Enhancement of Thermoelectric Performance for n-Type PbS through

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Enhancement of Thermoelectric Performance for n-type PbS through Synergy of Gap State and Fermi Level Pinning Zhong-Zhen Luo, Shiqiang Hao, Songting Cai, Trevor P. Bailey, Gangjian Tan, Yubo Luo, Ioannis Spanopoulos, Ctirad Uher, Christopher Wolverton, Vinayak P. Dravid, Qingyu Yan, and Mercouri G. Kanatzidis J. Am. Chem. Soc., Just Accepted Manuscript • Publication Date (Web): 27 Mar 2019 Downloaded from http://pubs.acs.org on March 27, 2019

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Journal of the American Chemical Society

Enhancement of Thermoelectric Performance for n-type PbS through Synergy of Gap State and Fermi Level Pinning Zhong-Zhen Luo,1,2 Shiqiang Hao,3 Songting Cai,2,3 Trevor P. Bailey,4 Gangjian Tan,5 Yubo Luo,1,2 Ioannis Spanopoulos,2 Ctirad Uher,4 Chris Wolverton,3 Vinayak P. Dravid,3 Qingyu Yan,1,* Mercouri G. Kanatzidis2,* 1School

of Materials Science and Engineering, Nanyang Technological University, 50 Nanyang Avenue 639798, Singapore 2Department

of Chemistry, Northwestern University, Evanston, Illinois 60208, United States

3Department

of Materials Science and Engineering, Northwestern University, Evanston, Illinois 60208, United States 4Department

of Physics, University of Michigan, Ann Arbor, Michigan 48109, United States 5State Key Laboratory of Advanced Technology for Materials Synthesis and Processing, Wuhan University of Technology, Wuhan, 430070, China *Corresponding Author: [email protected]; [email protected]

ABSTRACT We report that Ga-doped and Ga-In co-doped n-type PbS samples show excellent thermoelectric performance in the intermediate temperature range. First-principles electronic structure calculations reveal that Ga doping can cause Fermi level pinning in PbS by introducing a gap state between the conduction and valence bands. Furthermore, Ga-In co-doping introduces an extra conduction band. These added electronic features lead to high electron mobilities up to µH ~630 cm2V−1s−1 for n of 1.67 × 1019 cm−3 and significantly enhanced Seebeck coefficients in PbS. Consequently, we obtained a maximum power factor of ~32 Wcm−1K−2 at 300 K for Pb0.9875Ga0.0125S, which is the highest reported for PbS-based systems giving a room-temperature figure of merit, ZT of ~0.35 and ~0.82 at 923 K. For the co-doped Pb0.9865Ga0.0125In0.001S the maximum ZT rises to ~1.0 at 923 K and achieves a record-high average ZT (ZTavg) of ~0.74 in the temperature range of 400 K to 923 K. Keywords: thermoelectric, n-type PbS, Ga doping, Ga-In co-doping, Fermi level pinning

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INTRODUCTION Thermoelectrics are solid state materials offer direct conversion between thermal and electrical energy in the presence of a temperature gradient they feature no moving parts nor hazardous emissions, and show great potential in waste heat recovery. The efficiency of a thermoelectric material is evaluated by the dimensionless figure of merit, ZT = S2σT/κtot, where S is the Seebeck coefficient, σ is the electrical conductivity, T is the absolute temperature, and κtot is the total thermal conductivity (including respective electronic and lattice components, κele and κlat).1-11 The quantity S2σ defines the power factor (PF), a key quantity that determines the performance of thermoelectric materials. High ZT can be achieved through increasing the PF or decreasing the κtot or both. However, because the S, σ, and κele are interrelated and cannot easily be independently optimized, they present a bottleneck toward boosting thermoelectric performance. Furthermore, the efficiency of a thermoelectric device (η) depends not on ZT maximum at a given temperature but on the average ZT (ZTavg) value over a wide temperature range as η = [(TH − TC)/TH] [(1 + ZTavg)1/2 − 1]/[(1 + ZTavg)1/2 + TC/TH], where TH and TC are the hot side and cold side temperature, respectively. Thus, for practical device applications, the ZTavg is the critical quantity that must be maximized over the entire operation temperature range, rather than ZTmax. The cubic rock-salt-structured lead chalcogenides are very promising thermoelectric materials at intermediate temperatures (< 900K ) because of their unique electronic structure and intrinsically low thermal conductivity.12-15 In this context, PbTe and PbSe are the most extensively studied.16-31 However, with concerns regarding the high price and potential scarcity of tellurium and even selenium, it is essential to develop thermoelectric materials based on lower cost and more abundant elements.32-33 PbS, an analogue of PbTe and PbSe, is very attractive for large scale implementations due the lower cost, the greater abundance of sulfur and excellent chemical stability.34-36 PbS has the lowest vapor pressure and the highest melting temperature of 1,391 K among lead chalcogenides (PbTe, 1,197 K and PbSe, 1,351 K),37 which may enable higher operation temperatures. Recently, there have been several significant developments in 2


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PbS-based thermoelectric materials, such as p-type Pb0.975Na0.025S-3%SrS (ZT ~1.2 at 923 K),34 Pb0.975Na0.025S-3%CdS (ZT ~1.3 at 923 K),36 Pb0.985Ag0.015S (ZT ~0.6 at 850 K)38 and n-type PbS-1%Sb2S3-1%PbCl2 (ZT ~1.1 at 923 K),39 PbS1−xClx (ZT ~0.7 at 850 K).40 In these studies, the high ZTmax value is obtained only at a high temperature, but the more important ZTavg values are only modest. In lead chalcogenides the n-type materials are more difficult to improve in terms of the power factor than the p-type counterparts because they only have a single conduction band (CB) as opposed to two valence bands (VB) for the p-type counterparts.41 When only a single band is available, the strategy of band convergence is not viable and other approaches must be used to enhance the Seebeck coefficient.4247

Trapped electrons at gap states introduced by doping can be thermally promoted to

the CB at high temperature, leading to the high electrical conductivity and suppression of intrinsic excitations.48-50 Also, Fermi level pinning, which keeps the carrier concentration (n) fixed regardless of the dopant concentration,51 can increase the Seebeck coefficient in the low temperature range.52-54 Thus, engineering certain electronic gap states and Fermi level pinning could be promising approaches to enhance the electronic transport properties and power factor over the entire operating temperature range.55 The nature of gap states and resonant levels, caused by the amphoteric group III elements (Al, Ga, and In) as acceptors or donors, has been recognized in n-type PbTe and PbSe.42, 49, 56-60 For n-type PbS, however, with its above mentioned advantages over PbTe and PbSe, there are no studies reported to improve its thermoelectric properties with these strategies. Here, we report the preparation of Ga-doped, and Ga-In co-doped n-type PbS via the vacuum melting method combined with subsequent spark plasma sintering (SPS). We show that these introduce a gap state and Fermi level pinning via Ga doping into the PbS matrix which is in agreement with first-principles electronic structure calculations and confirmed by Hall measurements. We observe enhanced Seebeck coefficients and very high power factors of ~32 μWcm−1K−2 at 300 K for Pb0.9875Ga0.0125S, which exceeds those of all previously studied PbS-based materials.36, 39-40, 61 As a result, a high 3



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room-temperature ZT of ~0.35 and a high ZTavg of ~0.7 in the temperature range of 400 K to 923 K were achieved for Pb0.9875Ga0.0125S. When the less electronegative In is added for co-doping an additional conduction band is introduced (supported by our electronic structure calculations) and the electrical conducitivty and overall thermoelectric properties further improve. Meanwhile, the enhanced alloy phonon scattering introduced by the Ga and In dopants also depresses the lattice thermal conductivity. Finally, a record-high ZTavg of ~0.74 in the range of 400 K to 923 K with a peak ZT of ~1.0 at 923 K was achieved for co-doped n-type Pb0.9865Ga0.0125In0.001S.

EXPERIMENTAL SECTION Synthesis. The high purity starting materials were used as obtained: Pb wire (99.99%, American Elements, USA), S flakes (99.999%, American Elements, USA), Ga shots (99.99%, Sigma-Aldrich, USA) and In beads (99.999%, Sigma-Aldrich, USA). The nominal compositions of Pb1−xGaxS (x = 0.001, 0.003, 0.005, 0.007, 0.01, 0.0125 and 0.015), Pb0.9875−yGa0.0125InyS (y = 0.0005, 0.001, 0.002, 0.003, and 0.005) and PbS as a reference were synthesized by mixing the high purity starting materials in 13 mm diameter fused quartz tubes. The tubes were flame-sealed under a pressure of ~2 × 10−3 torr. The mixed raw materials inside the quartz tube were slowly heated to 723 K over 12 h in a box furnace, then to 1423 K in 7 h, held there for 6 h, and finally air quenched to room temperature. For a typical sample, the following amounts were used: Pb (10 g, 48.26 mmol), S (1.5687 g, 48.92 mmol), Ga (0.0426 g, 0.61 mmol), and In (0.0056 g, 0.049 mmol) to prepare a ~11.6 g ingot of Pb0.9865Ga0.0125In0.001S. Densification. The obtained ingots were hand ground to a fine powder using a mechanical mortar and pestle. The powders were subsequently sintered by using the Spark Plasma Sintering (SPS) technique (SPS-211LX, Fuji Electronic Industrial Co. Ltd.) at 773 K for 10 min under an axial compressive stress of 40 MPa in a vacuum. Disk-shaped pellets with a thickness of ~11 mm, diameter ~12.7 mm, and relative densities ~95% were obtained. Band gap measurement. The room temperature optical band gaps for selected 4


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Pb1−xGaxS and Pb0.9875−yGa0.0125InyS samples were determined using finely ground powder. The spectra were collected in the wave number range 4000 − 400 cm−1 with a Nicolet 6700 FT-IR spectrometer. The band gap was calculated from reflectance data using Kubelka-Munk equations: α/S’ = (1 − R)2/(2R), where R, α and S’ are the reflectance, absorption, and scattering coefficients, respectively.62 Electronic Transport Properties. The electrical conductivity and Seebeck coefficient of samples were simultaneously measured using an Ulvac Riko ZEM-3 system under a low-pressure helium atmosphere from 300 K to 923 K. For the test, the obtained SPSed pellets were cut into bars (~11 mm × 3 mm × 3 mm), then spray coated with a thin layer (0.1 − 0.2 mm) of boron nitride to avoid evaporation of sulfur and to protect the instrument. The uncertainties of the electrical conductivity and Seebeck coefficient are about 5% and 3% for this measurement, respectively.63 Hall Measurements. Room temperature Hall coefficient measurements were made using a Quantum Design Magnetic Property Measurement System (MPMS) connected to a Linear Research AC Resistance Bridge operating at 12 Hz. Polished samples of size ~1 mm × 2 mm × 6 mm were mounted with four probes, two to apply an excitation current and two to measure the transverse voltage under perpendicular applied magnetic fields. Both positive and negative fields of magnitude 0.5 Tesla were used to correct for small probe misalignment. For the high temperature Hall effect measurement, we implemented a similar procedure in a homemade system with an air-bore, heliumcooled superconducting magnet to generate the field within a high temperature oven that surrounds the Ar-filled sample probe. The estimated error is based on the standard deviation of several data points at a single temperature. The carrier concentration was calculated from the Hall coefficient assuming a single carrier, i.e. n = 1/(e|RH|), where e is the electron charge and RH is the Hall coefficient, with the error propagated from the Hall coefficient. The Hall mobility (µH) was determined as µH = σRH. Thermal Conductivity. The total thermal conductivity (κtot) was calculated with the relationship κtot = D·Cp·ρ, where D is the thermal diffusivity, Cp is the specific heat capacity, and ρ is the density. The thermal diffusivity was measured using the laser flash 5



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method (Netzsch LFA457) under a continuous nitrogen flow from 300 K to 923 K for all samples. The squared shape pellets with approximate dimensions of 10 × 10 × 2 mm3, which were coated with a thin layer of graphite to minimize errors from the emissivity of the material, were used for the measurement. The experimental data was analyzed using a Cowan model with pulse correction. The Cp was calculated using the equation Cp/kB per atom = 3.07 + 4.7 × 10−4 (T/K−300)64-65 obtained by fitting experimental data.66 The ρ was calculated using the mass and dimensions of the samples. Considering the uncertainties from D (~5%), ρ (~5%) and Cp (~15%), the combined uncertainty for all measurements involved in ZT determination is ~20%. In this study, all the charge and thermal transport properties were measured perpendicular to the sintering pressure direction. Band Structure Calculations. The total energies and relaxed geometries of Ga-doped and Ga-In co-doped PbS with 54 atom cell were calculated by density functional theory (DFT) within the generalized gradient approximation (GGA) of Perdew-BurkeErnzerhof with Projector Augmented Wave potentials.67 We use periodic boundary conditions and a plane wave basis set as implemented in the Vienna ab initio simulation package.68 The total energies were numerically converged to approximately 3 meV/cation using a basis set energy cutoff of 500 eV and dense k-meshes corresponding to 4000 k-points per reciprocal atom in the Brillouin zone. For the GaIn co-doped cases, we considered two Ga and one In (Pb24Ga2InS27) with many possible configurations to determine the most favorable configuration for further band structure calculations. Boltzmann transport calculations. We used the Boltzmann transport equation to calculate the Fermi level change and thermoelectric properties of Seebeck coefficient, S and electric conductivity, σ in the frame work of semiclassical transport theory.69 To describe scattering terms in the Boltzmann equation for the Seebeck coefficient and electric conductivity, conveniently define a relaxation-time n,k for a carrier in an energy level n at wavevector k. Then, we express the transport tensors as a function of temperature and the electron chemical potential  (which is depending on the doping 6


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level in a semiconductor). 𝜎𝑖𝑗(𝑇,𝜇) = 𝑒

∫

2

𝑒

∂𝑓𝜇(𝑇,𝜖) ― 𝜎𝑖𝑗(𝜖)𝑑𝜖 ∂𝜖

(

(𝜎𝑆)𝑖𝑗(𝑇,𝜇) = 𝑇∫ ―

∂𝑓𝜇(𝑇,𝜖) ∂𝜖

)(𝜖 ― 𝜇)𝜎 (𝜖)𝑑𝜖 𝑖𝑗

2 𝜋2 𝑘𝐵 𝜅𝑖𝑗(𝑇,𝜇) = 𝜎 (𝑇,𝜇)𝑇 3 𝑒

()

(1)

(2)

(2) (3)

𝑖𝑗

Here by defining the derivative of the Fermi-Dirac distribution function with respect to the energy ∂𝑓𝜇 ∂𝜖, we express the Seebeck and electric conductivity in terms of the transport distribution function 𝜎𝑖𝑗(𝜖): 1

𝜎𝑖𝑗(𝜖) = 𝑉∑𝑛,𝑘𝑣𝑖(𝑛,𝑘)𝑣𝑗(𝑛,𝑘)𝜏𝑛,𝑘𝛿(𝜖 ― 𝜖𝑛,𝑘)𝑑𝜖

(4)

where 𝜖𝑛,𝑘 stands for the energy at energy level n at k, 𝑣𝑖(𝑛,𝑘) is the i-th component of the energy band velocity at (𝑛,𝑘) as calculated by the energy derivative with respect to ki, 𝑣𝑖(𝑛,𝑘) = 2𝜋 ℎ∂𝜖𝑛,𝑘 ∂𝑘𝑖 and the summation goes over all bands n and in entire of the Brillouin zone. The chemical potential is related to the temperature and carrier concentration, and thus the transport tensors are also a function of temperature and carrier concentration. Calculated Seebeck and electric conductivity are plotted as a function of temperature at selected carrier concentrations.

RESULTS AND DISCUSSION Structural Characterization and band gaps. Powder X-ray diffraction (PXRD) measurements were used for the structural characterization and evaluation of phase purity the samples of Pb1−xGaxS (x = 0.001, 0.003, 0.005, 0.007, 0.01, 0.0125 and 0.015), and Pb0.9875−yGa0.0125InyS (y = 0.0005, 0.001, 0.002, 0.003, and 0.005) (Figure S1, Supporting Information). The PXRD patterns show that all samples are singlephase compounds crystalizing in the rock salt structure with a space group of Fm3m, (within the detection limit of the laboratory instrument). As displayed in Figure S2a (Supporting Information), the infrared spectra for Pb1−xGaxS indicate that the band gaps increase slightly from ~0.39 eV for pure PbS to ~0.4 eV for Ga-doped samples. For Ga7



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In co-doped samples, the band gaps are increased further to ~0.43 eV (Figure S2b, Supporting Information). For Pb0.9875−yGa0.0125InyS samples with y > 0.001, the bandgaps are difficult to observe spectroscopically because of interference from the high number of free carriers. Boosting the Performance via Ga Doping. Charge Transport Properties. Hall Coefficient. N-type Hall coefficients were recorded for all samples in the study, indicating the dominance of electrons in charge conduction with concentrations in the order of 1019 cm−3 for the majority of Pb1−xGaxS samples. As shown in Figure 1a, the substitution of Ga for Pb decreases the magnitude of the Hall coefficient until the Ga dopant level reaches ~0.5 at%. Above this level, RH and the corresponding charge carrier concentration remain mostly unchanged. The predicted carrier concentration values (assuming a Ga3+ ion substitutes for Pb2+ and adds a single electron) as a function of Ga content are much higher than the measured values. This suggests that Ga is an inefficient dopant at > 0.5 at%, either by i) not donating its electrons to the matrix material or ii) by creating a secondary phase or iii) by pinning the Fermi level by compensating defects and balancing out the donated electrons to keep the Hall coefficient roughly constant. Fermi level pinning is more in line with the DFT calculations, which will be discussed later. Electrical Conductivity and Seebeck Coefficients. The temperature-dependent electrical conductivity of Pb1−xGaxS samples increases with Ga content from ~300 Scm−1 for Pb0.999Ga0.001S to ~1385 Scm−1 for Pb0.985Ga0.015S at 300 K, Figure 2a. The increasing trend is primarily because of the increase of n from ~0.41 × 1019 (for Pb0.999Ga0.001S) to ~1.55 × 1019 cm−3 (for Pb0.9875Ga0.0125S) (Figure 1a). Moreover, the charge carrier mobilities remain high at ~500 cm2V−1s−1 with Ga content > 0.5 at% at 300 K (Figure 1d and S3a, Supporting Information). The electrical conductivity for all samples

monotonously

decreases

with

temperature,

displaying

degenerate

semiconductor behavior. As shown in Figure 1d, the Ga-doped samples have high carrier mobility, µH (347 – 502 cm2V−1s−1 with n from ~0.41 to 1.73 × 1019 cm−3). By 8


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comparison, the mobilities of some previously reported PbS-based n-type materials are Pb0.98-xSb0.02CuxS-yCu (17 – 90 cm2V−1s−1 with n from ~1.68 to 11.50 × 1019 cm−3), PbS-xPbCl2 (124 – 236 cm2V−1s−1 with n from ~4.12 to 9.52 × 1019 cm−3), PbS1%PbCl2-xBi2S3 (55 – 176 cm2V−1s−1 with n from ~6.56 to 6.72 × 1019 cm−3), PbS1%PbCl2-xSb2S3 (19 – 121 cm2V−1s−1 with n from ~6.55 to 6.70 × 1019 cm−3), and PbS1%PbCl2-1%Ca(Sr)S (254 – 402 cm2V−1s−1 with n from ~6.90 to 6.95 × 1019 cm−3) at room temperature.39, 70 The temperature-dependent Seebeck coefficients for Pb1−xGaxS are displayed in Figure 2b. The negative sign of the Seebeck coefficients throughout the tested temperature range indicates that the electrons are the dominant carriers, agreeing with the negative values of the Hall coefficients (Figures 1a and 1c, Supporting Information). Specifically, the Pb0.999Ga0.001S sample has the highest Seebeck coefficients throughout the entire measured temperature range. The Seebeck coefficient decreases significantly (from −252 to −167 μVK−1) when the Ga content increases from x = 0.001 to 0.003 at 300 K. Then, with additional Ga content (at x > 0.005), the Seebeck coefficient remains approximately constant at 300 K. Moreover, from 300 K to 773 K, the Seebeck coefficients increase to a maximum of −335 μVK−1 (x = 0.007) and thereafter start to decrease because of the excitation of minority carriers (holes). The Seebeck coefficient as a function of Hall carrier density n (Pisarenko plot) at 300 K for Pb1−xGaxS is displayed in Figure 2d. The solid purple curve is the theoretically calculated values based on the single parabolic band (SPB) model for n-type PbS with effective density of state (DOS) mass of electron of 0.55 me (me is the free electron mass), which fit the experimental data and the theoretically calculated value of 0.52 me well. Compared with the effective DOS masses of Sb-Cu co-doped PbS (~0.5 me) and Cl-doped PbS (~0.4 me),39 the Ga doped PbS samples have the highest effective DOS mass. Power Factor. The temperature-dependent power factors for the Pb1−xGaxS samples are shown in Figure 2c. Because of the substantially increased electrical conductivities and high Seebeck coefficient, the Pb1−xGaxS samples exhibit ultrahigh power factors for PbS material. Remarkably, the Pb0.9875Ga0.0125S sample has a power factor of ~32 9



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μWcm−1K−2 at 300 K, which is the highest reported for both n- and p-type PbS-based thermoelectric materials (Figure 3a).34, 36, 38-40, 61, 71-79 Below, we will show results from density functional theory calculations to help explain the high power factors found in the Pb1−xGaxS samples. Thermal Conductivity. The temperature-dependent total thermal conductivity (κtot) for the Pb1−xGaxS samples is shown in Figure 3b. The κtot continuously decreases with rising temperatures. In addition, the κtot values rise for samples with increasing Ga content (for x < 0.007) and then decrease when x > 0.007. At 300 K, Pb0.999Ga0.001S has the lowest value of 2.41 Wm−1K−1 and Pb0.993Ga0.007S has the highest value of 3.07 Wm−1K−1. The lowest value of 1.00 Wm−1K−1 is achieved at 923 K for Pb0.997Ga0.003S. The lattice thermal conductivity (κlat) is calculated by subtracting the electronic thermal conductivity (κele) from κtot. The κele is estimated by using the WiedemannFranz law,80 κele = LσT (where L is the Lorenz number estimated using the equation: L = 1.5 + exp[−|S|/116] × 10−8 V2K−2). Figure S6c (Supporting Information) shows the calculated Lorenz numbers. The κele values of Pb1−xGaxS show a significant rise with the increase fraction of Ga because of the sharp increase in electrical conductivity (Figure S6b, Supporting Information). As shown in Figure 3c, the κlat values for Pb1−xGaxS decrease at elevated temperatures as commonly occurs in semiconductors because of phonon-phonon umklapp scattering. In detail, Pb0.985Ga0.015S has the lowest value of 1.91 Wm−1K−1 and Pb0.993Ga0.007S has the highest value of 2.45 Wm−1K−1, respectively, at 300 K. Moreover, the lowest κlat value of ~0.86 Wm−1K−1 is obtained at 923 K for Pb0.997Ga0.003S. The κlat values of the Pb1−xGaxS samples along with those for pristine PbS, Cl-doped and Sb-doped ntype PbS-based solid solution thermoelectric materials are displayed in Figure 7a.71, 81 The κlat decreases by ~21% and 33% from 2.64 and 1.28 Wm−1K−1 for PbS to 2.09 and 0.86 Wm−1K−1 for Pb0.997Ga0.003S at 300 K and 923 K, respectively (Figure 7a). Obviously, Ga-doping is more effective in reducing the κlat than Cl- or Sb-doping. Ga-In co-doping: Synergistically optimized electrical and thermal transport properties 10


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In order to further improve the n-type PbS thermoelectric performance, we explored the modification of the electronic structure with Ga-In co-doping. The aim was to see if we can achieve higher electrical conductivity via In doping (through less electronegativity difference) while maintaining the large Seebeck coefficient via Ga doping (through the gap state and Fermi level pinning, see DFT calculations part). Moreover, co-doping can further reduce the κlat via extra atomic mass fluctuations in the Pb sublattice and strain field fluctuations between the dopants (Ga and In). Because Pb0.9875Ga0.0125S showed the best overall thermoelectric performance, in these investigations the doping content is fixed to x = 0.0125. As shown in Figures 1b and 1c, the co-doped samples have lower RH and higher n than Ga-doped samples. The results suggest that the In is a high-efficiency electron donor for PbS. Furthermore, the co-doped samples with y < 0.002 have high µH >500 cm2V−1s−1 at 300 K (Figure 1d and S3b, Supporting Information). In particular, the highest µH ~630 cm2V−1s−1 with n of 1.67 × 1019 cm−3 for Pb0.9865Ga0.0125In0.001S is obtained at room temperature, an enhancement of ~28% compared with that of Pb0.9875Ga0.0125S (~491 cm2V−1s−1 with n of 1.55 × 1019 cm−3). The resulting co-doped samples of Pb0.9875−yGa0.0125InyS (y = 0.0005, 0.001, 0.002, 0.003, and 0.005) exhibit enhanced electrical conductivities, e.g. ranging from 1218 Scm−1 for Pb0.9875Ga0.0125S to 2867 Scm−1 for Pb0.9825Ga0.0125In0.005S at 300 K (Figure 4a). The Ga-In co-doped samples exhibit lower Seebeck coefficients than the Pb0.9875Ga0.0125S samples at 300 K (Figure 4b) because of the higher carrier concentrations (Figures 1a and 1b) and lower effective DOS masses (Figure S4, Supporting information). The Seebeck coefficients are about −145, −103, −84, −60, and −56 µV/K at 300 K for samples with y = 0.0005, 0.001, 0.002, 0.003, and 0.005, respectively. For the y > 0.0005 samples, the power factors are higher than that of Pb0.9875Ga0.0125S at T > 673 K (Figure 4c). In detail, the power factors over than 10 μWcm−1K−2 (e.g. 10.4 μWcm−1K−2 for y = 0.001, 10.9 μWcm−1K−2 for y = 0.002, 10.3 μWcm−1K−2 for y = 0.003, and 11.5 μWcm−1K−2 for y = 0.005) were obtained at 923 K. The much higher σ values result in higher the κtot for the co-doped samples (Figure 11



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4d). However, the κlat for Ga-In co-doped samples is lower than that of Pb0.9875Ga0.0125S, which is likely due to enhanced point defect scattering (Figure 4e). Remarkably, the lowest κlat of 0.66 Wm−1K−1 is achieved for Pb0.9825Ga0.0125In0.005S at ~923 K. Compared with the minimum κlat value of PbS (1.28 Wm−1K−1 at 923 K),81 the Pb0.9825Ga0.0125In0.005S achieves nearly a ~50% reduction of κlat (Figure 7a). TEM analysis Microstructural and compositional analyses were performed for the Pb0.9875Ga0.0125S sample using scanning/transmission electron microscopy(S/TEM). A typical bright field TEM image of the sample is shown in Figure 5a with selected area diffraction pattern inset. The diffraction pattern can be indexed to rock-salt (NaCl) PbS (space group: Fm3m) with no additional spots or streaks observed. High-resolution TEM images at different magnifications of the selected area (Figures 5b and c) clearly illustrate the lattice fringes of the sample along [100] without any form of defects, namely Moirre fringes, phase boundaries, etc. In addition, the high angle annular dark field (HAADF) image (Figure 5d) along with elemental maps of the corresponding area also confirms that Ga forms a solid solution in the PbS matrix. The results suggest that the reduction of κlat was caused by the large mass fluctuations and strain field fluctuations between the dopant and matrix atoms. Electronic Structure DFT Calculations The electronic structure and charge transport behavior were further investigated by first-principles electronic band structure calculations based on DFT. Figures 6a, c and e show the DFT band structures of undoped PbS, Ga-doped PbS and two Ga and one In co-doped PbS, respectively (considering one Pb atom substitution by Ga in a 3×3×3 PbS supercell, equivalent to a 3.7 mol% doped PbS). For the pure PbS without any dopants, the band structure shows a direct band gap of 0.32 eV at the L point with valence band (VB) contributions from the 3p state of the S atom and the conduction band (CB) arising from the 6p state of the Pb atom. For the CB, the second CB minimum is along ΣK and has an energy difference with the L point of 0.35 eV. For the single Ga-doped PbS (Figure 6c), the Ga atom induces strong gap states contributed 12


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from Ga 4s states and hybrid S 3s and 3p states, as shown in the band structure and DOS of Figures 6b and d. For the single Ga-doped case, the Fermi level lies within the gap states, suggesting the Ga addition significantly enhances the carrier concentration, electrical conductivity and power factor, as we noted experimentally. To simulate more closely the co-doped case, we also calculated the electronic band structure of two Ga and one In atom in the PbS lattice (Pb24Ga2InS27). Before the band structure calculations were carried out, we first had to screen the most favorable Ga and In configurations in the PbS 54 atom unit cell. By considering the many possible configurations, we determined the least energetic one to be Ga and In residing as nearest neighbors. Interestingly, with respect to the pure PbS case two extra bands are introduced in the electronic band structure of the two Ga and one In co-doped case (Figure 6(e)). One is a gap state like the single Ga-doped case composed of Ga 4s and neighbor S 3p states, as described above. The In 5s states introduce an extra CB, which is adjacently higher than the Ga gap states (Figure 6(f)). For the two Ga and one In codoped case, the electrons are from In 5s states at L and Γ points, the energy difference between L and Γ being only 0.03 eV. Note that the ionization states of Ga and In are both consistent with 3+ states and there is no charger transfer suggested between Ga and In species. The calculated Fermi level change upon electron concentration for pure PbS, single Ga-doped PbS and one Ga and one In co-doped PbS at 300 K shown in Figure S8. The Fermi level at the concentration of 5 × 1017 cm−3 is adopted as a reference. For single Ga-doped PbS, the Fermi level change is at least one order of magnitude lower than pure PbS and one Ga and one In co-doped PbS at 300 K. As shown in Figures 6g and 6h, the electrical conductivity and Seebeck coefficient via the Boltzmann transport calculations, indicate that such a unique band structure for Ga-In co-doped sample has the higher electrical conductivity and larger Seebeck coefficient than the pure PbS band structure from 100 K to 300 K with the same carrier concentrations. Figure of Merit The

temperature-dependent

figures

of

merit,

ZT,

for

Pb1−xGaxS

and 13



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Pb0.9875−yGa0.0125InyS are displayed in Figures 3d and 4f. Pb0.9875Ga0.0125S possesses a high room-temperature ZT of ~0.35 and Pb0.9865Ga0.0125In0.001S develops a peak ZT of ~1.0 at 923 K. Moreover, to assess the expected performance of these materials in terms of a thermoelectric device, the ZTavg was calculated by the following relationship, 1

𝑇

𝑍𝑇avg = 𝑇H ― 𝑇C∫𝑇H𝑍𝑇d𝑇 C

(5)

This average value plays a more decisive role than the peak ZT for the thermoelectric conversion efficiency in a device. A comparison of ZTavg values for Pb0.9875Ga0.0125S and Pb0.9865Ga0.0125In0.001S with those in previous studies on PbS-based thermoelectric materials is illustrated in Figure 7c. The Ga-doped Pb0.9875Ga0.0125S samples have a high ZTavg of 0.7 in the temperature range of 400 K to 923 K while the Ga-In co-doped Pb0.9865Ga0.0125In0.001S samples have a ZTavg of ~0.74 between 400 K and 923 K, which is higher than any reported for both n- and p-type PbS based materials (Figure 7c).34, 36, 38-40, 61, 71-79

The high ZT of ~0.35 at room-temperature helps to increase the ZTavg.

CONCLUSIONS The n-type thermoelectric materials Pb1−xGaxS and Pb0.9875−yGa0.0125InyS are promising low cost thermoelectric materials. As electron dopant, Ga has significant effects: (i) tunes the carrier concentration by substituting Ga3+ for Pb2+; (ii) reduces the κlat via large mass fluctuations and strain field fluctuations between the dopants and matrix atoms; (iii) introduces a gap state between the VB and CB in PbS that was revealed by first-principles electronic band structure calculations. Moreover, the gap state and the Fermi level pinning lead to a significant enhancement of Seebeck coefficients of > −130 μVK−1 at 300 K for all Ga-doped samples. As a result, the high Seebeck coefficient leads to a record high power factor of ~32 μWcm−1K−2 and a high ZT of ~0.35 at roomtemperature for Pb0.9875Ga0.0125S. The Ga-In as the co-dopants, (i) introduce an extra CB, which improves the electrical conductivity; (ii) enhance the phonon scattering by increased point defect, leading to the low lattice thermal conductivity. Finally, in Pb0.9865Ga0.0125In0.001S, we observe the highest µH ~630 cm2V−1s−1 for n of 1.67 × 1019 cm−3 for Pb0.9865Ga0.0125In0.001S and a record-high ZTavg of ~0.74 between 400 K and 14


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923 K with a peak ZT of ~1.0 at 923 K. The high ZTavg value over the entire working temperature range is a key finding in this work, which begins to approach those found in PbSe type systems. Based on the formula, η = [(TH − TC)/TH] [(1 + ZTavg)1/2 − 1]/[(1 + ZTavg)1/2 + TC/TH] with TH = 923 K and TC = 400 K, an efficiency of 10.3% in Pb0.9865Ga0.0125In0.001S is estimated. This makes the PbS as the excellent thermoelectric material for thermoelectric generators for example by combining the best p-type Pb0.975Na0.025S-3%SrS with its high ZTavg of ~0.64 from 400 K to 923 K. Further improvements in the ZTavg of both n- and p-type PbS samples could lead to low cost thermoelectric generators.

Conflicts of interest There are no conflicts to declare. Acknowledgements This work was supported by the Department of Energy, Office of Science Basic Energy Sciences under grant DE-SC0014520, DOE Office of Science (sample preparation, synthesis, XRD, TE measurements, TEM measurements, DFT calculations). ZZL and QY gratefully acknowledge the National Natural Science Foundation of China (61728401). This work made use of the EPIC facility of Northwestern University’s NUANCE Center, which has received support from the Soft and Hybrid Nanotechnology Experimental (SHyNE) Resource (NSF ECCS-1542205); the MRSEC program (NSF DMR-1720139) at the Materials Research Center; the International Institute for Nanotechnology (IIN); the Keck Foundation; and the State of Illinois, through the IIN. User Facilities are supported by the Office of Science of the U.S. Department of Energy under Contract No. DE-AC02-06CH11357 and DE-AC0205CH11231. Access to facilities of high performance computational resources at the Northwestern University is acknowledged. The authors also acknowledge Singapore MOE AcRF Tier 2 under Grant Nos. 2018-T2-1-010, Singapore A*STAR Pharos Program SERC 1527200022, the support from FACTs of Nanyang Technological University for sample analysis. 15



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Supporting Information PXRD patterns, Hall coefficient, temperature-dependence Lorenz numbers, thermal diffusivity, heat capacity, electronic thermal conductivity, and a table of room temperature densities for Pb1−xGaxS and Pb0.9875−yGa0.0125InyS. Thermoelectric properties as a function of temperature for PbS. The Supporting Information is available free of charge on the ACS Publications website. References 1. Hsu, K. F.; Loo, S.; Guo, F.; Chen, W.; Dyck, J. S.; Uher, C.; Hogan, T.; Polychroniadis, E. K.; Kanatzidis, M. G. Cubic AgPbmSbTe2+m: Bulk Thermoelectric Materials with High Figure of Merit. Science 2004, 303 (5659), 818-821. 2. Tan, G.; Zhao, L.-D.; Kanatzidis, M. G. Rationally Designing High-Performance Bulk Thermoelectric Materials. Chem. Rev. 2016, 116 (19), 12123–12149. 3. Zhu, T.; Liu, Y.; Fu, C.; Heremans, J. P.; Snyder, J. G.; Zhao, X. Compromise and Synergy in High-Efficiency Thermoelectric Materials. Adv. Mater. 2017, 29 (14), 1605884. 4. He, J.; Tritt, T. M. Advances in thermoelectric materials research: Looking back and moving forward. Science 2017, 357 (6358). 5. Zhao, L.-D.; Dravid, V. P.; Kanatzidis, M. G. The panoscopic approach to high performance thermoelectrics. Energy Environ. Sci. 2014, 7 (1), 251-268. 6. Sootsman, J. R.; Chung, D. Y.; Kanatzidis, M. G. New and old concepts in thermoelectric materials. Angew. Chem. Int. Ed. 2009, 48 (46), 8616-39. 7. Minnich, A. J.; Dresselhaus, M. S.; Ren, Z. F.; Chen, G. Bulk nanostructured thermoelectric materials: current research and future prospects. Energy Environ. Sci. 2009, 2 (5), 466. 8. Snyder, G. J.; Toberer, E. S. Complex thermoelectric materials. Nat. Mater. 2008, 7, 105. 9. Zhao, L.-D.; Chang, C.; Tan, G.; Kanatzidis, M. G. SnSe: a remarkable new thermoelectric material. Energy Environ. Sci. 2016, 9 (10), 3044-3060. 10. Zeier, W. G.; Zevalkink, A.; Gibbs, Z. M.; Hautier, G.; Kanatzidis, M. G.; Snyder, G. J. Thinking Like a Chemist: Intuition in Thermoelectric Materials. Angew. Chem. Int. Ed. 2016, 55 (24), 6826-6841. 11. Luo, Z.-Z.; Zhang, Y.; Zhang, C.; Tan, H. T.; Li, Z.; Abutaha, A.; Wu, X.-L.; Xiong, Q.; Khor, K. A.; Hippalgaonkar, K.; Xu, J.; Hng, H. H.; Yan, Q. Multifunctional 0D2D Ni2P Nanocrystals-Black Phosphorus Heterostructure. Adv. Energy Mater. 2017, 7 (2), 1601285. 12. Sitter, H.; Lischka, K.; Heinrich, H. Structure of the second valence band in PbTe. Phys. Rev. B 1977, 16 (2), 680-687. 13. Delaire, O.; Ma, J.; Marty, K.; May, A. F.; McGuire, M. A.; Du, M. H.; Singh, D. 16


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Figures

Figure 1. Hall coefficient, RH, and carrier concentration, n at 300 K for (a) Pb1−xGaxS (x = 0.001, 0.003 0.005, 0.01 and 0.0125) and (b) Pb0.9875−yGa0.0125InyS (y = 0.0005, 0.001, 0.002, 0.003, and 0.005). The observed variation in RH and n with Ga concentration can be explained by the phenomenon of Fermi level pinning. The concentration of free electrons n increases with increasing Ga concentration until x ~ 0.005; above this concentration, adding Ga has less effect on the n. We therefore expect an enhancement in room temperature Seebeck coefficients for those samples with x ≥ 0.005; (c) RH from 300 K to 800 K for Pb0.9875Ga0.0125S and Pb0.9865Ga0.0125In0.001S; and (d) Comparison of carrier mobility, µH in this work (PbS-Ga and PbS-GaIn) with previous sample, Pb0.98-xSb0.02CuxS-yCu (PbS-Sb-Cu), PbS-xPbCl2 (PbS-Cl), PbS1%PbCl2-xBi2S3(PbS-Cl-Bi2S3), PbS-1%PbCl2-xSb2S3(PbS-Cl-Sb2S3), and PbS1%PbCl2-1%Ca(Sr)S (PbS-Cl-Ca/SrS). 39, 70

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Figure 2. Thermoelectric properties as a function of temperature for Pb1−xGaxS SPSed pellets: (a) Electrical conductivity; (b) Seebeck coefficient; and (c) Power Factor. (d) Seebeck coefficient as a function of Hall carrier concentration at 300 K. The solid purple curves in (d) is the theoretical Pisarenko curve for n-type PbS with effective DOS mass of electron of 0.55 me.

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Figure 3. (a) Power factors in the present study compared with those in previous n-type PbS-based thermoelectric materials. Thermoelectric properties as a function of temperature for Pb1−xGaxS SPSed pellets: (b) total thermal conductivity, κtot; (c) lattice thermal conductivity, κlat; and (d) figure of merit, ZT.

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Figure 4. Thermoelectric properties as a function of temperature for Pb0.9875−yGa0.0125InyS SPSed pellets; (a) Electrical conductivity; (b) Seebeck coefficient; (c) Power factor; (d) Total thermal conductivity; (e) Lattice thermal conductivity; and (f) ZT values.

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Figure 5. (a) Representative Bright field TEM image of the Pb0.9875Ga0.0125S sample with diffraction pattern along the [001] zone axis at inset. A clean surface can be observed within a relatively large length scale (the scale bar is 500 nm). (b)-(c) High resolution images of Pb0.9875Ga0.0125S with the crystal orientation highlighted by yellow arrows in (c). (d) High angle annular dark field (HAADF) image and its corresponding elemental maps, indicating the sample forms a solid solution.

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Figure 6. Band structure of (a) pure PbS; (c) Pb26GaS27 and (e) Pb24Ga2InS27 and corresponding density of states of (b) pure PbS; (d) Pb26GaS27 and (f) Pb24Ga2InS27; the calculated Seebeck coefficient (g) and electrical conductivity (h) of pure PbS and GaIn co-doped PbS from 100 K to 300 K with the carrier concentrations of 1 × 1018 cm−3 and 1 × 1019 cm−3.

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Figure 7. (a) Comparison of κlat values for pristine PbS and n-type PbS-based solid solution thermoelectric materials; (b) Comparison of ZT values for n-type PbS in the present study with those in previously explored n-type PbS-based thermoelectric materials; and (c) Comparison of ZTavg values with the temperature gradient of 400 K to 923 K for several n- and p-type PbS-based thermoelectric materials.

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TOC Figure

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Enhancement of Thermoelectric Performance for n-Type PbS through

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