Thermoelectric Property Investigation of the PbTe Binary System with Doping

Introduction

Thermoelectric (TE) materials are deeply rooted in the principles of condensed matter physics, where the behavior and interactions of electrons and phonons within solid-state systems critically determine their functional characteristics [1]–[10]. The ability to precisely control these interactions at the atomic level is vital for optimizing both thermal and electrical transport properties, positioning thermoelectric materials as key components in the advancement of modern electronic devices [11]–[23].

Thermoelectric materials are highly intriguing because of their capacity to transform thermal energy into electrical energy directly and the reverse process too. The effectiveness of these materials is measured by the dimensionless figure of merit, zT, which has spurred advancements in various applications, including power generation and waste heat recovery [24]–[29]. PbTe is acknowledged as a highly promising thermoelectric material, particularly within the mid-temperature range of 500 K–900 K, which positions it well for applications in deep space exploration and industrial heat recovery [30]–[34]. Though traditional thermoelectric materials, including Bi₂Te₃, are highly effective at near-room temperatures [35]–[37], PbTe operates efficiently in the mid-temperature range [38].

Notwithstanding the beneficial characteristics of a small bandgap, reduced lattice thermal conductivity, and an elevated melting point, the thermoelectric performance of n-type PbTe is inferior to that of its p-type equivalent [39]–[42]. This disparity stems from its more intricate band structure and diminished carrier transport efficiency. To tackle these issues, diverse tactics, including doping and nanostructuring, have been utilized to augment the figure of merit (zT) of PbTe, specifically by enhancing its electrical and thermal characteristics [43], [44].

Doping has emerged as a particularly effective approach to modify the electronic properties of PbTe. Prior research has demonstrated significant improvements in zT through the introduction of dopants such as indium (In), antimony (Sb), and iodine (I) [45]–[48]. Recently, the approach of co-doping, which entails the simultaneous introduction of multiple dopants, has been investigated as a strategy to synergistically enhance both electrical conductivity and thermal resistivity [49], [50]. The combination of bismuth (Bi) and iodine (I) yields noteworthy outcomes, as Bi improves carrier concentration while I decreases lattice thermal conductivity through enhanced phonon scattering.

This study investigates the effects of trace Bi and I co-doping on the thermoelectric properties of PbTe alloys. The objective is to clarify the mechanisms through which varying dopant concentrations enhance thermoelectric performance, especially in n-type PbTe.

Methodological Approaches

Fabrication of PbTe Alloys

Alloys of Pb_1−xBi_xTe_1−xI_x (where x = 0.00%, 0.05%, 0.10%, 0.20%, and 0.50%) were synthesized through a stepwise synthesis method. The elemental precursors, comprising high-purity Pb (99.999%), Te (99.9999%), Bi (99.99%), and PbI₂ (99.9%), were meticulously weighed in stoichiometric ratios and subsequently sealed within vacuum-sealed quartz ampoules. The ampoules underwent an initial heating at 1073 K for a duration of two hours, followed by a melting process at 1273 K for 6 hours. The materials produced were subjected to quenching in cold water, followed by annealing at 973 K for a duration of 48 hours. This was then followed by hot pressing at 823 K under a pressure of 44 MPa, resulting in the formation of dense pellets measuring 12.7 mm in diameter and 2 mm in thickness.

Characterization

The synthesized alloys were subjected to analysis of their structural properties through X-ray diffraction (XRD) to verify phase purity and crystallographic structure. The microstructure underwent examination via scanning electron microscopy (SEM), while elemental distribution was assessed through energy-dispersive X-ray spectroscopy (EDS). The Hall effect measurements were utilized to assess the electrical properties, specifically focusing on carrier concentration and mobility. The Seebeck coefficient and electrical resistivity were measured concurrently across the temperature range of 323 K–773 K utilizing a Linseis LSR-3 instrument. The determination of thermal diffusivity was achieved through the laser flash method, while the total thermal conductivity was computed using the equation:

where C_p represents heat capacity, λ denotes thermal diffusivity, and ρ indicates density [51]. Additionally, electronic thermal conductivity (κ_e) was obtained via the Wiedemann-Franz law [51]:

Results and Discussion

Structural Analysis

XRD patterns confirm that the PbTe alloys maintain a cubic phase structure across all dopant concentrations. The lattice parameters show negligible changes despite the incorporation of Bi and I. It happens due to their similar ionic radii to Pb and Te. The SEM images reveal that trace Bi and I co-doping reduces grain size and promotes the formation of nanoscale precipitates, which contribute to enhanced phonon scattering.

Electrical Resistivity

Fig. 1 illustrates that the electrical resistivity of the Pb_1−xBi_xTe_1−xI_x samples (x = 0.00%, 0.05%, 0.10%, 0.20%, and 0.50%) exhibits metallic behavior in the doped samples. This figure demonstrates the shift of an undoped sample from a metallic state to a semiconductor state as the temperature increases. The transition takes place at approximately 550 K. The co-doping of Bi and I leads to a significant reduction in resistivity through increased carrier concentration. This behavior demonstrates that the doping elements of Bi and I significantly enhance the carrier concentration while simultaneously minimizing the scattering of charge carriers. The sample with 0.05% co-doping demonstrates the lowest resistivity throughout the temperature spectrum. The decrease in resistivity, especially at elevated temperatures, boosts electrical conductivity while ensuring a balance with phonon scattering, resulting in enhanced thermoelectric performance.

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Fig. 1. Electrical resistivity of Pb_1−xBi_xTe_1−xI_x, with X = 0%~0.5%, as a function of temperature.

Seebeck Coefficient

The Seebeck coefficient, indicating the voltage produced per unit temperature difference across a material, exhibits a steady rise with temperature in all doped samples, as illustrated in Fig. 2. Instances of co-doped semiconductors demonstrate characteristics that are characteristic of degenerative semiconductors. The sample featuring a co-doped composition of 0.05% exhibits the highest Seebeck coefficient among the alloys, reaching a peak value of 244 μV/K at a temperature of 730 K. This illustrates that the carrier concentration has been refined, marked by an appropriate balance between the carrier density and the energy filtering resulting from phonon scattering induced by nanoparticles. This leads to a rise in the generation of thermoelectric voltage.

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Fig. 2. Seebeck coefficient of Pb_1−xBi_xTe_1−xI_x, with X = 0%~0.5%, as a function of temperature.

Power Factor

The power factor, directly related to the product of electrical conductivity and the square of the Seebeck coefficient, serves as a crucial parameter for thermoelectric efficiency. Fig. 3 illustrates that the peak power factor of around 25 μWK⁻²cm⁻¹ is recorded at 329 K for the 0.05% co-doped sample. As the dopant concentration rises at room temperature, there is a decline in the power factor; however, notable enhancements are observed at higher temperatures, especially in the mid-temperature range. The observed enhancement in performance at elevated temperatures highlights the synergistic impact of co-doping in refining both electrical and thermal transport characteristics.

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Fig. 3. Power factor of Pb_1−xBi_xTe_1−xI_x, with X = 0%~0.5%, as a function of temperature.

Lattice and Total Thermal Conductivity

The incorporation of Bi and I significantly diminishes the lattice thermal conductivity, mainly due to improved phonon scattering processes occurring at grain boundaries and nanoparticle locations. Fig. 4a illustrates that the lattice thermal conductivity attains its minimum value of 0.64 W/mK for the 0.50% co-doped sample at 674 K. This represents a 26% decrease compared to the undoped PbTe. The observed reduction can be linked to the heightened phonon scattering caused by the nanoscale precipitates and the reduction in grain size noted in the SEM analysis. The total thermal conductivity illustrated in Fig. 4b exhibits a comparable trend across all co-doped samples. The values observed are lower compared to the pristine PbTe. The 0.05% co-doped sample shows a total thermal conductivity of 1.21 W/mK at 732 K, achieving a reduction of about 14% in comparison to undoped PbTe.

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Fig. 4. Lattice thermal conductivity of Pb_1−xBi_xTe_1−xI_x, with X = 0%~0.5%, as a function of temperature (a), total thermal conductivity of Pb_1−xBi_xTe_1−xI_x, with X = 0%~0.5%, as a function of temperature (b).

Figure of Merit (zT)

The thermoelectric performance of Pb_1−xBi_xTe_1−xI_x alloys is represented by the figure of merit (zT). The zT notably improves across all doped compositions, as illustrated in Fig. 5a. A peak zT of 0.9 is recorded at 725 K for the 0.20% Bi and I co-doped sample, attributed to the synergistic effects of an elevated power factor and diminished lattice thermal conductivity. This indicates that co-doping with Bi and I optimally enhances the material’s thermoelectric characteristics at high temperatures.

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Fig. 5. Temperature dependence of (a) figure of merit and (b) average ZT values for Pb_1−xBi_xTe_1−xI_x (X = 0%~0.5%).

The average figure of merit (zT_avg) across the 323–723 K range is maximized at 0.7 for the 0.05% co-doped sample, as illustrated in Fig. 5b. This composition demonstrates optimal equilibrium among electrical resistivity, Seebeck coefficient, and thermal conductivity, rendering it especially effective for mid-range temperature applications. The enhancements in zT and zT_avg highlight the efficacy of trace co-doping as a feasible approach for improving the thermoelectric performance of n-type PbTe alloys.

Conclusion

This study shows that trace co-doping with bismuth (Bi) and iodine (I) significantly improves the thermoelectric performance of n-type PbTe alloys. The co-doped samples demonstrate notable enhancements in electrical conductivity, Seebeck coefficient, and power factor while concurrently decreasing lattice and total thermal conductivity. The 0.20% Bi and I co-doped sample attains a peak zT of 0.9 at 725 K, indicating the viability of these materials for mid-temperature thermoelectric applications. Furthermore, the 0.05% co-doped sample demonstrates the greatest average zT (~0.7) across an extensive temperature range, indicating that little co-doping can substantially enhance thermoelectric efficiency.

These findings create opportunities for the advancement of more efficient thermoelectric materials, especially for energy conversion technologies within the mid-temperature spectrum. Future research may investigate the optimization of doping concentrations and the possibility of integrating Bismuth and Iodine with additional dopants to enhance the electrical and thermal characteristics of PbTe.