Rhombohedral to Cubic Conversion of GeTe via MnTe alloying Leads

Article Cite This: J. Am. Chem. Soc. 2018, 140, 2673−2686

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Rhombohedral to Cubic Conversion of GeTe via MnTe Alloying Leads to Ultralow Thermal Conductivity, Electronic Band Convergence, and High Thermoelectric Performance Zheng Zheng,† Xianli Su,*,†,‡ Rigui Deng,† Constantinos Stoumpos,‡ Hongyao Xie,† Wei Liu,† Yonggao Yan,† Shiqiang Hao,§ Ctirad Uher,∥ Chris Wolverton,§ Mercouri G. Kanatzidis,*,‡,§ and Xinfeng Tang*,† Downloaded via UNIV OF KANSAS on January 4, 2019 at 15:38:09 (UTC). See https://pubs.acs.org/sharingguidelines for options on how to legitimately share published articles.

†

State Key Laboratory of Advanced Technology for Materials Synthesis and Processing, Wuhan University of Technology, Wuhan 430070, China ‡ Department of Chemistry, Northwestern University, Evanston, Illinois 60208, United States § Department of Materials Science and Engineering, Northwestern University, Evanston, Illinois 60208, United States ∥ Department of Physics, University of Michigan, Ann Arbor, Michigan 48109, United States S Supporting Information *

ABSTRACT: In this study, a series of Ge1−xMnxTe (x = 0− 0.21) compounds were prepared by a melting−quenching− annealing process combined with spark plasma sintering (SPS). The effect of alloying MnTe into GeTe on the structure and thermoelectric properties of Ge1−xMnxTe is profound. With increasing content of MnTe, the structure of the Ge 1−x Mn x Te compounds gradually changes from rhombohedral to cubic, and the known R3m to Fm-3m phase transition temperature of GeTe moves from 700 K closer to room temperature. First-principles density functional theory calculations show that alloying MnTe into GeTe decreases the energy difference between the light and heavy valence bands in both the R3m and Fm-3m structures, enhancing a multiband character of the valence band edge that increases the hole carrier effective mass. The effect of this band convergence is a significant enhancement in the carrier effective mass from 1.44 m0 (GeTe) to 6.15 m0 (Ge0.85Mn0.15Te). In addition, alloying with MnTe decreases the phonon relaxation time by enhancing alloy scattering, reduces the phonon velocity, and increases Ge vacancies all of which result in an ultralow lattice thermal conductivity of 0.13 W m−1 K−1 at 823 K. Subsequent doping of the Ge0.9Mn0.1Te compositions with Sb lowers the typical very high hole carrier concentration and brings it closer to its optimal value enhancing the power factor, which combined with the ultralow thermal conductivity yields a maximum ZT value of 1.61 at 823 K (for Ge0.86Mn0.10Sb0.04Te). The average ZT value of the compound over the temperature range 400−800 K is 1.09, making it the best GeTe-based thermoelectric material.

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of the Fermi level,19,20 and achieving band convergence.21,22 Coupled with a successful suppression of the thermal conductivity by forming solid solutions or introducing nanostructural features that enhance phonon scattering,23−26 a superior thermoelectric material can be designed.27,28 As the group 14 tellurides PbTe,29−32 SnTe,33−36 and GeTe37,38 are narrow band gap semiconductors with high thermoelectric performance, they can be utilized for power generation in the intermediate temperature region (∼500−800 K). PbTe, crystallizing with a rock salt structure, has been engineered to possess excellent thermoelectric properties. For example, Tan et al.31 synthesized Na-doped Pb0.98Na0.02Te-x% SrTe alloys by nonequilibrium methods and obtained a ZT

INTRODUCTION Thermoelectric solid state materials have attracted tremendous attention because they promise efficient and direct conversion of thermal energy to electricity and, as such, can enable a distributed technology that can augment the efforts for energy efficiency, conservation, and management.1−8 The conversion process is all electronic and offers an unprecedented reliability. The thermoelectric conversion efficiency is generally evaluated by the material’s figure of merit ZT, defined as ZT = α2σT/(κe + κL), where α is the Seebeck coefficient, σ is the electrical conductivity, T is the absolute temperature, κe is the electronic thermal conductivity, and κL is the lattice thermal conductivity.9−13 The performance of a thermoelectric material can be improved in a synergistic way by enhancing the electronic properties through doping,14−16 band structure modifications,17,18 introducing resonant states in the vicinity © 2018 American Chemical Society

Received: December 23, 2017 Published: January 19, 2018 2673

DOI: 10.1021/jacs.7b13611 J. Am. Chem. Soc. 2018, 140, 2673−2686

Journal of the American Chemical Society

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value of 2.5 at 923 K. Compared to PbTe, GeTe is a far less studied p-type narrow band gap semiconductor.39 Because of the high concentration of intrinsic Ge vacancies, the hole carrier concentration is quite high,40 on the order of 1021 cm−3, which leads to excessively high electrical conductivity (∼8500 S/cm), low Seebeck coefficient (∼34 μV/K), and high thermal conductivity (∼8 W/m K) at room temperature.40 Therefore, the thermoelectric properties of pristine GeTe are rather poor, with the maximum ZT of less than 0.8 at 720 K. The optimization of thermoelectric properties of GeTe has historically focused mostly on suppressing the high hole carrier concentration, and on enhancing alloy scattering to lower the thermal conductivity. Considerable progress has been achieved in recent years. For instance, Perumal et al.41 reported that Sbdoped GeTe (rhombohedral structure) exhibits decreased hole carrier concentration and improved valence band convergence (decreased the energy separation between the light and heavy valence bands) while Sb doping point defect phonon scattering, reducing the lattice thermal conductivity and leading to a ZT of 1.85 at 725 K. Wu et al.42 reported a large enhancement of ZT from 0.8 to 1.9 in GeTe via alloying with PbTe, which also led to improved valence band convergence, and suppressed the concentration of Ge vacancies and lowered the lattice thermal conductivity. GeTe exhibits a ferroelectric phase transition at 700 K from the low temperature polar rhombohedral structure (R3m) to the high temperature cubic rock-salt structure (Fm-3m).43 For thermoelectric materials intended for high temperature power generation, phase transformations are problematic, as they could speed up the deterioration in the thermoelectric performance and even lead to a mechanical failure of the device due to cracking and discontinuity in the thermal expansion coefficient. Therefore, for the long-term thermal stability and reliability of operation, it is important to lower the ferroelectric phase transition temperature or even suppress it altogether. In this work, we prepared a series of Ge1−xMnxTe (x = 0− 0.21) compounds by a melting−quenching technique followed by annealing and combined with spark plasma sintering (SPS), and we investigated the influence of MnTe content in GeTe on the structure and thermoelectric properties of Ge1−xMnxTe. With increasing content of Mn in the structure, Ge1−xMnxTe gradually transforms from the rhombohedral phase to the cubic phase and the transformation takes place at a progressively lower temperature. Moreover, alloying with MnTe promotes a convergence of the light and heavy valence bands of GeTe, leading to an increase in the hole effective mass. The convergence in this case occurs via two different mechanisms: first, the Mn substitution lowers the maximum of the light hole band relative to that of the heavy one, and second, the increase in crystal symmetry from rhombohedral to cubic increases the degeneracy of the valence band extrema by making several points on the Brillouin zone more equivalent. The effect of this band convergence is a large enhancement in the carrier effective mass from 1.44 m0 (GeTe) to 6.15 m0 (Ge0.85Mn0.15Te) which is reflected in an enhanced Seebeck coefficient. Alloying with MnTe also decreases the phonon relaxation time by enhancing alloying point defect scattering, and lowers the phonon velocity. This leads to an ultralow lattice thermal conductivity of 0.13 W m−1 K−1 at 823 K. ZT values as high as 1.61 at 823 K were achieved for the Ge0.86Mn0.10Sb0.04Te alloy when optimized via Sb doping.

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EXPERIMENTAL SECTION

Compounds with the nominal compositions of Ge1−xMnxTe (x = 0− 0.21) and Ge0.9−yMn0.1SbyTe (y = 0−0.10) were synthesized by vacuum melting combined with the SPS process. High purity Ge (bulk, 99.999%), Te (bulk, 99.999%), Mn (pellet, 99.99%), and Sb (bulk, 99.99%) were weighed and mixed in stoichiometric proportions to achieve the desired composition (5 g). The mixtures were sealed in evacuated quartz tubes (diameter of 15 mm) and heated to 1373 K in 10 h, kept at this temperature for 24 h, quenched in supersaturated salt water, and then annealed at 773 K for 3 d. The obtained ingots were ground into fine powders, which were vacuum sintered using a spark plasma sintering (SPS) apparatus under a pressure of 50 MPa at 773 K for 5 min to obtain fully dense bulk samples. Powder XRD analysis (PANalytical−Empyrean; Cu Kα) was used to identify the phase composition of the samples. The Rietveld refinements of the XRD patterns were performed using JANA software. The morphology of the bulk samples was studied using electron probe microanalysis (EPMA, JEOL JXA-8230) and highresolution transmission electron microscopy (HRTEM, JEM-2100F, JEOL). The chemical valence of elements was determined using X-ray photoelectron spectroscopy (XPS, VG Multilab 2000; Thermo Electron Corporation). The phase transition temperature of the samples was measured by using a differential scanning calorimeter (DSC Q20; TA Instruments) shown in Figure S1 in the Supporting Information. The electrical conductivity and the Seebeck coefficient were measured using a ZEM-3 apparatus (Ulvac Riko, Inc.) under a helium atmosphere from 300 to 823 K. The thermal conductivity was calculated from κ = λCpρ, where λ is the thermal diffusivity measured in an argon atmosphere by the laser flash diffusivity method (LFA 457; Netzsch), the specific heat capacity (Cp) was calculated by the Dulong−Petit law, and the density (ρ) of the samples was determined by the Archimedes method and was summarized in Table S1 which ranges from 5.86 to 6.15 g cm−3 with the relative density above 95% at room temperature. The electrical conductivity (σ), the Hall coefficient (RH), and the low-temperature heat capacity (Cp) were measured using a Physical Property Measurement System (PPMS-9: Quantum Design). The carrier concentration (n) and the carrier mobility (μH) were calculated from n = 1/eRH and μH = σ/ne. Electronic Band Structure Calculations. The total energies and relaxed geometries of GeTe and Ge1−xMnxTe were calculated by density functional theory (DFT) within the generalized gradient approximation (GGA) of Perdew−Burke−Ernzerhof with projector augmented wave potentials.44 We use periodic boundary conditions and a plane wave basis set as implemented in the Vienna ab initio simulation package.45 The total energies were numerically converged to approximately 3 meV/cation using a basis set energy cutoff of 500 eV and dense k-meshes corresponding to 4000 k-points per reciprocal atom in the Brillouin zone. We consider up to 2 Mn atoms in the GeTe 54-atom cell. For Ge25Mn2Te27, we consider multiple two Mn substitution Ge configurations and adopt the most favorable one with two nearest neighbor MnGe for electronic band structure calculations. Even though Mn has been explored as multivalent species (+2, +3, +4, etc.), we consider Mn in GeTe as an isovalent doping with Mn substituting for Ge.46 The scalar relativistic spin polarization effect has been considered with an initial magnetic moment of 5 μB for the substituted Mn. The substitution defects in GeTe completely change the symmetry of the original primitive cell. Thus, for the purposes of a more direct comparison with GeTe, we transformed the eigenstates for defect structures into a so-called effective band structure in the primitive Brillouin zone of the parent compound GeTe using a spectral decomposition method.47

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RESULTS AND DISCUSSION 1. Effect of Alloying with MnTe on the Structure, Phase Composition, Band Structure, and Thermoelectric Properties of Ge1−xMnxTe. 1.1. Phase Composition and Microstructure. Figure 1a and b are the XRD patterns of Ge1−xMnxTe powders before and after SPS at room temper2674


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structure, while in the rock-salt motif it is located in the center of the octahedron. Due to the off-center position of the Ge atom, the octahedra in the rhombohedral structure are asymmetric with six Ge−Te bonds split into three shorter bonds (red stick, 2.844 Å) and three longer bonds (green spring, 3.156 Å), while in the cubic structure all Ge−Te bonds are of equal length, as shown in Figure 3. In the rhombohedral structure, the Ge atoms form a strongly distorted octahedral (GeTe6) local structure, as shown in Figure 3a. Due to the bond distance difference, the bond angle between the shorter Ge−Te bonds and longer Ge−Te bonds deviates from 180 or 90°. During the phase transition, on heating, the Ge atom shifts on average from the off-center position (1/2−x, 1/2−x, 1/2− x) to the center position (1/2, 1/2, 1/2),48 resulting in equal Ge−Te bond distances of the cubic structure, as shown in Figure 3b. We used DSC analysis to characterize the phase transition temperature of the Ge1−xMnxTe (x = 0−0.45) samples, and the results are summarized in Figure 4. As shown in Figure 4a, the phase transition temperature from the rhombohedral to cubic structure decreases gradually from 665 to 416 K as the content of Mn increases in the single phase region. When the content of Mn exceeds 0.18, a secondary phase is detected, but the phase transition temperature further decreases to 338 K, approaching the room temperature. The JANA software was employed for the structure refinement. Detailed information is presented in Figure S3. With increasing content of Mn, the lattice parameter along the c-axis decreases from 10.67 Å for GeTe to 10.31 Å for Ge0.82Mn0.18Te. In contrast, the lattice parameter along the ab plane increases as the content of Mn increases. The overall effect is a decrease in the unit cell volume with increasing content of Mn because of the large decrease of the lattice parameter along the c-axis, as shown in Figure 4b. Moreover, alloying with MnTe shortens the long Ge−Te bond distances and lengthens the short bond distances, with a concomitant increase of the Te−Ge−Te bond angle approaching the 180° of the cubic structure; see Figure 4c. To assess the microstructure by TEM characterization, we have selected Ge0.86Mn0.10Sb0.04Te as a typical example in the series. In Figure 5a and b, we observe a number of characteristic herringbone structures with their fish-skeleton-like rows of short slanted parallel lines alternating row by row, which is a typical microtwinned structure in the GeTe system.49 The presence of herringbone structures with alternating dark and

Figure 1. XRD patterns of Ge1−xMnxTe (x = 0−0.21).

ature. Before SPS, all samples were single phase materials within the in-house XRD detection limit. After SPS, the samples with x ≤ 0.18 were single phases having the rhombohedral structure. In samples with x > 0.18, a small amount of second phase MnTe2 was detected. The XRD of the samples with x > 0.21 after SPS is shown in Figure S2. Typically, the presence of double peaks in the 2θ range of 23− 27° and 41−45° is a characteristic feature of the rhombohedral phase. With increasing content of Mn, the double peaks gradually merge and become wide single peaks, indicating R3m results from the rock-salt Fm-3m because of the strong tendency of Ge2+ ion to move off-center from the octahedral site in order to lower the energy of the 4s2 lone pair. As Mn, which does not have a stereoactive lone pair, substitutes on the Ge site in the R3m structure, it attempts to approach the center of the position, which essentially characterizes the cubic rocksalt structure. Beyond the regular XRD analysis, scanning electron microscope (SEM) and back scattered electron (BSE) images (see Figure 2) were carried out by EPMA for Ge1−xMnxTe (x = 0−0.15). No significant difference between the bright and dark contrast was observed in any of the samples. The distribution of elements in all samples was homogeneous on a microscale, with no detection of any secondary phases, further confirming that, when x ≤ 0.18, the samples are single phase materials, consistent with the XRD results. Figure 3 shows the typical rhombohedral and cubic structure of GeTe. The difference between the structures is that in the rhombohedral motif the Ge atom sits off-center of the octahedron formed by six Te atoms in the rhombohedral

Figure 2. SE and BSE images of the Ge1−xMnxTe polished surfaces (x = 0, 0.03, 0.09, 0.15). 2675


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Figure 3. Structure of GeTe: (a) rhombohedral structure; (b) cubic structure.

of the Ge-3d core state is 32.43 eV, corresponding to the 3d orbital of the Ge atom, Figure 6a. We can confirm that Ge is in the Ge2+ state in Ge1−xMnxTe. Figure 6b is the photoemission spectrum of the Te-3d core state, including Te-3d3/2 and Te3d5/2. The binding energies of Te-3d5/2 and Te-3d3/2 are 572.90 and 583.29 eV, respectively. The Te-3d region has well separated spin−orbit components (Δmetal = 10.4 eV). In addition, the shape of the peak is approximately symmetric, and the intensity ratio of the two peaks is 3:2, indicating that the valence of Te is −2 in Ge1−xMnxTe (x = 0−0.21). Figure 6c shows the photoemission spectrum of the Mn-2p core state, including Mn-2p1/2 and Mn-2p3/2. The binding energies of Mn2p3/2 and Mn-2p1/2 are 641.62 and 653.74 eV, respectively. The Mn-2p spin−orbit components are well separated (Δmetal = 11.2 eV), and the shape of the peaks is asymmetrical. We also note the presence of a satellite peak of Mn-2p3/2 observed at about 647 eV, which is the characteristic peak of Mn2+. Thus, Mn is in the Mn2+ state rather than the Mn4+/3+ state in Ge1−xMnxTe. Regardless of Mn content, no chemical shift is observed in the peak position of each element, indicating that the chemical environment of Mn2+ atoms has not changed at room temperature. The evolution toward the cubic structure with increasing MnTe fraction in GeTe and its influence on the transport properties is discussed in detail below. 1.2. Thermoelectric Performance of Ge 1−x Mn x Te. 1.2.1. Band Structure of Ge1−xMnxTe. Before we delve into the experimental measurements of thermoelectric transport, we present the results of DFT calculations of the electronic structure which provide useful insight on how the valence band structure is modified with the introduction of Mn in GeTe. The experimental results are then discussed in the context of the changes in the electronic structure. In order to better understand the impact of alloying of GeTe with MnTe on the electronic band structure, we calculated the band structure of Ge27−xMnxTe27 (x = 0, 1, 2) compounds in both the low temperature rhombohedral structure (Figure 7a−c) and the high temperature cubic structure (Figure 7e−g). Brillouin zones of GeTe with low temperature rhombohedral structure and high temperature cubic structure are shown in parts d and h of Figure 7, respectively, for comparison. The band calculations show that the conduction bands are formed mainly from Ge 4p states and the valence bands mainly from Te 5p states for both the rhombohedral and rock-salt structures. In the rhombohedral Ge1−xMnxTe structure, the energy difference between the first and second valence band maxima is almost unchanged from 0.15 eV for pure GeTe to 0.14 eV in Ge26MnTe27 but decreases to 0.04 eV for Ge25Mn2Te27, indicating that the band convergence of the two valence bands is occurring. In addition, alloying with MnTe introduces

Figure 4. (a) Transition temperatures as a function of Mn content in Ge1−xMnxTe (x = 0−0.45) obtained from DCS curves. (b) Lattice parameters and (c) bond distances and bond angles of Ge1−xMnxTe (x = 0−0.18).

bright stripes typically implies that each domain possesses a different crystal axis, crystallizing as a merohedral twin crystal. In Figure 5c, we can resolve the interplanar spacing of 0.34 nm, corresponding to the (0, 2, 1) plane of the rhombohedral structure of GeTe. In Figure 5d, region 1 is basically free of defects, and its inverse Fourier image is shown in Figure 5e. The lattice stripes are arranged regularly, with few defects, and in the corresponding Fourier images, the diffraction spots are along straight lines. Area 2 in Figure 5d is rich with defects. The diffraction spots of the Fourier image, the inset in Figure 5f, lie on a circle, and many defects, such as dislocations and stacking faults, are observed in the inverse Fourier image. It is the presence of these defects that is believed to enhance phonon scattering, resulting in very low lattice thermal conductivity. Figure 6 shows X-ray photoemission spectra of Ge, Te, and Mn in Ge1−xMnxTe (x = 0−0.21) samples. The binding energy 2676


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Figure 5. (a and b) Low magnification TEM micrographs of Ge0.86Mn0.10Sb0.04Te showing domain variants called herringbone structures. (c and d) HRTEM images of Ge0.86Mn0.10Sb0.04Te. (e) IFFT image of a defect-free area with the inset showing the FFT image. (f) IFFT image of a defect-rich area with the inset showing the FFT image.

new states in the band gap regardless of crystal structure, and they arise from Mn 3d states, shown in red dots in Figure 7. The Fermi level is right in the middle of the gap; however, it is well known that the presence of a large amount of Ge vacancies in GeTe shifts the Fermi level into the valence band, resulting in a p-type highly degenerate semiconductor.50 At high temperatures, the stable phase is the rock-salt cubic structure. Parts e−g of Figure 7 show the band structure of the Ge27−xMnxTe27 (x = 0, 1, 2) compounds in their high temperature cubic phase. The main contribution to the hole transport comes from the valence band maximum at the L and Σ points of the Brillouin zone. In pure GeTe with cubic structure, the energy difference between the valence band maxima at L and Σ points is 0.21 eV. As the content of MnTe increases, the energy difference decreases to 0.05 and 0.01 eV for Ge26MnTe27 and Ge25Mn2Te27, respectively. Clearly, alloying with MnTe promotes merging of the two valence bands regardless of whether Ge1−xMnxTe is in the rhombohedral or cubic phase. Moreover, alloying with MnTe gives rise to extra states in the gap in both the low temperature rhombohedral phase and the high temperature cubic phase. 1.2.2. Electronic Transport Properties. To shed light on the influence of the modified band structure on the charge transport, it is useful to compare the room temperature plots of the Seebeck coefficient S versus the carrier concentration n, in the so-called Pisarenko relation for the Ge1−xMnxTe compounds. The black dashed line is calculated by using a two-valence-band model.37 The blue solid trend lines are calculated using a single parabolic band model and assuming that scattering is dominated by acoustic phonons, as expressed in eq 1. S=

8π 2κB 2 ⎛ π ⎞2/3 ⎜ ⎟ m*T 3eh2 ⎝ 3n ⎠

(1)

Here, S is the Seebeck coefficient, kB is the Boltzmann constant, h is the Planck constant, e is the electron charge, n is the carrier concentration, and m* is the effective mass. Figure 8a shows the Pisarenko plot for Ge1−xMnxTe compounds together with those previously reported of Sb-doped Ge1−xSbxTe and undoped GeTe. For undoped GeTe and Sb-doped Ge1−xSbxTe,

Figure 6. Photoemission spectra of (a) Ge 3d core states, (b) Te 3d3/2 and 3d5/2 core states, and (c) Mn 2p1/2 and 2p3/2 core states in Ge1−xMnxTe (x = 0−0.21) samples. 2677


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Figure 7. Band structure of Ge27−xMnxTe27 (x = 0, 1, 2) compounds in (a−c) low temperature rhombohedral structure, (d) Brillouin zones of GeTe with low temperature rhombohedral structure, (e−g) high temperature cubic structure, and (h) Brillouin zones of GeTe with high temperature cubic structure. MnTe introduces some impurity states in the band gap, as shown in red dots.

Ge0.82Mn0.18Te. Such a huge change in density of states effective mass m* indicates the participant of heavy valence band for charge transport after alloying with MnTe (based on eq 15). This value is significantly greater than the one obtained from the Seebeck coefficient analysis which gives 4.01 m0 because of the contribution of the localized magnetic moments of Mn2+ ions from the d5 orbital manifold, as indicated by the band structure calculations in Figure 7. The unpaired electrons of the Mn2+ ions do not contribute to the charge transport in the materials but are contributing to the heat capacity, as reflected in the high Sommerfeld parameter γ. In addition, for the Ge0.90−xMn0.10SbxTe compounds, the trend line of the Pisarenko plot indicates the effective mass of 3.47 m0, which is larger than that of the pure GeTe and the Sb doped Ge1−xSbxTe. The reason for such a rapid increase in the

the trend line of the Pisarenko plot indicates an effective mass of 1.44 m0, while, for the Ge1−xMnxTe compounds, the effective mass increases dramatically with the increasing content of MnTe in the structure and the Seebeck coefficient is much larger than that predicted by the two-valence-band model.37 For instance, the trend line indicates that the effective mass of charge carriers in Ge0.85Mn0.15Te is closer to 4.69 m0, considerably larger than the effective mass in pure GeTe. The enhanced effective mass is also experimentally verified by the low temperature heat capacity measurements which derive the Sommerfeld constant γ which is proportional to the density of states effective mass. The value of γ increases dramatically from 3.27 mJ mol−1 K−1 for pure GeTe to 24.38 mJ mol−1 K−1 for Ge0.82Mn0.18Te, so the corresponding density of states effective mass increases from 2.88 m0 for pure GeTe to 42.1 m0 for 2678


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Figure 8. (a) Pisarenko plot for Ge1−xMnxTe (x = 0−0.18) compounds compared with the earlier reported data. The black dashed line shown in part a is the calculated line based on the two valence band models.37 The solid blue line shown in part a is the calculated line based on single parabolic band models with different effective masses of 1.44 m0, 2.04 m0, 3.47 m0, and 4.69 m0, respectively. (b) The constituency ratio (using electron probe microanalysis) and the carrier concentration at different Mn contents.

Table 1. Room Temperature Transport Parameters of Ge1−xMnxTe (x = 0−0.18) sample x x x x x x x

= = = = = = =

0 0.03 0.06 0.09 0.12 0.15 0.18

matrix composition

κL (W m−1 K−1)

σ (104 S m−1)

S (μV K−1)

nH (1020 cm−3)

μH (cm2 V−1 s−1)

m*/m0

Ge49.14Te50.83 Ge47.27Mn1.42Te51.32 Ge45.97Mn2.52Te51.51 Ge43.87Mn4.04Te52.09 Ge42.94Mn5.17Te51.89 Ge41.07Mn6.83Te52.10 Ge39.05Mn8.46Te52.48

3.37 2.03 2.05 1.80 1.70 1.64 1.75

60.42 46.38 36.55 33.55 28.61 29.02 25.09

34.09 40.34 46.63 38.69 42.10 43.54 40.64

7.84 10.23 18.30 38.03 45.15 47.82 27.95

54.17 28.19 12.25 3.71 3.84 4.41 4.69

1.44 2.04 3.47 4.69 5.73 6.15 4.01

MnTe, the carrier concentration becomes greater than the optimal carrier concentration ((1−3) × 1020 cm−3)51 and charge carrier scattering is enhanced, resulting in a significant decrease in the mobility of holes. 1.2.3. Thermal Conductivity. Figure 10a depicts the temperature dependence of the total thermal conductivity of the Ge1−xMnxTe (x = 0−0.18) compounds. Pure GeTe shows a rapidly decreasing thermal conductivity with the increasing temperature until it reaches the phase transformation temperature just above 700 K. At that point, the trend is interrupted and the conductivity starts to increase. The Ge1−xMnxTe composition with x = 0.03 has a substantially weaker temperature dependence of the thermal conductivity. The compositions with greater content of Mn actually have a thermal conductivity that initially increases, reaches a peak value in the 500−600 K range, and then decreases. The peaks fall within the temperature range where the structures undergo the phase transformation. The lattice thermal conductivity can be estimated by subtracting the electronic thermal conductivity from the measured total thermal conductivity

effective mass is the gradual convergence of the two valence band edges as the content of Mn increases, and the increasing role of the heavy valence band in the carrier transport. Room temperature transport parameters for the Ge1−xMnxTe samples, including the electrical conductivity, Seebeck coefficient, carrier concentration, carrier mobility, effective mass, and the lattice thermal conductivity, are shown in Table 1. At room temperature, the hole carrier concentration increases with the increasing MnTe content. Figure 8b shows the constituency ratio measured by using electron probe microanalysis and the carrier concentration in Ge1−xMnxTe compounds as a function of the content of Mn. The overall atomic ratio between cations (Ge + Mn) and anions (Te) decreases as the Mn content increases, which means that the concentration of Ge vacancies increases, resulting in an increase in the carrier concentration from 7.84 × 1020 cm−3 for pure GeTe to 4.78 × 1021 cm−3 for the Ge0.85Mn0.15Te compound. Figure 9a shows the temperature dependence of the electrical conductivity for Ge1−xMnxTe. Since compounds with MnTe content above 0.18 contain MnTe2 impurity phase, we did not measure their electronic transport properties. The electrical conductivity of all compounds decreases monotonically with increasing temperature, behaving as highly degenerate semiconductors. At room temperature, the decrease in the electrical conductivity with increasing content of Mn is attributed to increased scattering and, hence, reduced carrier mobility. The Seebeck coefficient of all compounds is positive, exhibiting a ptype character with holes as the dominant charge carrier; see Figure 9b. We should mention a slight upturn in the Seebeck coefficient near the phase transition; it is particularly evident in pure GeTe. With the increasing content of Mn, the Seebeck coefficient gradually decreases. Although the band degeneracy increases as discussed above, the significantly increased carrier concentration leads to an overall lower Seebeck coefficient. Figure 9c displays the power factor of the Ge1−xMnxTe compounds as a function of temperature. After alloying with

κL + κamb = κ − κe = κ − LσT

(2)

where κL is the lattice thermal conductivity, κamb is the bipolar thermal conductivity (here likely negligible, since no hint of intrinsic excitations has been detected in measurements of any one of the transport parameters within the covered temperature range), κ is the total thermal conductivity, and κe is the thermal conductivity contributed by charge carriers, respectively. The latter can be estimated by the Wiedemann−Franz law κe = LσT

(3)

where σ is the electrical conductivity and L is the Lorenz number. Assuming a single parabolic band model, the Lorenz number L is calculated from52 2679


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Figure 10. Temperature dependence of (a) the total thermal conductivity, (b) the lattice thermal conductivity, and (c) the figure of merit ZT for Ge1−xMnxTe (x = 0−0.18).

Figure 9. Temperature dependence of (a) the electrical conductivity, (b) the Seebeck coefficient, and (c) the power factor for Ge1−xMnxTe (x = 0−0.18).

⎛ ⎛ κB ⎞2 ⎜ r + L=⎜ ⎟⎜ ⎝e ⎠⎜ r+ ⎝

( (

⎡ r+ ⎢ −⎢ ⎣ r+

( (

5 2 3 2

7 2 3 2

)Fr+(5/2)(η) )Fr+(1/2)(η)

Figure 10b displays the temperature dependence of the lattice thermal conductivity. The lattice thermal conductivity decreases with the increasing temperature and decreases with the increasing content of Mn due to the enhanced alloy phonon scattering. Thus, while pure GeTe at room temperature has a lattice thermal conductivity of ∼3.37 W m−1 K−1, the lattice thermal conductivity of Mn0.15Ge0.85Te is only about half of that value, ∼1.64 W m−1 K−1, at room temperature. At 800 K, the lattice thermal conductivities of the samples alloying with MnTe become very low and fall in the range ∼0.25−0.5 W m−1 K−1. This is comparable or even lower than an estimate of the minimum lattice thermal conductivity for GeTe of about 0.5 W m−1 K−1 calculated on the basis of the glass limit model of Cahill et al.;53 see Figure 10b. The low values of the lattice thermal conductivity of Ge1−xMnxTe compounds in comparison to pure GeTe reflect the strongly enhanced alloy scattering. To further analyze the influence of introducing Mn atoms in the GeTe lattice on the thermal conductivity, we make use of the Callaway model.54,55 Assuming that the grain size is similar in all Ge1−xMnxTe samples, we only consider the influence of Umklapp scattering and point defect scattering on the lattice thermal conductivity. According to Callaway, the lattice thermal

2⎞

)Fr+(3/2)(η) ⎤⎥ ⎟ ⎟ )Fr+(1/2)(η) ⎥⎦ ⎟⎠

(4)

The reduced Fermi level η can be calculated from the temperature dependent Seebeck coefficient ⎛ κ ⎜ r+ S = ± B⎜ e r+ ⎝

( (

Fn(η) =

∫0

∞

5 2 3 2

)Fr+(3/2)(η) )Fr+(1/2)(η)

χn dχ 1 + e χ−η

⎞ ⎟ − η⎟ ⎠

(5)

(6)

where kB is the Boltzmann constant, e is the elemental electron charge, S is the Seebeck coefficient, and r is the scattering factor. We assume that acoustic phonon scattering is the predominant scattering mechanism; thus, r = −1/2. 2680


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Table 2. Disorder Scattering Parameters Γ, ΓS, and ΓM, Strain-Field-Related Adjustable Parameter ε1, Disorder Scaling Parameter u, and Calculated Lattice Thermal Conductivity for Ge1−xMnxTe (x = 0−0.18) sample

Γ (10−3)

ΓM (10−3)

ΓS(expt) (10−3)

ΓS(calc) (10−3)

ε1

u

κL (calc) (W m−1 K−1)

GeTe Ge0.97Mn0.03Te Ge0.94Mn0.06Te Ge0.91Mn0.09Te Ge0.88Mn0.12Te Ge0.85Mn0.15Te Ge0.82Mn0.18Te

55.46 54.20 109.96 117.26 154.06 121.94

0.46 0.89 1.30 1.69 2.05 2.38

55.00 53.30 108.66 115.57 152.02 119.55

60.86 104.84 149.72 189.84 225.39 256.55

505 505 505 505 505 505

1.74 2.28 2.73 3.08 3.35 3.58

3.37 2.03 1.71 1.51 1.38 1.29 1.22

conductivities of Ge1−xMnxTe (κL) and that of pure GeTe (κPL) are related via

κL κLP

tan−1 u u

=

π 2θDΩ

u2 =

hν 2

(7)

κLp Γ

(8)

where u is the disorder scattering parameter, θD is the Debye temperature (244 K for GeTe), Ω is the average atomic volume, h is the Planck constant, ν is the average sound velocity (2452 m/s for GeTe), and Γ is the scattering parameter. The scattering parameter Γ can be calculated using the model of Slack and Abeles,56 Γcalc = ΓM + ΓS, where ΓM and ΓS are the mass fluctuation scattering parameter and the strain field fluctuation scattering parameter, respectively, given by

ΓM =

M̅ i M̿

1 2 i i

Mi1 − Mi 2 M̅ i

2

)

n ∑i = 1 ci 2

( )

n

∑i = 1 ci

ΓS =

2

( )f f (

n

∑i = 1 ci

M̅ i M̿

fi1 fi 2 εi

n ∑i = 1 ci

(9) ri1 − ri 2 ri ̅

2

( )

(10)

where n stands for the number of different atoms in the lattice and ci is the degeneracy of atomic occupancy. For GeTe, there are two different atomic positions (the Ge site and the Te site); thus, n = 2 and c1 = c2 = 1. M̿ is the average relative atomic mass of the compound, M̅ i and ri̅ are the average atomic mass and radius on the ith sublattice, respectively, f ki is the fractional occupation of the kth atoms on the th sublattice, and Mki and rki are the atomic mass and radius, respectively. The above parameters are expressed as follows:

M̅ i =

∑ f ik Mik k

ri ̅ =

∑ f ik rik k

Figure 11. (a) Cp/T vs T2 plot in thte 2−30 K range. The blue solid line is calculated using the combined Debye−Einstein model. The individual contributions from electronic (γ), Debye (β), and the two Einstein terms (E1, E2) are also plotted. (b) The mass fluctuation scattering parameter ΓM and the strain field fluctuation scattering parameter ΓS as a function of the content of Mn. (c) Sound velocities of Ge1−xMnxTe (x = 0−0.18).

(11)

(12)

n

M̿ =

Moreover, with increasing Mn content, the strain field fluctuation scattering parameter increases because of the difference in the atomic radii between Ge and Mn and this in fact seems to dominate phonon scattering. It is also worth considering whether alloying could soften chemical bonds in the structure and thus further lower the thermal conductivity, since this effect is not considered in the Callaway model. This effect of modifying the stiffness of the crystal lattice can be probed by sound velocity measurements. Figure 11c shows room temperature measurements of the

∑i = 1 ciM̅ i n

∑i = 1 ci

(13)

The calculated scattering parameters, strain fluctuation, and mass fluctuation scattering parameters are shown in Table 2 and Figure 11b. The scattering parameter increases with the increasing content of MnTe. The mass fluctuation scattering parameter also increases gradually, indicating that the presence of Mn increases the Ge vacancies in the system and causes more mass fluctuations, thus enhancing phonon scattering. 2681


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been softened, consistent with the speed of sound measurements. Consequently, alloying GeTe with MnTe not only enhances alloy scattering, but it also induces chemical bond softening which further contributes to phonon scattering and leads to the very low thermal conductivity. 1.2.4. Figure of Merit ZT of Ge1−xMnxTe. Figure 10c shows that, with rising temperature, the ZT value of Ge1−xMnxTe (x = 0−0.18) compounds increases. This is particularly the case for pure GeTe, where the ZT reaches its maximum value of 1.09 at 673 K. The thermoelectric performance of Ge1−xMnxTe (x = 0−0.18), however, is inferior to GeTe. Although alloying with MnTe dramatically suppresses the thermal conductivity of Ge1−xMnxTe (x = 0−0.18) compounds, their lower power factors, caused by a suboptimal charge carrier density, preclude reaching competitive values of the figure of merit. In the following section, we show how to optimize the carrier concentration by doping with Sb on the Ge site, to significantly enhance the thermoelectric performance well beyond that of GeTe. 2. Enhancing Thermoelectric Performance of Ge1−xMnxTe Compounds via Optimization of the Carrier Concentration. After alloying with MnTe, the energy separation of the two valence band maxima decreases, which improves the energy convergence of the two valence band tops, leading to a great increment of the density of states effective mass from 1.44 m0 to 6.15 m0. According to the electronic band structure calculations, the energy separation of the valence band maximum between the L point and Σ point for Ge25Mn2Te27 is 0.01 eV, which is almost fully converged. However, the carrier concentration of the samples is too high for good thermoelectric performance. In an attempt to optimize the carrier concentration and improve the power factor of the Ge1−xMnxTe compounds, we chose Ge0.90Mn0.10Te, which is close to the composition of Ge25Mn2Te27, as a matrix material and doped it with Sb to form Ge0.9−yMn0.1SbyTe compounds with y = 0−0.10. Doping with Sb on the Ge sites is in fact electron doping and effectively decreases the high concentration of holes and allows some control on the hole carrier concentration. The purpose of this type of doping was to bring the concentration down and closer to its optimal value for maximizing ZT. The effect of Sb doping on the phase composition, microstructure, and thermoelectric performance is described in the following sections. 2.1. Phase Composition of Sb Doped Ge0.9−yMn0.1SbyTe. Figure 12a shows powder XRD patterns of Ge0.9−yMn0.1SbyTe after spark plasma sintering. All compounds possess the rhombohedral GeTe structure at room temperature. With increasing Sb doping, the split Bragg peaks between 23−27°

sound velocity as a function of MnTe fraction. As the content of Mn increases, the longitudinal velocity, transverse velocity, and average speed of sound all decrease, indicating that alloying with MnTe, indeed, softens chemical bonding in Ge1−xMnxTe. To further support this conclusion, we measured the low temperature heat capacity of GeTe and Ge1−xMnxTe and calculated the Debye temperature. Figure 11a shows the low temperature heat capacity of GeTe in the temperature range from 2 to 30 K. The plot of Cp/T versus T2 can be well fitted by using the combined Debye-2 Einstein model: Cp

= γ + βT 2 +

T

⎛

∑ ⎜A n(ΘE )2 (T 2)−3/2 n

⎝

n

⎞ e Θ En / T ⎟ (e Θ En / T − 1)2 ⎠ (14)

In the above equation, the first term denotes the electronic contribution. The Sommerfeld constant γ is given by the expression57 γ=

π2 2 m* κB N (E F) = 1.36 × 10−4 × Vmol 2/3nγ1/3 3 m0

(15)

where Vmol is the molar volume, nγ is the carrier concentration per atom, and m*/m0 is the effective mass. The second term denotes the Debye lattice contribution with β = C·(12π4NAkB/ 5)·(ΘD)−3, where NA, kb, and ΘD are the Avogadro number, Boltzmann constant, and characteristic Debye temperature, respectively. The parameter C is given as C = 1 − ∑n An/3NR, where N is the number of atoms per formula unit and R is the gas constant. The third term represents the contribution from Einstein oscillator modes, where An is the prefactor of the nth Einstein oscillator mode. The various fitting parameters are listed in Table 3. The measured low temperature heat capacity Table 3. Low Temperature Physical Parameters of GeTe, Ge0.82Mn0.18Te, and Ge0.86Mn0.10Sb0.04Te sample

γ (J mol−1 K−2)

β (mJ mol−1 K−2)

ΘD (K)

v (m/s)

GeTe Ge0.82Mn0.18Te Ge0.86Mn0.10Sb0.04Te

0.00327 0.02438 0.08022

0.129 0.175 0.208

244 221 209

2452 2221 2100

and the fitting line are shown in Figure S4. The Debye temperature of GeTe is 244 K, while the Debye temperature of the Ge1−xMnxTe compounds is lower, e.g., Ge0.82Mn0.18Te having a Debye temperature of 221 K. Thus, alloying with MnTe suppresses the Debye temperature of Ge1−xMnxTe compounds, manifesting that the chemical bonds have, indeed,

Figure 12. (a) XRD patterns and (b) lattice parameters of Ge0.9−yMn0.1SbyTe (y = 0−0.10). 2682


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Figure 13. Temperature dependence (10−300 K) of (a) the carrier concentration and (b) the carrier mobility for Ge0.9−yMn0.1SbyTe (y = 0−0.10).

Figure 13b depicts the temperature dependence of the carrier mobility in the temperature range from 10 to 300 K. Below 100 K, the carrier mobility of Ge0.9−yMn0.1SbyTe compounds follows a T−1 dependence. At temperatures above 100 K, the carrier mobility crosses over and its temperature dependence is closer to T−1/2, indicating that alloy scattering dominates the charge carrier transport.58 Again, the Ge0.80Mn0.10Sb0.10Te compound deviates from the trend and the temperature dependence of its mobility above 100 K drops more sharply, tending toward a T−3/2 dependence. As a function of the Sb content, the mobility of Ge0.9−yMn0.1SbyTe compounds at room temperature initially increases, reaches its maximum of 10.3 cm2 V−1 s−1 for y = 0.04, and then decreases (see Table 4), presumably due to defect scattering. The electrical conductivity of all Ge0.9−yMn0.1SbyTe compounds slowly decreases until about 475 K, at which temperature the conductivity starts to rise to a bump near 575 K, and then decreases, Figure 14a. The behavior is essentially that of a degenerate semiconductor. With increasing Sb doping, the electrical conductivity of Ge0.9−yMn0.1SbyTe decreases because the concentration of holes decreases, as shown in Figure 13a. All compounds possess positive Seebeck coefficients in accord with measurements of the Hall coefficient, documenting the p-type (holes) nature of transport, Figure 14b. With increased Sb doping, the Seebeck coefficient of all Ge0.9−yMn0.1SbyTe compounds increases gradually because of the decreasing carrier concentration. Compared to the Ge1−xMnxTe compounds, the Seebeck coefficient of the Sbdoped compounds is significantly larger, perhaps by as much as a factor of 2, the consequence of having a more optimized carrier concentration. Figure 14c displays the power factor of Ge0.9−yMn0.1SbyTe compounds as a function of temperature. Because of the enhanced Seebeck coefficients, the power factor of the Sbdoped compounds significantly exceeds the power factor of the undoped Ge1−xMnxTe compounds, especially at temperatures near the ambient. The maximum power factor of 30.7 μW cm−1 K−2 is obtained for the Ge0.84Mn0.1Sb0.06Te compound at 673 K. 2.2.2. Thermal Conductivity of Ge0.9−yMn0.1SbyTe. Figure 15a shows the temperature dependence of the thermal conductivity of Ge0.9−yMn0.1SbyTe compounds. The thermal conductivity decreases slowly as the temperature increases and shows a similar dip near 475 K followed by a local bump around 575 K, as was observed in the electrical conductivity data in Figure 14a. Using the Wiedemann−Franz relation, we calculated the lattice thermal conductivity of Ge0.9−yMn0.1SbyTe

and 41−45° gradually merged into a single peak, indicating that the structure evolves from the rhombohedral to the cubic phase. As shown in Figure 12b, this is accompanied by an increase of the a-axis lattice parameter and a decrease of the caxis lattice parameter. The overall volume of the unit cell increases with Sb doping. 2.2. Thermoelectric Performance of Sb Doped Ge0.9−yMn0.1SbyTe. 2.2.1. Electronic Transport Properties. The carrier concentration of Ge0.9−yMn0.1SbyTe compounds increases with increasing temperature in the entire temperature range covered. Interestingly, the rise in carrier concentration is much steeper at temperatures below 100 K (on warming from 10 K) than at higher temperatures where the temperature dependence is more or less diminished, Figure 13a. As the electronic band structure calculations indicate alloying with MnTe gives rise to impurity states in the gap in both the low temperature rhombohedral phase and the high temperature cubic phase, the increase of the carrier concentration is due to the ionization of impurity states at low temperatures, while above 100 K the ionization is substantially completed and the compound behaves as a degenerate semiconductor. Because Sb behaves as an electron donor, the carrier concentration of Ge0.9−yMn0.1SbyTe compounds decreases with increasing content of Sb. A notable exception is the Ge0.80Mn0.10Sb0.10Te composition with the highest Sb content where the carrier concentration breaks the trend and rises. This might be due to Sb exceeding its solubility in the compound, although we have no direct evidence based on the XRD data in Figure 12a. Room temperature transport properties of Ge0.9−yMn0.1SbyTe compounds are summarized in Table 4. Table 4. Room Temperature Transport Parameters of Ge0.9−yMn0.1SbyTe (y = 0−0.10) sample y y y y y y

= = = = = =

0 0.02 0.04 0.06 0.08 0.10

κL

σ

S

nH

μH

m*/m0

2.04 1.97 0.91 1.05 1.15 1.11

17.49 14.49 16.93 13.57 7.24 7.16

55.95 68.59 84.79 109.99 129.92 142.96

22.52 15.15 9.43 9.06 8.37 10.70

3.44 4.52 10.29 8.43 4.01 0.40

4.79 4.51 4.06 5.13 5.75 7.44

The influence of Sb on the carrier concentration can be gauged by comparing the concentration in Ge0.90Mn0.10Te with that in Ge0.82Mn0.10Sb0.08Te, i.e., 2.25 × 1021 cm−3 versus 8.37 × 1020 cm−3, a factor of 2.6 times lower carrier density of holes upon Sb doping. 2683


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from Ge vacancies, Sb substituting for Ge and alloy scattering from the presence of MnTe, and grain boundary scattering. TEM images of Ge0.86Mn0.10Sb0.04Te provide documentation for the presence of an abundant variety of defects, such as twin grain boundaries and dislocations that further enhance phonon scattering. Just as in the case of undoped Ge1−xMnxTe compounds, the lattice thermal conductivity of Sb-doped structures approaches the minimum thermal conductivity value (κmin) at high temperatures and the Ge0.86Mn0.10Sb0.04Te compound falls below that value already near 500 K. Apart from the role of scattering, the low thermal conductivity also benefits from softening of the chemical bonds upon GeTe alloying with MnTe, as discussed in section 1.2.3. For instance, the Debye temperature of Ge0.86Mn0.10Sb0.04Te derived from the low temperature heat capacity measurements is only 209 K, much lower than that of GeTe (244 K) and Ge0.82Mn0.18Te (221 K). 2.2.3. Figure of Merit ZT. Figure 16a presents the temperature dependence of ZT for Ge0.9−yMn0.1SbyTe. The ZT values are greatly enhanced upon Sb doping compared to GeTe and the Ge1−xMnxTe compounds, and several compounds (those with y > 0.02) well exceed the ZT value of unity at 800 K. The highest ZT of 1.61 belongs to Ge0.86Mn0.10Sb0.04Te at 823 K, and represents an enhancement of 47% compared to GeTe. From the practical point of view, it is the average ZT (ZTave) value that determines the overall efficiency of a thermoelectric module intended to operate over a range of temperatures. Figure 16b provides a comparison of ZTave values for several GeTe-based thermoelectric materials from 400 to 800 K. The maximum ZT ave value of 1.09 is obtained in our Ge0.86Mn0.10Sb0.04Te compound. It is much higher than the ZTave value of 0.81 reported for (Ge0.80Pb0.20)0.90Mn0.10Te,59 0.85 for Ge0.90Bi0.10Te,60 0.88 for Ge0.95Mn0.05Te,38 and 0.91 for Ge0.98In0.02Te.19

■

Figure 14. Temperature dependence of (a) the electrical conductivity, (b) the Seebeck coefficient, and (c) the power factor for Ge0.9−yMn0.1SbyTe (y = 0−0.10).

CONCLUDING REMARKS The effect of alloying GeTe with MnTe and subsequent doping by Sb on the structural and transport properties is significant. With increasing content of Mn, the structure of the Ge1−xMnxTe compounds gradually changes from the rhombohedral to the cubic phase and the phase transition temperature moves closer to room temperature. First-principles density functional theory calculations show that alloying MnTe into GeTe alters the energy separation between the two valence band edges and moves them closer together. The effect of this

compounds (shown in Figure 15b) under the same assumptions as in section 1.2.3. The lattice thermal conductivity decreases gradually with increasing temperature, but the trend is more linear (at least for samples with y > 0.02) rather than the expected T−1 behavior assuming the dominance of Umklapp processes. This is likely due to participation of other scattering mechanisms, such as point defect scattering

Figure 15. Temperature dependence of (a) the total thermal conductivity and (b) the lattice thermal conductivity for Ge0.9−yMn0.1SbyTe (y = 0− 0.10). 2684


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Figure 16. (a) Temperature dependence of the figure of merit ZT and (b) the average figure of merit ZT for Ge0.9−yMn0.1SbyTe (y = 0−0.10).

■

ACKNOWLEDGMENTS The authors thank Rong Jiang and Tingting Luo for help with the HRTEM analysis. The authors wish to acknowledge support from the Natural Science Foundation of China (Grant Nos. 51402222, 51521001, and 51632006), the Fundamental Research Funds for the Central Universities (WUT: 162459002, 2015 III 061, 2017 IVA 097), and the 111 Project of China (Grant No. B07040). At Northwestern University (X.S., S.H., C.W., and M.G.K.), thermoelectric property measurements and band structure calculations were supported by a grant from the U.S. Department of Energy, Office of Science, and Office of Basic Energy Sciences under Award No. DE-SC0014520.

band convergence is a significant enhancement in the carrier effective mass from 1.44 m 0 (GeTe) to 6.15 m 0 (Ge0.85Mn0.15Te). Alloying with MnTe enhances alloy scattering and softens the chemical bonds, leading to a much lower speed of sound and, consequently, a very low lattice thermal conductivity that approaches or even falls below the estimated minimum thermal conductivity in GeTe. Doping with Sb on the sites of Ge effectively decreases the concentration of holes and brings the carrier concentration closer to its optimal value. The presence of Sb in the structure also enhances point defect scattering and contributes to lowering of the lattice thermal conductivity. The resulting increases in the power factor together with the very low thermal conductivity yield ZT values well in excess of unity for most of the Ge0.9−yMn0.1SbyTe compounds. The highest ZT value of 1.61 at 823 K was achieved for the Ge0.86Mn0.10Sb0.04Te compound. The ZTave value of 1.09 over the temperature range 400−800 K is the highest value for any of the GeTe-based thermoelectric materials. This bodes well for assembling efficient thermoelectric generators based on Ge0.9−yMn0.1SbyTe compounds.

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■

ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/jacs.7b13611. DSC curves (Figure S1), XRD patterns (Figure S2), Rietveld refinement (Figure S3), Debye−Einstein model fitting (Figure S4), and the measured density of the samples (Table S1) (PDF)

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AUTHOR INFORMATION

Corresponding Authors

*[email protected] *[email protected] *[email protected] ORCID

Xianli Su: 0000-0003-4428-6461 Constantinos Stoumpos: 0000-0001-8396-9578 Chris Wolverton: 0000-0003-2248-474X Mercouri G. Kanatzidis: 0000-0003-2037-4168 Xinfeng Tang: 0000-0001-7555-919X Notes

The authors declare no competing financial interest. 2685


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