculated the E g of the Cu 3 Sb(Se 1−x S x ) 4 (x = 0-1) samples with the formula: E g = 2eS max T, where E g , e, S max , and T represent the band gap, elementary charge, maximal Seebeck coefficient, and the associated temperature, respectively [55].The calculated E g for the pristine Cu 3 SbSe 4 of ~0.30 eV aligned well with the reported literature [36,56]; the results are displayed in Figure S3.Consequently, the introduction of alloyed S played a role in enlarging E g from ~0.30 eV to ~0.69 eV, thus widening the band gap to alleviate the bipolar effect.For the semiconductors, we note that the increase in S (|S|) was directly proportional to the carrier effective mass and n −2/3 .We calculated the Pisarenko relation between |S| and n (indigo and red dashed lines with m* ~0.68 and 1.4 m e , respectively) based on the single parabolic band model (SPB), as follows [57,58]: where k B , h represent the Boltzmann constant, and Planck constant, respectively.The calculated m* was significantly enhanced from 0.68 for pristine Cu 3 SbSe 4 to 5.03 m e for the x = 0.6 sample (Table S1).As seen in Figure 4c, the calculated m* based on S (experimental values) of Cu 3 Sb(Se 1−x S x ) 4 (x = 0.1-1) samples were above the Pisarenko line.Furthermore, the m* depended directly on the E g ( , where E the energy of electron states), which deviated from a single Kane band model [21,59,60], thus confirming the large S was related to E g and m*.Consequently, the decreased carrier concentration (x > 0.5) and increased m*, resulted in the significant enhancement of S.
The temperature dependence of the power factors (S 2 σ) of the Cu 3 Sb(Se 1−x S x ) 4 (x = 0-1) samples are presented in Figure 4d.The S 2 σ of Cu 3 SbSe 4 -Cu 3 SbS 4 solid solutions exhibited a similar temperature-dependent behavior as the electrical conductivity (σ).The temperature-dependent trend observed in the S 2 σ was mirrored in the behavior of the σ for the Cu 3 SbSe 4 -Cu 3 SbS 4 solid solutions.Owing to their relatively elevated σ and S values, these samples demonstrated larger S 2 σ values compared to the pristine Cu 3 SbSe 4 , particularly within the lower temperature range.Notably, the x = 0.3 sample achieved a larger S 2 σ value than the other samples, and the peak S 2 σ value of Cu 3 SbSe 2.8 S 1.2 sample was ~670 µW m −1 K −2 at 673 K.
The calculated L values of the Cu 3 Sb(Se 1−x S x ) 4 (x = 0-1) samples ranged from 1.5 to 1.6 W Ω K −2 , and the results are listed in Figure S5.Owing to the enhanced carrier concentration (x < 0.6), the κ ele showed a slight increase at low temperature after S alloying, as described in Figure 5b.The κ lat of the Cu 3 Sb(Se 1−x S x ) 4 (x = 0-1) samples is plotted in Figure 5c, indicating a significant decrease within the measured temperature range after S alloying.
To explore the effects of S alloying on the phonon scattering and the significant reduction in κ lat , the κ lat of the Cu 3 Sb(Se 1−x S x ) 4 (x = 0-1) compounds was evaluated at room temperature by the Debye-Callaway model.The primary scattering mechanisms under consideration were point defect scattering and Umklapp scattering.Then, the κ lat of the pristine (κ pristine lat ) and S-alloyed (κ lat ) Cu 3 SbSe 4 compounds could be computed based on the Debye-Callaway model [48,65,66]: where u, θ D , Ω, h, and ν represent the scaling parameter, Debye temperature, volume per atom, Planck constant, and average speed of sound, respectively (herein, θ D = 131 K and ν= 1991.2m/s [46]).Γ is the imperfection scale parameter, which is associated with the Γ m (mass fluctuation) and Γ s (strain field fluctuation) [67]: where x, ∆M/M and ∆r/r are the S concentration in one molecular, the relative change of atomic mass, and atomic radius owing to the replacement of Se with S, respectively.The ε value can be computed using the following formula [68]: where, γ and υ p are the Grüneisen parameter and Poisson ratio, respectively (here, γ = 1.3 [46] and υ p = 0.35 [69]).The values of Γ m and Γ s for the Cu 3 Sb(Se 1−x S x ) 4 compounds are presented in Table S3. Figure 5d shows how the scattering parameters Γ m and Γ s changed with varying Se-alloying levels.It was observed that Γ m was smaller than Γ s when the S content x ≤ 0.6, indicating that the Γ s (strain field fluctuation) contributed greatly to the drop of κ lat .As for the x > 0.6 samples, the Γ m (mass fluctuation) was the dominant.It is commonly accepted that the atomic radius of S is different from that of the Se atom, inducing a localized lattice distortion and leading to local field fluctuations that hinder the propagation of heat-carrying phonons [70,71].However, with increasing S content, the mass fluctuation gradually became the dominant factor.The experimental κ lat closely aligned with the curve calculated by the Callaway model (Figure 5e), suggesting that point defects made a great contribution to suppress the κ lat in the Cu 3 Sb(Se 1−x S x ) 4 solid solutions [48].For a more comprehensive evaluation of our results, a comparison of the our κ lat data with the recently reported values of Cu 3 SbSe 4 are illustrated in Figure 5f [33,34,36,38,39].Remarkably, the Cu 3 Sb(Se 1−x S x ) 4 (x = 0.5) sample achieved an outstandingly low κ lat of ~0.50 W m −1 K −1 at 673 K.

Figure of Merit (ZT)
The temperature-dependent ZT of the Cu 3 Sb(Se 1−x S x ) 4 (x = 0-1) samples are illustrated in Figure 6a.With the benefit of the collaborative enhancement of electrical and thermal transport properties, the x = 0.3 sample attained a maximum ZT value of ~0.72 at 673 K, which was 44% higher than that of pristine Cu 3 SbSe 4 .To further analyze our TE properties, the comparison of the ZT max of the Cu 3 SbSe 4 -based materials is given in Figure 6b [33][34][35][36][37][38][39][40]72].Obviously, our ZT max of 0.72 was higher than that of other

Conclusions
In summary, a series of Cu 3 SbSe 4 -Cu 3 SbS 4 solid solutions were synthesized by vacuum melting and plasma-activated sintering (PAS) techniques, and the effects of S alloying on TE performance were investigated.S alloying can widen the band gap, effectively alleviating the bipolar effect.Additionally, the S (Seebeck coefficient) was significantly improved because of the increased m*.Furthermore, the substitution of S for Se in Cu 3 SbSe 4 lattice led to noticeable local distortions, yielding large strain and mass fluctuations to suppress the κ lat, thus decreasing the κ lat and κ tot to ~0.50 Wm −1 K −1 and ~0.52 Wm −1 K −1 at 673 K, respectively.Consequently, a peak ZT value of ~0.72 was obtained at 673 K for the Cu 3 Sb(Se 1−x S x ) 4 (x = 0.3) sample.Based on these results, it is speculated that further improvement in the figure of merit of Cu 3 Sb(Se 1−x S x ) 4 solid solutions can be obtained by enhanced electrical transport properties.Our research offers a new strategy to develop high-performance TE materials in solid solutions via elemental alloying.

Figure 2 .
Figure 2. (a) SEM image of the fracture surfaces of the Cu3SbSe2.8S1.2 sample; (b) high magnification images of (a); (c) the corresponding EDS mapping for all constituent elements of selected region in (b); (c) SEM images of the polished surfaces of the Cu3SbSe2.8S1.2 sample; (d) The corresponding elemental mapping by EDS, obtained by overlaying the respective EDS signals directly arising from Cu (e), Sb (f), Se (g), and S (h).

Figure 2 . 14 Figure 3 .
Figure 2. (a) SEM image of the fracture surfaces of the Cu 3 SbSe 2.8 S 1.2 sample; (b) high magnification images of (a); (c) the corresponding EDS mapping for all constituent elements of selected region in (b); (c) SEM images of the polished surfaces of the Cu 3 SbSe 2.8 S 1.2 sample; (d) The corresponding elemental mapping by EDS, obtained by overlaying the respective EDS signals directly arising from Cu (e), Sb (f), Se (g), and S (h).Nanomaterials 2023, 13, x FOR PEER REVIEW 6 of 14

14 Figure 4 .
Figure 4. Temperature-dependent (a) electrical conductivity σ; (b) Seebeck coefficient S, the inset is Eg; (c) Pisarenko relationship with m* in this work compared with other works at room temperature.The indigo and red broken line represent the Pisarenko relationship with m* ~ 0.68 and 1.4 me, respectively.(d) power factor S 2 σ of Cu3Sb(Se1−xSx)4 (x = 0-1) samples.

Figure
Figure 4b illustrates the temperature-dependent S of the Cu3Sb(Se1−xSx)4 (x = 0-1) samples.The p-type semiconductor behavior of solid solutions, characterized by dominant hole carriers, was evidenced by the positive S value observed across the entire temperature range.Notably, the S value of the samples exhibited an initial ascent followed by a subsequent descent as the temperature rose, ultimately reaching its zenith at ~473 K.This be-

Figure 4 .
Figure 4. Temperature-dependent (a) electrical conductivity σ; (b) Seebeck coefficient S, the inset is Eg; (c) Pisarenko relationship with in this work compared with other works at room temperature.The indigo and red broken line represent the Pisarenko relationship with m* ~0.68 and 1.4 m e , respectively.(d) power factor S 2 σ of Cu 3 Sb(Se 1−x S x ) 4 (x = 0-1) samples.

Figure
Figure4billustrates the temperature-dependent S of the Cu 3 Sb(Se 1−x S x ) 4 (x = 0-1) samples.The p-type semiconductor behavior of solid solutions, characterized by dominant hole carriers, was evidenced by the positive S value observed across the entire temperature range.Notably, the S value of the samples exhibited an initial ascent followed by a subsequent descent as the temperature rose, ultimately reaching its zenith at ~473 K.This behavior can be attributed to the influence of the bipolar effect[54].The maximum S of ~730 µVK −1 was obtained from the x = 0.6 solid solution.We calculated the E g of the Cu 3 Sb(Se 1−x S x ) 4 (x = 0-1) samples with the formula: E g = 2eS max T, where E g , e, S max , and T represent the band gap, elementary charge, maximal Seebeck coefficient, and the associated temperature, respectively[55].The calculated E g for the pristine Cu 3 SbSe 4 of ~0.30 eV aligned well with the reported literature[36,56]; the results are displayed in FigureS3.Consequently, the introduction of alloyed S played a role in enlarging E g from ~0.30 eV to ~0.69 eV, thus widening the band gap to alleviate the bipolar effect.For the semiconductors, we note that the increase in S (|S|) was directly proportional to the carrier effective mass and n −2/3 .We calculated the Pisarenko relation between |S| and n (indigo and red dashed lines with m* ~0.68 and 1.4 m e , respectively) based on the single parabolic band model (SPB), as follows[57,58]: