Article pubs.acs.org/JACS
Cite This: J. Am. Chem. Soc. 2018, 140, 9282−9290
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
‡
J. Am. Chem. Soc. 2018.140:9282-9290. Downloaded from pubs.acs.org by UNIV OF SUSSEX on 08/10/18. For personal use only.
S Supporting Information *
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 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. 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 toward high ZT are mostly aimed at either increasing 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
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). © 2018 American Chemical Society
Received: May 31, 2018 Published: June 29, 2018 9282
DOI: 10.1021/jacs.8b05741 J. Am. Chem. Soc. 2018, 140, 9282−9290
Article
Journal of the American Chemical Society
30% lower κlat than Pb0.95Sb0.33Se only with heavy dislocations. We 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.
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. 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 zerovalent vacancies for balancing charge in the vicinity of these aliovalent impurities in the Pb2+Se2− lattices. This induces heavy dislocations with a density (ND) of 2 × 1012 cm−2 for the sample with x = 0.05, that is, 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 vacancyabundant regions, that is, 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 toward ∼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
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
Figure 1. Temperature-dependent ZT for Pb0.95Sb0.033Se1−yTey (y = 0−0.4).
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 Pb0.95 Sb0.033Se. 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. 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 (Figures S2 and 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 ⟨100⟩ 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 9283
DOI: 10.1021/jacs.8b05741 J. Am. Chem. Soc. 2018, 140, 9282−9290
Article
Journal of the American Chemical Society
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 ED 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 rock-salt PbSe structure at the atomic level. The PbSe structure is drawn over the direct EDS signal of Pb in (d).
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 Pb0.95Sb0.033 Se0.6Te0.4 sample (Figure 3a,b). The characteristic continuous networks of tangled dislocation loops found in the Pb0.95 Sb0.033Se 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 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 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, and 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 STEM-EDS results suggest the formation mechanism for dislocations in Pb0.95Sb0.033Se and Pb0.95Sb0.033Se1−yTey. Vacancies
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). We employed atomic resolution spherical aberrationcorrected scanning TEM (Cs-corrected STEM) to unveil evolution mechanisms of the nanoscale defects in the Pb0.95Sb0.033 Se0.6Te0.4 sample. Figure 2a shows representative lowmagnification 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 a single set of Bragg diffraction spots that correspond to the PbSe structure along the ⟨100⟩ zone axis, indicating that the dislocations and nanoprecipitates have similar structure and lattice parameters to the matrix. Figure 2b,c presents 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 ⟨100⟩ zone axis. As a consequence, adjacent atoms, that is, Pb/Sb and Se/Te, exhibit a nearly identical contrast in the HAADF-STEM image, although an intensity of HAADFSTEM image is approximately proportional to the square of the atomic number (Z). Figure 2d−f depicts atomic resolution elemental mappings by STEM-energy 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 colors, respectively. These provide the direct 9284
DOI: 10.1021/jacs.8b05741 J. Am. Chem. Soc. 2018, 140, 9282−9290
Article
Journal of the American Chemical Society
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) Highmagnification 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 respective EDS signal directly recorded from (e) Sb, (f) Pb, (g) Se, and (h) Te atoms. High-magnification 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.
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).
seem 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. Figure 3i,j shows 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. These are 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 3l−n), and they are deficient in the main body. This observation can be 9285
DOI: 10.1021/jacs.8b05741 J. Am. Chem. Soc. 2018, 140, 9282−9290
Article
Journal of the American Chemical Society
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.
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 HAADFand ABF-STEM images reveal a coherent individual nanoprecipitate embedded in the matrix (Figure 4b,c). 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 STEM-EDS for the entire area in Figure 4b, Te atoms are more abundant in small nanoprecipitates than in the matrix. The other atoms do not give a discernible difference in abundance throughout them (Figure 4d−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. 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 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. Since the Pb0.95Sb0.033Se1−yTey samples are embedded with complex defect architecture composed of point defects, nanoprecipitates, and dislocations, we performed theoretical calculations to elucidate their effects on the markedly reduced κlat. We first calculated the dependence of κlat with respect to
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.
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 9286
DOI: 10.1021/jacs.8b05741 J. Am. Chem. Soc. 2018, 140, 9282−9290
Article
Journal of the American Chemical Society 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 Pb0.95 Sb0.033Se0.6Te0.4 and Pb0.95Sb0.033Se by the modified Debye− Callaway model49 (see Supporting Information for details). The κlat can be expressed as the eq 1: κlat =
kB ij kBT yz jj zz 2π 2v jk ℏ z{
3
∫0
θD
τtot(x)
x 4e x dx (e − 1)2 x
(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) according to the Matthiessen’s −1 −1 −1 −1 −1 −1 equation τ−1 tot = τN + τU + τPD + τNP + (τDC + τDS). 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 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 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: kB ij kBT yz x 4e x jj zzz τtot(x) x 2 j 2π v k ℏ { (e − 1)2
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 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.
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, Pb0.95Sb0.033 Se0.6Te0.4 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 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:
3
κs =
(2)
The κlat is the integral of the κs with respect to the ω according to eqs 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 depress κlat significantly at low- and mid-ω regions. The decreased ND of 3 × 1011 cm−2 in Pb0.95 Sb0.033Se0.6Te0.4 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
∞
e ∫0 μ= mI*
∂f ∂ε
(− )τ
tot(ε)(ε ∞
∫0
∂f ∂ε
+ αε 2)3/2 (1 + 2αε)−1dε
(− )(ε + αε )
2 3/2
(3) 9287
DOI: 10.1021/jacs.8b05741 J. Am. Chem. Soc. 2018, 140, 9282−9290
Article
Journal of the American Chemical Society
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.
where τtot is the total carrier scattering relaxation time, and 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 V−1 s−1 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 1−2 orders of magnitude to
