Inhibition of minority transport for elevating the thermoelectric figure of merit of CuO/BiSbTe nanocomposites at high temperatures

Abstract

Achieving a large thermoelectric figure of merit (ZT) value at elevated temperatures for Bi₂Te₃-based materials is significant for low-grade waste-heat (∼400–500 K) recovery applications. Here, we show that in Bi_0.4Sb_1.6Te₃ based composites incorporated with 0.2 vol% CuO nanoinclusions, the introduced asymmetric interface potentials can effectively inhibit the transport of minorities through stronger scattering than majorities, as well as the energy filtering effect, thus resulting in an obvious increase (∼8% rise) of power factor at high temperatures. In addition to enhanced phonon scattering at interfaces and nanoinclusions, the reduced thermal conductivity (∼65% decline) at elevated temperatures can be attributed to inhibition of bipolar contributions through strong scattering of minorities at the interface potentials. Consequently, in BiSbTe-based thermoelectric systems with 0.2 vol% CuO, a largest ZT = 1.37 is achieved at 496 K, which is ∼40% larger than that of the BiSbTe matrix at the same temperature.

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1. Introduction

The phenomenon of thermoelectricity (TE) is a technology that can convert heat into electricity directly via a solid-state conversion.^1,2 However, the efficiency of a TE material system is still too low for energy harvesting from low-grade waste heat (∼400–500 K), which is evaluated by the thermoelectric figure of merit quantity (ZT), defined as ZT = (S²T)/ρ(κ_c + κ_L), where ρ is electrical resistivity, S the Seebeck coefficient, κ_c the carrier thermal conductivity, κ_L the lattice thermal conductivity and T the absolute temperature.³

As the most promising thermoelectric materials at room temperature, Bi₂Te₃-based alloys attract more and more attention. Intrinsically, BiSbTe alloy is a narrow-gap (indirect band gap of ∼0.13–0.15 eV) layered semiconductor possessing a trigonal unit cell with space group R3̄m and lattice constants a = 4.38 Å and c = 30.36 Å; thus intrinsic excitation of minorities will easily occur at elevated temperatures (usually at T = ∼400 K).⁴ Therefore, its ZT value drops rapidly with further increasing temperature (T > 400 K). For authoritative instance, p-type Bi_xSb_2−xTe₃ nanocomposites prepared by high energy ball milling combined with hot-pressing have the maximum ZT value of 1.4 at ∼373 K, which, however, drops rapidly to ∼0.95 at 498 K with further increasing temperature;⁵ although dense dislocation arrays formed at low-energy grain boundaries in Bi_0.5Sb_1.5Te₃ lead to a substantially lower lattice thermal conductivity, dramatically improving the ZT to 1.86 at 320 K, the ZT value declines fleetly to ∼0.7 at 480 K.⁶ Consequently, their ZT values at high temperatures are still too small to be used in waste heat recovery (∼400–500 K).

In order to solve this problem, we introduce an alternative and feasible way, to inhibit the transport of minorities through strong scattering at introduced interface potentials. However, the introduced potential should be asymmetric, i.e. these potentials must cause relative weak scattering to the majorities. As a result, power factor (PF = S²/ρ) of BiSbTe alloy can possibly be increased at elevated temperatures. A prospective way to realize this goal is to incorporate nanoinclusions with larger band-gap into BiSbTe matrices to form nanocomposites, in which proper potentials will form at the interfaces (phase boundaries) and energy filtering effect (EFE) would be enhanced through (majority) carrier scattering at the interface potentials.^7,8 Hence, it is greatly challenging whether one can introduce in nanocomposites a proper interface potential that can not only bring about strong EFE but also inhibit transport of minorities at elevated temperatures, in addition to enhancing phonon blocking.

In this work, Bi_0.4Sb_1.6Te₃ (BST) based composites incorporated with CuO nanoparticles were prepared. CuO is a p-type semiconductor with a band gap of 1.2–1.9 eV. Hence, as it contacts with BST, p–p type potentials at the interfaces will form, which would inhibit transport of minorities and could bring about strong EFE, elevating S and PF at high temperatures. In fact, our results indicate that in the composite system with 0.2 vol% of CuO, ∼8% increase in PF and ∼65% decrease in κ_L are concurrently realized, leading to a largest ZT = 1.37 at 496 K, which makes this material suitable for low-grade waste-heat recovery applications.

2. Experimental section

Elemental Bi (99.99%), Sb (99.99%) and Te (99.99%) powders were weighted according to the composition of Bi_0.4Sb_1.6Te₃ with 3 wt% of excess Te. The powder mixture was loaded into quartz ampoule pumped under vacuum of 10⁻² Pa and then heated to 1073 K for 10 h in a muffle furnace. The obtained ingot was grinded into powders. The nanometer-sized CuO (99.99%, ∼40 nm sized) and obtained Bi_0.4Sb_1.6Te₃ powders were mixed in a planetary mill for 2 h in accordance with the volume ratios of 0.1 : 99.9, 0.2 : 99.8 and 0.3 : 99.7. Then the bulk nanocomposite samples were obtained by hot-pressing the blended powders under a pressure of 600 MPa in vacuum at 623 K for 1 h.

X-ray diffraction (Philips diffractometer, Cu K_α radiation) was used to study the phase structure of the obtained samples at room temperature. The fractographs were observed by field emission scanning electron microscopy (FE-SEM). Electrical resistivity and Seebeck coefficient were measured by the ZEM-3 system from ULVAC under helium atmosphere from 300 to 500 K. The thermal diffusivity D was measured using the laser flash method (Netzsch, LFA-457). It should be pointed out that due to the anisotropic characteristic of BiSbTe alloys, D was measured in the perpendicular direction to the pressing direction, ensuring that the thermal and electrical properties are measured in the same direction. The specific heat, C_p, was determined by differential scanning calorimetry (DSC Pyris Diamond). The density d was measured by the Archimedes' method. The resulting total thermal conductivity was calculated from the measured thermal diffusivity D, specific heat C_p, and density d according to the relationship κ = DdC_p. The Hall coefficients were measured using the van der Pauw technique under a magnetic field of 0.72 T. The accuracies in measurements of resistivity, Seebeck coefficient and thermal conductivity are around ±2%, ±5% and ±5%, respectively. The uncertainty of ZT is around ±11%.

3. Results and discussion

3.1. Microstructure characteristics

Fig. 1 shows the XRD patterns of BST, CuO and f(CuO)/BST (f = 0.1, 0.2 and 0.3 vol%) composite samples. As shown in Fig. 1 (curves (a) and (b)), all the main diffraction peaks match well with the standard JCPDS cards (BST: 72-1836; CuO: 01-1117). However, it should be pointed out that one cannot detect obvious diffraction peaks from CuO in the curves of (c) and (e) in Fig. 1, for a few CuO particles are added to BST matrix (0.1, 0.2 and 0.3 vol% correspond to curves (c)–(e)).

Fig. 1 XRD patterns at room temperature of (a) BST, (b) CuO and (c–e) f(CuO)/BST (f = 0.1, 0.2 and 0.3 vol%).

The fractographs of the sintered CuO/BST composite bulk samples are shown in Fig. 2. One can see that white granules with sizes of ∼40 nm distribute in the big gray grains, as shown in Fig. 2(a) and (b). Further analysis of the rectangle area in Fig. 2(a) with energy dispersive X-ray spectroscopy (EDX) indicates that the areas with white spots contain chemical elements Cu and O (see Fig. 2(c)), verifying that the white spots are actually CuO grains. This result confirms that nanophase CuO are successfully incorporated into BST matrix, forming CuO/BST bulk nanocomposites. Fig. 3(a) shows the bright-field TEM image of CuO/BST, which indicates that the CuO nanoparticles were embedded in the BST matrix. Fig. 3(b) shows the lattice image, revealing a typical phase boundary between the CuO inclusion and the BST matrix (as shown by the white dash line).

Fig. 2 FE-SEM micrographs of (a) fracture surface of CuO/BST bulk composite sample, (b) HRSEM image of the selected rectangle area in (a), (c) EDX pattern detected in the marked area in (a).

Fig. 3 (a) TEM bright-field image of CuO/BST, showing the BST matrix and the incorporated nanophase CuO. (b) HRTEM image of CuO/BST, revealing a typical phase boundary between the CuO inclusion and the BST matrix.

3.2. Thermoelectric properties

The thermoelectric properties (ρ and S) of the composites f(CuO)/BST (f = 0, 0.1, 0.2 and 0.3 vol%) are shown in Fig. 4(a) and (b). One can see from Fig. 4(a) that ρ for all the samples increases with increasing temperature, showing degenerate semiconductor behavior.⁹ In comparison, ρ of the composite samples decreases monotonically with increase in f. Moreover, it is found that the slopes (dρ/dT) for samples with different f differ obviously, which are 4.65 × 10⁻⁸, 3.37 × 10⁻⁸, 3.10 × 10⁻⁸ and 3.08 × 10⁻⁸ Ω m K⁻¹ for f = 0, 0.1, 0.2 and 0.3 vol%, respectively. Obviously, the slopes dρ/dT of the composite samples (f > 0) are smaller than that of the sample with f = 0, which could be caused by incorporating the second phase.

Fig. 4 Temperature dependences of (a) electrical resistivity and (b) Seebeck coefficient for composite samples f(CuO)/BST (f = 0, 0.1, 0.2 and 0.3 vol%). Temperature dependences of (c) total carrier mobility μ_T and (d) carrier mobility that corresponds to the scattering of carriers at the interfaces μ_in for composite samples f(CuO)/BST (f = 0, 0.1, 0.2 and 0.3 vol%). The inset of (d) is a logarithmic plot of μ_in × T^1/2 versus 1/T (300 K < T < 425 K), and from the slope the height of the potential barrier (or depth of the potential well) is extracted to be E_Bp = −75 meV.

S values for all of the samples are positive (Fig. 4(b)), indicating that the major charge carriers are holes. S for the sample with f = 0 increases first with increasing temperature at T < ∼425 K and then it decreases with further increase in temperature, due to the intrinsic excitation at high temperatures.^10,11 In contrast, S values of the composite samples (f > 0) increase monotonically with temperature in the whole temperature range investigated here. In addition, S decreases obviously with increasing CuO content.

In order to understand the behavior of ρ and S, carrier concentration p of all the samples are determined at room temperature. p increases from 4.01 × 10¹⁹ to 9.23 × 10¹⁹, 10.88 × 10¹⁹ and 12.37 × 10¹⁹ cm⁻³, as f increases from 0 to 0.1, 0.2 and 0.3 vol%, respectively (see Table 1). Simultaneously, the mobility μ decreases moderately from 218.7 to 114.8 cm² V⁻¹ s⁻¹. Therefore, the decrease in ρ results largely from the increase in p due to the relation ρ = 1/(peμ).¹²

Table 1 List of Hall mobility μ, carrier concentration p, scattering parameter λ, the relative density d_r and the Lorenz number L at room temperature for f(CuO)/BST (f = 0, 0.1, 0.2 and 0.3 vol%)

f(vol%)	μ^a (cm^2 V^−1 s^−1)	p^b (10^19 cm^−3)	λ^c	dr^d (%)	L^e
a μ is Hall mobility.b p is carrier concentration.c λ is scattering parameter.d dr is relative density, defined as dr = d/d0, where d is measured density and d0 (= 6.76 g cm^−3) is theoretical density of BST. For the composite samples f(CuO)/BST, its theoretical density is modified as: d0 = (1 − f)d1 + fd2, here d1 = d0 for BST and d2 (= 6.6 g cm^−3) is theoretical density of CuO.e L is the Lorenz number.
0	218.7	4.01	0	96	1.66
0.1	134.6	9.23	0.09	96	1.82
0.2	121.2	10.88	0.29	97	1.86
0.3	114.9	12.37	0.34	96	1.89

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As we know, for a degenerated semiconductor, the diffusive part of the Seebeck coefficient (or the T-linear Seebeck coefficient) can be described as:¹³

here, we assume the f(CuO)/BST (f = 0.2 vol%) compound to be a quasi-free electron system and formula (2) can be extended as:where n(ε) ∝ E^1/2, γ²(ε) ∝ E, τ(ε) ∝ E^−1/2 (assuming a constant mean free path). Thus, we obtain the Seebeck coefficient as:where k_B, E_f and e are the Boltzmann constant, Fermi level and electron charge, respectively. This formula indicates that the slope of the plot S vs. T is inversely proportional to the Fermi level E_f. By the best fitting of formula (3) to experimental data (see Fig. 4(b)) we obtain E_f = 0.081 eV for f(CuO)/BST (f = 0.2 vol%).

As mentioned above, the slopes dρ/dT of the composite samples (f > 0) are obviously smaller than that of the sample with f = 0. For a degenerate semiconductor, p do not change substantially before the intrinsic excitation (here T < ∼425 K), then we can calculate μ_T (the total carrier mobility) according to the relation ρ = (peμ)⁻¹ at different temperatures, as shown in Fig. 4(c). Assuming that the scattering events are independent with each other, then one has:¹⁴

where μ_T, μ_m and μ_in are the total carrier mobility of the composite samples, the mobility in the matrix and the mobility being related to scattering of interface potentials. Subsequently, one can extract μ_in by using formula (4), as shown in Fig. 4(d). Similar to the scattering of grain boundary potentials, μ_in can be approximately written as:^15,16where L is the mean spacing between two adjacent potential barriers, and E_Bp is the height of the potential barrier (or depth of the potential well) at the interfaces. The inset of Fig. 4(d) shows a logarithmic plot of μ_in × T^1/2 versus 1/T. From the inset of Fig. 4(d), one can find that the values of the slopes of the composite samples f(CuO)/BST (f = 0.1, 0.2 and 0.3 vol%) are very close to each other. Subsequently, the height of the potential barrier (or depth of the potential well) can be extracted to be E_Bp = −75 meV, where the minus suggests that actually there exists a potential well with the depth E_Wp = 75 meV.

The increase in p can qualitatively explain why S of composite samples decrease with increasing f according to the Mott formula:¹⁷

where q, k_B, E_f are the carrier charge, the Boltzmann constant, and Fermi energy, respectively. However, quantitative analysis indicates that energy-dependent scattering (or EFE) has occured,^18,19 as manifested by the increase in the scattering parameter λ, which is usually related to relaxation time τ with the relation: τ = τ₀E^λ−1/2 (here E and τ₀ are the energy of carriers and the energy-independent constant, respectively). By using a single parabolic band model, the density of state effective mass and the Seebeck coefficient S can be expressed as:²⁰with Fermi integral of order iwhere h is the Planck constant and ξ_F is the reduced Fermi level F_f/(k_BT). Then, we obtain (where m_e is the free electron mass) for BST at 300 K by assuming that λ = 0 for the BST matrix (i.e. acoustic scattering is dominant in BST). Moreover, in our calculation, we assume that do not change in different samples, and then we obtain the λ values for all the samples (see Table 1). Table 1 shows that λ increases with increasing CuO content, and this increase of λ leads to ∼7, ∼19 and ∼24 μV K⁻¹ rise in S at 300 K for the samples with f = 0.1, 0.2 and 0.3 vol%, respectively, as shown in Fig. 5(a) (where the solid line is the Pisarenko relation of BST at T = 300 K and shows the dependence of S on p calculated by using formulae (7)–(9)).

Fig. 5 (a) Variation of Seebeck coefficient with carrier concentration for f(CuO)/BST (f = 0, 0.1, 0.2 and 0.3 vol%) at 300 K. The solid line is Pisarenko relation for BST at 300 K. (b) Cross sectional schematics of the energy bands for CuO (band gap E_g1) and BST matrix (band gap E_g0) and p–p type interface potentials (potential well with an effective depth E_Wp and potential barrier with an effective height E_Bn) formed from band bending (where E_c0 and E_c1 are the conduction band bottoms; E_v0 and E_v1 are the valence band tops and d_p is the particle size of CuO).

Another interesting phenomenon is that in contrast to the BST matrix, S for the composite samples (f > 0) increase monotonically with temperature and do not show decrease up to 500 K. This phenomenon suggests that the heterojunction potentials at the interface between CuO and BST scatter electrons much strongly than holes, as schematically shown in Fig. 5(b). Since in the case of mixing conduction S can be written as follows:²¹

where the subscript T, p and n represent total (hole and electronic conduction), hole conduction and electronic conduction, respectively. If electrons are scattered more strongly than holes, μ_n will become negligibly small as compared to μ_p, which leads to σ_n ≪ σ_p, and the term |σ_nS_n| (S_n < 0) in formula (10) can be neglected as compared to σ_pS_p. Hence one has S_T ≈ S_p, which explains why S for the composite samples (f > 0) increase monotonically with temperature. Moreover, previous studies in Bi₂Te₃-related materials indicated that the antisites (i.e., Bi atoms go to Te sites) are more likely to occur at interfaces. Uncompensated recombination centers at interfaces associated with defect states and antisites are responsible for charge buildup at grain boundaries and thus increase the hole density in the grains.²² This explanation is consistent with the observed decrease in ρ as well as the reduction in S with the increasing CuO content (see Fig. 4(a) and (b)).

Fig. 6(a) shows PF of f(CuO)/BST as functions of temperature. One can see that PF of the BST matrix decrease rapidly with further increasing temperature, while PF of the composite samples show a relative slow descent. Clearly, PF of the slightly incorporated samples (f = 0.1 and 0.2 vol%) enhances obviously at elevated temperatures. Specially, PF of the sample with f = 0.2 vol% reaches 27.4 μW (cm K²)⁻¹ at 496 K, which is ∼8% larger than that of the BST matrix. The enhancement of PF for the composite sample can be ascribed to alleviated increase of ρ and monotonic increase of S at elevated temperatures due to the elevated energy filtering of carriers and inhibition of minority transport.

Fig. 6 Temperature dependences of (a) power factor, (b) total thermal conductivity (lattice thermal conductivity in the inset) and (c) ZT (the ZT measurement uncertainty is represented by the dotted deviation) for composite samples f(CuO)/BST (f = 0, 0.1, 0.2 and 0.3 vol%).

The total thermal conductivity κ for all the samples is given in Fig. 6(b) as a function of temperature. One can see that κ for the BST matrix decreases with increasing temperature and then increases with further increasing temperature. In comparison, κ for the composite samples (f = 0.1, 0.2 and 0.3 vol%) decreases with increasing temperature in the whole temperature range investigated. The total thermal conductivity κ consists of lattice thermal conductivity κ_L and the carrier thermal conductivity κ_c, i.e. κ = κ_L + κ_c, where the carrier thermal conductivity κ_c can be estimated by the Wiedemann–Franz relation (κ_c = LT/ρ), in which the Lorenz number L is estimated using formula (11) with the assumption of transport dominated by acoustic scattering and a single parabolic band:²³

the obtained values of L are 1.66–1.89 × 10⁻⁸ V² K⁻², as listed in Table 1. As shown in the inset of Fig. 6(b), the incorporation of nanophase CuO leads to substantial reduction of κ_L as compared to that of BST. For instance, κ_L decreases to 0.30 W (K m)⁻¹ (a ∼65% decline as compared to that of BST) for the sample with f = 0.2 vol% at 496 K. Obviously, the reduction of κ_L in the composite samples should be attributed to the additional phonon scattering from nanoinclusion and the phase boundaries. It is worthwhile to note that κ_L of the composite samples (f > 0) does not show obvious increase up to 500 K, indicating a smaller bipolar contribution caused by strong scattering of electrons (minorities) at interfaces, as mentioned above.⁵

Fig. 6(c) shows ZT for all the samples. One can see that ZT for the BST matrix increases with increasing temperature, and after reaching a maximum it decreases with further increasing temperature. Meanwhile, the temperature of maximum of ZT for composite samples is higher than that of BST matrix. Specially, ZT of the sample with f = 0.2 vol% reaches 1.37 at 496 K, which is ∼40% larger than that of the BST matrix at the same temperature. In addition to inhibition of κ_L, the enhancement of ZT at elevated temperatures can be mainly ascribed to the increase of PF, resulting from alleviated increase of ρ and monotonic increase of S at elevated temperatures due to elevated energy filtering of carriers and inhibition of minority transport.

4. Conclusion

In summary, incorporating 0.2 vol% nano-CuO particles into the BST matrix can concurrently result in increase in PF and reduction of κ_L. The elevated PF results mainly from alleviated increase of ρ and monotonic rise in S due to carrier scattering at interface potentials in the composite system. Simultaneously, CuO nanoinclusions cause reduction in κ_L at elevated temperatures owing to enhanced phonon scattering at interfaces and nanoinclusions as well as phase boundaries, which can be attributed to inhibition of bipolar contribution through strong scattering of minorities at the interface potentials. Owing to ∼8% increased PF and ∼65% reduced κ_L, ZT = 1.37 is achieved at 496 K in the composite system with 0.2 vol% of CuO. Present study demonstrates that the thermoelectric performance of CuO/BST nanocomposite system possesses great potentials in the application for energy harvesting from low-grade waste heat.

Acknowledgements

Financial supports from the National Natural Science Foundation of China (No. 11374306 and 11174292) are gratefully acknowledged.

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