Research Article  Open Access
Zhenghao Hou, Dongyang Wang, Jinfeng Wang, Guangtao Wang, Zhiwei Huang, LiDong Zhao, "Contrasting Thermoelectric Transport Behaviors of pType PbS Caused by Doping Alkali Metals (Li and Na)", Research, vol. 2020, Article ID 4084532, 11 pages, 2020. https://doi.org/10.34133/2020/4084532
Contrasting Thermoelectric Transport Behaviors of pType PbS Caused by Doping Alkali Metals (Li and Na)
Abstract
PbS is a latent substitute of PbTe thermoelectric materials, which is on account of its superiority in low cost and earth abundance. Here, the thermoelectric transport properties of ptype PbS by doping alkali metals (Na and Li) are investigated and it is verified that Li is a more effective dopant than Na. By introducing Li, the electrical and thermal transport properties were optimized collectively. The electrical transport properties were boosted remarkably via adjusting carrier concentration, and the maximum power factor (PF_{max}) of ~11.5 μW/cmK^{2} and average power factor (PF_{ave}) ~9.9 μW/cmK^{2} between 423 and 730 K in Pb_{0.99}Li_{0.01}S were achieved, which are much higher than those (~9.5 and ~7.7 μW/cmK^{2}) of Pb_{0.99}Na_{0.01}S. Doping Li and Na can weaken the lattice thermal conductivity effectively. Combining the enlarged PF with suppressed total thermal conductivity, a maximum ZT ~0.5 at 730 K and a large average ZT ~0.4 at 423730 K were obtained in ptype Pb_{0.99}Li_{0.01}S, which are higher than ~0.4 and ~0.3 in ptype Pb_{0.99}Na_{0.01}S, respectively.
1. Introduction
The search for reliable and environmentally friendly new energy has attracted worldwide attention because of the shortage of fossil energy. A thermoelectric device is capable of transforming heat into electric energy immediately, which has shown great prospect in clean energy field [1–5]. The thermoelectric device efficiency is positively associated with the dimensionless figure of merit [6–9], , where represents absolute temperature, expresses the Seebeck coefficient, denotes electrical conductivity, and represents total thermal conductivity comprising electronic () and lattice () contributions [2, 10, 11].
Lead telluride (PbTe) based materials, as a kind of mediumtemperature operating materials, have attracted extensive research interests on account of outstanding thermoelectric performance [12–14]. However, considering the high costs and low earth abundance of the Te element, the thermoelectric materials with rich resources should be developed. To date, one research hotpot in this field is to find an alternative material to substitute PbTe which possesses prominent thermoelectric properties [14–16]. As a similar alternative of PbTe, PbS possesses a NaCl structure and an alike band structure. Nevertheless, the poor electrical properties and large lattice thermal conductivity historically make PbS become an inferior thermoelectric material [11]. Aimed at solving the shortcomings of PbS, the approaches including carrier concentration optimization [17], band manipulation [18], and microstructure engineering [19–22] have been proved as effective strategies to manipulate electrical properties and thermal conductivity; the achievements realized through the above strategies well elucidate the potential performance of PbS.
Usually, doping is a powerful tactic to enhance ZT. Doping is essential in adjusting carrier concentration, and it is the prerequisite to gain a high ZT as all of those thermoelectric properties are interlinked by carrier concentration. On the assumption that the scattering or band structure is not modified obviously by a dopant, the Seebeck coefficient and electrical conductivity of degenerated semiconductor with a single parabolic band can be given using Equations (1) and (2) [23, 24]. where displays the Boltzmann constant, shows the electron charge, denotes the Planck constant, expresses effective mass, is the carrier concentration, and represents the carrier mobility. Apparently, and are in an inversely proportional relationship. Therefore, adjusting carrier concentration through balancing the relationship between and is an important method to boost power factors. Doping with different elements may induce diverse impact on carrier concentration optimization and band structure manipulation. For example, ptype Nadoped PbS with CdS as second phases attains a large ZT ~1.3 at 923 K owing to extensive phonon scattering by nanophase precipitates and better electrical transport [25]; the ZT of ptype Tldoped PbTe reaches ~1.5 at 773 K due to greatly enhanced Seebeck coefficients by deformation of electronic density of states [17]. It is meaningful to speculate the impacts by doping other alkali metals on thermoelectric performance in PbS.
In this article, we focused on PbS, which contains highly earthabundant elements and owns higher melting point compared to PbTe. The thermoelectric properties in PbS doped by Li and Na were investigated systematically. The consequences reveal that the electrical and thermal properties were optimized synchronously through alkali metal doping. The electrical properties were improved through adjusting carrier concentration, and the PF_{max} of Pb_{0.99}Li_{0.01}S reached ~11.5 μW/cmK^{2}, which is far greater than ~9.5 μW/cmK^{2} in Pb_{0.99}Na_{0.01}S. Both Li and Na can bring down the because of point defects in PbS matrix. Li was more effective than Na in reducing on account of larger mass and strain field fluctuations. Integrating enhanced PF and reduced , a higher ZT value ~0.5 at 730 K and average ZT ~0.4 at 423730 K can be reached in Pb_{0.99}Li_{0.01}S, which are higher than ~0.4 and~0.3 in ptype Pb_{0.99}Na_{0.01}S, respectively, indicating that Li doping can improve thermoelectric performance of PbS more effectively than Na doping.
2. Experimental Section
2.1. Preparation Method
Highpurity chemicals of Pb particle (99.99%), S (99.99%), Na (99.99%), and Li (99.99%) were weighed and loaded into carboncoated quartz ampules under a N_{2}filled glove box. The ampules of the chemicals were evacuated under vacuum and flamesealed. The pure chemicals were gradually warmed up to 723 K in 12 h, elevated to 1423 K in 7 h before keeping stable at 1423 K for 6 h, and finally naturally cooled to indoor temperature. The prepared specimens were pulverized and filtered with 400mesh sieves for sintering through spark plasma sintering (SPS211LX) using a pressure of 50 MPa at 923 K for 10 min.
2.2. Thermoelectric Properties
The acquired cylinder bulk materials were incised for measuring relevant thermoelectric properties. The CTA system was applied to measure electrical parameters ( and ) at 300730 K under He gas, and the samples were polished in a rectangular shape of . The surfaces of measured samples were sprayed with thinlayer BN, which can inhibit volatilization and protect instrument [26]. The cylindrical disks with thickness of 1 mm and diameter of 6 mm were used to measure the thermal diffusivity (). The thermal conductivity is computed through , and the thermal diffusivity was characterized using a Netzsch LFA457 instrument with a laser flash method [27]. A thin graphite film on the surface of samples was utilized to cut down errors of emissivity for testing . The density () was obtained based on mass and volume. All the densities of samples are around 7.2 g/cm^{3}. The heat capacity () was computed using the Debye model [28].
2.3. XRay Diffraction
The phase structure was investigated using an Xray diffraction technique with D/MAX2200pc system with CuKα at (Rigaku, Japan, 40 kV, 40 mA). The scanning speed and step size of the XRD measurement are 6° min^{1} and 0.02°, respectively.
2.4. Theoretical Calculations
The density functional theory (DFT) calculations were acquired through a projectoraugmented wave (PAW) strategy [29, 30] with the Vienna Ab initio Simulation Package (VASP) [31]. The PerdewBurkeErnzerhof (PBE) exchangecorrelation functional was used to model crystal and electronic structure. The used kinetic cutoff energy of plane waves is 500 eV. A supercell (Pb_{27}S_{27}) was constructed to evaluate the defect formation energy of Li (Pb_{26}LiS_{27}) and Na (Pb_{26}NaS_{27}) doped systems. The internal coordinates of all atoms are entirely relaxed while the maximum residual ionic force is lower than 0.01 eV Å^{1}, and the total energy difference approaches 10^{6} eV.
The formation energy of the defect (, Li) in charge is calculated by [32, 33] where and refer to the total energy of defect contained and undoped PbS in supercells with the same dimension, separately. , , and are the chemical potential, average energy of element in its most stable crystal structure, and the number of the atom added to () or taken from () the host, respectively. presents the Fermi level relative to energy location of valence band maximum (), which changes between 0 and band gap in PbS. The correction term is adopted to arrange the reference potential between the defectcontaining and pure supercells with the same size [34]. All characteristic values are recombined to the 1s core level of the atom farthest from the defect [32, 35].
The formation energy depends on the chemical potential of each element, which is related to the offstoichiometric degree (Pb or Srich condition). The different offstoichiometric degrees will result in different chemical potential and formation energy. The upper and lower boundary chemical potential () is determined by the offstoichiometric degree and the stability against precipitation of elemental Pb, S, Li, and Na:
The host compounds are obtained from the sum of the chemical potentials of Pb and S: where is the formation energy of PbS in a rocksalt structure.
The second phase of Na_{2}S, Li_{2}S, and PbS_{2} should be avoided, and the corresponding formation energy should be larger than the sum of elemental chemical potential:
3. Results and Discussion
Figure 1 demonstrates the detailed information of XRD results. All specimens possess a single phase of cubic PbS. The data peak transfers to low angle range as the Li and Na content was added, which indicates that Li and Na are doped into PbS lattice.
Figure 2 depicts electrical properties in PbS with Li and Na doping. It can be clearly observed from Figures 2(a) and 2(b) that the falls off when temperature rises, except for low doping samples of Pb_{1x}Na_{x}S ( and 0.0075).
For Lidoped samples, the possesses a tendency to increase first and then decrease with the stoichiometry of Li increasing and reaches to its maximum 777 S/cm in Pb_{0.995}Li_{0.005}S, as shown in Figure 2(a). However, the Na doping presents different results. As presented in Figure 2(b), the has an increased trend with increasing of Na content, and the maximum of 1274 S/cm can be realized in Pb_{0.98}Na_{0.02}S. The is positively correlated with and from Equation (2), which are determined by the solid solubility and the different scattering mechanisms, respectively. The continued increase in of Pb_{1x}Na_{x}S is mainly due to the fact that the higher solubility of Na than Li was caused by better ion radius matching (, , ).
As displayed in Figures 2(c) and 2(d), different from the undoped PbS, the Seebeck coefficients () for all doped samples are positive, indicating that Li and Na are effective ptype dopants in PbS. For Lidoped samples, the present the trend of first decreasing and then increasing with an increasing Li content. For Nadoped samples, the trend is reversed that the increase first and then decrease with an increasing Na content. These diametrically opposite trends reflect the contrary change of carrier concentration () in those materials since the are negatively correlated with .
To evaluate the doping efficiency of Li and Na in PbS, the formation energy of potential defect was calculated and shown in Figures 3(a) and 3(b). The lower formation energy of Na_{Pb} indicates the spontaneous formation of Na_{Pb} in any conditions, which is even lower than that in V_{Pb}. However, the Li_{Pb} has higher formation energy under Pb and S rich situations. In an equilibrium theory, the defect concentration can be evaluated by the formation energy , expressed as [36]. Thus, the larger formation energy of Li leads to a lower and a larger (Figure 2(c)).
As presented in Figure 2(e), for Lidoped samples, a higher PF can be obtained in Pb_{0.99}Li_{0.01}S in a broad temperature range, and the peak value can reach 11.5 μW/cmK^{2} at 450 K. The peak PF for Pb_{0.99}Li_{0.01}S is much higher than Pb_{0.99}Na_{0.01}S which is ascribed to the lower , namely, adjusting carrier concentration to an optimized scope. Figures 3(c) and 3(d) show the carrier mobility and carrier concentration at room temperature which are calculated by the carrier effective mass of PbS () [25]. According to Rowe and Bhandari’s study [37], the decreases and the increases as the increases and the PF maximizes at a suitable for a semiconductor. Therefore, adjusting the to a reasonable range is the key factor to obtain higher PF. Compared with Pb_{0.99}Na_{0.01}S, Li doping leads to a relative lower and higher PF. Figures 2(g) and 2(h) show the maximum power factor (PF_{max}) at 300730 K and average power factor (PF_{ave}) within 423730 K of ptype PbS samples. The PF_{ave} is calculated by Equation (7) in which the and are the temperatures of hot and cold ends. The PF_{ave} represents the overall capacity and level of electrical transports over a specified wide temperature range. The PF_{max} and PF_{ave} of the Pb_{0.99}Li_{0.01}S sample are 11.5 and 9.9 μW/cmK^{2}, respectively, higher than those of Pb_{0.99}Na_{0.01}S which are 9.5 and 7.7 μW/cmK^{2}. The present results reveal that the different dopants can reach the PF_{max} under their proper , which is strictly determined by the solid solubility of dopants in PbS.
Figures 4(a) and 4(b) depict the which decreases monotonically with the increase of temperature. The of Pb_{1x}Li_{x}S is lower than that in the undoped PbS, which is different from the larger content of Pb_{1x}Na_{x}S since is higher. The of Pb_{0.99}Li_{0.01}S and Pb_{0.99}Na_{0.01}S is 0.2094 J/g·K and 0.2092 J/g·K at 730 K, respectively. The of Lidoped samples is similar to the C_{p} of Nadoped samples at the same content and temperature. The includes lattice thermal conductivity and electronic thermal conductivity () [22, 25], where the relationship between , , and Lorenz number () described in Equation (8) indicates that the is proportional to [38, 39].
The Lorenz number was obtained through calculating the Seebeck coefficient and integral chemical potentials [40]. Figures 4(c) and 4(d) show the Lorenz number in all samples as function of temperature. Higher and lead to the larger than those in undoped PbS, as revealed through Figures 4(e) and 4(f). Thus, the reduction in is primarily caused by the decrease of .
Figures 5(a) and 5(b) show that the of all doped samples is lower than that of the undoped sample. The point defect scattering presumably reduces the by Li and Na doping. Obviously, the decreases with the increasing dopant content. More importantly, Li and Na are both effective in reducing the . To understand the phonon transports in Li (Na) doped PbS, we adopted the Callaway model to evaluate point defect scattering caused by Li and Na doping [28, 41, 42].
When the temperature is higher than the Debye temperature, the point defect is an intensive scattering center to reduce the . According to the Callaway model [28, 42, 43], the ratio of the between the defectcontaining material and host material can be written as in which and represent the lattice thermal conductivities in doped and parent materials, separately. The parameter is described using in which , , , and express the Planck constant, average atom volume, average sound velocity, and Debye temperature, separately. The imperfection scaling parameter () indicates that the phonon scattering intensity by atomic scale defects contains mass fluctuation and strain field fluctuation . The phenomenological adjustable parameter () regulates the uncertainty of . The imperfection scaling parameter and the phenomenological adjustable parameter are expressed by the following equations [42]: where displays the Poisson ratio, which is calculated using the longitudinal () and transverse () acoustic velocities. The acoustic velocity of PbS was adopted in Poisson ratio and Grüneisen parameter () calculation by the following equations:
When Pb sites are replaced by Li (Na), no change happens on the position of S, , which is defined by [44, 45] where , and . where , and .
Then,
The calculated mass fluctuations and strain field fluctuations have been given by Table 1. The higher deviations in atomic radius and mass between Pb and Li lead to larger Γ_{(Pb,Li)}than , indicating more effective decreasing of by Li doping. In Figures 5(c) and 5(d), the calculated results based on the Callaway model exhibit the same trend with the experimental data. The huge deviation may result from the formation of nanostructure even though in moderate doping concentration. This phenomenon confirms that Li and Na could both play effective roles in suppressing .

The temperaturedependent ZT of PbS doped by Li and Na are presented in Figures 6(a) and 6(b). Pb_{1x}Li_{x}S samples exhibit larger ZT than Pb_{1x}Na_{x}S samples. The maximum ZT (ZT_{max}) in Pb_{0.99}Li_{0.01}S attained ~0.5 when , which is higher than that in Pb_{0.99}Na_{0.01}S. The better thermoelectric performance of Lidoped samples is mainly due to the higher PF which results from the obtained proper range and the slightly lower from a more effective point defect scattering.
The variation trends of maximum ZT (ZT_{max}) and average ZT (ZT_{ave}), calculated by Equation (16), are consistent with PF_{max} and PF_{ave}, as displayed in Figures 6(c) and 6(d). The ZT_{max} from room temperature to 730 K and ZT_{ave} within 423730 K are 0.5 and 0.4 in Pb_{0.99}Li_{0.01}S, which is much higher than Pb_{0.99}Na_{0.01}S (0.4 and 0.3). The quality factor is a parameter for estimating the optimal thermoelectric properties of a specific material according to the effective mass model, and the quality factor is obtained by Equation (16). The weighted mobility is calculated by the electrical conductivity and Seebeck coefficient according to Equation (17) [46, 47]. in which and are unit mass of free electron and the electron charge, respectively. represents the Fermi integral with and is calculated by the following equations. in which shows the scattering factor and equals 1/2 here and is the reduced chemical potential [46].
The calculated quality factors of Pb_{0.99}Li_{0.01}S and Pb_{0.99}Na_{0.01}S at 730 K are 0.4 and 0.2, respectively. The quality factor of Pb_{0.99}Li_{0.01}S is about twice higher than that of Pb_{0.99}Na_{0.01}S, so the ZT of Pb_{0.99}Li_{0.01}S is higher, which is caused by the enhanced PF by adjusting in a reasonable range. The thermoelectric conversion efficiencies are calculated by Equation (20) [28]: in which and represent the temperature in hot and cold end, respectively. The maximum calculated thermoelectric conversion efficiency based on single leg is ~4.8% in Pb_{0.99}Li_{0.01}S which is higher than Pb_{0.99}Na_{0.01}S (~3.4%) when K and K, indicating Li is a valid dopant to regulate the thermoelectric performance through tuning .
4. Conclusion
This work indicates that Li doping is more effective than Na doping in thermoelectric performance optimization in PbS. The boosted thermoelectric performance of Lidoped PbS is completed by enhancing the PF through regulating in a reasonable range. The PF_{max} and PF_{ave} between 423 and 730 K of Pb_{0.99}Li_{0.01}S reached ~11.5 and~9.9 μW/cmK^{2}, which are much better compared with ~9.5 and ~7.7 μW/cmK^{2} of Pb_{0.99}Na_{0.01}S. Pb_{1x}Li_{x}S samples possess slightly smaller than that of Pb_{1x}Na_{x}S because of larger mass and strain field fluctuations. At last, higher ZT_{max} ~0.5 at 730 K and ZT_{ave} ~0.4 at 423 K730 K can be obtained in Pb_{0.99}Li_{0.01}S. The calculated thermoelectric conversion efficiency ~4.8% is achieved in Pb_{0.99}Li_{0.01}S with K and K. In the future, the ZT for Lidoped PbS can also be raised through nanostructuring, manipulating band structures, and other approaches.
Conflicts of Interest
The authors declare no competing financial interests.
Acknowledgments
We acknowledge the support on this topic from the National Natural Science Foundation of China (51772012 and 51671015), the National Key Research and Development Program of China (2018YFA0702100 and 2018YFB0703600), Beijing Natural Science Foundation (JQ18004), and 111 Project (B17002). L.D.Z. acknowledges the support of the National Science Fund for Distinguished Young Scholars (51925101). Z.H. thanks the financial support from the Academic Excellence Foundation of BUAA for PhD Students. D.W. thanks the financial support from the National Postdoctoral Program for Innovative Talents (BX20200028) and the support from highperformance computing (HPC) resources at Beihang University. J.W. and G.W. acknowledges the support of the High Performance Computing Center of Henan Normal University. Z.H. thanks the support from China Postdoctoral Science Foundation Grant (2019M650429).
References
 L. E. Bell, “Cooling, heating, generating power, and recovering waste heat with thermoelectric systems,” Science, vol. 321, no. 5895, pp. 1457–1461, 2008. View at: Publisher Site  Google Scholar
 G. Tan, L.D. Zhao, and M. G. Kanatzidis, “Rationally designing highperformance bulk thermoelectric materials,” Chemical Reviews, vol. 116, no. 19, pp. 12123–12149, 2016. View at: Publisher Site  Google Scholar
 Z. G. Chen, X. Shi, L. D. Zhao, and J. Zou, “Highperformance SnSe thermoelectric materials: progress and future challenge,” Progress in Materials Science, vol. 97, pp. 283–346, 2018. View at: Publisher Site  Google Scholar
 Y. Xiao, C. Chang, Y. Pei et al., “Origin of low thermal conductivity in SnSe,” Physical Review B, vol. 94, no. 12, article 125203, 2016. View at: Publisher Site  Google Scholar
 G. Tang, W. Wei, J. Zhang et al., “Realizing high figure of merit in phaseseparated polycrystalline Sn_{1x}Pb_{x}Se,” Journal of the American Chemical Society, vol. 138, no. 41, pp. 13647–13654, 2016. View at: Publisher Site  Google Scholar
 Y. Liu, L.D. Zhao, Y. Zhu et al., “Synergistically optimizing electrical and thermal transport properties of BiCuSeO via a dualdoping approach,” Advanced Energy Materials, vol. 6, no. 9, article 1502423, 2016. View at: Publisher Site  Google Scholar
 L.D. Zhao, X. Zhang, H. Wu et al., “Enhanced thermoelectric properties in the counterdoped SnTe system with strained endotaxial SrTe,” Journal of the American Chemical Society, vol. 138, no. 7, pp. 2366–2373, 2016. View at: Publisher Site  Google Scholar
 Y. Xiao, H. Wu, W. Li et al., “Remarkable roles of Cu to synergistically optimize phonon and carrier transport in ntype PbTeCu_{2}Te,” Journal of the American Chemical Society, vol. 139, no. 51, pp. 18732–18738, 2017. View at: Publisher Site  Google Scholar
 B. C. Qin, Y. Xiao, Y. M. Zhou, and L. D. Zhao, “Thermoelectric transport properties of PbSnTeSe system,” Rare Metals, vol. 37, no. 4, pp. 343–350, 2018. View at: Publisher Site  Google Scholar
 C. Chang, M. Wu, D. He et al., “3D charge and 2D phonon transports leading to high outofplaneZTin ntype SnSe crystals,” Science, vol. 360, no. 6390, pp. 778–783, 2018. View at: Publisher Site  Google Scholar
 Y. L. Pei and Y. Liu, “Electrical and thermal transport properties of Pbbased chalcogenides: PbTe, PbSe, and PbS,” Journal of Alloys and Compounds, vol. 514, pp. 40–44, 2012. View at: Publisher Site  Google Scholar
 Y. Xiao, H. Wu, J. Cui et al., “Realizing high performance ntype PbTe by synergistically optimizing effective mass and carrier mobility and suppressing bipolar thermal conductivity,” Energy & Environmental Science, vol. 11, no. 9, pp. 2486–2495, 2018. View at: Publisher Site  Google Scholar
 Y. Xiao, H. Wu, D. Wang et al., “Amphoteric indium enables carrier engineering to enhance the power factor and thermoelectric performance inn‐Type AgnPb100InnTe100+2n(LIST),” Advanced Energy Materials, vol. 9, no. 17, article 1900414, 2019. View at: Publisher Site  Google Scholar
 L.D. Zhao, H. J. Wu, S. Q. Hao et al., “Allscale hierarchical thermoelectrics: MgTe in PbTe facilitates valence band convergence and suppresses bipolar thermal transport for high performance,” Energy & Environmental Science, vol. 6, no. 11, pp. 3346–3355, 2013. View at: Publisher Site  Google Scholar
 K. Hsu, S. Loo, F. Guo et al., “Cubic AgPb_{m}SbTe_{2+m}: bulk thermoelectric materials with high figure of merit,” Science, vol. 303, no. 5659, pp. 818–821, 2004. View at: Publisher Site  Google Scholar
 K. Biswas, J. He, I. D. Blum et al., “Highperformance bulk thermoelectrics with allscale hierarchical architectures,” Nature, vol. 489, no. 7416, pp. 414–418, 2012. View at: Publisher Site  Google Scholar
 J. P. Heremans, V. Jovovic, E. S. Toberer et al., “Enhancement of thermoelectric efficiency in PbTe by distortion of the electronic density of states,” Science, vol. 321, no. 5888, pp. 554–557, 2008. View at: Publisher Site  Google Scholar
 G. Tan, F. Shi, S. Hao et al., “Codoping in SnTe: enhancement of thermoelectric performance through synergy of resonance levels and band convergence,” Journal of the American Chemical Society, vol. 137, no. 15, pp. 5100–5112, 2015. View at: Publisher Site  Google Scholar
 M. Zhao, C. Chang, Y. Xiao, R. Gu, J. He, and L. D. Zhao, “Investigations on distinct thermoelectric transport behaviors of Cu in ntype PbS,” Journal of Alloys and Compounds, vol. 781, pp. 820–830, 2019. View at: Publisher Site  Google Scholar
 Y. Wang, J. Wen, Z. Fan et al., “Energyfilteringinduced high power factor in PbSnanoparticlesembedded TiS_{2},” AIP Advances, vol. 5, no. 4, article 047126, 2015. View at: Publisher Site  Google Scholar
 C. Chang, Y. Xiao, X. Zhang et al., “High performance thermoelectrics from earthabundant materials: enhanced figure of merit in PbS through nanostructuring grain size,” Journal of Alloys and Compounds, vol. 664, pp. 411–416, 2016. View at: Publisher Site  Google Scholar
 X. Qian, L. Zheng, Y. Xiao, C. Chang, and L. D. Zhao, “Enhancing thermoelectric performance of ntype PbSe via additional mesoscale phonon scattering,” Inorganic Chemistry Frontiers, vol. 4, no. 4, pp. 719–726, 2017. View at: Publisher Site  Google Scholar
 M. Cutler, J. F. Leavy, and R. L. Fitzpatrick, “Electronic transport in semimetallic cerium sulfide,” Physical Review, vol. 133, no. 4A, pp. A1143–A1152, 1964. View at: Publisher Site  Google Scholar
 B. Poudel, Q. Hao, Y. Ma et al., “Highthermoelectric performance of nanostructured bismuth antimony telluride bulk alloys,” Science, vol. 320, no. 5876, pp. 634–638, 2008. View at: Publisher Site  Google Scholar
 L.D. Zhao, J. He, S. Hao et al., “Raising the thermoelectric performance of ptype PbS with endotaxial nanostructuring and valenceband offset engineering using CdS and ZnS,” Journal of the American Chemical Society, vol. 134, no. 39, pp. 16327–16336, 2012. View at: Publisher Site  Google Scholar
 L.D. Zhao, J. He, C. I. Wu et al., “Thermoelectrics with earth abundant elements: high performance ptype PbS nanostructured with SrS and CaS,” Journal of the American Chemical Society, vol. 134, no. 18, pp. 7902–7912, 2012. View at: Publisher Site  Google Scholar
 S. Johnsen, J. He, J. Androulakis et al., “Nanostructures boost the thermoelectric performance of PbS,” Journal of the American Chemical Society, vol. 133, no. 10, pp. 3460–3470, 2011. View at: Publisher Site  Google Scholar
 B. Qin, D. Wang, W. He et al., “Realizing high thermoelectric performance in ptype SnSe through crystal structure modification,” Journal of the American Chemical Society, vol. 141, no. 2, pp. 1141–1149, 2019. View at: Publisher Site  Google Scholar
 P. E. Blöchl, “Projector augmentedwave method,” Physical Review B, vol. 50, no. 24, pp. 17953–17979, 1994. View at: Publisher Site  Google Scholar
 G. Kresse and D. Joubert, “From ultrasoft pseudopotentials to the projector augmentedwave method,” Physical Review B, vol. 59, no. 3, pp. 1758–1775, 1999. View at: Publisher Site  Google Scholar
 G. Kresse and J. Furthmüller, “Efficient iterative schemes for ab initio totalenergy calculations using a planewave basis set,” Physical Review B, vol. 54, no. 16, pp. 11169–11186, 1996. View at: Publisher Site  Google Scholar
 Y. Zhou, W. Li, M. Wu et al., “Influence of defects on the thermoelectricity in SnSe: a comprehensive theoretical study,” Physical Review B, vol. 97, no. 24, article 245202, 2018. View at: Publisher Site  Google Scholar
 S. H. Wei, “Overcoming the doping bottleneck in semiconductors,” Computational Materials Science, vol. 30, no. 34, pp. 337–348, 2004. View at: Publisher Site  Google Scholar
 Z.K. Yuan, S. Chen, Y. Xie et al., “Nadiffusion enhanced ptype conductivity in Cu(In, Ga) Se_{2}: a new mechanism for efficient doping in semiconductors,” Advanced Energy Materials, vol. 6, no. 24, article 1601191, 2016. View at: Publisher Site  Google Scholar
 C. Xia, Y. Jia, and Q. Zhang, “Firstprinciples electronic structure and formation energies of group V and VII impurities in the αFe_{2}O_{3} alloys,” Journal of Applied Physics, vol. 116, no. 11, article 113706, 2014. View at: Publisher Site  Google Scholar
 S. B. Zhang, S.H. Wei, and A. Zunger, “Overcoming doping bottlenecks in semiconductors and widegap materials,” Physica BCondensed Matter, vol. 273274, pp. 976–980, 1999. View at: Publisher Site  Google Scholar
 G. A. Moore, “Modern thermoelectrics,” Electronics and Power, vol. 30, no. 9, p. 733, 1984. View at: Publisher Site  Google Scholar
 H. Mori, H. Usui, M. Ochi, and K. Kuroki, “Temperature and dopingdependent roles of valleys in the thermoelectric performance of SnSe: a firstprinciples study,” Physical Review B, vol. 96, no. 8, p. 10, 2017. View at: Publisher Site  Google Scholar
 Y. Pei, A. D. LaLonde, N. A. Heinz et al., “Stabilizing the optimal carrier concentration for high thermoelectric efficiency,” Advanced Materials, vol. 23, no. 47, pp. 5674–5678, 2011. View at: Publisher Site  Google Scholar
 L.D. Zhao, V. P. Dravid, and M. G. Kanatzidis, “The panoscopic approach to high performance thermoelectrics,” Energy & Environmental Science, vol. 7, no. 1, pp. 251–268, 2014. View at: Publisher Site  Google Scholar
 K. Ahn, K. Biswas, J. He, I. Chung, V. Dravid, and M. G. Kanatzidis, “Enhanced thermoelectric properties of ptype nanostructured PbTeMTe (M = Cd, Hg) materials,” Energy & Environmental Science, vol. 6, no. 5, pp. 1529–1537, 2013. View at: Publisher Site  Google Scholar
 M. Zhao, C. Chang, Y. Xiao, and L. D. Zhao, “High performance of ntype (PbS)_{1xy}(PbSe)_{x}(PbTe)_{y} thermoelectric materials,” Journal of Alloys and Compounds, vol. 744, pp. 769–777, 2018. View at: Publisher Site  Google Scholar
 C. L. Wan, W. Pan, Q. Xu et al., “Effect of point defects on the thermal transport properties of(La_{x}Gd_{1−x})_{2}Zr_{2}O_{7}: experiment and theoretical model,” Physical Review B, vol. 74, no. 14, article 144109, 2006. View at: Publisher Site  Google Scholar
 Y.L. Pei, J. He, J. F. Li et al., “High thermoelectric performance of oxyselenides: intrinsically low thermal conductivity of Cadoped BiCuSeO,” NPG Asia Materials, vol. 5, no. 5, article e47, 2013. View at: Publisher Site  Google Scholar
 G. Tan, F. Shi, H. Sun et al., “SnTe–AgBiTe_{2} as an efficient thermoelectric material with low thermal conductivity,” Journal of Materials Chemistry A, vol. 2, no. 48, pp. 20849–20854, 2014. View at: Publisher Site  Google Scholar
 Y. Xiao, D. Wang, Y. Zhang et al., “Band sharpening and band alignment enable high quality factor to enhance thermoelectric performance in ntype PbS,” Journal of the American Chemical Society, vol. 142, no. 8, pp. 4051–4060, 2020. View at: Publisher Site  Google Scholar
 B. Qin, W. He, and L.D. Zhao, “Estimation of the potential performance in ptype SnSe crystals through evaluating weighted mobility and effective mass,” Journal of Materiomics, vol. 6, no. 4, pp. 671–676, 2020. View at: Publisher Site  Google Scholar
Copyright
Copyright © 2020 Zhenghao Hou et al. Exclusive Licensee Science and Technology Review Publishing House. Distributed under a Creative Commons Attribution License (CC BY 4.0).