Insight into the transport properties and enhanced thermoelectric performance of n-type Pb1−xSbxTe
Introduction
Thermoelectric materials are used in devices converting heat into electricity or for the construction of solid-state heat pumps [1], [2], [3]. The main advantages of these devices are high reliability and a significantly long period of continuous operation. The efficiency of thermoelectric conversion is determined by a dimensionless thermoelectric figure of merit represented as ZT = σS2T/(κel+ κlat), where σ is electrical conductivity, S is the Seebeck coefficient, T is absolute temperature, κel and κlat are the electronic and lattice components of thermal conductivity, respectively [4], [5], [6], [7]. Obviously, an excellent thermoelectric material should have a high thermoelectric power factor (PF) PF = S2σ and low lattice thermal conductivity κlat [5].
The enhancement of the power factor has been realized by different strategies for different types of materials: density of electronic states (DOS) modifications at the Fermi level EF [2], [8], [9], [10], [11], convergence of electronic bands [12], [13], nano-structuration [14], [15], electron filtering [16], [17], etc. As regards the reduction of lattice thermal conductivity, the most established methods are the formation of solid solutions, the introduction of nano-precipitates, and microstructure modification by means of point defects [18], [19], [20].
Lead telluride (PbTe) is one of the most attractive materials in terms of its thermoelectric properties in the temperature range of 500–900 K [4], [5], [6], [14], [15], [16], [17], [18], [20], [21], [22], [23], [24]. This narrow bandgap semiconductor (Eg = 0.19 eV at 0 K and Eg = 0.31 eV at 300 K [4]) consists of heavy atoms, which is one of the requirements for low lattice thermal conductivity. It has high dielectric permittivity and low effective mass of carriers, resulting in high mobility of carriers. PbTe is a polar semiconductor with predominant covalent bonding; therefore, scattering on the acoustic phonons is the most probable scattering mechanism [25], [26]. The band structure of PbTe was proposed by Allgaier and Houston [27] and confirmed by Crocker and Rogers [28]. They suggested that two bands determine the properties of valence band EV: light-hole band L+ and heavy-hole band Σ, which is flatter; these are separated by the energy shift of 0.18 eV at 0 K [13]. The light-hole band has the determining effect on carrier formation if its concentration is small. As carrier concentration increases, the position of Fermi level EF moves to the heavy-hole band, which makes its influence significant. With the temperature rise, the effect of the heavy band also becomes significant, as the light valence band moves down with temperature [4]. A single L-conduction band defines the properties of the conduction band because the nearest band is located above a significant energy distance of ~0.3 eV [4], [29]. For optimal carrier concentration (reduced Fermi energy μ* ≈ 0) and main carrier scattering on the acoustic phonons, the thermoelectric figure of merit mostly depends on three parameters Z = N × u/кlat, where N is band degeneracy, and u is carrier mobility. Therefore, due to the overlapping of light and heavy carriers, band engineering for p-PbTe is more effective compared with n-PbTe [16].
If the reported values of the ZT parameter for p-type PbTe-based materials exceed ~2.0 [30], [31], the thermoelectric figure of merit for the n-type component of the PbTe-based thermoelement is much lower. One of the promising n-type doping elements in PbTe is Sb [15], [16]. The electronic structure, transport properties, and nano-structuration effect of Sb-doped PbTe-based materials have been considered in the literature [14], [15], [16], [20], [24], [32], [33], [34], [35], [36]. Antimony in PbTe has a weak temperature dependence of solubility that provokes an excess of Sb in the form of nanoparticles at low temperatures and point defects at high temperatures [37]. In accordance with the equilibrium phase diagram, the solubility limit of Sb2Te3 in the pseudo-binary system of PbTe-Sb2Te3 is 2.13 ± 0.21 (at% of Sb) at 723 K [38]. First-principle calculations, together with experimental nuclear magnetic resonance (NMR) measurements of magic-angle spinning (MAS) for 125Te and 207Pb isotopes, show that Sb in the PbTe lattice can behave as an amphoteric dopant [39]. In materials with Te deficiency, Sb substitutes Te atoms, and for Pb-deficient materials, Sb occupies the Pb position.
Even if there is a lot of data available about the Sb dopant in PbTe, there are still some aspects which require additional analysis. According to studies [20], [40], the lattice parameter for Pb1−xSbxTe decreases as Sb nominal concentration increases. Authors of work [25] suggest that the lattice parameter increases up to nominal x = 0.01, and then goes down with the further increase in Sb nominal concentration. Recently, authors of work [41] have found that the fluctuations (increase and decrease) of the lattice parameter with Sb increase from x = 0.002 till x = 0.015. Also, the transport properties for the same nominal composition of Sb in PbTe show significantly different values in different works. For example, the electrical conductivity of Pb0.995Sb0.005Te fluctuates from ~40 S/cm [21] at ~300 K to ~1000 S/cm [41] at the same temperature.
In this work, we carried out detailed research on microstructural and transport properties for Pb1−xSbxTe. We also analyzed the solubility of Sb in PbTe as well as the possibility of occupation of both sublattices. The effect of different scattering mechanisms on the transport properties of n-type Pb1−xSbxTe was studied using the developed electronic transport model. The possible reasons for the uncertain transport properties in literature were discussed in detail. We also estimated the thermoelectric efficiency of Sb-doped PbTe samples and their potential use for the construction of a segmented or functionally graded n-type thermoelectric leg.
Section snippets
Synthesis
Materials were synthesized in quartz ampoules evacuated to a residual pressure of 10−4 mbar. The ampoules were subjected to rigorous purification, which included washing in HNO3:HCl concentrated acid mixture and frequent cleaning with distilled water and isopropanol. Polycrystalline Pb1−xSbxTe, x = 0.001, 0.005, 0.01, 0.02, 0.03 samples were synthesized by melting Pb (Alfa Aesar, 99.999%), Te (Alfa Aesar, 99.999%) and Sb (Alfa Aesar, 99.999%) at 1273 K in a rocking furnace, followed by
Powder X-ray diffraction analysis
Powder XRD analysis of samples after synthesis shows sharp peaks indicating the polycrystal nature of the obtained materials (Fig. 1). For the Pb1−xSbxTe samples with the chemical composition of ≤ 1at% of Sb, the additional phases were not detected, indicating the single-phase nature of the obtained materials. At a concentration of ≥ 2 at% of Sb, a minor presence of the Sb-based phase could be observed (reflection at 2Θ = 28.2°), which is consistent with the reported limits of Sb solubility in
Conclusions
In this work, the crystal structure and thermoelectric properties of Pb1−xSbxTe alloys were investigated in detail. The lattice parameter refinement of Pb1−xSbxTe (x = 0, 0.001, 0.005, 0.01, 0.02, 0.03), contrary to the literature data, showed the decrease of the lattice parameter over the investigated concentration range of Sb doping, with the sample that had the lowest Sb nominal concentration considered in this work (x = 0.001), indicating the possible Sb substitution of both sublattices,
CRediT authorship contribution statement
T. Parashchuk: Conceptualization, Visualization, Writing - original draft. I. Horichok: Formal analyses, Data curation, Methodology. A. Kosonowski: Software, Formal analysis. O. Cherniushok: Investigation, Visualization, Data Curation. P. Wyzga: Investigation. G. Cempura: Visualization. A. Kruk: Validation. K. T. Wojciechowski: Principal Investigator, Project managment and conceptualization, Writing - review & editing, Supervision.
Declaration of Competing Interest
The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.
Acknowledgements
The authors would like to thank the Foundation for Polish Science (Fundacja na rzecz Nauki Polskiej) for financial support (TEAM-TECH/2016–2/14 grant “New approach for the development of efficient materials for direct conversion of heat into electricity”). under the European Regional Development Fund. The beneficiary institution of the grant is the Lukasiewicz Research Network – Krakow Institute of Technology.
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