Comprehensive Investigation on the Thermoelectric Properties of p‐Type PbTe‐PbSe‐PbS Alloys

Abstract

these parameters complicates the efforts in enhancing the thermoelectric performance. [1,3] To date, high ZT values have been obtained through enhancing electrical transport properties, reducing lattice thermal conductivities, and exploring the thermoelectric materials with intrinsically low thermal conductivity. [7][8][9][10][11][12][13][14][15][16][17][18][19] Lead chalcogenides are kinds of superior thermoelectrics because of their special physical and chemical properties. [20] In particular, PbTe and PbSe possess complex band structures (such as small energy offsets between light L and heavy Σ hole valence bands), which lead to larger band effective mass, higher Seebeck coefficients, and favor better electrical performance than that with single valence band. [9,[20][21][22] Besides, the intrinsic lattice thermal conductivities of lead chalcogenides are quite low due to the phonon anharmonicity. [20] Even that PbS possesses simple band structures and poor electrical and thermal transport properties, the features of low-cost, earth-abundant, higher melting point (1391 K), and larger energy band gap (0.41 eV) make PbS also an attractive thermoelectric candidate. [23][24][25] In the past few years, several approaches have been employed to enhance the thermoelectric performance of lead chalcogenides, such as enhancing electrical properties through introducing resonant states [8,26,27] and manipulating band structures, [28] suppressing thermal conductivities through introducing nanostructures, [25,[29][30][31][32] and all-scale hierarchical structures. [10,33] Among these methods, elements alloying for the solid solution with atomic-scale substitutions have been the most generally employed. Indeed, promising thermoelectric performance was achieved through simple elements alloying in the Pb-Sn-Te-Se solid solution system. [34] Similarly, extraordinary thermoelectric performance has been achieved in PbTe-PbSe, [28,35] PbTe-PbS, [36][37][38] PbTe-MTe (M = Mg, Sr), [10,33,39] PbSe-PbS, [40,41] PbSe-CdSe, and PbS-CaS solid solutions. [22,25] The above achievements in lead chalcogenides motivate us to fully investigate the thermoelectric transport properties of p-type PbTe-PbSe-PbS alloys and deeply understand this system, in which the carrier concentration was fixed with 2 mol% Na doping. Specifically, an ultrahigh power factor ≈25 µW cm −1 K −2 and a low lattice thermal conductivity ≈0.5 Wm −1 K −1 at 873 K, and thus a high ZT ≈ 1.9 are obtained in Solid solution alloying is one of the quite powerful approaches to enhance thermoelectric performance because it can simultaneously optimize electrical and thermal transport properties. Herein, a comprehensive investigation on p-type PbTe-PbSe-PbS alloys is reported, in which the carrier concentration is fixed with 2 mol% Na doping. High thermoelectric performance is achieved via synergistically tuning carrier concentration, manipulating electronic band structure, introducing nanostructures, and separating phases. Thus, a high ZT value ≈1.9 is obtained in (PbTe) 1−x (PbSe) x...

Synergetic Approach for Superior Thermoelectric Performance in PbTe-PbSe-PbS Quaternary Alloys and Composites

“…The lowest power factor is observed in alloy samples with x = 0.35 because an increase in the Se content results in a decrease in the mobility of charge carriers due to the scattering of charge carriers by impurities, which is not beneficial to the increase in the power factor [36]. In order to confirm the contribution of L and Σ bands' convergence to thermoelectric properties, the Pisarenko plot is shown based on two valence bands' model compared with PbTe [20,43,44], Pb 1−x K x Te [10], and Na-doped PbTe [43], as shown in Figure 6d. Instead of the single parabolic band model, the Pisarenko plot corresponds to the two valence bands' model with effective masses of light, L, and heavy, Σ, bands equal to 0.36 m e and 1.6 m e , respectively, which means that the Fermi levels lie deep within the valence band and the two valance bands contribute significantly to the Seebeck coefficient [8].…”

“…where Z is the figure-of-merit, T c is the cold side temperature, T h is the hot side temperature, T avg is the average temperature (T h + T c )/2, and ∆T is the temperature difference between hot and cold sides (T h − T c ). The calculated ZT avg values of PbTe, (PbTe) 0.75 (PbS) 0.25 [34], (PbTe) 0.88 (PbS) 0.12 [36], and (PbTe) 0.84 (PbSe) 0.07 (PbS) 0.07 doped with 2% Na [20] is shown in Figure 9b. It shows the highest average ZT avg of the (PbTe) 0.75 (PbSe) 0.2 (PbS) 0.05 alloy compared to the other compounds quoted in the previous reports [20,34,36].…”

“…The power factor of Pb 1−x K x Te 0.7 Se 0.25 S 0.05 and Pb 0.98 K 0.02 Te alloys displays the maximum value equal to 27.78 µW m −1 K −2 at 600 K when x = 0.01, which is attributed to the significant reduction in electrical resistivity. The Pisarenko plot made on two valence bands' model for Pb 1−x K x Te 0.7 Se 0.25 S 0.05 alloys, Na-doped PbTe, and Pb 1−x K x Te is shown in Figure 11d [10,20,43,44] and the values of effective masses of the heavy hole m * h = 1.2 m e (Σ band) and light hole m * l = 0.36 m e (L band) with an energy band gap ∆E ≈ 0.12 eV is shown. The experimental data points of Pb 1−x K x Te 0.7 Se 0.25 S 0.05 alloys lie below the theoretical curve plotted using the two valence bands' model, indicating a lower effective mass of the charge carriers in the alloys.…”

“…In addition, the thermoelectric performance in PbTe 1−x Se x ternary alloys can be increased by nanostructuring, resulting in low lattice thermal conductivity. Nanostructuring in the PbTe-PbS system can be achieved using bulk phase separation either by nucleation or spinodal decomposition depending on the relative phase fraction [19].Recent advances report that the lattice thermal conductivity in the quaternary system of (PbTe) 1−x−y (PbSe) x (PbSe) y can be reduced by point defect, which is produced by triple disorder in the rock salt structure [20][21][22]. High ZT ≈ 2.2 at 800 K was obtained in p-type (PbTe) 1−2x (PbSe) x (PbS) x quaternary alloys due to band engineering and phonon scattering from point defects [20,23,24].…”

“…Recent advances report that the lattice thermal conductivity in the quaternary system of (PbTe) 1−x−y (PbSe) x (PbSe) y can be reduced by point defect, which is produced by triple disorder in the rock salt structure [20][21][22]. High ZT ≈ 2.2 at 800 K was obtained in p-type (PbTe) 1−2x (PbSe) x (PbS) x quaternary alloys due to band engineering and phonon scattering from point defects [20,23,24]. Quaternary alloys PbTe-PbSe-PbS manifest themselves as effective n-type materials as well.…”