# Electronic, Thermal, and Thermoelectric Transport Properties of ReSe2 and Re2Te5

Authors: Joonho Bang; Okmin Park; Hyun-Sik Kim; Seung-Mee Hwang; Se Woong Lee; Sang Jeoung Park; Sang-il Kim
Journal: International Journal of Energy Research
 (2023)

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## Abstract

Re-based chalcogenides have been studied in various fields such as strain engineering, photodetection, spintronics, and electromechanics, as well as in piezoelectric and photonic devices. In this study, the electrical, thermal, and thermoelectric transport properties of two representative Re-based chalcogenides, ReSe2 and Re2Te5, are investigated systematically. Furthermore, their electronic band dispersions are calculated using density functional theory and compared with the phenomenological data. The maximum power factor values for the ReSe2 and Re2Te5 were measured 0.0066 and 0.11 mW/mK2 at 880 K, respectively. Thermal conductivity of layered ReSe2 at room temperature was between 1.93 and 8.73 W/mK according to the measuring direction. For Re2Te5 with a complex orthorhombic crystal structure, the thermal conductivity was quite low in the range between 0.62 and 1.23 W/mK at room temperature. As a result, the maximum zT values of ReSe2 were quite low as 0.0016 at 880 K due to very low power factor and high thermal conductivity. Meanwhile, the relatively high zT of 0.145 in Re2Te5 is obtained at 880 K, which is originated from the acceptable power factor value and the low thermal conductivity.


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## Body

## 1. Introduction

Metal chalcogenides have been receiving increasing attention as potential energy materials due to their tunable electronic properties and unique crystal structures, as well as relatively higher electrical conductivity in comparison to their transition metal oxide counterparts [1–3]. In particular, semiconductor chalcogenides have been widely used in thermoelectric (TE) fields because they have high electrical conductivity and low thermal conductivity, or even due to their unique crystal structures [4–6]. Among them, the layered structure that occupies most of the chalcogenides secures low thermal conductivity due to weak layer-to-layer van der Waals bonding. This is a key point because TE materials’ performance is evaluated using a dimensionless thermoelectric figure of merit, zT=S2σT/κ (where S, σ, κ, and T are the Seebeck coefficient, electrical conductivity, thermal conductivity, and absolute temperature, respectively). Therefore, several studies on layered chalcogenides are still being conducted to search for new thermoelectric materials. In fact, layered chalcogenides such as Bi-Te-based materials, InSe, In4Se3, HfTe2, and SnSe2 are famous TE materials that have high σ and low κ [7–13]. Bi-Te-based materials with high zT at 300-400 K have been reported in various studies [7–9]. In4Se3 was reported to have a zT value of 1.48 at 705 K [11].Transition metal chalcogenides (TMCs), which have mostly layered structures, are also applicable in the same context. Recently, TMCs have been applied to a wide range of applications including nanoelectronics, sensors, energy conversion, and energy storage as 2D materials [14]. In addition, among the layered TMCs, chalcogenide materials that are based on Zr, Ti, W, and Mo have been widely used in the TE field [15, 16].ReSe2 is a one-layered TMC and has been studied in various fields such as strain engineering, photodetection, spintronics, and electromechanics, as well as in piezoelectric and photonic devices [17–20]. In addition, ReSe2 is semiconductor that has a distinct band gap (1.26 eV for bulk ReSe2) according to the density functional theory (DFT) of generalized gradient approximation (GGA) calculations from Hafeez et al. and Wolverson et al. [21, 22]. Thus, ReSe2 may exhibit good TE properties and could be more advantageous due to the interlayer distance being 0.7 nm longer than other layered TMCs such as MoS2 and WS2 [17, 23], which leads to lower κ. Since the interlayer distance is long, κ of ReSe2 can be predicted to being substantially large between the ab- and c-axes. Mahmoud and Joubert calculated lattice thermal conductivity (κlatt) based on bulk ReSe2 through first principles. In their study, κlatt of the (100) and (010) directions were 18.47 and 17.44 W/mK at 300 K, respectively. However, κlatt of the (001) direction was 0.69 W/mK [24]. If these characteristics are used well, ReSe2 can be judged to having sufficient potential as a TE material.Re2Te5, which is another rhenium chalcogenide semiconductor, is not a layered TMC but has a complex orthorhombic crystal structure with 84 atoms ([Re24] and [Te60]) per unit cell. These atoms exhibit a cluster-type Chevrel phase with [Re6] surrounded by [Te8] [25–27]. One notable structural property of the Chevrel phase is the presence of 4 large vacancies. This causes the scattering of phonons, which effectively reduces κlatt. Because of this, κ of Re2Te5 is 1.3 W/mK, which is similar to that of layered TMCs [28, 29]. In addition, it has the merit of being able to enhance thermoelectric properties through various doping in the 4 vacancies. In fact, Caillat et al. reported that rattling was found in elements doped into the vacancies, resulting in reduced κ due to phonon scattering [30].In this study, the electrical, thermal, and thermoelectric transport properties of ReSe2 and Re2Te5 samples were investigated. Notably, the electrical transport properties of ReSe2 and Re2Te5 can be analyzed in more detail using a single parabolic band model. Based on this, the density-of-state effective mass, md∗, was calculated, and zT was evaluated to confirm the thermoelectric performances. In addition, the measured electrical transport properties were compared with calculated from first-principle DFT calculations.


## 2. Experimental Method

The ReSe2 and Re2Te5 samples were synthesized via a conventional solid-state reaction process in a vacuum-sealed quartz tube. High-purity elements Te (99.999%), Se (99.999%), and Re (99.99%) powders were weighed with stoichiometric compositions, and mixed powder was loaded in the vacuum-sealed quartz tube. The loaded quartz ampoules were then heated to 950°C for 6 h and this temperature was maintained for 70 h. The synthesized ReSe2 and Re2Te5 were pulverized into powders through high-energy ball milling (SPEX 8000D, SPEX) in Ar atmosphere. The ReSe2 and Re2Te5 powders were placed into a graphite mold and pressed for sintering by spark plasma sintering (SPS, SPS-1030, Sumitomo Coal Mining Co., Ltd.). The ReSe2 and Re2Te5 loaded into graphite molds were sintered at 950°C for 20 min under 70 MPa and 850°C for 10 min under 70 MPa, respectively. During the sintering, vacuum was maintained in the inside of the SPS chamber (~10-5 Torr).The crystalline phases of the samples were identified using powder X-ray diffraction (XRD) with a Bruker D8 Discover (Cu Kα, λ=1.54059Å) diffractometer at room temperature. XRD measurements for the sintered pellet samples were carried out in two different directions, perpendicular (⟂) and parallel (‖) directions to the SPS pressing direction. The thermoelectric transport properties (σ and S) were measured simultaneously using a thermoelectric-property measurement system (ZEM-3, Advanced-Riko) in the two different directions within a temperature range of 300–880 K on the samples in He atmosphere. Power factor (PF) was calculated based on the measured σ and S values. The Hall carrier concentrations and mobilities were calculated using the Hall-Van der Pauw measurement system (HMS5300, Ecopia) under a 0.548 T magnetic field. The κtot values of each sample were calculated from its sample density (ρs), heat capacity (Cp), and thermal diffusivity (α). ρs was used as theoretical densities for ReSe2 and Re2Te5. Cp, as presented in Table 1, was measured using a differential scanning calorimeter (DSC8000, Perkin Elmer). Laser-flash analysis was conducted to measure α (LFA457, Netzsch). zT was evaluated based on the measured data.Table 1
Experimental and calculated lattice parameters of the ReSe2 and Re2Te5.
a (Å)b (Å)c (Å)Volume (Å3)ReSe2Exp.6.72116.64056.7386249.973Calc.6.78706.61696.7394245.165Re2Te5Exp.12.976212.973414.17382386.095Calc.13.515213.439714.47842629.847First-principle DFT calculations were performed using the generalized gradient approximation with the Perdew-Burke-Ernzerhof functional and the projector augmented plane-wave method implemented in the Vienna Ab initio Simulation program code [31–33]. The 5d/6s electrons of Re, the 4s/4p electrons of Se, and the 5s/5p electrons of Te were used as valence electrons. The plan-wave-basis cut-off energy was set to 600 eV. Self-consistency was carried out using unit cells containing 12 and 84 atoms, and 8×8×8 and 4×4×4 k-point meshes were used for the structural relaxation and the electronic structure calculation of ReSe2 and Re2Te5, respectively. A van der Waals correction was included using the DFT-D3 method with Becke-Johnson rational damping [34, 35]. Structural relaxation was performed until the Hellmann-Feynman forces were less than 1×10−3 eV A−1. The atomic positions of the relaxed structures are provided in Table S1 in Supporting Materials.The transport properties of ReSe2 and Re2Te5 were estimated using the Shankland-Koelling-Wood interpolation as implemented in the BoltzTraP2 code [36, 37]. First, the band structures obtained by DFT calculations were interpolated using the extended Shankland algorithm [38–40]. Next, the Onsager transport coefficients were determined using the linearized Boltzmann transport equation based on the rigid-band approximation [35]. For the calculation of the transport properties, dense 12×12×12 and 6×6×6 k-point meshes were used for ReSe2 and Re2Te5, respectively.


## 3. Results and Discussions

Figures1(a) and 1(c) depict the triclinic (space group: P1[2]) and orthorhombic (space group: Pbca [61]) crystal structures of ReSe2 and Re2Te5, respectively. Figures 1(b) and 1(d) show XRD patterns of the ReSe2 and Re2Te5 polycrystalline bulk samples at the 2θ range from 10° to 50°. In addition, to consider anisotropy for the samples, the measurements were performed along the directions perpendicular (⟂) and parallel (‖) to the sintering pressure direction. From the measured XRD patterns, it was observed that ReSe2 and Re2Te5 have a single triclinic phase and a single orthorhombic phase without impurity, respectively. The lattice parameters are presented in Table 1 with the calculated lattice parameter by DFT calculation. The lattice parameters derived from the experiment were matched to those of JCPDS within an error less than 0.3%. In addition, the lattice parameters were similar with the calculated lattice parameters, while it is commonly known that the calculated lattice parameters by first-principle DFT had a larger value than those of the experimental data.Figure 1
(a, c) Crystal structure of the (a) ReSe2 and (c) Re2Te5, respectively. (b, d) XRD patterns of the (b) ReSe2 and (d) Re2Te5 samples.
(a)(b)(c)(d)Figure2 shows the measured thermoelectric transport properties for the ReSe2 and Re2Te5 according to measurement directions. ReSe2 and Re2Te5 demonstrated semiconductor transport behavior. As shown in Figures 2(a) and 2(d), the σ of ⟂ReSe2 and ‖ReSe2 are 0.0021 and 7.12×10−5 S/cm at 370 K, respectively, and ⟂Re2Te5 and ‖Re2Te5 are 0.12 and 0.10 S/cm at 300 K, respectively. σ of ⟂ReSe2 (‖ReSe2) and ⟂Re2Te5 (‖Re2Te5) gradually increased to 0.56 (0.28) and 32 (25.8) S/cm at 880 K, respectively. In the case of ReSe2, the ab-axis was superior to c-axis; this is typical in the transport properties of a general layered structure material. Meanwhile, Re2Te5 did not differ significantly between the two directions. The maximum S of the ReSe2 in Figure 2(b) was 948 μV/K at 370 K, which was measured in ⟂ direction. However, in the case of Re2Te5 shown in Figure 2(e), S at 300 K has a maximum value of 515 μV/K. Consequently, the calculated PF shows a maximum value in the ⟂ direction in both cases. The maximum PF values for the ReSe2 and Re2Te5 were 0.0066 and 0.11 mW/mK2, respectively.Figure 2
(a, d) Electrical conductivities, (b, e) Seebeck coefficients, and (c, f) power factors as a function of temperature for (a, b, c) ReSe2 and (d, e, f) Re2Te5. Insets of (b) and (e) show common logarithmic carrier concentration as a function of absolute Seebeck coefficient, and insets of (c) and (f) show weighted mobilities.
(a)(b)(c)(d)(e)(f)Table2 indicates the results of the Hall measurement and md∗ at room temperature. As presented, the large difference in σ is caused mainly by the fact that nH of Re2Te5 is 104 times larger than the nH of ReSe2 (nH denotes hole concentration). The md∗, which was calculated using Equation (1) [38], for ReSe2 and Re2Te5, was 0.154 and 1.97 m0 (m0 is the rest mass of an electron), respectively. The fact that the nH of ReSe2 is significantly low is also the reason why the md∗ of the ReSe2 is smaller than Re2Te5 by a factor of 12 despite its S being higher than that of Re2Te5. Furthermore, log10n as function of ⟂S at 300 K was plotted for the ReSe2 and Re2Te5 into insets of Figures 2(b) and 2(e).
(1)log10md∗T300=23log10n−2320.3−0.00508×S+1.58×0.967S.Table 2
Hall measurement results, density of state effective mass, and heat capacity for ReSe2 and Re2Te5 at room temperature.
SamplesnH (cm-3)⟂μH (cm2/Vs)μH (cm2/Vs)md∗ (m0)Cp (J/gK)ReSe22.55×10143.120.2510.1540.212Re2Te51.87×10180.3080.2731.970.157Commonly,md∗ was estimated using Equation (2). However, because the md∗ is only accurate when S is lower than 137 μV K-1 [41], using Equation (2) for ReSe2 and Re2Te5 (S>500 μV K-1) is not appropriate. Therefore, Equation (1), which is accurate for all degeneracy, was used instead.
(2)S=8π2kB23eh2md∗Tπ3n2/3.Meanwhile, according to the measuring direction, the⟂μH and μH values of layered ReSe2 were 3.12 and 0.251 cm2/Vs, respectively. The ⟂μH and μH values of Re2Te5 were confirmed as 0.308 and 0.273 cm2/Vs, respectively.Insets of Figures2(c) and 2(f) are results that calculated weighted mobilities μw as a function of the temperature for the ReSe2 and Re2Te5. The μw values were calculated from the measured σ and S; μw can be obtained via a simple analytical expression, wherein the exact Drude-Sommerfeld free-electron model is approximated using Equation (3) for S>20 μV/K [42].
(3)μw=3h3σ8πe2mekT3/2expS/k/e−21+exp−5S/k/e−1+3/π2S/k/e1+exp5S/k/e−1,where me is the mass of an electron. μw is proportional to the maximum PF that a sample can reach when nH is optimized. Therefore, μw of ReSe2 shows as significant difference as in PF with regard to the direction. However, unlike PF, maximum values of these were observed at 480 K (14.5 cm2/Vs, ⟂μw) and at 580 K (1.40 cm2/Vs, μw), respectively. While the difference between ⟂μw and μw of ReSe2 decreases for temperatures higher than 480 K, the difference between corresponding PF increases for all temperatures. The large difference in PF observed at 880 K despite the small difference in ⟂μw and μw suggests that the nH of ReSe2 is rapidly shifting away from the optimal nH. In the case of Re2Te5, μw values about the two directions were 2.47 and 2.036 cm2/Vs, respectively. This is similar to the PF trend at 880 K.Figures3(a) and 3(b) show the temperature dependence of the S and σ/τ (τ: relaxation time) values for ReSe2 and Re2Te5, respectively. For this calculation, we adopt the nH values of 2.55×1014cm−3 for ReSe2 and 1.87×1018cm−3 for Re2Te5, which are obtained by the Hall effect measurements at 300 K (see Table 2). Both compounds exhibit similar behavior; i.e., the S value decreases as temperature increases, whereas the σ/τ (τ: relaxation time) value is increased with the increase of temperature. Such trends are in good agreement with the experimental observations (Figures 2(a), 2(b), 2(d), and 2(e)), indicating that our calculational approach is suitable for the present systems. It is noted that there are distinct differences in the transport properties between ReSe2 and Re2Te5: (i) the σ/τ values of Re2Te5 are higher than that of ReSe2 throughout the whole temperature range, and (ii) the maximum S value of ReSe2 (~1293 μV K−1 at 330 K) is about two times higher than that of Re2Te5 (~601 μV K−1 at 500 K).Figure 3
Calculated transport properties and electronic structures. (a, b) Temperature (T) dependence of S and σ/τ for ReSe2 (a) and Re2Te5 (b). (c, d) nH dependence of S, σ/τ, and σS2/τ for ReSe2 (c) and Re2Te5 (d). Dashed red lines indicate the nH values of 2.55×1014cm−3 for ReSe2 and 1.87×1018cm−3 for Re2Te5. (e, f) Band structures and total/projected DOSs of ReSe2 (e) and Re2Te5 (f).
(a)(b)(c)(d)(e)(f)We also calculated the doping dependence of theS and σ/τ (τ: relaxation time) values for both compounds (Figures 3(c) and 3(d)). The calculated S values are 1330 μV/K for ReSe2 and 594 μV/K for Re2Te5 when the nH values are 2.55×1014cm−3 and 1.87×1018cm−3, respectively. These S values reasonably agree with the experimental data (see Table 2 and Figures 2(b), 2(c), and 2(e)) but are slightly overestimated. When the nH increases, the S values of both compounds decrease, whereas the σ/τ values sharply increase. As a result, the σS2/τ values, which are directly correlated with the PF, increase rapidly at the higher nH until the maximum σS2/τ is reached. This result indicates that the higher PF of Re2Te5 compared with that of ReSe2 in our experimental observation (Figures 2(c) and 2(f)) mainly originates from the ~104 times higher nH of Re2Te5, rather than other parameters such as maximum PF. The optimal nH values to achieve the maximum PF can be estimated as ~1020 cm−3 for both compounds, suggesting that the thermoelectric performance can be further improved by introducing additional hole carriers into ReSe2 and Re2Te5.The electronic band structures and density of states (DOS) for ReSe2 and Re2Te5 are calculated to elucidate the correlation between the thermoelectric properties and the electronic structure. The calculated band structures and DOS for ReSe2 and Re2Te5 are shown in Figures 3(e) and 3(f), respectively. Both compounds have finite band gaps with values of ~0.9 eV and ~0.7 eV, consistent with the experimentally observed semiconducting transport behavior (Figures 2(a) and 2(d)). By comparing the electronic band structures of ReSe2 and Re2Te5, it was found that Re2Te5 has a more complex band structure near the valence band maximum as compared with that of ReSe2. Such higher band degeneracy facilitates the substantial enhancement of the DOS near the valence band maximum, which mainly consists of Te 5p orbitals (right panel in Figure 3(f)). The high band degeneracy and effective DOS near the valence band maximum are beneficial to achieve a higher power factor in the p-type doping regime [43]. This distinct difference in electronic structures can be understood by comparing their different crystal structure; i.e., the Re cations in ReSe2 are only bound to the nearby Se anions (Figure 1(a)), whereas the crystal structure of Re2Te5 consists of the mixture of the homopolar Te–Te bonds and heteropolar Re–Te bonds (Figure 1(c)), inducing a complex electronic structure.Figures4(a) and 4(d) show calculated κ of ReSe2 and Re2Te5. κ values of ReSe2 were gradually decreased in both ⟂ and ‖ directions as the temperature changed. ⟂κ and κ were 1.93 and 8.73 W/mK at 300 K, respectively, which are quite large. The large difference between two directions is due to the layered structure. The ⟂κ and κ were gradually decreased to 0.920 and 3.75 W/mK at 880 K. For Re2Te5, which has the complex crystal structure, the κ value was in the range between 0.62 and 1.23 W/mK. The κ of Re2Te5 can be further reduced by possible doping in 4 large vacancies in the unit cell, which can cause rattling effect [27].Figure 4
(a, d)κtot and (b, e) zT as a function of the temperature for (a, b) ReSe2 and (d, e) Re2Te5. Insets of (c) and (f) show calculated B factor. (c, f) Predicted zT of the (c) ReSe2 and (f) Re2Te5 at 300 K calculated based on the single parabolic band model as a function of nH̲.
(a)(b)(c)(d)(e)(f)Figures4(b) and 4(e) show evaluated zT as a function of temperature, while the insets show a dimensionless thermoelectric quality factor B for ReSe2 and Re2Te5. The maximum zT values of ReSe2 and Re2Te5 were 0.0016 and 0.145, respectively, in the ⟂ direction at 880 K. The zT of ReSe2 is very low due to low σ and high κ, which are not adequate for the good thermoelectric materials. Meanwhile, the relatively high zT of 0.145 in Re2Te5 is originated from the acceptable PF higher than 0.1 mW/mK2 and the low-enough κ smaller than 1.0 W/mK.The dimensionless thermoelectric quality factorB [39] (the insets of Figures 4(b) and 4(e)) is another measure of thermoelectric performance of materials, which can be obtained using the following [39]:
(4)B=ke28πe2mekT3/23h3∙μwκlattT.B of ReSe2 is quite low and shows similar trend to μw, which shows the maximum values at midtemperature. B of Re2Se5 shows the maximum value of 0.039 at 880 K.Figures4(c) and 4(f) depict the plot of the experimental ⟂zT of ReSe2 and Re2Te5 (in symbol) and the calculated ⟂zT of ReSe2 and Re2Te5 (in line) as a function of nH at 300 K using a single parabolic band (SPB) model under acoustic phonon scattering assumption:
(5)zT=B2F1η/F0η−η2F0η1+B3F2η/F0η−2F1η/F0η2F0η,where Fxη (η is the reduced electrochemical potential) is the Fermi integral of order x.
(6)Fxη=∫0∞εxdε1+eε−η.According to the SPB model, both⟂zT of ReSe2 and Re2Te5 can be significantly improved once nH is optimized. For example, the maximum ⟂zT at 300 K predicted for ReSe2 and Re2Te5 are 9.3×10−4 and 3.2×10−3 at 300 K, respectively. Based on appropriate nH tuning, ⟂zT of ReSe2 and Re2Te5 can be improved by more than a factor of 83 (9.3×10−7⟶7.8×10−5) and 4 (7.2×10−4⟶3.2×10−3), respectively. The optimization of nH by proper doping in Re2Te5 by various strategies, including cation/anion doping and impurity control, may further increase the zT.In this study, the electrical, thermal, and thermoelectric transport properties of ReSe2 and Re2Te5 polycrystalline alloys are systematically investigated. The maximum power factor values for the ReSe2 and Re2Te5 were measured 0.0066 and 0.11 mW/mK2 at 880 K, respectively. The differences in electronic transport properties between ReSe2 and Re2Te5 were verified with density of state and electronic dispersion calculated from first-principle density functional theory. Thermal conductivity of layered ReSe2 at room temperature was between 1.93 and 8.73 W/mK according to the measuring direction, which of both are relatively high. For Re2Te5 with the complex crystal structure, the thermal conductivity was low in the range between 0.62 and 1.23 W/mK at room temperature. As a result, the maximum thermoelectric figure of merit zT values of ReSe2 was quite low as 0.0016 at 880 K due to very low power factor and high thermal conductivity. On the other hand, the relatively high zT of 0.145 in Re2Te5 is seen due to the decent power factor value and the low thermal conductivity. Indeed, adequate doping can enhance the zT of Re2Te5 by further enhancing the power factor by controlling the carrier concentration and reducing the thermal conductivity by filling the 4 large vacancies in the unit cell by rattling effect.



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