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Synergistic Enhancement of Thermoelectric Performances by Cl-Doping and Pb-Excess in (Pb,Sn)Se Topological Crystal Insulator

We investigated the thermoelectric properties of the Pb0.75Sn0.25Se and Pb0.79Sn0.25Se1−xClx (x = 0.0, 0.2, 0.3, 0.5, 1.0, 2.0 mol.%) compounds, synthesized by hot-press sintering. The electrical transport properties showed that low concentration doping of Cl (below 0.3 mol.%) in the Pb-excess (Pb,Sn)Se samples increased the carrier concentration and the Hall mobility by the increase of carriers’ mean free path. The effective mass of the carrier was also enhanced from the measurements of the Seebeck coefficient. The enhanced effective masses of the carrier by the Cl-doping can be understood by the enhanced electron-phonon interaction, caused by the crystalline mirror symmetry breaking. The significantly decreased lattice thermal conductivities showed that the crystalline mirror symmetry breaking decreased the lattice thermal conductivity of the Pb-excess (Pb,Sn)Se. By the Cl-doping and the Pb-excess’s synergistic effect, which can suppress the bipolar effect, the zT values of x = 0.2 and 0.3 mol.% reached 0.8 at 773 K. Therefore, we suggest that Pb-excess and the crystalline mirror symmetry breaking by Cl-doping are effective for high thermoelectric performance in the (Pb,Sn)Se.


Introduction
Thermoelectric devices based on the Seebeck, Peltier, and Thomson effects can be used for thermoelectric power generation or solid-state cooling, including flexible or wearable thermoelectric devices [1,2]. The thermoelectric performance of the device is mainly determined by the dimensionless thermoelectric figure of merit (zT), which is defined by zT = S 2 σT/κ, where S, σ, T, and κ are the Seebeck coefficient, electrical conductivity, absolute temperature, and thermal conductivity, respectively. The high-performance thermoelectric materials (Bi 2 Te 3 , Bi 2 Se 3 , Sb 2 Te 3 , SnTe, etc.) have been revealed to have topologically protected states such as the topological insulator (TI) or the topological crystalline insulator (TCI) states, etc. [3].
The PbTe is the thermoelectric material with high zT values in both the n-type (1.8 at 773 K [4]) and p-type (2.5 at 923 K [5]). Even though the PbTe has good thermoelectric properties, the low abundance of tellurium in the earth's crust is one of the disadvantages of practical thermoelectric applications [6]. Because of the abundance of Se compared with the Te and the similar crystal structure of PbSe compared with PbTe, the PbSe is a promising candidate to replace the PbTe. Furthermore, recent investigations show that the thermoelectric performance of the n-type PbSe are comparable with those of the PbTe [6].
The PbSe shows a topological phase transition from a trivial insulator to a TCI by Sn substitution at low temperature [7]. The TCI is one of the topological states caused by crystalline mirror symmetry and the mirror Chern number. The theoretical calculation density. The Hall carrier density nH was obtained from the Hall resistivity measurement from the relation of nH = −1/(eRH), RH = ρxy/H, where RH is the Hall coefficient and H is the applied magnetic fields ranging from −5 to 5 T. The Hall resistivity was measured by the four-probe contact method using a physical property measurement system (PPMS Dynacool 14T, Quantum Design, San Diego, CA, USA). The thermal conductivity κ was calculated from the relation of κ = λρsCp, where λ is the thermal diffusivity measured by a laser flash method (LFA-456, NETZSCH, Selb, Germany), ρs is the sample density, and the Cp is the specific heat, which is estimated by the high-temperature extrapolation, measured by the PPMS Dynacool 14T.

Results
The structural characterization of the Pb0.79Sn0.25Se1−xClx (x = 0.0, 0.2, 0.3, 0.5, 1.0, 2.0 mol.%) and Pb0.75Sn0.25Se compounds was performed by the powder XRD, as shown in Figure 1. The XRD peaks of all the samples were indexed by the rock salt-type cubic structure (Fm-3m, space group No. 225) without any impurity peaks. The XRD peaks of the Pbexcess and Cl-doped samples were not shifted significantly comparing with the Pb0.75Sn0.25Se sample. The lattice parameter (a = 6.095 Å) of the samples was comparable with the values (a = 6.085 Å [16], 6.093 Å [17], 6.098 Å [7]) of the Pb1−xSnxSe compounds.  The temperature-dependent electrical conductivities of the Pb0.79Sn0.25Se1−xClx (x = 0.0, 0.2, 0.3, 0.5, 1.0, 2.0 mol.%) and Pb0.75Sn0.25Se compounds are shown in Figure 3a. The electrical conductivity of all sintered samples showed metallic or highly degenerated semiconductor behavior. The Pb-excess sample's electrical conductivities (Pb0.79Sn0.25Se) were decreased compared with the non-Pb-excess sample (Pb0.75Sn0.25Se). The reduced electrical conductivities by the Pb-excess sample were mainly affected by the decreased Hall carrier concentration, as shown in Figure 3b. Since the PbSe has intrinsic vacancy defects [15], the Pb-addition decreases the Hall carrier concentration by the reduction of acceptors and changes the Hall coefficients from positive to negative values, similar to the Pb-addition on PbSe [14]. The electrical conductivities of the Pb-excess and Cl-doped samples (x = 0.0, 0.2, 0.3, 0.5, 1.0, 2.0 mol.%) were increased with the increasing Cl-doping concentration by the enhanced Hall carrier concentration. The Hall carrier concentration and Hall mobility are affected by the Cl-doping on the Pb 0.79 Sn 0.25 Se as the following relation σ = neµ [18]. The theoretical Hall carrier concentration (n H = n/r H ) and Hall mobility (µ H = µ/r H ) are calculated using the following equations: where m * , r H , η, and F n (η) are the effective mass of the carrier, the Hall factor, the reduced Fermi energy (η = E F /k B T), and the n-th order Fermi integral given by F n (η) = ∞ 0 x n 1+e x−η dx, respectively [18].
The carrier's effective masses are calculated using the measured Hall carrier concentration and the calculated reduced Fermi energy from the experimentally measured Seebeck coefficient with the following equation: where r is the scattering factor. The main scattering mechanism of the carriers can be estimated roughly from the σ(T) with the relation of the σ ∝ T n [19,20]. Because the n values of the Pb 0.79 Sn 0.25 Se 1−x Cl x (x = 0.0, 0.2, 0.3, 0.5, 1.0, 2.0 mol.%) and Pb 0.75 Sn 0.25 Se compounds were close to -1.5 near room temperature, as shown in the inset of Figure 3c, the main scattering mechanism of the samples could be regarded as the acoustic phonon scattering. For acoustic phonon scattering, r is −1/2 [18]. The Hall carrier concentration and Hall mobility are affected by the Cl-doping on the Pb0.79Sn0.25Se as the following relation σ = neμ [18]. The theoretical Hall carrier concentration ( = / ) and Hall mobility ( = / ) are calculated using the following equations: where m*, rH, η, and Fn(η) are the effective mass of the carrier, the Hall factor, the reduced Fermi energy (η = EF/kBT), and the n-th order Fermi integral given by ( ) = ∞ , respectively [18]. The carrier's effective masses are calculated using the measured Hall carrier concentration and the calculated reduced Fermi energy from the experimentally measured Seebeck coefficient with the following equation: The Hall mobility can be affected by the mean free path Λ of the carrier, which is calculated by the following equation [21,22]: The density-functional theory shows that the Pb-vacancy of PbSe can act as an acceptor, while the Se-vacancy is a donor [15]. The experimental result is consistent with the theoretical calculation, in that the p-type PbSe was changed to the n-type by the Pb-addition [14].  Using Equations (2) and (4), the effective masses of the carrier were obtained and are presented in Figure 4b,c. The decreased effective mass of the carrier of the Pb-excess sample was attributed to the reduced Pb-vacancy defects as compared with the non-Pb-excess sample. The increased effective masses of the carrier by the Cl-doping can be understood by the crystalline mirror symmetry breaking in the Cl-doped Pb0.7Sn0.3Se [13]. The enhanced carrier scattering by Cl-doping can increase the effective mass of the carrier. As a result, the power factor is significantly enhanced at low Cl-doping concentrations, as shown in Figure 4d. The Pb-excess samples can increase the power factor by the enhanced Seebeck coefficient associated with the reduced Pb-vacancy. However, since the electrical Using Equations (2) and (4), the effective masses of the carrier were obtained and are presented in Figure 4b,c. The decreased effective mass of the carrier of the Pb-excess sample was attributed to the reduced Pb-vacancy defects as compared with the non-Pbexcess sample. The increased effective masses of the carrier by the Cl-doping can be understood by the crystalline mirror symmetry breaking in the Cl-doped Pb 0.7 Sn 0.3 Se [13]. The enhanced carrier scattering by Cl-doping can increase the effective mass of the carrier. As a result, the power factor is significantly enhanced at low Cl-doping concentrations, as shown in Figure 4d. The Pb-excess samples can increase the power factor by the enhanced Seebeck coefficient associated with the reduced Pb-vacancy. However, since the electrical conductivity was also decreased by the reduced carrier concentration, the Pb-excess was not found to be efficient to increase the power factor. Instead, the Cl-doping in the Pb-excess samples (Pb 0.79 Sn 0.25 Se) effectively increased the carrier concentration and increased the effective mass of the carrier by the crystalline mirror symmetry breaking.
The To obtain the lattice thermal conductivity, we calculated the Lorenz numbers of the Pb0.79Sn0.25Se1−xClx (x = 0.0, 0.2, 0.3, 0.5, 1.0, 2.0 mol.%) and Pb0.75Sn0.25Se compounds by using Equation (4) and the following equation [23]: The temperature-dependent Lorenz numbers L(T) of the Pb0.79Sn0.25Se1−xClx (x = 0.0, 0.2, 0.3, 0.5, 1.0, 2.0 mol.%) and Pb0.75Sn0.25Se compounds are shown in Figure 5b. The electrical contribution in the total thermal conductivity was obtained by the Wiedemann-Franz law (κel = L0σT), where κel, L0, σ, and T are the electrical thermal conductivity, Lorenz number, electrical conductivity, and absolute temperature, respectively [23]. Figure 5c presents the thermal conductivities of the lattice and bipolar contribution To obtain the lattice thermal conductivity, we calculated the Lorenz numbers of the Pb 0.79 Sn 0.25 Se 1−x Cl x (x = 0.0, 0.2, 0.3, 0.5, 1.0, 2.0 mol.%) and Pb 0.75 Sn 0.25 Se compounds by using Equation (4) and the following equation [23]: The temperature-dependent Lorenz numbers L(T) of the Pb 0.79 Sn 0.25 Se 1−x Cl x (x = 0.0, 0.2, 0.3, 0.5, 1.0, 2.0 mol.%) and Pb 0.75 Sn 0.25 Se compounds are shown in Figure 5b. The electrical contribution in the total thermal conductivity was obtained by the Wiedemann-Franz law (κ el = L 0 σT), where κ el , L 0 , σ, and T are the electrical thermal conductivity, Lorenz number, electrical conductivity, and absolute temperature, respectively [23]. Figure 5c presents the thermal conductivities of the lattice and bipolar contribution (κ lattice + bipolar ), which were obtained by subtracting the electrical thermal conductivity from the total thermal conductivity. The lattice and bipolar thermal conductivities κ lattice + bipolar of the Pb 0.75 Sn 0.25 Se slightly decreased with the increasing temperature near room temperature, and then increased by the bipolar effect at high temperature, similar to the bulk PbSe [14]. The lattice and bipolar thermal conductivities κ lattice + κ bipolar of the Pb 0.79 Sn 0.25 Se 1−x Cl x (x = 0.0, 0.2, 0.3, 0.5, 1.0, 2.0 mol.%) also showed the conventional κ 1/T behavior below 525 K and the bipolar effect at high temperature (T ≥ 550 K). The Umklapp processes of acoustic phonon mainly cause the 1/T behavior of the thermal conductivity at high temperature [24]. The bipolar effect is associated with the small bandgap of the PbSe [14]. A previous study showed that the Cl-doping suppresses the bipolar effect in Pb 0.7 Sn 0.3 Se 1−x Cl x because of the bandgap [13]. On the other hand, the bipolar effect was not suppressed by the Cl-doping in this result. This indicates that the bipolar effect depends on the Pb-excess rather than the Cl-doping. It suggests that the bipolar effect of the Pb 0.79 Sn 0.25 Se 1−x Cl x (x = 0.0, 0.2, 0.3, 0.5, 1.0, 2.0 mol.%) and Pb 0.75 Sn 0.25 Se compounds are related with the minority carrier excitation, rather than the bandgap energy.
As compared with the non-Pb-excess sample (Pb 0.75 Sn 0.25 Se), the κ lattice + κ bipolar of the Pb-excess sample (Pb 0.79 Sn 0.25 Se) were enhanced, and the κ lattice + κ bipolar of the Cl-doped Pb-excess samples decreased with the increasing Cl-doping concentration, as shown in Figure 5d. In contrast, the Pb-excess increased the κ lattice + κ bipolar by the Pb-vacancy defect reduction, and the κ lattice + κ bipolar of the Cl-doped samples significantly decreased by the crystalline mirror symmetry breaking. Figure 6a shows As compared with the non-Pb-excess sample (Pb0.75Sn0.25Se), the κlattice + κbipolar of the Pbexcess sample (Pb0.79Sn0.25Se) were enhanced, and the κlattice + κbipolar of the Cl-doped Pb-excess samples decreased with the increasing Cl-doping concentration, as shown in Figure  5d. In contrast, the Pb-excess increased the κlattice + κbipolar by the Pb-vacancy defect reduction, and the κlattice + κbipolar of the Cl-doped samples significantly decreased by the crystalline mirror symmetry breaking. Figure 6a shows

Conclusions
In summary, the thermoelectric properties of the sintered bulk samples of the Pb0.79Sn0.25Se1−xClx (x = 0.0, 0.2, 0.3, 0.5, 1.0, 2.0 mol.%) and Pb0.75Sn0.25Se compounds were investigated. The electrical resistivity and the Hall carrier concentration results clearly show that the Cl-doping in the Pb-excess (Pb,Sn)Se samples can increase the carrier concentration. Additionally, the relatively high Hall mobility is possible by the carrier's en-

Conclusions
In summary, the thermoelectric properties of the sintered bulk samples of the Pb 0.79 Sn 0.25 Se 1−x Cl x (x = 0.0, 0.2, 0.3, 0.5, 1.0, 2.0 mol.%) and Pb 0.75 Sn 0.25 Se compounds were investigated. The electrical resistivity and the Hall carrier concentration results clearly show that the Cl-doping in the Pb-excess (Pb,Sn)Se samples can increase the carrier concentration. Additionally, the relatively high Hall mobility is possible by the carrier's enhanced mean free path at low Cl-doping concentrations (below 0.3 mol.%). The Seebeck coefficients decreased with the increasing Cl-doping concentration and carrier concentration. On the other hand, the carrier's enhanced effective masses can be understood by the crystalline mirror symmetry breaking from Cl-doping. From the thermal conductivity measurements, the crystalline mirror symmetry breaking by the Cl-doping can significantly decrease the lattice thermal conductivity of the Pb-excess (Pb,Sn)Se. Furthermore, the bipolar effect was suppressed in the Pb-excess samples. As a result, the zT values of x = 0.2 and 0.3 mol.% increased up to 0.8 at 773 K. Therefore, we suggest that Pb-excess and crystal mirror symmetry breaking by Cl-doping effectively increases the thermoelectric performance in the (Pb,Sn)Se system.