Enhancement of the thermoelectric properties of MnSb₂Se₄ through Cu resonant doping

Abstract

MnSb₂Se₄ is a narrow band semiconductor having large Seebeck coefficients and intrinsically low thermal conductivities, but modest thermoelectric zT values due to having low carrier concentrations and high electrical resistivity. Here, we report that Cu substituted Mn_1−xCu_xSb₂Se₄ (0 ≤ x ≤ 0.35) materials display resonant doping behavior, leading to significantly enhanced power factors (PFs) and overall thermoelectric zT values in the measured temperature range. For the optimized composition Mn_0.75Cu_0.25Sb₂Se₄, the PF reaches 0.26 mW m⁻¹ K⁻² at 773 K, coupled with low thermal conductivities of 0.61 W K⁻¹ m⁻¹ to 0.32 W K⁻¹ m⁻¹ over the measured temperature range. A peak zT of 0.64 at 773 K is achieved, which is a 100% increase in comparison to undoped MnSb₂Se₄. Such a high zT has rarely been seen in thermoelectric materials with a low symmetry of crystallization, implying that Cu-doped MnSb₂Se₄ could be considered as a new platform in thermoelectric research for intermediate temperature power generation.

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1. Introduction

Thermoelectric (TE) materials can play a key role in efficient energy conversion by directly converting waste heat into electricity or conversely, creating a heat gradient by applying an electrical current. The conversion efficiency of TE materials is governed by the dimensionless figure of merit, zT = (S²/ρκ)T, where S, ρ, κ, and T are the Seebeck coefficient, electrical resistivity, thermal conductivity, and absolute temperature, respectively.¹ To obtain a high zT, the general route focuses on minimizing κ while maximizing the power factor, S²/ρ. On the one hand, the power factor can be optimized as a function of the carrier concentration (n), which should typically be approximately 10¹⁹ cm⁻³ and can be realized through doping in intrinsic semiconductor TE materials.² Meanwhile, other strategies that can be used to improve the power factor include band convergence,³ energy barrier filtering,⁴ resonant states,^5,6 and modulation doping.⁷ On the other hand, κ is mainly composed of κ_lat and κ_ele, where κ_lat and κ_ele are the lattice and electronic contributions of the thermal conductivity, respectively. κ_ele is directly related to ρ and T through the Wiedemann–Franz law κ_ele = LT/ρ, where L is the Lorenz number.⁸ A lower κ_lat can be realized by several phonon scattering mechanisms, such as point defect scattering, nano-structuring, “rattling”, grain-boundary scattering, interface scattering, etc.⁹

Traditional thermoelectric research mainly focuses on material systems with a high symmetry of crystallization, such as Bi₂Te₃ (trigonal),¹⁰ PbTe (cubic),¹¹ SiGe (cubic),¹² half-Heusler (cubic),¹³ Mg₂Si (cubic),¹⁴ and α-MgAgSb (tetragonal).¹⁵ Highly symmetric TE materials usually possess a desirable electronic band structure, which is beneficial for achieving high-mobility carriers, high electrical conductivity, as well as a large Seebeck coefficient. Typically, the room temperature carrier mobility and Seebeck coefficient of n-type and p-type Bi₂Te₃ are μ_n ∼ 270 cm² V⁻¹ s⁻¹, S ∼ −250 μV K⁻¹, and μ_p ∼ 420 cm² V⁻¹ s⁻¹, S ∼ 260 μV K⁻¹, respectively.^16,17 However, on the other hand, TE materials with high symmetry of crystallization and strongly covalent chemical bonds usually favor high lattice thermal conductivities. Compounds with low lattice thermal conductivity are generally associated with heavy compositional elements, low symmetric crystallization, complex unit cells, etc.¹⁸ Namely, when acoustic phonon scattering dominates the carrier transport and the Fermi level is optimized through doping, the maximum zT is determined by the quality factor B, , where k_B is the Boltzmann constant, ħ is the reduced Planck constant, C_l is the combined elastic moduli, N_v is the number of degenerate valleys, m^*_I is the band effective mass, and E_def is the deformation potential coefficient characterizing the strength of the carriers scattered by acoustic phonons.^19,20 The quality factor B suggests that low lattice thermal conductivity and multiple degenerate valleys with low band effective mass are beneficial for high zT. Thus, searching for new pristine TE materials with intrinsically low thermal conductivities has been a hot topic in thermoelectric research in recent years.^21,22

MPn₂Q₄ (M = Mn, Fe; Pn = Sb, Bi; and Q = S, Se) compounds are a fascinating class of ternary magnetic semiconductors that exhibit interesting physical properties, which also show potential in thermoelectricity, spintronics and photoelectronics, as well as for solid-state electrolytes.^23,24 Despite the close similarity in their crystal structures (monoclinic space group C2/m, no. 12), the dominant magnetic ordering and charge carrier type in MPn₂Q₄ compounds can be diversified. For instance, antiferromagnetic (AFM) ordering can be observed in MnSb₂S₄,^25,26 MnSb₂Se₄,²⁷ and MnBi₂Se₄,²⁸ whereas FeSb₂Se₄ (ref. 29) and FeBi₂Se₄ (ref. 24) show ferromagnetic (FM) behavior. Moreover, p-type semiconducting behavior is observed in MnSb₂Se₄ (ref. 27) and FeSb₂Se₄,²⁹ but MnBi₂Se₄ (ref. 28) and FeBi₂Se₄ (ref. 24) exhibit n-type semiconducting behavior. Recently MnSb₂Se₄ was reported to possess a large Seebeck coefficient (S = +945 μV K⁻¹), high electrical resistivity (ρ ∼ 8.9 Ω m) and an intrinsically low thermal conductivity (κ = 1.4 W m⁻¹ K⁻¹) at 300 K.²⁷ Based on electronic band structure calculations, infrared diffuse reflectance spectroscopy, and magnetic susceptibility measurements, it was found that MnSb₂Se₄ is a semiconductor with an energy band gap of ∼0.31 eV, exhibiting paramagnetic behavior at 300 K and with a Néel temperature of 20 K.²⁷ The thermoelectric properties were measured only for a low temperature range. It has been realized that the poor thermoelectric properties in MnSb₂Se₄ mainly originate from its large resistivityρ. However, research activity to reduce ρ in this material has been rare so far, with one report on Sn-doped MnSb₂Se₄ leading to a much increased electrical resistivity.³⁰

In this study, we demonstrate that Cu substituted Mn_1−xCu_xSb₂Se₄ (0 ≤ x ≤ 0.35) materials display heavily doped p-type semiconducting behavior with increased carrier concentrations of approximately 10¹⁹ cm⁻³, and furthermore the resonant states in the valence band caused by Cu doping lead to significantly enhanced power factors (PF) and overall thermoelectric figure of merit zT values in the whole temperature range. For the optimized composition Mn_0.75Cu_0.25Sb₂Se₄, the PF reaches 0.26 mW m⁻¹ K⁻² at 773 K, coupled with low thermal conductivities of 0.61 W K⁻¹ m⁻¹ to 0.32 W K⁻¹ m⁻¹ over the whole temperature range. A peak zT of ∼0.64 at 773 K is achieved, which is a 100% increase in comparison to undoped MnSb₂Se₄. This result implies that Cu-doped MnSb₂Se₄ could be considered as a new platform in thermoelectric research for intermediate temperature power generation.

2. Experimental

Cu doped MnSb₂Se₄ samples were synthesized as a single phase using high purity Mn powder (99.95%, Beijing Xiao Yang Technology Development Co., Ltd. China), Cu powder (99.9%, Alfa Aesar, US), Sb powder (99.999%, Beijing Xiao Yang Technology Development Co., Ltd. China), and Se powder (99.99%, Beijing Xiao Yang Technology Development Co., Ltd. China) as the starting materials. The stoichiometric mixture of all of the starting powders was thoroughly mixed using an agate mortar with a pestle and sealed in an evacuated quartz tube. The sealed tube was then placed into a furnace, slowly heated up to 573 K, and held at this temperature for 10 h. The furnace temperature was then increased to 773 K in 2 h and held at this temperature for 24 h, before finally being cooled down to room temperature by turning off the furnace power. The ingots were ground into fine powders using an agate mortar with a pestle, and then approximately 9 g of the powder was sintered using the spark plasma sintering (SPS) method at 773 K for 10 min under an axial pressure of 65 MPa in a 12.7 mm diameter graphite die under evacuated conditions. The relative density of the pressed pellets was about 94% with respect to its theoretical value, and the resulting pellets were obtained with a thickness of 13 mm and a diameter of 12.7 mm.

The X-ray diffraction (XRD) patterns of the synthesized Cu doped MnSb₂Se₄ polycrystalline powder were recorded on a Panalytical X′ Pert Pro using monochromatic Cu Kα radiation (λ = 1.5418 Å) and operating under 40 kV and 40 mA. Scanning electron microscopy (SEM) images were recorded using an XL30 S-FEG SEM (FEI, US).

Magnetic measurements were performed on polycrystalline powder of MnSb₂Se₄ (34.3 mg) and Mn_0.75Cu_0.25Sb₂Se₄ (33.6 mg) using a Quantum Design Magnetic Property Measurement System (MPMS) SQUID magnetometer. The magnetic measurement data was recorded at alternating current (AC) at 100 Hz between 2 K and 300 K in an applied field of 5 Oe. Heat capacity (C_p) values between 5 K and 280 K were measured under a zero applied field using a Quantum Design Physical Property Measurement System (PPMS).

Electrical and thermal transport properties were measured from 300 K to 773 K. The pellets were cut into 2.5 mm × 2.5 mm × 12 mm bars for measurement of the electrical resistivity and the Seebeck coefficient using a commercial LSR-3 Seebeck coefficient/electrical resistivity measurement system (Linseis, Germany) under a low-pressure helium atmosphere. The uncertainty of the electrical resistivity and Seebeck coefficient measurement is ±5%. The thermal conductivity was calculated from κ = DC_pd, where D is the thermal diffusivity coefficient, C_p is the specific heat capacity, and d is the density. The pellets were cut and polished into a square shape of 10 mm × 10 mm × 2 mm for thermal diffusivity measurements. The thermal diffusivity was measured under an argon atmosphere using the laser diffusivity method in a Netzsch LFA 457. The heat capacities between 300 K and 773 K were measured using a differential scanning calorimeter (DSC) in a TA Q200 instrument, and the density was determined using the dimensions and mass of the sample. The uncertainty of C_p is around 7%. The uncertainty of the thermal conductivity is estimated to be within 8%, considering the uncertainties from D, C_p, and d. The combined uncertainty for all measurements involved in the calculation of zT is less than 12%. The Hall coefficient measurements were carried out using the van der Pauw technique under a reversible magnetic field of 0.5 T using pressure-assisted tungsten electrodes on a Nanometrics Hall System. The instrument uncertainty for the Hall coefficient data is ±5%.

The first principles calculations were performed with the plane-wave pseudopotential method using CASTEP program code.³¹ We adopted the generalized gradient approximation (GGA) in the form of the Perdew–Burke–Ernzerhof for the exchange–correlation potentials.³² Spin-polarized and LDA+U calculations were made to correctly deal with our system. The ultrasoft pseudopotential with a plane-wave energy cutoff of 440 eV and a 2 × 6 × 2 Monkhorst Pack k-point mesh in the reciprocal space were used for all of the calculations.³³ The self-consistent field was set as 5 × 10⁻⁷ eV per atom. To simplify the mixed occupancy situation, we assigned mixed occupancy sites only for the high occupancy atoms. We substituted one Mn atom with one Cu atom in the MnSb₂Se₄ cell to study Mn_0.75Cu_0.25Sb₂Se₄.

3. Results and discussion

Phase and structural analysis

As shown in Fig. 1a and b, the crystal structure of MnSb₂Se₄ can be described as a one dimensional edge-sharing arrangement of [(Mn)(Sb)₂(Se)₄]_∞ chains along the b axis, or a three-dimensional structure composed by both magnetic and semiconducting sub-lattices, which are linked with each other along the c axis by a long Sb–Se bond. The magnetic behavior of MnSb₂Se₄ originates from the geometrical details of the [MnSe₆]_∞ chains in the 3D structure and the coupling between localized spins on adjacent Mn atoms. The electronic transport properties are dominated by the semiconducting sub-units of the [Sb₂Se] network which separate adjacent MnSe₆ chains. In addition, the anti-site occupancy between Mn, and Sb was observed in the crystal structure of MnSb₂Se₄,²⁷ which would have an elaborate impact on the physical properties. The room-temperature powder X-ray diffraction (XRD) patterns corresponding to all of the Mn_1−xCu_xSb₂Se₄ (0 ≤ x ≤ 0.35) samples are consistent with the characteristics of a monoclinic MnSb₂Se₄ structure (Fig. 1c). No impure phase was observed within the detection limits of the equipment, and all of the reflection peaks can be indexed with the space group C2/m (no. 12). The lattice parameters for the MnSb₂Se₄ sample were observed to be a = 13.331 (3) Å, b = 3.967 (2) Å, c = 15.441 (4) Å, and β = 116.1 (5) °, which is significantly larger than previously reported data [a = 13.076 (3) Å, b = 3.965 (1) Å, c = 15.236 (3) Å, and β = 115.1 (3) °], especially in both the a and c directions.²⁷ As shown in Fig. 1d, for the Cu-doped samples, both a and b increased slightly and c decreases until x reaches 0.25, beyond which the doping saturates, in comparison to the lattice parameters of MnSb₂Se₄. This indicates that the substitution of Mn by the larger sized Cu (the ionic radius of Mn²⁺ and Cu¹⁺ are ∼0.67 Å and ∼0.77 Å respectively³⁴) in MnSb₂Se₄ will slightly increase the volume size of the crystal cell. The c constant of the lattice decreases with the increase of the Cu dopant in that the octahedral Mn(Cu)Se₆ structural unit in Mn_1−xCu_xSb₂Se₄ is subjected to a tilting distortion, which can lead to the decrease of the β angle, and the shortening of the c axis. As for the microstructure of the Mn_1−xCu_xSb₂Se₄ samples, the SEM (scanning electron microscopy) images in Fig. 1e and f show the detailed information. The image in Fig. 1e reveals a dense structure with a well-organized morphology composed of plate-like crystallites, and the average crystal size at the surface is around 50 μm. Fig. 1f clearly shows the layered structure in an enlarged area of the grains in Fig. 1e, which is coincident with the nature of the crystal structure.

Fig. 1 Crystal structure of MnSb₂Se₄ projected along the (a) [010] and (b) [100] directions, (c) room temperature powder XRD patterns for the samples of Mn_1−xCu_xSb₂Se₄ (0 ≤ x ≤ 0.35), (d) lattice parameters as a function of the doping content x, (e) a typical SEM image of the Mn_0.75Cu_0.25Sb₂Se₄ samples, (f) an enlarged SEM image of a selected area in (e).

Magnetism and specific heat

Previous work shows that MnSb₂Se₄ has an effective magnetic moment of μ_eff = 5.82(2) μ_B and is paramagnetic at 300 K, and also has an order/disorder AFM transition with a Néel temperature of approximately 20 K, where μ_B is Bohr magneton.²⁷ Fig. 2a shows the temperature dependence of the magnetization of the MnSb₂Se₄ and Mn_0.75Cu_0.25Sb₂Se₄ samples. It reveals that MnSb₂Se₄ and Mn_0.75Cu_0.25Sb₂Se₄ are both paramagnetic at 300 K. However, an AFM transition with a Néel temperature of approximately 20 K is only observed for the MnSb₂Se₄ sample, but not for Mn_0.75Cu_0.25Sb₂Se₄. The effective magnetic moment μ_eff is measured to be 5.92 μ_B for MnSb₂Se₄, and 5.01 μ_B for Mn_0.75Cu_0.25Sb₂Se₄. The variation of the magnetic properties in both samples is consistent with the partial substitution of magnetic Mn atoms with nonmagnetic Cu atoms in Mn_0.75Cu_0.25Sb₂Se₄.

Fig. 2 (a) Temperature dependence of the magnetization for both MnSb₂Se₄ and Mn_0.75Cu_0.25Sb₂Se₄ (alternating current at 100 Hz in an applied field of 5 Oe); (b) temperature dependence of the heat capacity for the Mn_0.75Cu_0.25Sb₂Se₄ sample. The dashed line represents the Dulong–Petit estimation. The inset shows the heat capacity below 10 K in the C_p/T vs. T² representation. The dashed line in the inset is the fitted curve for C_p/T = φ + βT².

Fig. 2b shows the temperature dependence of C_p for Mn_0.75Cu_0.25Sb₂Se₄ in the temperature range of 5 K to 773 K. The measured C_p value at 280 K is 0.28 J K⁻¹ g⁻¹, which is consistent with the Dulong–Petit estimation. The inset in Fig. 2b shows C_p below 10 K in the C_p/T vs. T² representation. Based on the Debey model,³⁵ the total C_p includes the carrier contribution (φT) and the phonon contribution (βT³), in which C_p ∝ T³ at the low temperature limit. The dashed line is the fitted curve for C_p/T = φ + βT² in the inset of Fig. 2b. The fitted parameters are 0.589 mJ g⁻¹ K⁻² for φ, and 0.0077 mJ g⁻¹ K⁻⁴ for β. The small φ value indicates that the electron density of states near the Fermi level is quite weak at low temperatures, which is consistent with the very large ρ observed at low temperatures. The Debye temperature (Θ_D) can be obtained from the equation Θ_D = (12π⁴pR/5β)^1/3, where p is the atom number per chemical formula, and R is the molar gas constant.^35,36 The Θ_D value of Mn_0.75Cu_0.25Sb₂Se₄ is obtained as 120.9 K. The theoretical κ_lat can be estimated using the Umklapp process:³⁷ , where M is the average mass per atom, V is the average atomic volume, and γ is the Grüneisen parameter. A low Debye temperature is beneficial for obtaining a relatively low thermal conductivity. Compared to the Θ_D of other high-performance thermoelectric materials, such as PbTe (160 K),¹² SnTe (140 K),³⁸ and CuGaTe₂ (229 K),³⁹ the Θ_D of Mn_0.75Cu_0.25Sb₂Se₄ is relatively low, implying a lower intrinsic thermal conductivity.

Electrical transport properties

Fig. 3a shows the temperature dependence of the electrical resistivity (ρ) between 300 K and 773 K. At room temperature, MnSb₂Se₄ displays high electrical resistivity and is out of the test range of the instrument. The electrical resistivity of all of the samples decreases with increasing temperature, which is due to thermal activation of the intrinsic carriers, as shown in Fig. 3a, indicating typical semiconductor behavior. In the Mn_1−xCu_xSb₂Se₄ (0 ≤ x ≤ 0.35) samples, Cu behaves as an effective p-type dopant and each Cu substitution can provide a free hole according to valence counting. In Fig. 3a, the electrical resistivity of all of the Cu-doped samples is reduced to below 10% of the value in MnSb₂Se₄. The ρ value decreases significantly from ∼28 030 mΩ cm at 573 K (compared to ∼890 000 mΩ cm at 300 K in ref. 27) in pristine MnSb₂Se₄ to 737.98 mΩ cm at 573 K for the x = 0.25 sample, owing to the increase of the carrier concentration in Cu-doped samples. Fig. 3b shows the Hall carrier concentrations (n) and carrier mobility (μ) of the Mn_1−xCu_xSb₂Se₄ samples measured at room temperature. Undoped MnSb₂Se₄ contains a low concentration of hole carriers (n ∼ 2.16 × 10¹⁷ cm⁻³). The carrier concentration increases drastically with Cu substitution and reaches a maximum of ∼2.5 × 10¹⁹ cm⁻³ for the x = 0.25 sample. The carrier mobility is as low as 0.4 cm² V⁻¹ s⁻¹ for MnSb₂Se₄, and then increases to ∼1.4 cm² V⁻¹ s⁻¹ for Mn_0.95Cu_0.05Sb₂Se₄. With increased doping, the carrier mobility drops slightly to ∼1.3 cm² V⁻¹ s⁻¹ for Mn_0.75Cu_0.25Sb₂Se₄, and then increases to ∼3 cm² V⁻¹ s⁻¹ for Mn_0.65Cu_0.35Sb₂Se₄. Here the lower mobility in MnSb₂Se₄ can be ascribed to the very large scattering of the carriers and the spatially localized nature of the transition metal 3d orbital in Mn related compounds.^40,41 The larger carrier mobility upon Cu doping compared to that of undoped MnSb₂Se₄ is probably due to the assumption that Cu substitution not only adds more hole carriers, but also disrupts the spatially localized nature of the Mn 3d orbital, leading to the increase of the hole mobility. Fig. 3c shows the temperature dependence of the Seebeck coefficient for all of the samples. It can be seen that with the increase of the amount of Cu the room temperature Seebeck coefficient decreases prominently. The values of S are all positive, indicating that the majority of the charge carriers are holes. The S value of undoped MnSb₂Se₄ reaches 650 μV K⁻¹ at 573 K, which is comparable to 945 μV K⁻¹ at 300 K in the literature.²⁷ The S values of the Cu-doped samples decrease but still maintain large values, and the maximum S exceeds 300 μV K⁻¹ at 573 K. Benefiting from the reduced ρ and larger S, the Cu-doped samples have much higher power factors than the pristine MnSb₂Se₄ sample, with a maximum value of ∼0.26 mW m⁻¹ K⁻² at 773 K as shown in Fig. 3d, which is ∼100% improvement over the undoped MnSb₂Se₄ sample. However, in comparison to other notable thermoelectric materials, the power factor of Cu-doped MnSb₂Se₄ is still lower due to its low carrier mobility and relatively high electrical resistivity.

Fig. 3 (a) The temperature dependence of the electrical resistivity ρ, the inset shows the temperature dependence of ρ for the MnSb₂Se₄ and Mn_0.95Cu_0.05Sb₂Se₄ samples; (b) room temperature Hall carrier concentration (n) and carrier mobility (μ) for the Mn_1−xCu_xSb₂Se₄ (0 ≤ x ≤ 0.35) samples; (c) the temperature dependence of the Seebeck coefficient S; and (d) the temperature dependence of the power factor S²/ρ for the Mn_1−xCu_xSb₂Se₄ (0 ≤ x ≤ 0.35) samples.

The electrical resistivity ρ can be calculated from the carrier concentration n and carrier mobility μ using:¹⁸ 1/ρ = neμ = ne²τ/m*, where e is the electron charge, τ is the scattering time, and m* is the density of states effective mass. From the Arrhenius plot in Fig. 4a, the temperature dependence of the electrical resistivity displays the intrinsic behavior commonly observed for semiconductors between 300 and 473 K. Assuming that the decrease in ρ is due to the thermal excitation of the charge carriers across the energy gap, the band gap values obtained are E_g ∼ 0.57 eV for Mn_0.85Cu_0.15Sb₂Se₄ and E_g ∼ 0.50 eV for Mn_0.75Cu_0.25Sb₂Se₄. It is noted that the values of E_g are larger than the value estimated from ab initio electronic structure calculations (E_g ∼ 0.3 eV).²⁷ Band structure calculations indicate that there are two valence bands with nearly identical dispersions near the Fermi level for MnSb₂Se₄, and furthermore they show that the energy difference between the two valence band edges is less than 0.01 eV. According to the two-valence-band model,⁴² if the energy difference between the two valence band edges is close to zero and the effective masses for both bands are approximately equal, the single parabolic band (SPB) model can be used to depict the electrical transport properties. The Pisarenko relation based on the SPB model for the room temperature Seebeck coefficient as a function of carrier concentration for MnSb₂Se₄ is shown in Fig. 4b. The solid curve is generated based on a SPB model with dominant acoustic phonon scattering. The density of states effective mass is calculated from the carrier concentration and the Seebeck coefficient, using the equations from Fermi–Dirac statistics:⁴³ , and , with the Fermi integrals F_i(η) defined by , where ξ is the reduced carrier energy, η is the reduced Fermi energy, h is the Planck constant, e is the electron charge, and λ is the scattering parameter. Assuming that the carrier mobility is limited by acoustic phonon scattering (λ = 0), m* is calculated to be 0.23 m_e for MnSb₂Se₄ at 300 K. As the room temperature carrier concentration increases from 2.16 × 10¹⁷ cm⁻³ for MnSb₂Se₄ to 2.5 × 10¹⁹ cm⁻³ for Mn_0.75Cu_0.25Sb₂Se₄, the Seebeck coefficient drops from 945 μV K⁻¹ to 327 μV K⁻¹, while still being about 6 times higher than the estimated value based on the SPB model. The m* is estimated to be 3.22 m_e for Mn_0.75Cu_0.25Sb₂Se₄ at 300 K. This enlarged m* could normally originate from resonant state doping or band convergence in TE materials. Since MnSb₂Se₄ has two nearly identical valence bands at the Fermi level, it is not realistic for band convergence to occur upon Cu doping, we can only attribute the enlarged m* to the increase of the local density of states (DOS) in the Fermi level by the presence of resonant states upon Cu doping. Indeed, the band structure calculation clearly shows the existence of a resonant state in the DOS of Mn_0.75Cu_0.25Sb₂Se₄. Based on the band structure calculation, the DOS was obtained as shown in Fig. 4c. A small hump near the Fermi level in Mn_0.75Cu_0.25Sb₂Se₄ is observed compared to the undoped MnSb₂Se₄. A partial DOS for each atom including Mn, Cu, Sb, and Se is shown in Fig. 4d, a resonant state is shown near the Fermi level, which is apparently caused by the Cu atoms.

Fig. 4 (a) The plot of ln(ρ) versus 1000/T; (b) fitting of the Seebeck coefficient as a function of the carrier concentration based on the Pisarenko relation, the black solid line represents the theoretical Pisarenko line; (c) local DOS of MnSb₂Se₄ and Mn_0.75Cu_0.25Sb₂Se₄; (d) local p-DOS for each atom of MnSb₂Se₄ and Mn_0.75Cu_0.25Sb₂Se₄. A resonant state is shown near the Fermi level, which is caused by Cu doping.

Thermal transport properties

Fig. 5 shows the total thermal conductivity of the Mn_1−xCu_xSb₂Se₄ samples. All of the samples exhibit abnormally ultralow thermal conductivity ranging from 0.32 to 0.61 W K⁻¹ m⁻¹ in the measured temperature range. The ultralow thermal conductivity is a great advantage for achieving high zT thermoelectric materials. The κ_tot values at 300 K for all of the samples decrease with an increase in the amount of Cu, and those κ_tot values decrease with the increase of temperature without significant up-turning at high temperature, which reveals that the Umklapp scattering is the dominant process and the bipolar diffusion is negligible. Generally, κ_tot consists of the lattice contributions κ_lat and electronic contributions κ_ele. Here, κ_lat is assumed to be equal to κ_tot because of the small contribution of κ_ele calculated by the Wiedemann–Franz law (κ_ele = LT/ρ). The κ_lat of Mn_1−xCu_xSb₂Se₄ is found to be significantly low and at the same level as the values reported for promising thermoelectric materials such as Cu₂Se (∼0.4 W K⁻¹ m⁻¹ at 1000 K)⁴⁴ and SnSe (∼0.23 W K⁻¹ m⁻¹ at 973 K).²¹

Fig. 5 The temperature dependence of the total thermal conductivity for the Mn_1−xCu_xSb₂Se₄ (0 ≤ x ≤ 0.35) samples.

The κ_lat can be expressed by the simple relationship:³⁷ , where C_v is the heat capacity at constant volume, υ_a is the average sound velocity, and l is the phonon mean free path. The minimum lattice thermal conductivity (κ_min) can be calculated using the model proposed by Cahill et al.:⁴⁵ , where V is the average atomic volume. Θ_D is related to υ_a and V via . The value of κ_min is calculated to be ∼0.23 W K⁻¹ m⁻¹ for MnSb₂Se₄, which is apparently an ultralow value among thermoelectric materials. The ultralow κ_lat in the Mn_1−xCu_xSb₂Se₄ samples is very interesting and can be attributed to the follow aspects: on the one hand, the large cell volume in the crystallization, and the layered complex structure, as well as the compositional heavy elements such as Sb and Se are the common factors contributing to low thermal conductivity in the crystal compounds;^18,46 on the other hand, the disorder arising from anti-site occupancy between Mn, Cu, and Sb may induce additional scattering of short wavelength phonons at high temperature and be responsible for the ultralow κ_lat.²⁷

Thermoelectric figure of merit zT

The thermoelectric figure of merit zT as a function of temperature for the Mn_1−xCu_xSb₂Se₄ samples is shown in Fig. 6a. The zT values increase with elevated temperature and Cu content, with the highest value reaching ∼0.64 at 773 K for the Mn_0.75Cu_0.25Sb₂Se₄ sample. This is ∼100% improvement over the undoped MnSb₂Se₄ sample. This enhancement of zT mainly originates from the significantly improved power factor via Cu doping and the intrinsically ultralow thermal conductivity in the materials. Due to the anisotropic transport properties in layered structure materials, the TE properties of the Mn_1−xCu_xSb₂Se₄ samples are measured in the perpendicular (in-plane) and parallel (out-of-plane) directions. It is observed that zT in the out-of-plane direction is higher than that for the in-plane direction, for which the latter one reaches 0.54 at 773 K, as shown in Fig. 6b. Fig. 7a–d show the temperature dependence of the electrical resistivity, Seebeck coefficient, power factor, and thermal conductivity in the direction perpendicular to pressing (in-plane) for the Mn_1−xCu_xSb₂Se₄ (0 ≤ x ≤ 0.35) samples. It can be seen that the main reason accounting for the anisotropic zT values lies in the difference in thermal conductivity for both directions, as shown in Fig. 5 and 7d.

Fig. 6 The temperature dependence of the zT values for the Mn_1−xCu_xSb₂Se₄ (0 ≤ x ≤ 0.35) samples for (a) the parallel (out-of-plane), and (b) perpendicular direction (in-plane) with respect to the pressing direction.

Fig. 7 (a) The temperature dependence of the electrical resistivity ρ; (b) the temperature dependence of the Seebeck coefficient S; (c) the temperature dependence of the power factor (PF) S²/ρ; and (d) the temperature dependence of the thermal conductivity κ_tot in the in-plane direction for the Mn_1−xCu_xSb₂Se₄ (0 ≤ x ≤ 0.35) samples.

It is noticed that the power factors of Mn_1−xCu_xSb₂Se₄ are lower than other notable thermoelectric materials. However, the ultralow κ_tot boosts zT in the Mn_1−xCu_xSb₂Se₄ materials, and further enhancement of zT should focus on the continuing improvement of the power factor in this material. Since the low power factor is mostly due to the low carrier mobility, the power factor could be further improved by reducing carrier scattering and breaking the localization of the carriers in Mn_1−xCu_xSb₂Se₄. One possible way is the growth of single crystal samples or high quality film samples.²¹ Another way is to break the localization by substantially substituting the 3d Mn atom or changing the concentration of holes.^41,47

4. Conclusions

In conclusion, Cu-doped MnSb₂Se₄ samples have been successfully synthesized and the thermoelectric properties between 300 K and 773 K have been investigated. The electrical conductivity and power factor can be significantly boosted by increasing the carrier concentration and increasing the local density of states near the Fermi level through Cu resonant doping. In combination with the intrinsically ultralow thermal conductivity in the materials over the temperature range of 300 K to 773 K, the highest thermoelectric figure of merit zT of 0.64 at 773 K was obtained for the Mn_0.75Cu_0.25Sb₂Se₄ sample in the optimized orientation, which is a 100% enhancement over the undoped polycrystalline MnSb₂Se₄ sample. This work suggests that MnSb₂Se₄-based materials could be promising candidates for thermoelectric power generation in the intermediate temperature range.

Acknowledgements

This work is supported by startup funding from the Institute of Physics at the Chinese Academy of Sciences.

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