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Vacancy manipulation for thermoelectric enhancements in GeTe alloysXinyue Zhang, Juan Li, Xiao Wang, Zhiwei Chen, Jianjun Mao, Yue Chen, and Yanzhong Pei

J. Am. Chem. Soc., Just Accepted Manuscript • Publication Date (Web): 28 Sep 2018

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Vacancy manipulation for thermoelectric enhancements in GeTe alloys Xinyue Zhang1,#, Juan Li1,#, Xiao Wang1, Zhiwei Chen1, Jianjun Mao2, Yue Chen2 and Yanzhong Pei1,*

1Interdisciplinary Materials Research Center, School of Materials Science and Engineering, Tongji Univ., 4800 Caoan Rd., Shanghai, 201804, China 2Department of Mechanical Engineering, The University of Hong Kong, Pokfulam Road, Hong Kong SAR, China

#These authors contributed equally to this work, *Email: yanzhong@tongji.edu.cn

Abstract Optimization of carrier concentration plays an important role on maximizing thermoelectric performance. Existing efforts

mainly focus on aliovalent doping, while intrinsic defects (e.g. vacancies) provide extra possibilities. Thermoelectric GeTe intrinsically forms in off-stoichiometric with Ge-vacancies and Ge-precipitates, leading to a hole concentration significantly higher than required. In this work, Sb2Te3 having a smaller cation-to-anion ratio, is used as a solvend to form solid solutions with GeTe for manipulating the vacancies. This is enabled by the fact that each substitution of 3 Ge2+ by only 2 Sb3+ creates 1 Ge vacancy, because of the overall 1:1 cation-to-anion ratio of crystallographic sites in the structure and by the charge neutrality. The increase in the overall Ge-vacancy concentration facilitates Ge-precipitates to be dissolved into the matrix for reducing the hole concentration. In a combination with known reduction in hole concentration by Pb/Ge-substitution, a full optimization on hole concentration is realized. In addition, the resultant high-concentration point defects including both vacancies and substitutions strongly scatter phonons and reduce the lattice thermal conductivity to the amorphous limit. These enable a significantly improved thermoelectric figure of merit at working temperatures of thermoelectric GeTe. Introduction

Without emissions or moving parts, thermoelectrics (TE) directly convert waste heat to electricity1, which have commonly been considered as a clean and sustainable technology for energy crisis. Typical thermoelectrics for power generation applications include half-Heuslers2, lead telluride3, bismuth telluride4, etc. The fundamental limitation for large-scale applications is their relatively low efficiency, which is determined by the materials’ dimensionless figure of merit zT, zT= S2

T/ρ(κE+κL), where S, T, ρ, κE and κL are the Seebeck coefficient, the absolute temperature, the electrical resistivity, the electronic and lattice component of the thermal conductivity, respectively.

Proven strategies for improving zT are typified either by an enhancement of power factor S2/ρ via band engineering such as band convergence3a,5, nestification6 or by a suppression of lattice thermal conductivity (κL)7 which can be realized through phonon scattering due to various sources including 0D point defects8, 1D dislocations9 and 2D boundary interfaces10 and through seeking novel materials with intrinsically low κL stemming from soft chemical bonds11 and/or complex crystal structure12.

However, above strategies guarantee the highest possible zT only if the carrier concentration is fully optimized13. This is because that, S, ρ, and κE are strongly coupled with each other through the carrier concentration14. Both power factor (S2/ρ) and zT can be maximized only in a narrow energy range of Fermi level, corresponding to a narrow range of carrier concentration15. This leads carrier concentration optimization to be always important for improving thermoelectrics. Extrinsic doping, particularly chemical doping by aliovalent impurities2a,16, is the most common approach to tune carrier concentration. In addition, intrinsic defects, including vacancies17, interstitials18 and antisite defects19, could provide an extra degree of freedom, but have been much less focused on.

Vacancy is one fundamental type of thermodynamically stable point defects in semiconductors, particularly in p-type conduction because the formation energy of a cation vacancy is usually lower than that of anion one due to the smaller size of a cation20. Being similar to other intrinsic defects, vacancies have an equilibrium concentration in a solid material at a given temperature, which usually corresponds to the lowest free energy under equilibrium and any vacancy

concentrations higher or lower than this equilibrium one tends to be thermodynamically unstable. These naturally-formed vacancies in semiconductors usually produce charge carriers as well as phonon scattering centers, enabling vacancies to dominate the transport of both carriers and phonons depending on the concentration and valence states. Fortunately, the vacancy concentration can be largely manipulated by external effects including the variations of composition, temperature and pressure, leaving availabilities for tuning both the charge and the phonon transport in semiconductors21.

Thermoelectric GeTe, is a typical case for a semiconductor having high-concentration intrinsic cation vacancies by thermodynamics22. This leads this compound to be intrinsically off-stoichiometric17d,20a with Ge-vacancies and Ge-precipitations22a,23. Under equilibrium, the existence of ~2.5% Ge-vacancies leads the hole concentration in pristine GeTe to be as high as ~1021 cm-3, which is in good agreement with a simple charge counting rule of each Ge-vacancy producing 2 holes17d,22a. Although the high concentration Ge-vacancies enable a strong phonon scattering intrinsically due to the resultant large fluctuations in both mass and strain24, the intrinsic hole concentration is significantly higher than that required for optimal thermoelectric performance20a,25. This inspires us a guiding strategy that an optimized carrier concentration at a sufficiently high concentration of cation-vacancies for improving thermoelectric GeTe.

It is generally believed that an intentional increase of lattice vacancies at Ge-sites would help Ge-precipitates to be dissolved, thus leading to a significant reduction in hole concentration. The creation in extrinsic cation vacancies can be realized through formation of solid solutions with a solvend having a smaller cation-to-anion ratio as compared to the matrix24b,24c. Alternatively, the formation of intrinsic Ge vacancies in GeTe is found to closely relate to the mean size of cations. An increase in cation size such as by Pb/Ge substitutions has been reported to increase the formation energy of Ge-vacancy, which leads to an effective dissolution of Ge-precipitates for reducing the hole concentration20a. Therefore, a combination of both the creation of external cation vacancies and Pb/Ge substitution is expected to fully optimize the carrier concentration in GeTe thermoelectrics.

The resultant high-concentration vacancies and substitutions, both of which ensure large mass and strain fluctuations for phonon scattering, could simultaneously

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enable an effective reduction in lattice thermal conductivity. It is therefore indicated that the manipulation of cation vacancies as an effective strategy for improving thermoelectric GeTe. This is demonstrated here in Ge1-x-ySb2x/3PbyTe solid solutions, where each 3 Ge2+ sites are occupied by only 2 Sb3+ ions leaving the third site vacant, in order to maintain the charge balance and the crystal structure unchanged from GeTe matrix. These lead to a successful realization of well-improved performance in GeTe thermoelectrics. Results and discussion

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Figure 1. Lattice parameter (a) and interaxial angle (b) for Ge1-x-ySb2x/3PbyTe alloys. Literature results of Sb-doped GeTe (Ge1-xSbxTe) are also included for comparison25d.

Figure 2. SEM images and EDS mappings for Ge1-xSb2x/3Te,

showing a removal of Ge precipitates (a-c) and the homogeneity for matrix phase (d).

The details about material synthesis and characterization, property measurements as well as vacancy formation energy calculations are given in supplementary. Room temperature X-ray diffraction (XRD) patterns for Ge1-x-ySb2x/3PbyTe alloys obtained in this work are shown in Figure S1. All the diffraction peaks can be well indexed to the rhombohedral structure of GeTe (a=b=c and α=β=γ<90°). Such a rhombohedral structure can be approximated as a slightly distorted rock-salt structure along the [111] direction26. The influence of alloying with Sb2Te3 and PbTe on the crystal structure can be characterized by the lattice parameter (a) and the interaxial angle (α), where a linear increase in both a and α is observed in both cases (Figure 1). The XRD results

indicate a solubility of x up to 0.22, which is higher than that reported in literature phase diagram21. A further alloying with PbTe leads to a significant lattice expansion while a slight increase in interaxial angle.

Scanning electron microscope (SEM) and energy dispersive spectroscopy (EDS) analyses are carried out to further characterize the phase compositions (Figure 2 and Figure S2). No Sb2Te3 precipitates or Sb-rich phases are observed when x<0.16, and the composition mapping by EDS confirms the homogeneity for the matrix phase. Being consistent with literatures23,25d,27, Ge-precipitates can be observed in GeTe alloys here as well, due to the low formation energy of Ge-vacancy20a. Importantly, Ge precipitates are observed to decrease with increasing x and are nearly removed when x>0.16. Further alloying with PbTe <10% leads to no additional impurity phases (Figure S2).

As the cation-to-anion ratio in Sb2Te3 is 1/3 smaller than that in GeTe, formation of a rhombohedral structured Ge1-xSb2x/3Se solid solution would lead to x/3 negatively charged vacancies (VGe

2-) at Ge site per formula unit. The introduced x/3 negatively charged vacancy (VGe

2-) and 2x/3 positively charged Sb cations (SbGe

+) would compensate with each other, which means that Sb2Te3-alloying does not generate free carriers28. The resulting increase in overall vacancy concentration due to Sb2Te3-alloying, would drive the Ge precipitates to be dissolved into matrix to occupy the VGe

2- sites, as evidenced by the SEM observations (Figure 2). This is also confirmed by the DFT calculations, which show an increase in formation energy of Ge vacancies due to Sb2Te3-alloying (Figure 3a).

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Due to the dissolution of Ge precipitates in Ge1-xSb2x/3Te alloys, the room temperature Hall carrier concentration (nH) decreases linearly with increasing x and then saturates at x>0.12 (Figure 3b). A further PbTe-alloying with Ge0.88Sb0.08Te (x=0.12) further decreases the hole concentration, which can as well be understood by the increase in formation energy of Ge-vacancy induced by the substitution with a larger cation20a. The combination of both Sb2Te3- and PbTe-alloying enables a Hall carrier concentration to be as low as 1×1020 cm−3, covering the optimal carrier concentration of 1~2×1020 cm−3 for GeTe thermoelectrics25b-d,29. Therefore, Ge1-xSb2x/3Te solid solutions with and without PbTe-alloying in the solid solution region are focused on in this work.

The linear region of carrier concentration versus x and y enables a precise control of carrier concentration ranging from 1~7×1020 cm−3 in Ge1-x-ySb2x/3PbyTe alloys. Moreover, an extremely high cation vacancy concentration of >5% can be simultaneously maintained even keeping the carrier

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concentration optimized (1~2×1020 cm−3), which is quite important for guaranteeing a well-reduced lattice thermal conductivity with the additional help of Sb/Ge and Pb/Ge substitutions.

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Figure 4. Normalized absorption versus photon energy (a, b); Hall carrier concentration dependent Seebeck coefficient (c) and Hall mobility (d) for Ge1-x-ySb2x/3PbyTe at room temperature. Literature results of Ge1-xSbxTe are included for comparison25b,25d,30.

The decrease in carrier concentration leads the optical absorption peak of free carriers to shift to lower energies, indicating a lower Fermi level as confirmed by the optical measurements at room temperature (Figure 4a-b). With known carrier concentration, mobility and dielectric constant, the inertial effective mass (mI

*) at Fermi level under an effective single band approximation can be estimated from the location of absorption peaks (via equation 9 in Ref. 31, more details given in supplementary), according to Lyden method31. The estimated inertial effective masses for these solid solutions with different carrier concentrations are listed in Table S1, along with literature results32 for pristine GeTe.

Hall carrier concentration dependent Seebeck coefficient (Figure 4c) and Hall mobility (Figure 4d) for Ge1-xSb2x/3Te at room temperature, show no obvious deviations from that of Sb-doped GeTe25b,25d,30 and agrees well with the two-valence-band model prediction25d. This indicates negligible difference in band structure between Sb2Te3-alloying and Sb-doping. Ge0.88-ySb0.08PbyTe alloys tend to show slightly lower Seebeck coefficient but a higher mobility, which can be understood by the slightly lighter inertial effective masses as compared to those of Ge1-xSb2x/3Te alloys with a large x (Table S1). Temperature dependent Hall mobility for Ge1-x-ySb2x/3PbyTe alloys is shown in Figure S3. Similar to that of other GeTe thermoelectrics25a,25d, Ge1-x-ySb2x/3PbyTe alloys roughly show a T-1.5 dependence of Hall mobility, suggesting a dominant carrier scattering by acoustic phonons.

Temperature dependent thermoelectric transport properties for the high zT materials are shown in Figure 5, while those for all compositions are given in Figure S4 and S5. The high thermoelectric performance is highly reproducible, which is ensured by multiple measurements on the same sample under several thermal cycles. The observed hysteresis in thermoelectric properties from 500 to 650 K, depending on the composition, is related to the phase

transition from rhombohedral to cubic that leads to a switch in energy between L and Σ valence bands33. The lattice thermal conductivity (κL) is estimated by subtracting the electronic component (κE=LT/ρ) from the total thermal conductivity (a Dulong-Petit heat capacity is used, Figure S6), where the Lorenz factor (L) is estimated based on a single parabolic band model approximation with acoustic phonon scattering (Figure S7).

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Due to the existence of high-concentration cation vacancies and substitutions for phonon scattering, the lattice thermal conductivity can be reduced to be as low as ~0.7 W/m-K at room temperature. In a broad temperature range, the achieved κL here is comparable with the amorphous limit (Figure S4c and S5c) according to the Cahill model34. To quantitatively understand the influence of vacancies on the lattice thermal conductivity in Ge1-x-ySb2x/3PbyTe alloys, a Debye-Callaway model35 is developed to predict the composition dependent lattice thermal conductivity. This model takes into account both phonon–phonon and point defect scattering (more details in the Supplementary), enabling a successful prediction on the lattice thermal conductivity reduction due to Sb2Te3- and PbTe-alloying (Figure 6). The slightly stronger effect on κL-reduction by Pb/Ge substitution, is due to the extremely large mass fluctuations introduced as well as the bond softening36 indicated by the decrease in sound velocities (Figure S8)..

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Due to the simultaneous effects of both optimization in

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carrier concentration (nH) and reduction in lattice thermal conductivity (Figure 3b and 6), thermoelectric figure of merit, zT, is found to be enhanced significantly (Figure 7a). Due to the existence of extra cation-vacancies that further reduces the lattice thermal conductivity, Ge1-xSb2x/3Te alloys indeed show higher thermoelectric performance than Ge1-xSbxTe with similar Hall carrier concentration25d. A further combination with Pb/Ge substitution enables both a stronger κL-reduction and a preciser nH-optimization, leading to extraordinary peak zT and a roughly 400 % enhancement in average zT as compared to that of pristine GeTe (Figure 7b).

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This work focuses on vacancy manipulation for a precise optimization of carrier concentration for thermoelectric GeTe, through the control of vacancy thermodynamics. Locating an optimized carrier concentration at an alloy composition having sufficiently high-concentration cation vacancies and substitutions, simultaneously enables a significant reduction in lattice thermal conductivity to approach the amorphous limit. This realizes a significant improvement in thermoelectric GeTe, where the strategy might be applicable for other thermoelectrics. Acknowledgement

This work is supported by the National Natural Science Foundation of China (Grant No. 11474219 and 51772215), the National Key Research and Development Program of China (2018YFB0703600). JM and YC are grateful for the financial support from RGC under project numbers 27202516 and 17200017, and the research computing facilities offered by ITS, HKU. References (1) Bell, L. E. Science 2008, 321, 1457. (2) (a) Fu, C.; Bai, S.; Liu, Y.; Tang, Y.; Chen, L.; Zhao, X.; Zhu, T. Nat Commun 2015, 6, 8144.(b) Appel, O.; Zilber, T.; Kalabukhov, S.; Beeri, O.; Gelbstein, Y. J. Mater. Chem. C 2015, 3, 11653.(c) Appel, O.; Schwall, M.; Mogilyansky, D.; Köhne, M.; Balke, B.; Gelbstein, Y. J. Electron. Mater. 2012, 42, 1340.(d) Dedegkaev, T. T.; Yaskov, D. A.; Lagkuev, D. K. Zhurnal Tekhnicheskoi Fiziki 1981, 51, 1539. (3) (a) Pei, Y.; Shi, X.; LaLonde, A.; Wang, H.; Chen, L.; Snyder, G. J. Nature 2011, 473, 66.(b) Gelbstein, Y. J. Electron. Mater. 2010, 40, 533. (4) (a) Goldsmid, H. J. Proc. Phys. Soc. 1958, 71, 633.(b) Vizel, R.; Bargig, T.; Beeri, O.; Gelbstein, Y. J. Electron. Mater. 2015, 45, 1296. (5) (a) Tang, Y.; Gibbs, Z. M.; Agapito, L. A.; Li, G.; Kim, H. S.; Nardelli, M. B.; Curtarolo, S.; Snyder, G. J. Nat Mater 2015, 14, 1223.(b) Li, W.; Chen, Z.; Lin, S.; Chang, Y.; Ge, B.; Chen, Y.; Pei, Y. Journal of Materiomics 2015, 1, 307.(c) Tang, J.; Gao, B.; Lin, S.; Li, J.; Chen, Z.; Xiong, F.; Li, W.; Chen, Y.; Pei, Y. Adv. Funct. Mater. 2018, 1803586.

(6) Lin, S.; Li, W.; Chen, Z.; Shen, J.; Ge, B.; Pei, Y. Nat Commun 2016, 7, 10287. (7) Chen, Z.; Zhang, X.; Lin, S.; Chen, L.; Pei, Y. National Science Review 2018. (8) (a) Vining, C. B.; Laskow, W.; Hanson, J. O.; Van der Beck, R. R.; Gorsuch, P. D. J. Appl. Phys. 1991, 69, 4333.(b) Zaitsev, V.; Fedorov, M.; Gurieva, E.; Eremin, I.; Konstantinov, P.; Samunin, A. Y.; Vedernikov, M. Phys. Rev. B 2006, 74, 045207. (9) (a) Kim, S. I.; Lee, K. H.; Mun, H. A.; Kim, H. S.; Hwang, S. W.; Roh, J. W.; Yang, D. J.; Shin, W. H.; Li, X. S.; Lee, Y. H.; Snyder, G. J.; Kim, S. W. Science 2015, 348, 109.(b) Chen, Z.; Ge, B.; Li, W.; Lin, S.; Shen, J.; Chang, Y.; Hanus, R.; Snyder, G. J.; Pei, Y. Nat Commun 2017, 8, 13828. (10) (a) Joshi, G.; Lee, H.; Lan, Y.; Wang, X.; Zhu, G.; Wang, D.; Gould, R. W.; Cuff, D. C.; Tang, M. Y.; Dresselhaus, M. S.; Chen, G.; Ren, Z. Nano Lett. 2008, 8, 4670.(b) Hsu, K. F.; Loo, S.; Guo, F.; Chen, W.; Dyck, J. S.; Uher, C.; Hogan, T.; Polychroniadis, E. K.; Kanatzidis, M. G. Science 2004, 303, 818.(c) Biswas, K.; He, J.; Blum, I. D.; Wu, C.-I.; Hogan, T. P.; Seidman, D. N.; Dravid, V. P.; Kanatzidis, M. G. Nature 2012, 489, 414.(d) Poudel, B.; Hao, Q.; Ma, Y.; Lan, Y. C.; Minnich, A.; Yu, B.; Yan, X. A.; Wang, D. Z.; Muto, A.; Vashaee, D.; Chen, X. Y.; Liu, J. M.; Dresselhaus, M. S.; Chen, G.; Ren, Z. F. Science 2008, 320, 634. (11) (a) Ying, P.; Li, X.; Wang, Y.; Yang, J.; Fu, C.; Zhang, W.; Zhao, X.; Zhu, T. Adv. Funct. Mater. 2017, 27, 1604145.(b) Li, W.; Lin, S.; Weiss, M.; Chen, Z.; Li, J.; Xu, Y.; Zeier, W. G.; Pei, Y. Adv. Energy Mater. 2018, 1800030. (12) (a) Ohno, S.; Aydemir, U.; Amsler, M.; Pöhls, J.-H.; Chanakian, S.; Zevalkink, A.; White, M. A.; Bux, S. K.; Wolverton, C.; Snyder, G. J. Adv. Funct. Mater. 2017, 27, 1606361.(b) Zhang, X.; Chen, Z.; Lin, S.; Zhou, B.; Gao, B.; Pei, Y. ACS Energy Lett. 2017, 2, 2470. (13) Pei, Y.; Gibbs, Z. M.; Balke, B.; Zeier, W. G.; Snyder, G. J. Adv. Energy Mater. 2014, 4, 1400486. (14) Goldsmid, H. J. Introduction to Thermoelectricity; Springer: Heidelberg, 2009. (15) Zhang, X.; Pei, Y. npj Quantum Materials 2017, 2, 68. (16) (a) Pei, Y.; LaLonde, A.; Iwanaga, S.; Snyder, G. J. Energy Environ. Sci. 2011, 4, 2085.(b) Zhang, J.; Song, L.; Pedersen, S. H.; Yin, H.; Hung, L. T.; Iversen, B. B. Nat Commun 2017, 8, 13901. (17) (a) Pomrehn, G. S.; Zevalkink, A.; Zeier, W. G.; van de Walle, A.; Snyder, G. J. Angew. Chem. Int. Ed. Engl. 2014, 53, 3422.(b) Xin, J.; Wu, H.; Liu, X.; Zhu, T.; Yu, G.; Zhao, X. Nano Energy 2017, 34, 428.(c) Al Rahal Al Orabi, R.; Hwang, J.; Lin, C.-C.; Gautier, R.; Fontaine, B.; Kim, W.; Rhyee, J.-S.; Wee, D.; Fornari, M. Chem. Mater. 2016, 29, 612.(d) Lewis, J. E. physica status solidi (b) 1969, 35, 737.(e) Kimura, Y.; Tanoguchi, T.; Kita, T. Acta Mater. 2010, 58, 4354. (18) (a) Du, Z.; Zhu, T.; Chen, Y.; He, J.; Gao, H.; Jiang, G.; Tritt, T. M.; Zhao, X. J. Mater. Chem. 2012, 22, 6838.(b) Ohno, S.; Imasato, K.; Anand, S.; Tamaki, H.; Kang, S. D.; Gorai, P.; Sato, H. K.; Toberer, E. S.; Kanno, T.; Snyder, G. J. Joule 2018, 2, 141. (19) (a) Stary, Z.; Horak, J.; Stordeur, M.; Stolzer, M. J. Phys. Chem. Solids 1988, 49, 29.(b) Horak, J.; Stary, Z.; Lostak, P.; Pancir, J. J. Phys. Chem. Solids 1990, 51, 1353. (20) (a) Li, J.; Chen, Z.; Zhang, X.; Yu, H.; Wu, Z.; Xie, H.; Chen, Y.; Pei, Y. Adv Sci (Weinh) 2017, 4, 1700341.(b) F., B. R. J. Phys. Chem. Solids 1963, 24, 27. (21) Abrikosov, N. K.; Bankina, V.; Poretskaya, L.; Shelimova, L.; Skudnova, E. NY: Plenum Press 1969, 249, 14. (22) (a) Damon, D. H.; Lubell, M. S.; R., M. J. Phys. Chem. Solids 1967, 28, 520.(b) Sist, M.; Kasai, H.; Hedegaard, E. M. J.; Iversen, B. B. Phys. Rev. B 2018, 97, 094116.(c) Tong, F.; Miao, X. S.; Wu, Y.; Chen, Z. P.; Tong, H.; Cheng, X. M. Appl. Phys. Lett. 2010, 97, 261904.

Page 4 of 5

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Journal of the American Chemical Society

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(23) (a) Hazan, E.; Madar, N.; Parag, M.; Casian, V.; Ben-Yehuda, O.; Gelbstein, Y. Adv. Electron. Mater. 2015, 1, 1500228.(b) Gelbstein, Y.; Davidow, J. Phys. Chem. Chem. Phys. 2014, 16, 20120. (24) (a) Shen, J.; Zhang, X.; Lin, S.; Li, J.; Chen, Z.; Li, W.; Pei, Y. J. Mater. Chem. A 2016, 4, 15464.(b) Yang, H.; Morelli, D. T. J. Electron. Mater. 2012, 41, 1720.(c) Pei, Y.; Morelli, D. Appl. Phys. Lett. 2009, 94, 122112. (25) (a) Li, J.; Zhang, X.; Chen, Z.; Lin, S.; Li, W.; Shen, J.; Witting, I. T.; Faghaninia, A.; Chen, Y.; Jain, A.; Chen, L.; Snyder, G. J.; Pei, Y. Joule 2018, 2, 976-987.(b) Hong, M.; Chen, Z.-G.; Yang, L.; Zou, Y.-C.; Dargusch, M. S.; Wang, H.; Zou, J. Adv. Mater. 2018, 1705942.(c) Samanta, M.; Biswas, K. J. Am. Chem. Soc. 2017, 139, 9382.(d) Li, J.; Zhang, X.; Lin, S.; Chen, Z.; Pei, Y. Chem. Mater. 2017, 29, 605. (26) Chattopadhyay, T.; Boucherle, J. X.; Schnering, H. G. v. J. Phys. C: Solid State Phys. 1987, 20, 1431. (27) Fahrnbauer, F.; Souchay, D.; Wagner, G.; Oeckler, O. J. Am. Chem. Soc. 2015, 137, 12633. (28) Matsunaga, T.; Morita, H.; Kojima, R.; Yamada, N.;

Kifune, K.; Kubota, Y.; Tabata, Y.; Kim, J. J.; Kobata, M.; Ikenaga, E.; Kobayashi, K. J. Appl. Phys. 2008, 103, 093511. (29) (a) Wu, D.; Zhao, L. D.; Hao, S.; Jiang, Q.; Zheng, F.; Doak, J. W.; Wu, H.; Chi, H.; Gelbstein, Y.; Uher, C.; Wolverton, C.; Kanatzidis, M.; He, J. J. Am. Chem. Soc. 2014, 136, 11412.(b) Perumal, S.; Bellare, P.; Shenoy, U. S.; Waghmare, U. V.; Biswas, K. Chem. Mater. 2017, 29, 10426. (30) Perumal, S.; Roychowdhury, S.; Negi, D. S.; Datta, R.; Biswas, K. Chem. Mater. 2015, 27, 7171. (31) Lyden, H. A. Phys. Rev. 1964, 134, A1106. (32) Lewis, J. E. physica status solidi (b) 1973, 59, 367. (33) Li, J.; Chen, Z.; Zhang, X.; Sun, Y.; Yang, J.; Pei, Y. NPG Asia Mater. 2017, 9, e353. (34) Cahill, D. G.; Watson, S. K.; Pohl, R. O. Phys. Rev. B 1992, 46, 6131. (35) (a) Klemens, P. G. Phys. Rev. 1960, 119, 507.(b) Callaway, J.; Vonbaeyer, H. C. Phys. Rev. 1960, 120, 1149.(c) Klemens, P. G. Proc. Phys. Soc. Sec. A 1955, 68, 1113. (36) Murphy, R. M.; Murray, É. D.; Fahy, S.; Savić, I. Phys. Rev. B 2017, 95, 144302.

0.00 0.04 0.08 0.12 0.16 0.20 0.24

0.5

1.0

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2.5

Vacancy Engineering

Ge1-x-y

Sb2x/3

PbyTe

κκ κκL (W/m

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x+y300 400 500 600 700 800

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2.5

GeTe

Ge 0.

76Sb 0.

08Pb

0.12Te

zT

T (K)

Vacancy

Engineering

For Table of Contents Only

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