Defect Engineering for High-Performance n-Type PbSe

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Defect Engineering for High Performance N-type PbSe Thermoelectrics Chongjian Zhou, Yong Kyu Lee, Joonil Cha, Byeongjun Yoo, Sung-Pyo Cho, Taeghwan Hyeon, and In Chung J. Am. Chem. Soc., Just Accepted Manuscript • DOI: 10.1021/jacs.8b05741 • Publication Date (Web): 29 Jun 2018 Downloaded from http://pubs.acs.org on July 1, 2018

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Journal of the American Chemical Society

Defect Engineering for High Performance N-type PbSe Thermoelectrics

Chongjian Zhou,†,‡ Yong Kyu Lee,†,‡ Joonil Cha,†,‡ Byeongjun Yoo,†,‡ Sung-Pyo Cho,§ Taeghwan Hyeon,†,‡ and In Chung†,‡,#,*

†

Center for Nanoparticle Research, Institute for Basic Science (IBS), Seoul 08826, Republic

of Korea. ‡

School of Chemical and Biological Engineering, #Institute of Chemical Processes, and §

National Center for Inter-University Research Facilities, Seoul National University, Seoul 08826, Republic of Korea.

ABSTRACT: Introducing structural defects such as vacancies, nanoprecipitates, and dislocations is a proven means of reducing lattice thermal conductivity. However, these defects tend to be detrimental to carrier mobility. Consequently, the overall effects for enhancing ZT are often compromised. Indeed, developing strategies allowing for strong phonon scattering and high carrier mobility at the same time is a prime task in thermoelectrics. Here we present a high performance thermoelectric system of Pb0.95(Sb0.033□0.017)Se1-yTey (□ = vacancy; y = 0 – 0.4) embedded with unique defect architecture. Given the mean free paths of phonons and electrons, we rationally integrate multiple defects that involve point defects, vacancy-driven dense dislocations, and Te-induced nanoprecipitates with different sizes and mass fluctuations. They collectively scatter thermal phonons in a wide range of frequencies to give lattice thermal conductivity of ~0.4 W m-1 K-1, which approaches to the amorphous limit. Remarkably, Te alloying increases a density of nanoprecipitates that affect mobility negligibly and impede phonons significantly, and it also decreases a density of dislocations that scatter both electrons and phonons heavily. As y is increased to 0.4, electron mobility is 1 ACS Paragon Plus Environment

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enhanced and lattice thermal conductivity is decreased simultaneously. As a result, Pb0.95(Sb0.033□0.017)Se0.6Te0.4 exhibits the highest ZT ~1.5 at 823 K, which is attributed to the markedly enhanced power factor and reduced lattice thermal conductivity, in comparison with a ZT ~0.9 for Pb0.95(Sb0.033 □ 0.017)Se that contains heavy dislocations only. These results highlight the potential of defect engineering to modulate electrical and thermal transport properties independently. We also reveal the defect formation mechanisms for dislocations and nanoprecipitates embedded in Pb0.95(Sb0.033 □ 0.017)Se0.6Te0.4 by atomic resolution spherical aberration-corrected scanning transmission electron microscopy.

1. Introduction Fossil fuels are a main source for producing useful forms of energy. However, more than 50% of generated energy is rejected as a waste heat.1,2 Recovering such a huge amount of energy loss can contribute to resolving the global energy crisis for a sustainable world. Thermoelectrics emerges as a viable technology for this purpose on account of its capability of direct conversion of heat into electric energy and environmentally friendly nature.3–8 Because a thermoelectric (TE) device consists of n- and p-type semiconductors, its conversion efficiency directly depends on the performance of constituent TE materials. Their dimensionless figure of merit ZT is expressed by S2σT/κtot,9–11 where S is the Seebeck coefficient, σ is the electrical conductivity, their product S2σ is the power factor (PF), T is the absolute temperature, and κtot is the total thermal conductivity from both the electrical (κele) and the lattice vibration contribution (κlat). Ideally, the materials must exhibit both high PF and low κtot for the best TE performance. However, the critical parameters of ZT, such as σ, S, and κtot, are so strongly intercorrelated that it is nearly impossible to decouple and control them independently to maximize ZT.12 As a result, strategies towards high ZT are mostly aimed at either increasing 2 ACS Paragon Plus Environment

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PF or decreasing κlat with a minimal sacrifice of σ. The representative examples of the former are band engineering,13–17 tuning effective mass,18 energy filtering,19 and off-stoichiometric compositions.20 The latter is a popular and proven way of improving ZT since the discovery of the nanostructured AgPbmSbTe2+m (LAST) system.21 The common examples are scattering thermal phonons by alloying,22–27 nanostructuring,16,20,28–32 hierarchical architectures,33–35 and lattice anharmonicity.14,36–43 It should be noted that the aforementioned examples have their own mechanisms to scatter phonons. To be specific, point defects, grain boundaries, and inherent phonon-phonon interactions are responsible for the scattering by alloying, nanostructuring, and lattice anharmonicity, respectively.44,45 It follows that the respective mechanism can disrupt phonon transport in the specified range of frequency (ω). For example, nanostructuring is effective for low-ω phonons; alloying for mid- to high-ω phonons; and the anharmonic lattice vibration such as Umklapp and normal processes independent of ω. Their respective relaxation time is differently proportional to ω0, ω-4, and ω-2. Dislocations in a grain boundary uniquely involve two distinctive mechanisms of dislocation strain fields and dislocation cores. Their relaxation time is proportional to ω-1 and ω-3, respectively. In accordance, they are coupled to scatter mid-ω phonons to reduce κlat dramatically, which are marginally interrupted by the other defects.46–48 In this regard, integrating multiple defects can shorten a total relaxation time of phonons in a wide range of ω, thereby minimizing κlat.49 At the same time, such defects can damage carrier mobility and σ.50 For example, the mobility of PbSe decreases considerably from ~500 cm2 V-1 s-1 to ~50 cm2 V-1 s-1 when highly dense dislocations are introduced.51 Due to this ambivalent effect of defects, especially dislocations, it is of prime importance to rationally design defect structures in consideration of the mean free paths of phonons and electrons for maximizing a ratio of mobility to κlat.

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Here we report a high performance n-type thermoelectric system of PbSe embedded with the unique defect architecture involving dislocations and multiscale nanoprecipitates. Their integration allows for broad-band phonon scattering, leaving a slit for electron transport, thereby resulting in effectively decoupling carrier mobility from κlat. Our design strategy for the defect architecture starts with creating a large degree of vacancies (□) in the PbSe matrix. We doped a charge-compensating amount of Sb to obtain Pb1-x(Sb2x/3 □ x/3)Se. It is thermodynamically favorable for the higher-valent Sb3+ cations to pair with zero-valent vacancies for balancing charge in the vicinity of these aliovalent impurities in the Pb2+Se2lattices. This induces heavy dislocations with a density (ND) of 2 × 1012 cm-2 for the sample with x = 0.05, i.e., Pb0.95(Sb0.033□0.017)Se. This level of ND damages carrier mobility seriously and gives a modest ZT of ~0.9 at 823 K, despite very low κlat of ~0.6 W m-1 K-1. Afterward, we further alloy Te in the Se lattice sites in Pb0.95(Sb0.033□0.017)Se to synthesize Pb0.95(Sb0.033 □0.017)Se1-yTey. For the rest of the manuscript, □ will be omitted and instead Pb0.95Sb0.033Se and Pb0.95Sb0.033Se1-yTey will be used for the simplicity. Te atoms preferably reside near the vacancy-abundant regions, i.e., dislocation lines, to reduce overall lattice strains. This spontaneously nucleates Te-rich nanoprecipitates and subsequently terminates the propagation of dislocations. Consequentially, Te alloying trades dislocations for nanoprecipitates, accompanied by a reduction in ND towards ~1011 cm-2. The declined ND markedly enhances carrier mobility, because nanoprecipitates that are endotaxially placed in the matrix marginally affect it. Despite the declined ND, κlat further diminishes to the amorphous limit by collaborative phonon scattering by dislocations and nanoprecipitates. These results validate our defect engineering strategy to decouple electrical and phonon transport properties. Because of a maximized ratio of carrier mobility to κlat, the Pb0.95Sb0.33Se0.6Te0.4 sample exhibits a high ZT value of ~1.5 at 823 K for n-type PbSe-based materials. It shows 50% higher power factor and 30% lower κlat than Pb0.95Sb0.33Se only with heavy dislocations. We 4 ACS Paragon Plus Environment

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also characterized the formation mechanism of dislocations and nanoprecipitates in Pb0.95Sb0.33Se0.6Te0.4 and their influences on TE properties using atomic resolution spherical aberration-corrected scanning transmission electron microscopy. These results provide fundamental understandings for how nanoscale defects form in bulk materials.

2. Results and discussion 2.1. Crystal structure and ZT values All synthesized members of Pb0.95Sb0.33Se1-yTey (y = 0, 0.1, 0.2, 0.3, and 0.4) crystallize in the rock-salt structure (Fm-3m space group) with no noticeable impurity according to their powder X-ray diffraction (PXRD) patterns (Figure S1a). The cell volume increases with the larger fraction of Te alloying. The trend of lattice dimension follows the Vegard’s law (Figure S1b), demonstrating the formation of solid solutions as observed in PbTe1-ySey. However, we observed the presence of a considerable degree of dislocations and nanoprecipitates. Figure 1 clearly demonstrates that a ZT of Pb0.95Sb0.033Se is greatly improved by Te alloying. The y = 0.4 sample exhibits a maximum ZT of ~1.5 at 823 K, in comparison with ~0.8 for Pb0.95Sb0.033Se. The observed ZT is one of the highest among n-type PbSe-based materials. To better understand this remarkable effect of Te alloying in Pb0.95Sb0.033Se1-yTey, we performed atomic resolution transmission electron microscopy (TEM) and theoretical calculations, coupled with characterizations for electrical and thermal transport properties.



Figure 1. Temperature-dependent ZT for Pb0.95Sb0.033Se1-yTey (y = 0 – 0.4).

2.2. Formation mechanisms of dislocations and nanoprecipitates Typical low-magnification TEM images of the Pb0.95Sb0.033Se samples taken before and after an SPS process show similar heavy dislocations that are tangled to form complex networks (Figure S2 and Figure S3a). This indicates that heavy dislocations are not induced during an SPS process. The corresponding electron diffraction (ED) pattern, which includes both the matrix and dislocations, can be indexed as the rock-salt structure down the zone axis without any noticeable second phase (inset in Figure S3a). Their average density (ND) is estimated to be ~2 × 1012 cm-2 from the image. In comparison, ND of typical semiconductors is ~103-106 cm-2.52 This exceedingly high ND plausibly forces individual dislocations to grow with a zigzag morphology (Figure S3b).52 The corresponding inverse fast Fourier transform (IFFT) image shows a high degree of edge dislocations along the {100} atomic planes (marked by the red symbols in Figure S3c). For high ZT, it is necessary to have optimal ND, since too high value deteriorates electrical transport properties. It would not be effective to tune concentration of vacancies for that purpose, given that they tend to segregate spontaneously and then induce dislocations. Instead, we introduced a ‘misfit’ impurity Te to the Se lattices in Pb0.95Sb0.033Se, synthesizing a new system Pb0.95Sb0.033Se1-yTey (y = 0.1, 0.2, 0.3, and 0.4).


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We employed atomic resolution spherical aberration-corrected scanning TEM (Cscorrected STEM) to unveil evolution mechanisms of the nanoscale defects in the Pb0.95Sb0.033Se0.6Te0.4 sample. Figure 2a shows representative low-magnification annular bright-field (ABF) STEM image. Short fragments of dislocation lines and multiscale nanoprecipitates are embedded in the solid solution matrix. The corresponding ED pattern (inset in Figure 2a) shows only single set of Bragg diffraction spots that correspond to the PbSe structure along the zone axis, indicating that the dislocations and nanoprecipitates have similar structure and lattice parameters to the matrix.

Figure 2. Typical STEM images and elemental mappings for the Pb0.95Sb0.033Se0.6Te0.4 sample. (a) Low-magnification ABF-STEM image. The inset shows the corresponding electron diffraction pattern taken on the entire area in (a). High-magnification atomic resolution (b) ABF- and (c) HAADF-STEM images taken on the solid-solution area marked in (a). (d-f) Elemental mappings of Pb, Se, and Te atoms depicted in yellow, green, and purple color, respectively, by STEM-EDS scanned on the red rectangle region in (c), confirming the rocksalt PbSe structure at the atomic level. The PbSe structure is drawn over the direct EDS signal of Pb in (d).



Figures 2b-c present atomic resolution high-magnification ABF- and high-angle annular dark-field (HAADF) STEM images, respectively, on the seemingly defect-free (solid solution) region (marked by the red circle in Figure 2a). The nearly perfect PbSe structure without a discernible contrast difference is observed. It should be noted that in the rock-salt structure a respective ion is surrounded by octahedron of six counterions, and that cations and anions are alternately repeated down the zone axis. As a consequence, adjacent atoms, i.e., Pb/Sb and Se/Te, exhibit a nearly identical contrast in the HAADF-STEM image although an intensity of HAADF-STEM image is approximately proportional to the square of the atomic number (Z). Figures 2d-f depict atomic resolution elemental mappings by STEMenergy dispersive spectroscopy (EDS) recorded from the red rectangle in Figure 2c. EDS signals of Pb, Se, and Te atoms are represented in yellow, green, and purple color, respectively. These provide the direct observation of crystal structure of Pb0.95Sb0.033Se0.6Te0.4 at the atomic level. Elemental segregation is not observed. Typical medium-resolution HAADF-STEM image clearly shows distinguished nanoscale features in the Pb0.95Sb0.033Se0.6Te0.4 sample (Figures 3a-b). The characteristic continuous networks of tangled dislocation loops found in the Pb0.95Sb0.033Se sample are broken into much shorter and linear fragments (Figure S4). Their ND estimated from TEM images is reduced by an order of magnitude to ~3 × 1011 cm-2 compared with that of Pb0.95Sb0.033Se. Larger and darker nanoprecipitates (>10 nm) are observed at the tip of fragmented dislocation lines, and smaller and brighter nanoprecipitates (~5 nm) aggregate along dislocation lines. Those nanoprecipitates are not observed in the Pb0.95Sb0.033Se sample that has only heavy dislocations. Figure 3b focuses on two individual dislocation lines grown in the matrix. A sharp contrast difference between the dislocation lines and the matrix indicates mass fluctuations across them according to the Z-contrast profile. A darker contrast on the dislocation lines can be attributed to vacancies in the PbSe crystal structure as discussed earlier. High-magnification HAADF-STEM image taken in the middle of the 8 ACS Paragon Plus Environment

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dislocation line clearly demonstrates that atomic arrays collapse in this vacancy-abundant region and thereby trigger the edge dislocations (Figure 3c). The dislocation lines and the matrix form a highly coherent interface with the crystallographic alignment.

Figure 3. Typical STEM images and elemental mappings for dislocation lines in the Pb0.95Sb0.033Se0.6Te0.4 sample. (a) Medium-magnification STEM image showing the defect architecture embedded in the matrix. Dark lines are dislocation lines. On their tips, large nanoprecipitates (marked by a red circle) are nucleated, indicating their capability of terminating the propagation of dislocations. Small, bright nanoprecipitates are segregated along dislocation lines. (b) High-magnification HAADF-STEM image showing two individual dislocation lines embedded in the matrix. Signal intensity of Z-contrast across them and the matrix taken by a line profile is displayed over the corresponding HAADF-STEM image. (c) High-magnification atomic-resolution HAADF-STEM image taken on the middle of dislocation lines. Edge dislocations and discontinuities of atomic arrays are clearly seen. (d) Atomic resolution elemental mapping by STEM-EDS scanned on the entire area in (c), presenting distribution of respective constituent atom. It is created by combining the 9 ACS Paragon Plus Environment


respective EDS signal directly recorded from (e) Sb, (f) Pb, (g) Se, and (h) Te atoms. Highmagnification atomic-resolution (i) HAADF-STEM and (j) ABF-STEM images taken on the tip of the dislocation line. Edge dislocations and discontinuities of atomic arrays are clearly observed. (k) Atomic resolution elemental mapping by STEM-EDS scanned on the whole region in (i), clearly revealing the Te-rich nanoprecipitate nucleated at the tip of the dislocation line. This is joint image of each EDS signal directly given by (l) Pb, (m) Se, and (n) Te atoms. Figure 3c shows atomic resolution elemental mappings by STEM-EDS (Figure 3d). It is created by overlapping the respective EDS signal from the constituent Sb, Pb, Se, and Te atoms displayed in Figures 3e-h. These results directly show elemental distribution across the dislocation line and the matrix. Importantly, Pb, Se, Te atoms are definitely deficient in the dislocation line. Contrarily, Sb atoms are more abundant in that region than the matrix, demonstrating significant mass fluctuations between them. Our HAADF-STEM and STEMEDS results suggest the formation mechanism for dislocations in Pb0.95Sb0.033Se and Pb0.95Sb0.033Se1-yTey. Vacancies seems to help dislocations bypass obstacles and propagate ceaselessly by a dislocation climb process.53 Indeed, we observed a large degree of vacancies in dislocation lines, confirming the mechanism of vacancy-driven dislocations. It must be thermodynamically favorable for Sb3+ to pair with vacancies for reducing charge imbalance and lattice strains in the Pb2+Se2- lattice. Sb3+ and Pb2+ also show the significantly different preference for coordination geometry, namely, trigonal pyramid and stiff octahedron, respectively. Accordingly, Sb atoms are forced to reside in dislocation lines. Figures 3i and 3j show representative HAADF- and ABF-STEM images taken at the tip of dislocation lines. It should be noted that large nanoprecipitates are typically attached at this tip (Figure 3a) and that the edge dislocations are clearly observed. The atomic arrays are well-aligned between the dislocation tip and the matrix, exhibiting highly coherent interfaces as observed in the main body of the dislocation lines. Figure 3k shows the corresponding atomic resolution elemental mappings by STEM-EDS. This is the overlapped EDS signals from respective Pb, Se, and Te atoms. Pb and Se atoms are nearly missing in the tip as in the main body. Interestingly, Te atoms are more abundant in the tip than in the matrix (Figure 3l10 ACS Paragon Plus Environment

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n), and they are deficient in the main body. This observation can be explained by the considerable difference in bond distance and bond enthalpy of Pb-Q bonds (Q = S, Se, Te): 3.03, 3.17, and 3.4 Å;54 320.7, 302.9, and 249.8 kJ mol-1 in an octahedral geometry,55 respectively. It requires large energy to break Pb-Se bonds and distribute Te homogeneously into the Se lattices in Pb0.95Sb0.033Se1-yTey. Consequently, it is thermodynamically favorable for Te atoms to flocculate into vacancy-rich dislocation lines. Furthermore, the dislocation tip penetrates and continuously propagates into crystal lattices, consequently having a higher degree of Gibbs free energy than the main body of dislocations and the matrix. As a result, Te-rich particles would nucleate and grow at the tip preferentially to reduce lattice imperfections and overall Gibbs free energy of the materials. Indeed, elemental analysis by STEM-EDS shows a ~46% higher Te/Se ratio in the tip than in the main body of dislocations (Table S1). When Te atoms are accumulated at the tip above a certain level, their growth by a dislocation climb process is no longer allowed and is ceased. These mechanisms are consistent with our STEM results. We further confirmed the proposed mechanisms by alloying Te more than 50%. For the Pb0.95Sb0.033Se0.5Te0.5 sample, dislocations disappear completely. Instead, a significant degree of large Te-rich nanoparticles (~20 - 50 nm) are observed (Figure S5). Figure 4a shows HAADF-STEM image taken on small nanoprecipitates generated along dislocation lines as observed in Figure 3a. They are brighter than dislocation lines and the matrix with a number density of Np ~1018 cm-3 and a typical diameter of ~5 nm (Figure 4a). High-magnification HAADF- and ABF-STEM images reveal a coherent individual nanoprecipitate embedded in the matrix (Figures 4b and 4c). Neither edge dislocations nor discontinuities at the interface confirm an endotaxial relationship between the small nanoprecipitates and the matrix. However, a sharp contrast difference indicates mass fluctuations between them. According to atomic resolution elemental mappings by STEMEDS for the entire area in Figure 4b, Te atoms are more abundant in small nanoprecipitates 11 ACS Paragon Plus Environment


than in the matrix. The other atoms do not give a discernible difference in abundance throughout them (Figures 4d and e-g). Richer Te contents and no apparent vacancies on small nanoprecipitates are ascribed to brighter signals in HAADF-STEM image and vice-versa in ABF-STEM image. They exhibit a ~14% smaller Te/Se ratio than the tips of dislocation lines.

Figure 4. Typical STEM images and elemental mappings for small nanoprecipitates generated along dislocation lines in the Pb0.95Sb0.033Se0.6Te0.4 sample. (a) HAADF-STEM image taken on the area near dislocation lines, showing ~5 nm nanoprecipitates, marked by the red circles. They appear brighter than the matrix. (b) Atomic resolution HAADF-STEM image of the individual nanoprecipitate. Signal intensity of Z-contrast across the nanoprecipitate taken by a line profile, showing a higher brightness at the nanoprecipitate. (c) The corresponding ABF-STEM image to (b). Atomic resolution elemental mapping by STEM-EDS scanned on the entire area in (b), clearly revealing Te is more abundant in the nanoprecipitate than the matrix. It is created by combining EDS signals directly recorded from (e) Pb, (f) Se, and (g) Te atoms, respectively.

2.3. Thermal transport properties Figure 5a shows the temperature-dependent κlat for Pb0.95Sb0.033Se1-yTey (y = 0. 0.1, 0.2, 0.3, and 0.4) samples. It is compared with the literature values of PbSe0.995Cl0.00556 and Pb0.995Sb0.005Se28 that contain point defects by normal doping. The latter also contains extensive nanoprecipitates. Pb0.95Sb0.033Se exhibits much lower κlat than PbSe0.995Cl0.005 and 12 ACS Paragon Plus Environment

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Pb0.995Sb0.005Se over the nearly entire temperature range, demonstrating that heavy dislocations can reduce κlat more effectively than point defects and nanoprecipitates. Subsequent Te alloying in Pb0.95Sb0.033Se further decreases κlat, especially above 625 K. The sample with y = 0.4 displays distinctively lower κlat than the other samples, showing a minimum value of ~0.4 W m-1 K-1 at 823 K, which approaches to the amorphous limit of κlat.

Figure 5. (a) Experimental temperature-dependent lattice thermal conductivities (κlat) of Pb0.95Sb0.033SeyTe1-y in comparison with the reported values of PbSe0.995Cl0.00556 and Pb0.995Sb0.005Se.28 (b) The calculated κlat at 300 K with respect to the degree of Te alloying based on the Klemens model (blue curve). PbSe1-yTey is assumed to form perfect solid solutions. The red square denotes the experimental κlat for PbSe1-yTey from the literature,22 excellently consistent with our calculation results. Experimental κlat for Pb0.95Sb0.033SeyTe1-y (orange circle) exhibits much lower values than those of PbSe1-yTey. Since the Pb0.95Sb0.033Se1-yTey samples are embedded with complex defect architecture composed of point defects, nanoprecipitates, and dislocations, we performed theoretical 13 ACS Paragon Plus Environment


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calculations to elucidate their effects on the markedly reduced κlat. We first calculated the dependence of κlat with respect to the mole fraction of Te in PbSeyTe1-y (0 ≤ y ≤ 1) based on the Klemens model57 (see Supporting Information for the details) to understand the role of point defects by Te alloying. We assumed that PbSeyTe1-y forms perfect solid solutions. The calculation results agree well with the experimental κlat for PbSeyTe1-y in the literature (Figure 5b).22 However, the experimental κlat of Pb0.95Sb0.033Se1-yTey samples is much lower than the theoretical and experimental κlat of PbSeyTe1-y, even considering the difference in their chemical compositions. This result indicates that the very low κlat of Pb0.95Sb0.033Se1-yTey samples can benefit from various defects uniquely integrated in them. We then calculated the temperature-dependent κlat of Pb0.95Sb0.033Se0.6Te0.4 and Pb0.95Sb0.033Se by the modified Debye-Callaway model49 (see Supporting Information for details). The κlat can be expressed as the eq 1: ௞

௞ಳ ் ଷ ఏీ ௫ర௘ ೣ ) ‫׬‬଴ ߬୲୭୲ (‫ )ݔ‬ೣ మ ݀‫ݔ‬ ℏ (௘ ିଵ)

κ୪ୟ୲ = ଶగామ ௩ (

(1)

where kB is the Boltzmann constant, ħ is the reduced Planck constant, ω is the phonon frequency, x is defined as ħω/kBT, and τtot is the total phonon scattering relaxation time. Here we considered various defects present in the samples observed by our STEM studies. Hence, τtot can be attributed to the scattering from normal (N) and Umklapp (U) processes, point defects (PD), nanoprecipitates (NP), dislocation cores (DC), and dislocation strains (DS) -1 according to the Matthiessen’s equation τ-1tot = τ-1N + τ-1U + τ-1PD + τNP + (τ-1DC + τ-1DS).

The blue and orange lines in Figure 6a represent the calculated κlat for Pb0.95Sb0.033Se and Pb0.95Sb0.033Se0.6Te0.4 considering dislocations with ND of 2 × 1012 and 3 × 1011 cm-2, respectively, according to our STEM studies. Umklapp and normal processes are the default for all our calculations. The calculated κlat of the former matches well with the experimental data up to 675 K, indicating that phonons are mainly scattered by dislocations. The gradual deviation above 675 K seems to result from bipolar diffusion or a disappearance of 14 ACS Paragon Plus Environment

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dislocations in high temperatures. The calculated κlat of the latter would be higher than that of the former if only dislocations with the decreased ND are considered, which greatly diverges from the experimental values. It agrees well with the experimental values when the contribution of nanoprecipitates and point defects by Te alloying are applied to the calculations. It should be noted that the effect of point defects is a minor factor in κlat. These results show the effectiveness of the defect architecture for lowering κlat.

Figure 6. (a) The calculated temperature-dependent lattice thermal conductivity (κlat) by the modified Debye-Callaway model based on various phonon scattering mechanisms (solid lines). The orange and blue lines reflect the contribution only from dislocations with a density (ND) of 3 × 1011 for Pb0.95Sb0.033Se0.6Te0.4 and 2 × 1012 cm-2 for Pb0.95Sb0.033Se, respectively. The red line involves scattering by dislocations (DS, ND = 3 × 1011 cm-2), point defects (PD), and nanoprecipitates (NP). Umklapp (U) and normal (N) processes are the default for all calculations. Experimental κlat for Pb0.95Sb0.033Se (green dots) and Pb0.95Sb0.033Se0.6Te0.4 (orange dots) is given for comparison. (b) The calculated spectral thermal conductivity (κs) with respect to the phonon frequency at 300 K, based on various phonon scattering mechanisms. The area below the line corresponds to the κlat. Black line, involving only U 15 ACS Paragon Plus Environment


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contribution; blue line, only DS with ND of 3 × 1011 cm-2; purple line, only DS with ND = 2 × 1012 cm-2; red line, DS with ND = 3 × 1011 cm-2 and NP; navy line, DS with ND = 3 × 1011 cm-2, NP, and PD. Figure 6b shows the calculated spectral lattice thermal conductivity (κs) of Pb0.95Sb0.033Se and Pb0.95Sb0.033Se0.6Te0.4 with respect to the phonon frequency (ω) at 300 K (see the Supporting Information for the details). The κs can be expressed by the eq 2: ௞

κୱ = ଶగామ ௩ (

௞ಳ ் ଷ ௫ర ௘ೣ ) ߬୲୭୲ (‫ )ݔ‬ೣ మ ℏ (௘ ିଵ)

(2)

The κlat is the integral of the κs with respect to the ω according to the eq 1 and 2. The area under a κs curve corresponds to κlat, which is attributed to the contribution of the specified defects involved in the calculations. Heavy dislocations with ND of 2 × 1012 cm-2 in Pb0.95Sb0.033Se depresses κlat significantly at low- and mid-ω regions. The decreased ND of 3 × 1011 cm-2 in Pb0.95Sb0.033Se0.6Te0.4 should have resulted in a weaker depression in κlat. However, the defect architecture involving nanoprecipitates and point defects in Pb0.95Sb0.033Se0.6Te0.4 suppresses κlat considerably in low- and high-ω regions. This integrated effect lowers its κlat in a wide range of ω, consistent with our experimental observations. 2.4. Electrical transport properties We conducted the temperature-dependent Hall effect measurement for the Pb0.95Sb0.033Se and Pb0.95Sb0.033Se0.6Te0.4 samples to investigate the effect of the defect architecture on electrical transport properties (Figure 7a). Defects caused by alloying can ambivalently influence ZT in that they typically reduce κlat and carrier mobility (µ) simultaneously. Hence, it is important to find alloying elements that can maximally reduce κlat and minimally sacrifice µ. Very unusually, Te alloying on Pb0.95Sb0.033Se significantly improves

both

the

Hall

mobility

(µH)

and

concentration

(nH).

For

example,

Pb0.95Sb0.033Se0.6Te0.4 shows nearly four times larger µH and nH than Pb0.95Sb0.033Se at 300 K. Typically µH decreases with increasing nH because of a more frequent collision of charge carriers. Also, isovalent Te alloying would not be expected to change nH. At presence, it is 16 ACS Paragon Plus Environment

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unclear why nH increases with the higher faction of Te alloying. Because each defect can influence µH differently, we calculated the dependence of µH with respect to nH based on the single Kane band model58 using the eq 3: ಮ

ങ೑

మ య/మ షభ ௘ ‫׬‬బ (ିങഄ )ఛ౪౥౪ (ఌ)(ఌାఈఌ ) (ଵାଶఈఌ) ௗఌ ಮ ങ೑ ‫׬‬బ (ି ങഄ )(ఌାఈఌ మ )య/మ ಺

ߤ = ௠∗

(3)

where τtot is the total carrier scattering relaxation time, ε is the reduced carrier energy defined as E/kBT. The relaxation time for acoustic phonon (τA), point defects (τPD), nanoprecipitates (τNP), and dislocations (τDS) is used for calculations (See Supporting Information for the details). The calculated µH based on only acoustic phonon scattering is larger than ~400 cm2 V1 -1

s in a wide range of nH (red line, Figure 7b). It fits well with the reported values for pristine

PbSe.22,59 Pb1-xSbxSe (x = 0.00075 and 0.00125) with extensive nanoprecipitates also shows an excellent agreement with the calculation results, demonstrating weak electron scattering by the nanoprecipitates.28 Heavy dislocations with ND of 2 × 1012 cm-2 considerably decrease the

µH by one to two orders of magnitude to less than 50 cm2 V-1 s-1 (pink line). Dense dislocations with the tuned ND of 3 × 1011 cm-2, coupled with nanoprecipitates and point defects, does not considerably depress µH. The calculated µH of Pb0.95Sb0.033Se0.6Te0.4 becomes close to those of defect-free, pristine PbSe. The calculation results are consistent with our experimental observations. These clearly demonstrate the validity of the defect architecture that rationally integrate multiple scattering mechanisms for phonons and electrons to maximize a ratio of µH to κlat for attaining high ZT.



Figure 7. (a) Experimental temperature-dependent carrier mobility (µH) and concentration (nH) by the Hall effect measurement for Pb0.95Sb0.033Se and Pb0.95Sb0.033Se0.6Te0.4. (b) The calculated µH with respect to nH (solid lines) based on various phonon scattering mechanisms. The red line reflects only acoustic (A) contribution; pink line acoustic and dense dislocations (DS) (ND = 2 × 1012 cm-2); blue line acoustic, dislocations (ND = 3 × 1011 cm-2), point defects (PD), and nanoprecipitates (NP). Experimental values for pristine PbSe (purple dots) and PbSe with extensive nanoprecipitates (pink dots) from the literatures22,28,59 are given for comparison. The green dots present the experimental µH for Pb0.95Sb0.033Se0.6Te0.4.

Te alloying in Pb0.95Sb0.033Se1-yTey markedly improves the electrical conductivity (σ) over the entire range of temperature (Figure 8a). It suppresses growth of dislocations into shortened fragments, thereby gradually decreasing ND and improving µH. As a consequence, σ increases with the higher degree of Te alloying. σ at 300 K is ~300 and ~1200 S cm-1 for the sample with y = 0 and 0.4, respectively. Though the increased σ results in the decreased Seebeck coefficient due to the single conduction band nature of n-type PbSe (Figure 8b), the 18 ACS Paragon Plus Environment

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PF is considerably enhanced by Te alloying (Figure 8c). It significantly enhances the σ and the consequent PF as well as depresses the κlat at the same time, ultimately boosting ZT from ~0.8 for Pb0.95Sb0.033Se to ~1.5 for Pb0.95Sb0.033Se0.6Te0.4 at 823 K (Figure 1). The achieved ZT is much higher than that of PbSe systems containing only either dense dislocations51 or nanoprecipitates28 in the literatures and in this work. We also prepared and characterized the three individual samples of Pb0.95Sb0.033Se0.6Te0.4 from the independent syntheses, and confirmed that high thermoelectric properties of Pb0.95Sb0.033Se0.6Te0.4 are highly reproducible (Figure S7). A negligible deviation is found for σ, S, and κtot of Pb0.95Sb0.033Se0.6Te0.4 with respect to temperature during heating and cooling processes, indicating high thermal and chemical robustness of this material (Figure S8).



Figure 8. Temperature-dependent (a) electrical conductivity, (b) Seebeck coefficient, (c) power factor for Pb0.95Sb0.033Se1-yTey. 3. Conclusion Pb0.95Sb0.033Se1−yTey (y = 0 – 0.4) has complex defect architecture composed of point defects, nanoprecipitates, and dense dislocations. The multiple mechanisms for phonon scattering leads to glass-like lattice thermal conductivity of ~0.4 W m−1 K−1 at 823 K for the x = 0.4 sample. Te alloying is a key to the defect system. It spontaneously generates 20 ACS Paragon Plus Environment

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nanoprecipitates that impede growth of dislocations. On that account, a fine manipulation of its fraction is a means of balancing the density of dislocations and nanoprecipitates. Consequently, it enables to attain a maximized ratio of carrier mobility to lattice thermal conductivity, because endotaxial nanoprecipitates in the matrix for our system marginally affects carrier mobility. Indeed, as the Te content increases in Pb0.95Sb0.033Se1-yTey, carrier mobility increases and lattice thermal conductivity decreases. Consequentially, the y = 0.4 sample exhibits a remarkably high ZT of ~1.5 at 823 K for n-type PbSe materials, resulting from the enhanced power factor and depressed lattice thermal conductivity. Importantly, the defect architecture in this work is rationally designed given thermodynamic stabilization of vacancy, higher valent Sb3+, and larger Te2- impurities in the Pb2+Se2- matrix. As a consequence, it can be readily stabilized in bulk thermoelectrics without complicated synthesis procedures, thereby suitable for mass production of thermoelectric materials. We also unveil the formation mechanisms of dislocations and nanoprecipitates embedded in the matrix employing atomic resolution Cs-corrected STEM. Our results can provide a platform to readily design desirable nanoscale defect structures in bulk materials with the high level of predictability.

4. Experiment Section Synthesis. Elemental Pb, Sb, Te, and Se (99.999%, American Elements) were used as received. Ingots (~12g) with nominal compositions Pb0.95Sb0.033Se1-yTey (y = 0, 0.1, 0.2, 0.3, 0.4) were synthesized by reacting a corresponding molar ratio of constituent elements in an evacuated fused silica tube (~10−5 torr) at 1423 K for 6 h, followed by quenching to ice water. The obtained ingots were annealed at 923 K for 48 h and naturally cooled to room temperature. The products were hand-ground by an agate mortar and pestle into fine powders in an Ar-filled glove box. The resulting powder was densified at 923 K for 5 min under an axial pressure of 50 MPa in a vacuum using spark plasma sintering (SPS) (SPS-211Lx, Fuji 21 ACS Paragon Plus Environment


Electronic Industrial Co., Japan). After SPS, a cylindrical sample with a thickness of ~12.7 mm and a diameter of 12 mm was obtained.

Characterization. Powder X-ray diffraction patterns for all samples were obtained using Cu Kα (λ = 1.5418 Å) graphite monochromatized radiation on a SmartLab Rigaku powder X-ray diffractometer operating at 40 kV and 20 mA. To measure charge transport properties, the SPS processed samples were cut and polished into various shapes and dimensions. The Seebeck coefficient and electrical conductivity were simultaneously recorded for bar-shaped samples with dimensions of ~12 × 3 × 3 mm3 by an ULVAC-RIKO ZEM-3 instrument under a low-pressure He atmosphere from room temperature to 873 K. Temperature-dependent thermal diffusivities were measured for disks with a diameter of 8 mm and a thickness of 1.5 mm using the laser flash diffusivity method in a Netzsch LFA 457 instrument. The samples were spray-coated by graphite. The thermal conductivity was calculated by the relation κtot = ρDCp, where ρ is the mass density calculated from the geometrical dimensions and masses of the samples (Table S4), D is the measured thermal diffusivity, and Cp is the temperaturedependent heat capacity obtained from the previous report.60 The electronic contribution to total thermal conductivity was calculated based on the relation κele = LσT, where L is the Lorenz number calculated from the single parabolic band model (See Supporting Information for details), σ is the electrical conductivity, and T is the absolute temperature. Lattice vibration contribution κlat was calculated by the relation κlat = κtot − κele. The temperaturedependent Hall effect measurement were performed from 300 to 873 K under an ultrahigh vacuum (

Defect Engineering for High-Performance n-Type PbSe

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