Synergistic optimization of the thermoelectric performance of BiSbSe₃ using doping and multi-scale defect engineering

Abstract

Thermoelectric materials are anticipated to emerge as novel sustainable energy sources in the near future. Te-free BiSbSe₃ with an orthogonal crystal structure is considered as a promising candidate for medium-temperature thermoelectric materials due to its ultra-low thermal conductivity. However, the poor electrical transport performance limits its advance. In this work, BiSbSe_3−x−yBr_xI_y (x = 0, 0.12, 0.18; y = 0, 0.04, 0.06) samples were prepared through a combination of melting and hot-pressing sintering, and their thermoelectric properties were optimized by doping and multi-scale defect engineering. Specifically, the codoping of Br and I elements can effectively provide additional electrons and significantly enhance electrical conductivity. Based on defect engineering, an “all-scale hierarchical defects - full-frequency phonon scattering” mechanism was proposed to minimize the lattice thermal conductivity. As a result, an ultralow lattice thermal conductivity of ∼0.19 W m⁻¹ K⁻¹ and a peak ZT of ∼0.66 at 673 K are achieved for BiSbSe_2.76Br_0.18I_0.06. This work reveals the critical synergistic effect of codoping and multi-scale defect engineering on enhancing the thermoelectric properties of Te-free BiSbSe₃ materials.

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1. Introduction

Thermoelectric devices have the capability of converting waste heat into electrical energy, providing a new type of green energy that can help alleviate the energy crisis.¹ These devices demonstrate numerous advantages, such as the absence of noise, being free of pollution, and having long service life, small size, and no moving parts,² making them ideal for use in waste heat recovery, thermal power generation, solid-state cooling, and other applications.³ Numerous thermoelectric materials have been discovered and studied, including cage compounds,^2,4,5 Half-Heusler alloys,^6,7 oxide thermoelectric materials,^8,9 Bi₂Te₃-based alloys,^10–16 PbX (S, Se, Te) based alloys,^17–20 SiGe alloys,^21,22 and so on. These materials can be divided into n-type and p-type and are assembled into thermoelectric modules to achieve direct conversion of thermal energy and electrical energy.²³ The thermoelectric performance is mainly evaluated by using the dimensionless figure of merit ZT, ZT = PF T/κ_t, PF = S²σ, where S, σ, and κ_t, are the Seebeck coefficient, electrical conductivity, and thermal conductivity, respectively. A competitive thermoelectric material should have a synergistic combination of a high Seebeck coefficient, higher electrical conductivity, and lower thermal conductivity. These parameters are correlated with the following formula:

σ = neμ (2)

κ_t = κ_l + κ_e = κ_l + LTσ (3)

where κ_B, e, h, m*, n, μ, κ_l, and κ_e are the Boltzmann constant, electron charge, the Planck constant, the density of states effective mass of carriers, carrier concentration, carrier mobility, and lattice and electronic thermal conductivities, respectively. To enhance the thermoelectric properties of these materials, several effective strategies have been adopted, such as band regulation, band degeneration and introducing resonance state to decouple the electrical parameters, defect regulation and searching for compounds with a special crystal structure to reduce the lattice thermal conductivity, and heterovalent and homovalent doping to optimize the carrier concentration.^3,24–26 In addition, an alternative way to achieve high thermoelectric performance is to search for materials with intrinsically low thermal conductivity and a high Seebeck coefficient, such as BiCuSeO,²⁷ Cu₂Se,^28,29 SnSe,³⁰ and so on.

Bi₂Te₃-based thermoelectric materials possess a unique layered structure, abundant structural defects and excellent thermoelectric performance at room temperature,¹³ with a maximum ZT of ∼2.0.¹² Benefiting from their predominant thermoelectric performance near room temperature, Bi₂Te₃-based compounds are well-known commercial thermoelectric materials for large-scale applications.¹⁶ The Te element is known as the “vitamin of modern industry”, but its scarcity has led to increasing raw material cost, which limits the wide application of Bi₂Te₃-based thermoelectric materials.³¹ In this scenario, it is essential to seek low-cost thermoelectric materials. Both Bi₂Se₃ and Bi₂Te₃ are in the rhombohedral phase with the identical space groups of D_3d⁵ (R3̄m).³² Additionally, both Bi₂Se₃ and Bi₂Te₃ are three-dimensional topological insulators,³³ and can be completely mutually soluble at high temperatures.³⁴ As a substitute for Bi₂Te₃, low-cost Bi₂Se₃ has become a promising thermoelectric material. However, the high thermal conductivity and poor Seebeck coefficient of Bi₂Se₃ lead to a ZT value of only ∼0.05 at room temperature.³⁵ Bi₂Se₃ is a narrow band gap compound (∼0.3 ev), and the band degeneracy N_V = 1.³⁶ As a result, low density of states (DOS) and a poor power factor are obtained for Bi₂Se₃.³⁷ Wang et al. demonstrated that the structural transition of Bi₂Se₃ can be realized by composition-induced alloying with the Sb element. The obtained BiSbSe₃ with an orthorhombic phase increases the band degeneracy N_V from 1 to 2, leading to a large DOS effective mass and significantly enhanced power factor.³⁸ Furthermore, the lattice thermal conductivity of BiSbSe₃ is much lower than that of Bi₂Se₃ due to the weakening of chemical bonds, phonon softening and large amount of lattice anharmonic dynamics caused by structural transformation. With its complex chain-like structure, as shown in Fig. 1(a), it may exhibit anisotropy behavior. Thus, BiSbSe₃ exhibits a high Seebeck coefficient and low intrinsic thermal conductivity, making it a high-quality thermoelectric material at medium temperatures. However, the low conductivity of BiSbSe₃ limits its thermoelectric performance due to the extremely low carrier concentration and the mismatched relationship between the effective mass and carrier concentration. Therefore, enhancing its conductivity is crucial for improving the thermoelectric performance of BiSbSe₃-based thermoelectric materials.³⁹ Due to its multi-conduction band characteristics, BiSbSe₃ can be doped with donor elements to introduce a high carrier concentration and enhance its electrical transport performance. For instance, replacing selenium sites with halogen atoms can effectively increase the carrier concentration, further pushing the Fermi level into the conduction band, and activating more conduction bands to participate in electron transport with high carrier concentrations.^40–42 Recently, Wang et al. introduced chlorine at the selenium site, the carrier concentration was enhanced to ∼9.58 × 10¹⁹ cm⁻³, and a maximum ZT of ∼1.0 at 800 K was obtained.⁴³ However, enhancing electrical performance often compromises thermal performance, due to the intricate coupling between electrical and thermal conductivity. Therefore, synergistically optimizing their relationship presents a significant challenge.

Fig. 1 (a) Crystal structures of BiSbSe₃, (b)–(d) XRD patterns of BiSbSe_3−x−yBr_xI_y (x = 0, 0.12, 0.18; y = 0, 0.04, 0.06), (b) powder XRD patterns, (c) XRD patterns perpendicular to the HP direction, and (d) XRD patterns parallel to the HP direction.

In this work, a series of BiSbSe_3−x−yBr_xI_y (x = 0, 0.12, 0.18; y = 0, 0.04, 0.06) samples with secondary phases were synthesized by combining melting with hot-pressing sintering. The enhanced electrical conductivity and reduced lattice thermal conductivity were achieved through codoping and multi-scale defect engineering. Additionally, due to the chain-like structure of BiSbSe_3, the texture was formed utilized HP sintering, and it is confirmed that the effect of texture on thermal conductivity is more pronounced than that on electrical conductivity. Consequently, the peak ZT increases from ∼0.05 for pristine BiSbSe₃ to ∼0.67 for BiSbSe_2.78Br_0.18I_0.04 parallel to the HP direction at 673 K with a calculated thermoelectric conversion efficiency η of ∼9.3%. This work indicates that the synergistic optimization of electrical and thermal performance through codoping and multi-scale defect engineering provides a promising approach to enhance thermoelectric properties of BiSbSe₃-based materials.

2. Experiments

2.1 Synthesis

BiSbSe_3−x−yBr_xI_y samples codoped with iodine and bromine were prepared by melting, annealing and hot pressed sintering (HP). According to the stoichiometric ratio of BiSbSe_3−x−yBr_xI_y (x = 0, 0.12, 0.18; y = 0, 0.04, 0.06), the high-purity powders of Bi (99.999%), Sb (99.999%), Se (99.999%), I (99.99%), and BiBr₃ (99%) were weighed in a glove box, loaded into quartz tubes and sealed (vacuum 10⁻³ torr). The quartz tubes were then placed into a muffle furnace, soaked at 1173 K for 12 h, quickly quenched in water, and then annealed in a box furnace at 673 K for 24 h. The obtained ingots were ball-milled into a fine powder for 11 h. The obtained powders were hot pressed and sintered in Φ 20 mm graphite dies at 673 K for 180 min at a uniaxial pressure of 30 MPa.

2.2 Characterization and measurement

The phase composition of all samples was checked by X-ray diffraction (XRD, Bruker D8 Advance, Germany) with Cu Kα. The microstructures and elemental compositions were analyzed by using a field emission scanning electron microscope (SU5000, Hitachi, Japan) coupled with an energy dispersive spectrometer (EDS). The electron backscatter diffraction (EBSD) analysis was conducted on the samples after argon ion polishing (PECS II 685, Gatan, USA) using a high-resolution field emission scanning electron microscope (JSM-IT800, IEOL, Japan). Scanning transmission electron microscopy (STEM) samples were prepared using a dual-beam focused ion beam (FIB) (Helios G4 UX, Thermo Fisher, USA). Atomic resolution high-angle annular dark feld (HAADF) imaging was performed using a probe-corrected scanning transmission electron microscope (FEI Titan G2 60-300, FEl, USA). A Seebeck coefficient/conductivity comprehensive test system (LSR-3, Linseis, Germany) was used to measure the conductivity (σ) and Seebeck coefficient (S) of samples under a helium atmosphere from 323 K ∼673 K simultaneously. The thermal diffusivity (D) was measured by the laser flash method using laser thermal conductivity (LFA457, Netzsch, Germany) under an argon atmosphere. The density (ρ) is measured by using an electronic balance (ME204E, Mettler Toledo, Switzerland) and the principle of Archimedes drainage method. The heat capacity of the phonon harmonic term under the Debye model is taken as the total heat capacity (C_p) of the sample. The longitudinal (v_l) and shear (ν_t) phonon velocities and Young's modulus (E) were measured by using an UMS-100 tester, which is based on the standard “non-destructive testing-measurement method for materials elastic modulus and Poisson's ratio using ultrasonic velocity” (GB/T 38897-2020). The thermal conductivity (κ_t) was calculated through κ_t = ρDC_p. The accuracies of the S, σ, and κ measurements are ±5%, ±3%, and ±7%, respectively.

2.3 Theoretical calculations

First-principles density functional theory (DFT) calculations were performed to investigate the effects of the codoped Br and I on the properties of BiSbSe₃. These calculations were performed using DFT with the Perdew Burke Ernzerh exchange-correlation functional within the generalized gradient approximation,⁴⁴ as implemented in the Vienna Ab initio Simulation Package code.⁴⁵ The projected augmented wave potential was employed to describe the ion–electron interaction.⁴⁶ A k-point grid of 2π × 0.02 Å⁻¹ spacing was used for the Brillouin zone integrations, and the plane-wave cutoff energy was set to 500 eV. The iterative process was continued until the forces per atoms were less than 0.02 eV Å⁻¹ and the energy convergence threshold was 1.0 × 10⁻⁷ eV per atom. The calculated band structure of the supercell was unfolded back into the original unit-cell Brillouin zone by the techniques implemented in the KPROJ code.⁴⁷

3. Results and discussion

3.1 Phase composition and microstructure

Fig. 1(a) displays the crystal structure of BiSbSe₃, showing a chain-like structure that may exhibit anisotropy. Fig. 1(b) shows the room-temperature powder XRD patterns of BiSbSe_3−x−yBr_xI_y (x = 0, 0.12, 0.18; y = 0, 0.04, 0.06). All the diffraction peaks match well with those of BiSbSe₃ (PDF#751462), and a secondary precipitate Bi₂Se₃ is detected. As shown in Fig. 1(c) and (d), the diffraction peaks of samples sintered by HP show various relative intensities perpendicular (⊥BiSbSe_3−x−yBr_xI_y) and parallel (//BiSbSe_3−x−yBr_xI_y) to the HP directions, suggesting the preferred orientation of grains during the HP process. The fracture surface of sintered samples was observed using scanning electron microscopy (SEM) to analyze the microstructures. Fig. 2(a) and (b) display the morphologies of BiSbSe_2.82Br_0.12I_0.06 perpendicular and parallel to the HP directions, respectively. A distinct orientation can be observed in Fig. 2(b). Additionally, EDS was conducted to analyze the elemental distribution, as shown in Fig. 3(c). The Bi-rich phases were identified by elemental mappings and point scanning. The corresponding atomic percentages of areas 1, 2 and 3 in Fig. 3(d) are presented in Table 1. The ratios of Bi to Se elements in areas 1, 2 (Bi-rich phases) and 3 are ∼2 : 3, ∼2 : 3 and ∼1 : 1, respectively. It is reasonable to infer that the Bi-rich phase is Bi₂Se₃, which is consistent with the XRD results. To obtain a more comprehensive understanding of the sample's anisotropy, electron backscatter diffraction (EBSD) was conducted on the same sample perpendicular and parallel to the HP directions, as shown in Fig. 3. The band contrast image in Fig. 3(a) and (d) reveals that the grains predominantly display a rod-like morphology. This can be attributed to the accelerated growth along the short axis b during sintering, leading to rod-like grains along the <010> direction (Fig. 3(g)). From Fig. 3(b) and (e), the smaller grains are observed parallel to the HP direction. The disparity regarding grain size along the different directions may be attributed to the preferred grain orientation and growth, as well as the compressive deformation along the perpendicular HP direction.⁴⁸ In Fig. 3(b) and (c), a specific preferred orientation is identified for the grains in the sample perpendicular to the HP direction, where the <100> direction of most grains aligns parallel to the HP direction. Similarly, in the sample parallel to the HP direction the <100> direction of most grains also aligns parallel to the HP direction, leading to an obvious texture, as shown in Fig. 3(e) and (f). As a result, the sintered samples are composed of stacked layers of grains with the <100> direction predominantly parallel to the HP direction.

Fig. 2 SEM micrographs of the fracture section of (a) BiSbSe_2.82Br_0.12I_0.06 perpendicular to the HP direction, (b) BiSbSe_2.82Br_0.12I_0.06 parallel to the HP direction, (c) BiSbSe_2.84Br_0.12I_0.04 perpendicular to the HP direction, (d)–(h) Energy Dispersive Spectrometry (EDS) of BiSbSe_2.84Br_0.12I_0.04.

Fig. 3 EBSD characterization of sample BiSbSe_2.82Br_0.12I_0.06, (a)–(c) perpendicular to the HP direction, (d)–(f) parallel to the HP direction, (a) and (d) band contrast, (b) and (e) inverse pole figure (IPF) color maps along the Z direction, and(c) and (f) inverse pole figures along the X, Y and Z directions. (g) Schematic diagram of texture formation.

Table 1 Atomic percentage in regions 1, 2, and 3

Element	Bi	Sb	Se	Br	I
1	34.27%	14.49%	48.93%	1.99%	0.32%
2	33.24%	15.14%	49.06%	2.28%	0.28%
3	18.29%	22.34%	56.96%	2.24%	0.17%

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To further confirm the phase and interfacial structures, HAADF-STEM analysis was conducted on the BiSbSe_2.76Br_0.18I_0.06 sample. As shown in Fig. 4(a), a distinct phase boundary is visible, with region I corresponding to the matrix phase (Fig. 4(b)), and region II corresponding to the secondary precipitate (Fig. 4(c)). Significant Bi-rich phases are observed in the elemental mapping image (Fig. 4(d1)). The HAADF-STEM image in Fig. 4(c) and the FFT pattern in the inset further confirm that the secondary precipitate in region II is Bi₂Se₃, and its formation are related to multiple factors. Specifically, the formation energy of antisite defect E_AS follows this order: E_AS(Sb–Te) < E_AS(Bi–Te) < E_AS(Sb–Se) < E_AS(Bi–Se), with Sb–Se having a smaller antisite defect energy than Bi–Se,⁴⁹ indicating a higher inclination for Sb atoms to occupy the Se sites and form antisite defects. The occupation of Se sites by Sb atoms leads to a reduction in the number of Sb atoms in the samples, resulting in insufficient Sb atoms available for bonding with Bi atoms, thereby leading to the formation of Bi₂Se₃. Furthermore, excessive doping may have surpassed the solubility limit, resulting in the secondary precipitates. The geometric phase analysis (GPA) depicted in Fig. 4(f1) and (f2) reveals significant fluctuations in the strain fields. Fig. 4(g) displays the inverse fast-Fourier transform (IFFT) image of the (001) plane shown in Fig. 4(f), which readily shows abundant dislocations and lattice distortions. These high-density distortions and strains greatly contribute to phonon scattering.⁵⁰ Additionally, both phase boundaries (Fig. 4(a)) and grain boundaries (Fig. 4(e)) can also scatter phonons and reduce lattice thermal conductivity to a certain extent, which will be discussed later.

Fig. 4 TEM image of the BiSbSe_2.76Br_0.18I_0.06 sample. (a) Low-magnification TEM image, the inset picture shows the electron diffraction patterns of two phases, (b) the HAADF-STEM image of the I area in (a), the inset picture shows the fast-Fourier transform (FFT) image, (c) the HAADF-STEM image of the II area in (a), the inset picture shows the FFT image, (d) the HAADF-STEM image of the interface between two phases of the selected square area in (a), (d1)–(d5) the corresponding elemental mapping images of Bi, Sb, Se, Br, and I, (e) low-magnification TEM image, the inset picture shows the electron diffraction pattern, (f) the HAADF-STEM image, the inset picture shows the FFT image, (f1) and (f2) GPA results along the ε_xy and ε_yy directions, and (g) inverse fast-Fourier transform (IFFT) image of plane (001) of (f).

3.2 Electrical transport properties

The temperature-dependence of the electrical conductivity of BiSbSe_3−x−yBr_xI_y samples is shown in Fig. 5(a). Substituting Br and I for Se sites introduces extra electrons, leading to a significant increase in carrier concentration, from ∼1.17 × 10¹⁶ cm⁻³ for the matrix to ∼2.89 × 10¹⁹ cm⁻³ for ⊥BiSbSe_2.84Br_0.12I_0.04 (Table 2), increased by three orders of magnitude. The calculated electronic band structures of pristine BiSbSe₃ and the I–Br codoped sample are shown in Fig. 6. After codoping, the Fermi level moves deeper into the conduction band, and more conduction bands will participate in electron transport, enhancing the carrier concentration. The defect equations are as follows:where represents the substitution of Bi (BiBr₃) at Bi (BiSbSe₃) sites without extra electrons; and represent the substitutions of Br at Se sites and I at Se sites. Positively charged substitution defects are formed, which can generate excess electrons. The electrical conductivity of all doped samples exhibits a trend of initially increasing, then decreasing, and subsequently increasing with increasing temperature. This complex trend can be attributed to impurity ionization and intrinsic excitation in impurity semiconductors.⁵¹ Below 373 K, the ionization of donor impurities plays a dominant role, enhancing the electrical conductivity by releasing electrons. As the temperature increases, the samples exhibit degenerate semiconductor characteristics, with the electrical conductivity decreasing as the temperature increases.⁵² However, at temperatures above 523 K, the mixed conduction of electrons and holes generated by intrinsic excitation results in an increase in the electrical conductivity.⁵³ Furthermore, the conductivity perpendicular to the HP direction is higher than that parallel to the HP direction for the same sample, suggesting superior electric transport performance perpendicular to the HP direction. For all the samples with identical I doping contents, irrespective of the direction, the conductivity decreases with increasing Br doping content. This may be mainly because excessive Br doping intensified the carrier scattering.⁴⁰ It is worth noting that the Seebeck coefficients of the samples display an almost isotropic behavior, irrespective of the direction, as shown in Fig. 5(b).⁵⁴ The temperature-dependent power factor for all samples is shown in Fig. 5(c), and a peak power factor of ∼4.1 μW cm⁻¹ K⁻² is achieved at 673 K for ⊥BiSbSe_2.84Br_0.12I_0.04. The Pisarenko curves are calculated to describe the relationship between S and n, based on the Boltzmann transport equation for electrons in the single parabolic band (SPB) model, as shown in Fig. 5(d). Various band effective masses are observed perpendicular and parallel to the HP directions. The band effective mass (m*) is inversely proportional to the band curvature.⁵⁵ Typically, carriers transported along the light-band direction with large curvature demonstrate smaller effective mass. Conversely, carriers transported along the heavy-band direction with small curvature exhibit larger effective mass. Under the SPB model, when acoustic phonon scattering dominates the carrier transport, the Seebeck coefficient can be expressed as:where k_B, e, F₁(η), and η are the Boltzmann constant, the elemental charge, the Fermi integral, and the reduced Fermi level, respectively. It has been found that S is only related to the position of the reduced Fermi level η (η = E_F/k_BT) and is independent of the m*, which is consistent with experimental results, demonstrating almost isotropy perpendicular and parallel to the HP directions.⁵⁶

Fig. 5 Temperature-dependence of the BiSbSe_3−x−yBr_xI_y (x = 0, 0.12, 0.18; y = 0, 0.04, 0.06) samples: (a) electrical conductivity, (b) Seebeck coefficient, and (c) power factor. (d) Room temperature Pisarenko plot.

Table 2 The room temperature carrier density (n_H), Hall mobility (μ_H), Young's modulus (E), longitudinal phonon velocities (ν_l), shear phonon velocities (ν_t), average phonon velocity (ν) and Debye temperature (θ_D) of BiSbSe_3−x−yBr_xI_y (x = 0, 0.12, 0.18; y = 0, 0.04, 0.06) samples

Samples	n H (10^19 cm^−3)	μ H (cm^2 V^−1 s^−1)	E (GPa)	v l (ms^−1)	ν t (ms^−1)	v (ms^−1)	θ D (K)
⊥x = 0, y = 0	0.001	19.0	33.7	2454	1406	1561	153.5
//x = 0, y = 0	0.001	1.2	36.9	2728	1441	1611	158.3
⊥x = 0.12, y = 0.04	2.89	25.4	25.9	2409	1269	1419	134.7
//x = 0.12, y = 0.04	2.58	26.4	23.8	2057	1278	1409	133.8
⊥x = 0.12, y = 0.06	2.96	24.4	26.7	2476	1295	1449	136.9
//x = 0.12, y = 0.06	2.56	24.0	23.6	2051	1286	1416	133.8
⊥x = 0.18, y = 0.04	1.98	35.5	27.5	2383	1320	1471	139.7
//x = 0.18, y = 0.04	1.98	32.0	24.5	2064	1307	1438	136.5
⊥x = 0.18, y = 0.06	3.71	16.7	31.0	2445	1439	1595	150.6
//x = 0.18, y = 0.06	3.18	19.1	25.6	2144	1336	1472	139.0

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Fig. 6 Calculated electronic band structures of (a) pristine BiSbSe₃ and (b) I–Br codoped samples.

3.3 Thermal transport properties

Fig. 8(a) shows the temperature-dependence of the total thermal conductivities for all samples. Compared with the pristine BiSbSe₃ matrix, the total thermal conductivity of BiSbSe_3−x−yBr_xI_y samples was substantially suppressed over the entire temperature range after codoping. Furthermore, the total thermal conductivity monotonously decreases with increasing temperature and this decline becomes negligible beyond 523 K. This can be attributed to the bipolar thermal effect, wherein the hole–electron pairs generated by thermal excitation further enhance thermal transport. According to the following formula, the thermal conductivity is proportional to E:⁵⁷where ρ, E, M, m are the density, Young's modulus, atomic weight of the molecule of the compound, number of atoms in the molecule, respectively. The E of all samples, as presented in Table 2, exhibits relative lower values compared to that of other state-of-the-art thermoelectric materials with ultra-low thermal conductivity such as SnSe (30.0 GPa)⁵⁸ and BiCuSeO (76.5 GPa),²⁶ expect for the pristine matrix. This suggests the potential for achieving a high ZT value. The lattice thermal conductivity κ_l is calculated by subtracting the electronic thermal conductivity κ_e (Fig. 8(d)) from the total thermal conductivity κ_t. As depicted in Fig. 8(b), it is evident that κ_l decreases with increasing temperature, roughly following the trend of κ_l ∝ T^−0.5, indicating the predominant influence of phonon–phonon interactions on reducing κ_l. The contribution of phonons to the thermal conductivity can be expressed as:where C_v, v, and l_p are constant volume heat capacity per unit volume, velocity of the phonon-group, and mean free path of phonons. BiSbSe₃ possesses a relatively complex crystal structure, with a certain degree of repulsion between the 5s² lone-pair electrons of Sb and the 3p orbital of Se. Similarly, the chemical bond is softened after codoping, leading to the formation of a phonon blocking mechanism through the interaction between Br and Bi and lone pair electrons.⁵⁹ As a result, high anharmonic lattice vibrations and strong scattering lattice waves are generated, thereby reducing the mean free path of phonon l_p.⁶⁰ Additionally, the intra-chain bond lengths of Sb–Se and Bi–Se in BiSbSe₃ are ∼2.6–2.8 Å and ∼2.7–2.9 Å, respectively, indicating strong covalent bonding. However, the inter-chain bond length is ∼3–3.15 Å, which significantly surpasses the sum of the covalent radii of Bi–Se (2.62 Å) and Sb–Se (2.54 Å), indicating weak inter-chain interactions³⁸ and resulting in low phonon velocities, as shown in Table 2. Therefore, the doped BiSbSe₃ samples exhibit low lattice thermal conductivities as a result of the strong anharmonicity and low sound velocity.

To further reduce the lattice thermal conductivity, a multi-scale defect modulation strategy is employed to scatter phonons with various frequencies. Thus, based on defect engineering, a mechanism “all-scale hierarchical defects (atomic scale, nanoscale and microscale) – full-frequency phonon scattering (high-frequency, mid-frequency and low-frequency)” is proposed, as shown in Fig. 8(e). The Debye–Callaway model can quantitatively describe the relationship between κ_l and multiple-phonon scattering mechanisms:⁶¹

where k_B is Boltzmann's constant, v is the average phonon-group velocity, T is the absolute temperature, h is the Planck constant, θ_D is the Debye temperature, τ_tot is the relaxation time, x is defined as hω/k_B (ω is the phonon frequency). According to Matthiessen's rule, the τ_tot encompasses various phonon scattering processes, including the Umklapp processes (τ_U), point defects (τ_PD), grain boundaries (τ_GB), dislocations (τ_DS), strains (τ_S), and precipitates(τ_P), and can be expressed as:⁶²

τ⁻¹_tot = τ⁻¹_U + τ⁻¹_PD + τ⁻¹_GB + τ⁻¹_DS + τ⁻¹_S + τ⁻¹_P (10)

The coexistence of point defects, grain boundaries, dislocations, strains, and secondary precipitates enables wide-frequency phonon scattering for samples.⁶³ Specifically, at the atomic scale, the boiling point of Se is lower than that of Bi and Sb, so Se is susceptible to volatilization, which results in a large number of intrinsic anion vacancies and an excess of cations in the samples. As previously mentioned, the occupation of anionic positions by excess cations leads to the formation of antisite defects . These 0-D point defects can effectively scatter high-frequency phonons with a short mean free path.⁶³ During the solidification of all samples, defects were trapped in the growing crystals, potentially leading to the presence of dislocations even after HP sintering.³⁷ Additionally, the ingots after quenching were crushed by ball milling, which also introduced a large number of dislocations. In Fig. 4(g), numerous 1-D defective dislocations were observed in the sample, which leads to lattice distortions and strains. The geometrically necessary dislocation (GND) analysis in Fig. 7 provides further explanations of the dislocations and strains. The consistent average ρ^GND of ∼0.8 × 10¹⁴ m⁻², irrespective of perpendicular or parallel to the HP directions, indicates the existence of a high-density uniform distribution of dislocations over a large field of view (tens of micrometer scale). These dislocations and strains can effectively scatter mid-frequency phonons.⁶³ In addition, the texture was formed during HP sintering, resulting in smaller grains parallel to the HP direction and numerous grain boundaries, which is in favor of phonon scattering.⁶⁴ Furthermore, the codoping of iodine and bromine may lead to the formation of pores due to their low boiling points and easy volatilization, as shown in Fig. 3(a) and (b). Additionally, the microscale secondary Bi₂Se₃ phase is observed, which introduces phase boundaries and interfacial dislocations.⁶⁵ Therefore, the presence of all-scale hierarchical defects including 0-D point defects, 1-D dislocations, 2-D textures and interfaces and 3-D secondary phases and pores collectively contributes to the effective scattering of full-frequency phonons. As shown in Fig. 8(a) and (b), the ultralow total thermal conductivity of ∼0.29 W m⁻¹ K⁻¹ and lattice thermal conductivity of ∼0.19 W m⁻¹ K⁻¹ are achieved at 673 K for //BiSbSe_2.78Br_0.18I_0.04, which is the lowest value compared to that of reported n-type BiSbSe₃-based materials to our knowledge, as shown in Fig. 8(c).

Fig. 7 GND maps of sample BiSbSe_2.82Br_0.12I_0.06, (a) and (b) perpendicular to the HP direction, (c) and (d) parallel to the HP direction, (a) and (c) GND maps, and (b) and (d) histograms of GND densities.

Fig. 8 (a), (b) and (d) represent the temperature-dependence of the BiSbSe_3−x−yBr_xI_y (x = 0, 0.12, 0.18; y = 0, 0.04, 0.06) samples, (a) total thermal conductivity (κ_t), (b) lattice thermal conductivity (κ_l), (c) a comparison of κ_l in n-type BiSbSe₃,^{38,39,48,49,66,67} (d) electronic thermal conductivity (κ_e), and (e) the phonon scattering mechanism.

3.4 Dimensionless figure of merit ZT

The temperature-dependent dimensionless thermoelectric figure of merit ZT for BiSbSe_3−x−yBr_xI_y samples is presented in Fig. 9(a). Benefiting from the optimization of electrical transport and thermal transport properties, a significant ZT improvement can be achieved. The peak ZT is enhanced from ∼0.05 for pristine //BiSbSe₃ to ∼0.67 for //BiSbSe_2.78Br_0.18I_0.04 at 673 K. As shown in Fig. 8(b), the ratio of κ⊥/κ// ranges from 1.3–1.6 and the ratio of σ⊥/σ// ranges from 1.1–1.3, indicating that the influence of texture on thermal conductivity is more pronounced than that on electrical conductivity. Thus, the ZT values of samples parallel to the HP direction are higher than that of the counterparts perpendicular to the HP direction.

Fig. 9 (a) Temperature-dependence of ZT values for BiSbSe_3−x−yBr_xI_y (x = 0.12,0.18; y = 0.04,0.06) samples, and (b) the ratio of electrical and thermal conductivity along the different directions.

In addition to the high ZT value, the thermoelectric conversion efficiency η is a crucial factor for industrial application. The theoretical maximum power generation efficiency η_max of a thermoelectric power generation device can be defined as:⁶⁸

where T_H is the hot-side thermoelectric leg temperature and T_C is the cold-side thermoelectric leg temperature. Fig. S3† shows that the //BiSbSe_2.78Br_0.18I_0.04 sample demonstrates a η of 9.3% at 673 K, as calculated from the above formula, suggesting good application prospects.

4. Conclusions

In summary, a series of BiSbSe_3−x−yBr_xI_y (x = 0, 0.12, 0.18; y = 0, 0.04, 0.06) samples with deformation textures were successfully prepared by the combination of melting and HP sintering. Through codoping and multi-scale defect engineering, enhanced electrical conductivity and reduced the lattice thermal conductivity were obtained simultaneously, achieving a peak ZT of ∼0.67 at 673 K and a thermoelectric conversion efficiency η of 9.3% for //BiSbSe_2.78Br_0.18I_0.04. Electrically, the codoping of I and Br effectively increased the carrier concentration and enhanced the power factor. Thermally, an “all-scale hierarchical defects (atomic scale, nanoscale and microscale) – full-frequency phonon scattering (high-frequency, mid-frequency and low-frequency)” mechanism was proposed. And the all-scale hierarchical defects including 0-D point defects, 1-D dislocations, 2-D defect textures and interfaces, and 3-D defect secondary phases and pores, collectively contribute to the full-frequency phonon scattering for the samples. As a result, an ultralow κ_l of ∼0.19 W m⁻¹ K⁻¹ was achieved for //BiSbSe_2.76Br_0.18I_0.06. Additionally, the texture displays a more pronounced anisotropy for thermal conductivity than electrical conductivity for the samples. Overall, the synergistic effect of codoping and multi-scale defect strategy can effectively enhance the thermoelectric properties, potentially offering insightful ideas to surpass the performance limitations of thermoelectric materials.

Data availability

The data that support the findings of this study are available from the corresponding author upon reasonable request.

Author contributions

Xiaowei Shi: conceptualization, methodology, data curation, writing – original draft. Zhen Tian: validation, investigation. Quanwei Jiang: validation. Yu Yan: investigation. Huijun Kang: conceptualization, investigation, writing – review & editing, supervision. Enyu Guo: investigation, writing – review & editing. Zongning Chen: investigation, writing – review & editing. Tongmin Wang: conceptualization, investigation, writing – review & editing, supervision.

Conflicts of interest

The authors declare no competing financial interest.

Acknowledgements

This work was financially supported by the National Natural Science Foundation of China (No. 52271025, 51927801, and U22A20174), Science and Technology Planning Project of Liaoning Province (2023JH2/101700295) and Innovation Foundation of Science and the Technology of Dalian (No. 2023JJ12GX021).

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Footnote

† Electronic supplementary information (ESI) available. See DOI: https://doi.org/10.1039/d4ta03432e

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