Enhanced Density-of-States Effective Mass and Strained Endotaxial

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Functional Inorganic Materials and Devices

Enhanced Density-of-states Effective Mass and Strained Endotaxial Nanostructures in Sb-doped Pb0.97Cd0.03Te Thermoelectric Alloys Gangjian Tan, Xiaomi Zhang, Shiqiang Hao, Hang Chi, Trevor Paul Bailey, Xianli Su, Ctirad Uher, Vinayak P. Dravid, Christopher Wolverton, and Mercouri G. Kanatzidis ACS Appl. Mater. Interfaces, Just Accepted Manuscript • DOI: 10.1021/acsami.8b21524 • Publication Date (Web): 04 Feb 2019 Downloaded from http://pubs.acs.org on February 7, 2019

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ACS Applied Materials & Interfaces

Enhanced

Density-of-states

Effective

Mass

and

Strained Endotaxial Nanostructures in Sb-doped Pb0.97Cd0.03Te Thermoelectric Alloys Gangjian Tan1,*, Xiaomi Zhang2, Shiqiang Hao2, Hang Chi3, Trevor P. Bailey3, Xianli Su1,4, Ctirad Uher3, Vinayak P. Dravid2, Chris Wolverton2, and Mercouri G. Kanatzidis4,*

1State

Key Laboratory of Advanced Technology for Materials Synthesis and Processing, Wuhan University of Technology, Wuhan 430070, China 2Department

of Materials Science and Engineering, Northwestern University, Evanston, Illinois 60208, United States 3Department

of Physics, University of Michigan, Ann Arbor, Michigan 48109, United

States 4Department

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

States

Corresponding Authors: [email protected] (G. T.), [email protected] (M. K.)

1 ACS Paragon Plus Environment

ACS Applied Materials & Interfaces 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Here we report that CdTe alloying and Sb doping increase the density-of-states effective mass and introduce endotaxial nanostructuring in n-type PbTe resulting in enhanced thermoelectric performance. A prior theoretical prediction for the presence of resonance states in the conduction band of this system, however, could not be confirmed. An amount of 3 mol% CdTe alloying widens the band gap of PbTe by 50%, leading to enhanced carrier effective mass and Seebeck coefficient. This effect is even more pronounced at high temperatures where the solubility of CdTe increases. At 800 K, when the carrier concentration is the same (4×1019 cm-3), the Seebeck coefficient of CdTealloyed PbTe is -195 μVK-1, 16% higher than that of Cd-free control sample (-168 μVK1).

Sb doping considerably increases the electron concentration of Pb0.97Cd0.03Te, giving

rise to optimized power factors of ~17 μWcm-1K-2 at 800 K. More importantly, Sb induces strained endotaxial nanostructures evenly distributed in the matrix. These Sb-rich nanostructures account for the ~40% reduction in the lattice thermal conductivity over the whole measured temperature range. As a result, a maximum ZT of 1.2 is attained at 750 K in 0.5 mol% Sb-doped Pb0.97Cd0.03Te alloys. Keywords: Thermoelectric; Lead telluride; Nanostructuring; Electronic structure; Thermal conductivity


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INTRODUCTION With more than two-thirds of utilized energy being lost as waste heat, there is compelling motivation for developing high-performance thermoelectric materials that can directly convert heat into electricity.1 The thermal-to-electrical energy conversion efficiency

is

evaluated

by

the

materials’

dimensionless

figure

of

merit

ZT=S2T/tot=S2T/(car+lat), where S is the Seebeck coefficient,  is the electrical conductivity, T is absolute temperature, and tot is the total thermal conductivity which is the sum of contributions from carrier migrations (car) and lattice vibrations (lat). These physical parameters are strongly interrelated, for example, car relates to  through the Wiedemann-Franz law car=LT (L is Lorenz number), which makes it quite challenging to independently optimize ZT.2-3 It has been demonstrated that band structure engineering (to improve S without obviously deteriorating )4-6 and/or nanostructuring (to decrease

lat without degrading  too much)7-10 can to some extent decouple those parameters and enhance ZT of IV-VI group semiconductors and many other materials. In the mid-temperature range (400-900 K) where thermoelectric power generation becomes highly relevant, p-type PbTe has the highest performance reported so far, with the maximum ZT exceeding 2 and average ZT exceeding 1.5.9-11 The high thermoelectric performance of hole-doped PbTe mainly stems from its unique valence band structure12 which has been validated by angle resolved photoemission spectroscopy (ARPES) studies.13 There is a primary light hole band at the L point (L valence band, valley degeneracy NV=4) of PbTe, followed by a second lower-lying heavy hole band at the Ʃ point (Ʃ valence band, valley degeneracy NV=12). At 300 K, the two valence bands are separated by an energy difference (∆EL-Ʃ) of only ~0.15-0.20 eV.14 Upon heating15 or alloying with some specific elements such as Mg,16 Sr,11 Cd17 or Mn,18 ∆EL-Ʃ can be further reduced to within a few kBT (kB is the Boltzmann constant). This leads to effective valence band convergence,5 i.e., an increase of total band valley degeneracy NV from 4 to ~16, which enables much enhanced S but has little detrimental influence on . Therefore, valence band convergence is believed to significantly improve the power factors of ptype PbTe.5, 11



Though ultrahigh ZT values have been demonstrated in p-type PbTe, the n-type counterpart seems to be less efficient as thermoelectric materials. ZT around unity19-21 is commonly reported for n-type PbTe, though in a very few studies people claim higher values of ~1.5.22-24 It is known that for practical thermoelectric use, both n- and p-type materials with comparable thermoelectric properties are required. It is therefore important to continue to develop high performance n-type PbTe materials with excellent repeatability. The ZT mismatch between n- and p-type PbTe is mainly originated from the difference in the conduction and valence band electronic structures. The conduction band at the L point of the Brillouin zone of PbTe is nonparabolic and has a low valley degeneracy NV of only 4.25 This L conduction band is the only band involved in charge transport of n-type PbTe, and a single Kane band model26-27 is adequate to describe the electronic transport behavior with reasonable accuracy. For this reason, n-type PbTe has much lower Seebeck coefficients than its p-type counterparts at comparable doping levels.21 To improve the S of n-type PbTe, researchers have tried to introduce resonant levels near the Fermi energy in the conduction band, for example, by Cd,19 Ti,28 Cr29 , Zn30 or Ga31 doping. However, experimentally, no significant enhancement of S has been observed in n-type PbTe doped with these elements. For example, previously, motivated by a theoretical hypothesis32 that Cd atoms on Pb sites of the rock salt lattice can increase the Seebeck coefficient of n-type PbTe via the formation of a resonant level in the density of states, we investigated the thermoelectric transport properties of a series of PbTe-CdTe alloys doped heavily with PbI2 or Sb (electron concentration n>2×1019 cm-3)19. We found that all samples follow the Pisarenko relationship at room temperature, and no enhancement of the Seebeck coefficient could be attributed to a resonant level. However, one should keep in mind that Seebeck coefficient enhancement from resonant level effects is very sensitive to the position of the Fermi level (doping concentration)4, 33. In this study, we revisit the n-type PbTe-CdTe system and explore lower electron densities spanning from 5×1018 cm-3 to 4×1019 cm-3 using Sb as the dopant. We find that at room temperature, when doping levels are relatively low (n1×1019 cm-3, the enhancement of S becomes trivial,


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which is consistent with our earlier findings. We attribute the unusual increase of S to two facts: (i) CdTe alloying largely increases the band gap of PbTe and subsequently enhances S because of the increased effective mass; (ii) The alloying solubility of CdTe in PbTe decreases as Sb content is increased, which weakens the bandgap enlargement effect. However, at elevated temperatures (T=600-800 K), regardless of Sb content, all PbTe-CdTe alloys show significantly larger S than the referential PbTe sample. This can be ascribed to the positive temperature coefficient of the solubility of CdTe in PbTe resulting in continuous bandgap enlargement. We conclude that Cd does not introduce resonant levels inside the conduction band of PbTe that increase Seebeck coefficient particularly around room temperature. Based on our electron microscopy observations, Sb doping induces strained endotaxial nano-precipitates (PbmSb2nTem+3n) in PbTe, which strongly decrease lat by ~40% in the entire measured temperature range. The enhanced Seebeck coefficient coupled with decreased lattice thermal conductivity leads to a maximum ZT of 1.2 at 750 K in n-type Sb-doped Pb0.97Cd0.03Te.

RESULTS AND DISCUSSION Phase purities and microstructures Previous studies have shown that the solubility of CdTe in PbTe is strongly temperature dependent34 and usually 3 mol% of CdTe is chosen as suitable for investigating the thermoelectric properties of PbTe-CdTe alloys17, 35. Sb is employed as electron dopant to tune the carrier concentration of Pb0.97Cd0.03Te. The synthesis and sintering procedures can be found in Experimental section in the Supporting Information. The SPS-processed PbTe and Pb0.97-xSbxCd0.03Te (x=0-0.01) alloys are highly dense (>97% of theoretical density, Table S1) and show single phase rock salt structure within the detection limit of laboratory powder X-ray diffraction (XRD), Figure 1(a). We obtained the room temperature carrier concentrations (n) of our Pb0.97-xSbxCd0.03Te samples using Hall measurements, and compared them with those of I-26 and La-doped27 PbTe samples reported in the literature, Figure 1(b). In all samples, n increases gradually with increasing doping concentration (x), consistent with the electron donor role of Sb and La replacing Pb and I substituting Te. Moreover, for La- and I-doped PbTe, the experimental



n falls exactly on the theoretical curve (solid black line) on the assumption that each substitutional atom releases one free electron into the conduction band due to the valence rule. However, our Sb-doped samples have much lower n values than theoretically expected. The lower doping efficiency of Sb is attributed to the nanostructuring it introduces into the PbTe system, which will be detailed later. Cd alloying shrinks the PbTe lattice, Figure 2(a), because the ionic radius of Cd2+ (0.95 Å) is smaller than that of Pb2+ (1.19 Å). We also note that the lattice constant of Pb0.97Cd0.03Te is higher than expected from Vegard’s law (solid curve). This means that Cd is not fully alloyed and is in good agreement with our previous study19 (see open circle symbols in Figure 2(a)). Indeed, the pseudo-binary phase diagram34 (Figure 2(b)) suggests that the solubility limit of CdTe in PbTe, which is strongly temperature dependent, is less than 3 mol% below 800 K. This is supported by our transmission electron microscope (TEM) study, Figure 2(c), where >200 nm Cd-containing precipitates (see energy-dispersive X-ray spectroscopy (EDS) mappings in Figure 2(d)) are observed, though these second phases cannot be detected by XRD because of their low volume fraction. This is also consistent with an earlier study by Pei et al.17 where submicron sized CdTe precipitates (observed at room temperature) exist in the hot pressed p-type Pb0.97Cd0.03Te pellet under scanning electron microscopy (SEM).

Electrical properties and band structure tailoring Despite a lower than 3 mol% actual alloying fraction, Pb0.97Cd0.03Te (0.32 eV) has a much larger optical band gap than pristine PbTe (0.24 eV), Figure 3. This bandgap enlargement is also supported by our first-principles band structure calculations (see Experimental section in the Supporting Information for calculation details), Figure 4. For example, in pristine PbTe, both the conduction band minimum (CBM) and valence band maximum (VBM) are at L point, separated by a direct energy gap (Eg) of ~0.11 eV, Figure 4(a). With increasing Cd alloying fraction, the CBM of PbTe shifts upwards, while the VBM shifts downwards in energy (Figures 4(b) and 4(c)), leading to an increase of Eg that changes from direct to indirect with high Cd content (Figure 4(d)). Band gap widening in PbTe was previously observed when isoelectronically replacing Pb with Mg16, Sr11, or Yb36 elements.


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In Figure 3 we also observe an increase of absorption with doping fraction of Sb in Pb0.97Cd0.03Te at energies below 0.2 eV (see purple arrow to guide the eye). This indicates an increase of free carrier concentration and agrees with our Hall measurement result shown in Figure 1(b). Interestingly, as the Sb doping concentration is increased, the apparent optical band gap of Pb0.97Cd0.03Te decreases from 0.32 eV to 0.29 eV (x=0.005), and then to 0.27 eV (x=0.01). As we will discuss later, this is due to a secondary process where Sb doping decreases the solubility of Cd in PbTe (therefore lowers Eg), in a similar fashion as Na doping in the p-type PbTe-CdTe system17. The temperature-dependent  and S values for Pb0.97-xSbxCd0.03Te are shown in Figures 5(a) and (b), respectively. For all samples,  decreases and S increases with temperature behaving like degenerate semiconductors, except x=0.001 and 0.002 samples where a saturation of S at ~650 K is clearly seen because of bipolar diffusion from minority carriers37. The power factor (PF=S2) is plotted in Figure 5(c). Properly doping Pb0.97Cd0.03Te with Sb significantly enhances the PFs as a result of optimized electrical transport properties. For example, x=0.005 and 0.007 samples display three times higher PFs than undoped Pb0.97Cd0.03Te at 800 K, achieving ~17 Wcm-1K-2, a decent value comparing to various reported n-type PbTe samples19-21, 26-30. Figure 5(d) shows the room temperature S of Pb0.97-xSbxCd0.03Te as a function of n. As we previously demonstrated Sb is a pure dopant in PbTe without obviously affecting the electronic band structure (or effective mass)21, we can simply attribute any changes of S (in comparison to pristine PbTe) to Cd alloying. The black, blue and red curves represent the theoretical Pisarenko plots for PbTe calculated using a single Kane band model (details can be found in Supporting Information and in Refs. 26-27) with effective masses (m*) of 0.25, 0.30 and 0.35 me (me is the electron rest mass), respectively. It can be seen that, with increasing doping levels (or Sb concentrations), m* of Pb0.97Cd0.03Te decreases gradually from 0.35 me to 0.25 me. As more Sb is doped, less Cd is soluble around room temperature, which leads to lower Eg (Figure 3) and smaller values of m* (Figure 5(d)). For degenerate semiconductors with Kane-type band dispersion like PbTe38, the effective mass of carriers (m*) is proportional to the band gap (Eg) through the relation:



h2 k 2

2m*

 E (1  E

Eg

),

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(1)

where h is the reduced Plank’s constant, k the crystal momentum, and E the energy of electron states. It therefore becomes clear that, at room temperature, the increased Eg of PbTe by Cd alloying (Figure 3) can reasonably explain the enhancement of m* at low doping concentrations of Sb. This is quite similar to what we previously found in n-type PbTe-PbS system.21 There is no clear trend to suggest that resonant levels are at play in our PbTe-CdTe samples. As the phase diagram34 in Figure 2(b) indicates, the solubility of CdTe in PbTe increases reaching ~3 mol% at 800 K. The enhanced solubility of Cd at elevated temperatures would undoubtedly widen the Eg of PbTe, leading to higher m* (according to Eq. (1)) and larger S. To examine this, we modeled the temperature dependent S of PbTe with different m* under n of 4×1019 cm-3 using a self-consistent single nonparabolic Kane band model26-27, and compared them to experimental data from Sb-doped Pb0.97Cd0.03Te and I-doped PbTe26 samples having the same n, Figure 6. It should be emphasized that such a single Kane band model takes into account the known temperature dependent band gap of PbTe, where the details can be found in Refs.26-27. We note that in the entire simulated temperature range, the experimental values of S in Idoped PbTe agree well with the fitting data with m*=0.25 me, demonstrating the validity of our simulation model. However, for our Sb-doped Pb0.97Cd0.03Te sample, the temperature dependent S cannot be simply described by a single m* value. Specifically, at lower temperatures (T < 500 K) the experimental S values mostly fall on the simulation curve with m* = 0.25 me, while at higher temperatures (T > 600 K), the simulation curve with m* = 0.35 me is more reasonable to describe the experimental data. The large enhancement of m* at high temperatures arising from increased solubility of Cd in PbTe contributes to much higher S of Sb-doped Pb0.97Cd0.03Te, in comparison with those of Idoped PbTe26.

Thermal conductivity and nanostructuring The details of calculating tot and lat can be found in experimental section in the Supporting Information, including data of thermal diffusivity (Figure S1) and Lorenz


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number (Figure S2). Figures 7(a) and 7(b) show tot and lat of Pb0.97-xSbxCd0.03Te as a function of temperature, respectively. tot increases as the doping level of Sb is increased, largely due to the increased electronic contribution to the heat transport. What really surprises us is the remarkable suppression of lat even by a dilute amount of Sb addition. For example, when Sb amount is slightly increased from 0.001 to 0.005, the values of lat significantly decrease from ~1.9 Wm-1K-1 to ~1.2 Wm-1K-1 at 300 K, and from ~1.2 Wm-1K-1 to ~0.7 Wm-1K-1 at 800 K, both of which represent a ~40% reduction. The origin of this strongly reduced lat upon Sb doping in Pb0.97Cd0.03Te, was explored with high resolution transmission electron microscope (HRTEM) examination as described below. The thermoelectric performance of PbTe can be enhanced by lowering lat, for instance, through nanostructuring.1,

8-11, 39-40

To mitigate the negative impacts of

nanostructuring on carrier mobility, the precipitate/matrix interfaces should be coherent or at least semicoherent but strained at the same time.9,

39

Strained endotaxial

nanostructures are believed to strongly scatter heat carrying phonons but no so much electrons.41-43 MTe (M=Ca, Sr, Ba)9-11,

44

have been demonstrated to be the best

candidates for nanostructuring in p-type PbTe. Figure S3(a) shows a TEM image of 0.5 mol% Sb-doped Pb0.97Cd0.03Te. There are two different kinds of precipitates: one with submicron size (~0.3 m) and the other much smaller (~5-20 nm). EDS mapping (Figure S3(b)) results clearly show that the spherical shaped large precipitates are rich in Cd and deficient in Pb (very likely CdTe), which is similar to what we observed in the undoped Pb0.97Cd0.03Te sample (Figure 2(c)). These CdTe precipitates are considered to be too big in size (larger than the mean free path of acoustic phonons in PbTe ~100 nm)45 to have any significant influence on the thermal conductivity reduction. The addition of Sb into Pb0.97Cd0.03Te induces the growth of a decent number of faceted nanoscale precipitates (5-20 nm), as we present in Figure 8(a). Figure 8(b) is a high angle annular dark field scanning transmission electron microscopy (HAADF-STEM) image which gives the “Z-contrast”. The precipitates appear to be darker in contrast which indicates a lower average atomic number than the matrix. Point EDS spectra were obtained from both matrix and precipitates. After



normalizing the spectra with the Te L peaks, Figure 8 (c), these faceted precipitates are rich in Sb element in contrast to the matrix composition. A zoom-in image (Figure 8(d)) of the precipitate reveals its rock salt structure. This is somewhat beyond our expectation because no known Sb-based binary tellurides display cubic crystal structures in ambient conditions. However, our previous study46 shows that rock-salt-type PbmSb2nTem+3n materials which have no bulk analogues can actually stabilize on the nanoscale. More importantly, the cubic PbmSb2nTem+3n phases have small lattice mismatch (

Enhanced Density-of-States Effective Mass and Strained Endotaxial

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