# Electronic and Thermal Transport Properties of Complex Structured Cu-Bi-Se Thermoelectric Compound with Low Lattice Thermal Conductivity

Authors: Jae-Yeol Hwang; Hyeona Mun; Jung Young Cho; Sang Sun Yang; Kyu Hyoung Lee; Sung Wng Kim
Journal: Journal of Nanomaterials
 (2013)

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## Abstract

Monoclinic Cux+yBi5−ySe8 structure has multiple disorders, such as randomly distributed substitutional and interstitial disorders by Cu as well as asymmetrical disorders by Se. Herein, we report the correlation of electronic and thermal properties with the structural complexities of Cux+yBi5−ySe8. It is found that the interstitial Cu site plays an important role not only to increase the electrical conductivity due to the generation of electron carriers but also to reduce the thermal conductivity mainly due to the phonon scattering by mass fluctuation. With impurity doping at the interstitial Cu site, an extremely low lattice thermal conductivity of 0.32 W·m−1·K−1 was achieved at 560 K. These synergetic effects result in the enhanced dimensionless figure of merit (ZT).


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## Body

## 1. Introduction

In thermoelectric (TE) materials, thermal energy is directly converted into electrical energy and vice versa through the flow of charge carriers (electrons or holes) in solid state without any moving parts [1, 2]. The performance of TE device depends on the temperature gradient (ΔT) and the dimensionless figure of merit (ZT) in TE material. The conversion efficiency of TE material is governed by ZT, which is defined as ZT=S2·σ·T/κ, where S is the thermopower (Seebeck coefficient), σ is the electrical conductivity, κ is the thermal conductivity, and T is the absolute temperature. Intuitively, good TE materials should have sufficiently large S, high σ, and low κ. Based on this relation, there are two different kinds of straightforward strategies for achieving high ZT. The first one is maximizing power factor (PF=S2·σ) by the modification of the electronic states through the optimization of doping, introduction of nanoscale materials, and so forth. The other one is minimizing κ by the perturbation of structural arrangements for enhancing phonon scattering through solid-solution alloying [3–6], nanostructuring [7, 8], and the development of new materials with intrinsically low κ. However, since σ, S, and κ are the functions of charge carriers as well as these physical parameters are intercorrelated to each other, it is very difficult to control these parameters individually. Recent TE researches have been mainly focused on breaking the trade-off relationship between σ and κ by reducing the lattice thermal conductivity (κlatt) due to the relative easiness of reducing κlatt without considerably affecting other electronic transport parameters (Sand σ). Thus, extensive researches have been focused on reducing κlatt by utilizing nanostructures and compositional inhomogeneities of state-of-the-art TE materials such as Bi2Te3, PbTe, and SiGe [3–8]. It has been reported that dramatically reduced κlatt in TE materials is due to one of the following mechanisms: alloy scattering [3–6], resonant scattering [9–13], anharmonic scattering [14], and interface scattering of phonons [15–17] or their combination.Recently, much effort has been focused on discovering new semiconducting materials with intrinsically lowκlatt. Such materials have a solid potential compared to conventional TE materials because their κlatt can be further reduced by compositional and microstructural engineering without sacrificing the other electronic properties. The common structural characteristics of low κlatt materials are complex structures, which have relatively large unit cells, sublattice disorders, low crystal symmetry, and/or a variety of atom types combined with random distributions. These result in the effective phonon scatterings, which make these materials promising candidates for TE applications.By understanding the origin of lowκ in complex structured system, it is possible to find a clue for novel TE materials with an appropriate structure and to manipulate structural arrangement for the achievement of low κ in conventional TE materials. In a previous article [18], we reported new TE materials, which are the pavonite homologues Cux+yBi5-ySe8 (1.2 ≤ x≤ 1.5, 0.1 ≤ y≤ 0.4) with low κlatt (0.41–0.55 W·m−1·K−1 at 300 K) owing to the structural complexity. In the present study, we investigated the electronic and thermal transport properties in the view point of the correlation with crystal structure in order to clarify the origin of TE properties in the homologous Cux+yBi5-ySe8 compounds.


## 2. Experimental

Crystal ingots ofCux+yBi5-ySe8 compounds were fabricated by conventional melting technique by the use of high-purity elemental Cu (99.999%, CERAC), Bi (99.999%, 5N Plus), and Se (99.9%, 5N Plus) as starting materials. The stoichiometric mixtures of the elements were loaded into a quartz tube of 14 mm in diameter. The tube was vacuum-sealed and the mixed contents were melted in a furnace for 10 hrs at 1273 K; then, they were water quenched. The ingots were ground using ball mill, and compacted bulk samples of 10 mm in diameter and 13 mm in thickness were prepared using spark plasma sintering (SPS) technique under dynamic vacuum and with the application of 50 MPa of uniaxial pressure at 663 K. The relative densities of the resulting consolidated samples were found to range from 7.22 to 7.48 g·cm−3, which are more than 95% of the theoretical value. We used Cu1.7Bi4.7Se8 (Cux+yBi5-ySe8, x = 1.4, y = 0.3) as a reference material, and small amount (w and z = 0.0085 and 0.025 for the interstitial and substitutional M sites, resp.) of Zn or In was introduced in host Cu1.7-wMwBi4.7Se8 or Cu1.7Bi4.7-zMzSe8 matrix to elucidate the electronic and thermal properties according to the different carrier concentrations. The electronic transport properties including σ and S were measured from 300 K to 560 K using an ULVAC ZEM-3 system. The κ values (κ=ρs·Cp·λ) were calculated from measurements taken separately: sample density (ρs), heat capacity (Cp), and thermal diffusivity (λ) measured under vacuum by laser-flash method (TC-9000, ULVAC, Japan), in which Cp was used as the constant value of 0.225 J·g−1·K−1 estimated from the Dulong-Petit fitting using low temperature Cp data. All measured data, which were acquired at the same dimension and configuration, are obtained within the experimental error of about 5%.


## 3. Results and Discussions

Figure1 shows TE properties for the homologous Cux+yBi5-ySe8 (1.2 ≤ x≤ 1.5, 0.1 ≤ y≤ 0.4) system at 560 K with varying compositional ratio between Cu and Bi. The absolute value of S decreases linearly with increasing σ, indicating that the semiconducting transport properties do not significantly change with varying the Cu/Bi ratio. Based on theoretical calculations of the previous report, interstitial Cu is regarded as the main source of electron carriers in the Cux+yBi5-ySe8 system [18]. Because the electron distributions around interstitial Cu ions, which are shown in the crystal structure of Cu-Bi-Se pavonite compound (Figure 2(a)), overlapped each other along b-axis, the degree of overlapping depends on the content of the interstitial Cu. This might be a possible reason for the changes in electrical properties by perturbing Cu sites, since the interstitial Cu sites locate along b-axis and work as an electrical conduction path, leading to an improvement of electron transfer across the basal plane. On the other hand, κ decreases from 0.65 to 0.51 W·m−1·K−1 by increasing Cu content. The highest ZT value of 0.27 at 560 K was obtained in the Cu1.9Bi4.6Se8 composition, which has the highest Cu concentration among samples, mainly due to its low κ. Thus, it is suggested that statistically distributed interstitial Cu along b-axis may be the main factor affecting the electronic (by generating electron carriers) and thermal transport (by enhancing phonon scattering) properties in this system. In order to understand the TE transport behavior based on the roles of the interstitial Cu and substitutional Bi sites, we individually modified those sites by impurity doping.Figure 1
Electrical conductivity (σ), Seebeck coefficient (S), thermal conductivity (κ), and ZT as functions of Cu/Bi ratio in Cux+yBi5-ySe8 (1.2 ≤ x≤ 1.5, 0.1 ≤ y≤ 0.4) pavonite homologues. All data were acquired at 560 K.(a) Crystal structure of Cu1.7Bi4.7Se8 with interstitial Cu and substitutional Bi sites. (b) Seebeck coefficient as a function of electrical conductivity (σ) for Cu-Bi-Se system. Blue and red dots indicate Cu1.7-wMwBi4.7Se8 and Cu1.7Bi4.7-zMzSe8 systems, respectively. Black dot is a base Cu1.7Bi4.7Se8 compound. The inset is Pisarenko plot at 300 K, representing the Seebeck coefficient (S) as a function of carrier concentration (nc). The dashed line corresponds to the theoretically expected curve for Cu1.7Bi4.7Se8 with effective mass of m*~0.21m0.
(a)
(b)Cu1.7Bi4.7Se8 was chosen as a base composition for doping, since this composition showed stable structure and reproducible physical properties. Figure 2(b) shows the Jonker plot of Cu-Bi-Se system. Most of the experimental data points for Cu1.7Bi4.7-zMzSe8 compounds lie on the straight line (cyan dashed) with the slope of 198 μV·K−1. However, in case of the interstitial Cu site modified Cu1.7-wMwBi4.7Se8 compounds, the slope (green dashed line) was changed in the region of largely increased σ (Figure 2(b)), indicating that the electronic state was altered to a highly degenerate state by doping at the interstitial Cu sites. In Pisarenko plot (the inset of Figure 2(b)), all data points lie below the theoretically expected Pisarenko curve (cyan) for undoped Cu1.7Bi4.7Se8 with effective mass of m* (~0.21m0). These electronic transport properties might be related to the changes in the Hall mobility (μH) and m* of doped compounds. In order to clarify the origin for affecting S in doped compounds, m* values were calculated using the measured S and the carrier concentration (nc) for the whole samples. The m* is one of the critical factors determining S and estimated with the following equation:
(1)m*=h22kBT[nc4πF1/2(η)]2/3,
where h,kB,Fn, and η are the Planck constant, Boltzmann constant, nth order Fermi integral, and the reduced Fermi energy, respectively.As shown in Figure3, m* was decreased by the doping compared to that of undoped compound. It should be noted that m* values of the interstitial Cu site modified Cu1.7-wMwBi4.7Se8 compounds were much lower than those of Cu1.7Bi4.7-zMzSe8. Furthermore, μH was inversely proportional to m* due to the reduced mass. In principle, the reduced m* enables the energetic movement of charge carriers in the highly degenerate semiconductors, resulting in the decrease of S. Considering the slight change of nc in the inset of Figure 2(b), it is concluded that the decrease in S is largely affected by the reduced m* via the modification of interstitial Cu site.Figure 3
Effective mass (m*/m0) and Hall mobility (μH) as functions of Seebeck coefficient (S) for Cu1.7-wMwBi4.7Se8 and Cu1.7Bi4.7-zMzSe8 with varying doping levels and dopants.In Figure4(a), σ of Cu1.7-wMwBi4.7Se8 was drastically changed by the modification of Cu sites compared to that of Bi sites (Cu1.7Bi4.7-zMzSe8). According to the theoretical calculation, interstitial Cu generates electron carriers in Cux+yBi5-ySe8 system [18]. Therefore, more electrons can be generated by the elemental doping at the interstitial Cu site. Indeed, higher nc, μH, and the smaller m* were observed in Cu1.7-wMwBi4.7Se8 compared to those of Cu1.7Bi4.7-zMzSe8. In Figures 4(a) and 4(b), with increasing the doping level, the region of intrinsic conduction also shifts to higher temperatures. This is a typical behavior of a degenerate semiconductor, since the increased extrinsic majority carriers suppress the contribution of the minority carriers and hence increase the onset temperature of intrinsic conduction. As shown in Figures 4(c) and 4(d), negative S values for all samples were observed over the entire temperature range, suggesting that the electrical conduction was dominated by n-type carriers. In Figure 5, it was confirmed that the change in S at 560 K was due to the combined effect of decreased m* and increased μH. Regardless of doping level and sites, carrier relaxation time (τ) was nearly the same (a few femtoseconds) for all samples. Figure 6 shows κlatt as a function of temperature. The value of κlatt was calculated from the relation of κ=κlatt+κelec, in which κelec is the electronic contribution. The value of κelec was estimated using the Wiedemann-Franz law, κelec=L·T·σ, in which L denotes the Lorenz number, taken to be L=(π2/3)(kB/e)2~2.45×10-8V2·K-2. However, this value is valid for the estimation of κlatt in metals, not in heavily doped semiconductors like TE materials especially at high temperature. In semiconductors, the L depends on η and scattering factor (r), which can be derived from the temperature dependence of μH (μH∝T-(3/2)+r) and decreases as η decreases with increasing temperature. The L is given as
(2)L=(kbe)2([(r+(5/2))Fr+(3/2)(η)(r+(3/2))Fr+(1/2)(η)]2(r+7/2)Fr+(5/2)(η)(r+3/2)Fr+(1/2)(η)-[(r+(5/2))Fr+(3/2)(η)(r+(3/2))Fr+(1/2)(η)]2),
where Fn(η) is the nth order Fermi integral, Fn(η)=∫0∞(xn/(1+ex-η))dx [19].Electrical conductivity (σ) as a function of temperature for (a) Cu1.7-wMwBi4.7Se8 and (b) Cu1.7Bi4.7-zMzSe8. Seebeck coefficient (S) as a function of temperature for (c) Cu1.7-wMwBi4.7Se8 and (d) Cu1.7Bi4.7-zMzSe8.
(a)
(b)
(c)
(d)(a) Seebeck coefficient (S), (b) Hall mobility (μH), (c) effective mass (m*/m0), and (d) carrier relaxation time (τ) as a function of temperature for Cu1.7-wMwBi4.7Se8 and Cu1.7Bi4.7-zMzSe8 with varying doping levels and dopants.
(a)
(b)
(c)
(d)Figure 6
Lattice thermal conductivity (κlatt) as a function of temperature for (a) Cu1.7-wMwBi4.7Se8 and (b) Cu1.7Bi4.7-zMzSe8 with varying doping levels and dopants.CalculatedL was nearly constant in all compounds and was in the range of 2.48–2.58 × 10−8 V2·K−2. As shown in Figure 6, κlatt was much decreased by the modification of Cu sites compared to that of Bi sites. This is mainly ascribed to the mass difference between site ions (Cu or Bi) and dopants. Indeed, the mass difference for interstitial Cu and In is 114.82 compared to 29.2 for the substitutional Bi and In. The values of κ, ranging from 0.47 W·m−1·K−1 to 0.69 W·m−1·K−1, were found for all compounds, and κ showed a weak temperature dependence. These κ values are much lower than those of state-of-the-art low κlatt systems, such as Zn4Sb3 (κ ~ 1.05 W·m−1·K−1 at 300 K) [20] and Cu2-xSe (κ ~ 1 W·m−1·K−1 at 400 K) [21]. We suggest that the reason of the extremely low κ values in this system is due to the strong phonon scattering and the short phonon mean free path of below 1 nm, which is much shorter than the size of unit cell of this structure. The strong phonon scattering is mainly attributed to the structural complexities based on the combined effect of point defects and intrinsic disorders. The maximum ZT values achieved in this study for Cu site and Bi site modified Cu1.6915In0.0085Bi4.7Se8 and Cu1.7Bi4.6915Zn0.0085Se8 were 0.25 and 0.18 at 560 K, respectively. It is expected from the low σ values of Cu-Bi-Se system that the present TE properties can be much enhanced by optimizing PF through tuning nc. The modification of Cu site is an effective way to reduce κlatt compared to that of Bi site. It is worth noting that intrinsically low κ of this material is less sensitive to temperature gradient because of the complex mixture of extraordinary structural disorders. There is still remaining a possibility for the further improvement of TE performance by the optimization of resonant level doping to enhance PF without sacrificing κ.


## 4. Conclusions

The electronic and thermal transport properties of Cu1.7Bi4.7Se8 pavonite homologues (N=3) with monoclinic C2/m space group were investigated in the view point of the correlation with complex crystal structure via the modification of Cu or Bi sites with dopants. σ and κlatt were much affected by the modification of Cu sites compared to that of Bi sites. This is due to the origin of n-type conduction and the intrinsically low κlatt, which is highly related to the structural configuration of the interstitial Cu sites in this system. Though the Cu1.7Bi4.7Se8 compound showed an extremely low κlatt, additional ~30% reduction in κlatt was achieved by the modification of Cu sites. Therefore, we anticipate that the further fine-tuning of the electronic and thermal properties based on the correlated findings about structural modifications gives a possible enhancement of TE performance in the Cu-Bi-Se system.



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