Shan Li1, Yumei Wang2, Chen Chen1, Xiaofang Li1, Wenhua Xue2, Xinyu Wang1, Zongwei Zhang1, Feng Cao3, Jiehe Sui4, Xingjun Liu1,4, Qian Zhang1. 1. Department of Materials Science and Engineering Harbin Institute of Technology Shenzhen Guangdong 518055 P. R. China. 2. Beijing National Laboratory for Condensed Matter Physics Institute of Physics Chinese Academy of Science Beijing 100190 P. R. China. 3. School of Science Harbin Institute of Technology Shenzhen Guangdong 518055 P. R. China. 4. State Key Laboratory of Advanced Welding and Joining Harbin Institute of Technology Harbin Heilongjiang 150001 P. R. China.
Abstract
Single crystal tin selenide (SnSe) has attracted much attention for its excellent thermoelectric performance. However, polycrystalline SnSe exhibits unsatisfactory figure-of-merit due to the inferior electrical properties, especially for n-type SnSe. In this work, a high concentration of Br doping (6-12 atm%) on the Se site effectively increases the Hall carrier concentration from 1.6 × 1017 cm-3 (p-type) in undoped SnSe to 1.3 × 1019 cm-3 (n-type) in Br-doped SnSe0.88Br0.12, leading to an increased electrical conductivity close to that of a single crystal. Combined with the decreased lattice thermal conductivity due to the enhanced phonon scattering by composition fluctuation and dislocations, a peak ZT of ≈1.3 at 773 K, together with the enhanced average ZT is obtained in SnSe0.9Br0.1 along the hot pressing direction.
Single crystal tin selenide (SnSe) has attracted much attention for its excellent thermoelectric performance. However, polycrystalline SnSe exhibits unsatisfactory figure-of-merit due to the inferior electrical properties, especially for n-type SnSe. In this work, a high concentration of Br doping (6-12 atm%) on the Se site effectively increases the Hall carrier concentration from 1.6 × 1017 cm-3 (p-type) in undoped SnSe to 1.3 × 1019 cm-3 (n-type) in Br-doped SnSe0.88Br0.12, leading to an increased electrical conductivity close to that of a single crystal. Combined with the decreased lattice thermal conductivity due to the enhanced phonon scattering by composition fluctuation and dislocations, a peak ZT of ≈1.3 at 773 K, together with the enhanced average ZT is obtained in SnSe0.9Br0.1 along the hot pressing direction.
The global problem of energy crisis and environmental issues impels the development of sustainable and clean energy technology. Thermoelectric (TE) materials can directly convert heat into electricity without moving parts and gaseous emission, having aroused wide attention for a global sustainable energy solution. The conversion efficiency of TE device is characterized by the dimensionless figure of merit ZT = S
2
σT/(κe+κL), where S is the Seebeck coefficient, σ the electrical conductivity, T the absolute temperature, κL the lattice thermal conductivity, and κe the electronic thermal conductivity.1, 2 Numerous approaches have been explored to enhance TE performance, including increased power factor (S
2σ) by band engineering (resonant doping, band convergence, and band flattening, etc.)3, 4, 5 and decreased thermal conductivity by defect engineering,6 and nanoengineering.7, 8, 9 An alternative way to achieve high ZT values is to seek new classes of TE materials with intrinsically low thermal conductivity, such as clathrates, skutterudites, sulfur‐based compounds, Ag9GaSe6, and SnSe etc.10, 11, 12, 13, 14SnSe was well studied in solar cells and electronic memory applications, but ignored as the TE materials due to the large room temperature electrical resistivity (101–105 Ω cm).15, 16 However, a promising high ZT ≈2.6 at 923 K was obtained along the crystallographic b axis in single crystal SnSe due to the intrinsic ultralow thermal conductivity induced by strongly anharmonic bonding.17 Although there are some controversy regarding the actual thermal conductivity of SnSe single crystals, this enhancement is also attributed to the decreased electrical resistivity in single crystals (0.1 Ω cm) with higher Hall mobility, which is subsequently pursued in the polycrystalline SnSe. Since the electrical resistivity is in inverse proportion to the carrier concentration and mobility, the easiest way is to dope in polycrystalline SnSe for higher carrier concentration, considering the inevitably defects in polycrystals. Relatively high electrical conductivity and ZT values have been achieved in p‐type polycrystalline SnSedoped with Ag, Na, and K, etc.18, 19, 20, 21 Specifically, multiple valence bands have been activated by doping with Na for the further enhanced Seebeck coefficient and TE performance in SnSe. However, since intrinsic Sn vacancy shows p‐type conducting behavior, it is difficult to convert SnSe to n‐type conductor, much more difficult to activate the heavy conduction band22 if compared with p‐type SnSe. I,23 BiCl3,24 Bi,25 and Br26 have been proved capable of changing the Hall coefficient from positive to negative. A decent ZT of ≈0.8 at about 773 K was obtained in SnSe0.96I0.04 with room temperature electron carrier concentration ≈2.0 × 1017 cm−3.23 And an improved ZT value of ≈1.1 at 773 K was achieved in SnSe0.97Br0.03 with room temperature electron carrier concentration up to ≈1.83 × 1018 cm−3.26 To be noted that this carrier concentration is still too low and the electrical conductivity of this Br‐dopedpolycrystalline SnSe is still much lower than that of single crystal.In this work, heavy (6–12 atm%) Br‐doped n‐type polycrystalline SnSe1–
Br was prepared by melting and hot pressing. The Hall carrier concentration increased dramatically from 1.6 × 1017 cm−3 (p‐type) in undoped SnSe to 1.3 × 1019 cm−3 (n‐type) in Br‐doped SnSe0.88Br0.12, leading to an increased electrical conductivity close to that of single crystal SnSe. Combined with a lowered lattice thermal conductivity at high temperature by effective defect scattering and suppression of the bipolar effect, both the average ZT and the highest ZT were improved. A highest ZT value of ≈1.3 was achieved at 773 K for SnSe0.9Br0.1 along the hot pressing direction.
Results and Discussion
Since SnSe undergoes a structure transition from orthorhombic (Pnma) to orthorhombic (Cmcm) at about 780 K,27, 28 all the TE properties were measured below 780 K. Figure
shows the temperature dependence of a) electrical conductivity, b) Seebeck coefficient, and c) power factor for heavy Br‐doped SnSe1–
Br (x = 0, 0.06, 0.08, 0.1, and 0.12) measured parallel to the hot pressing direction. The electrical conductivity of SnSe0.97I0.03
23 (dotted line), SnSe0.97Br0.03
26 (dashed line), and single crystal SnSe17 (solid line) is included for comparison. The optical absorption spectra of all the samples were measured to verify the doping effect of Br (shown in Figure 1d). With increasing temperature, the electrical conductivity increased for undoped SnSe and all electron‐dopedSnSe, showing typical semiconductor behavior. The room temperature electrical conductivity dramatically increased from ≈50 S m−1 in undoped SnSe to ≈800 S m−1 in Br‐doped SnSe0.9Br0.1, higher than those of I‐doped SnSe0.97I0.03 (≈10 S m−1),23 less Br‐doped SnSe0.97Br0.03 (≈50 S m−1),26 and even close to that of single crystal SnSe along the b axis (≈1000 S m−1).17 The Seebeck coefficient is positive for undoped SnSe, indicating a p‐type semiconductor. Br doping changed the conductive type from p to n in the whole temperature range, which is consistent with the Hall measurement as shown in Figure
a. Contributed from the enhancement in electrical conductivity, the SnSe1–
Br samples exhibited improvement in power factors, as shown in Figure 1c. The highest power factor is ≈4.5 µW cm−1 K−2 at 773 K for 10 atm% Br‐dopedSnSe, which is four times higher than that of the undoped SnSe (≈1.1 µW cm−1 K−2). With increasing content of Br, the calculated band gap decreased from 0.91 eV for undoped SnSe to 0.88 eV for 10 atm% Br‐dopedSnSe, further suggesting the doping of Br (see Figure 1d).
Figure 1
Temperature dependence of a) electrical conductivity b) Seebeck coefficient, and c) power factor for SnSe1–
Br (x = 0, 0.06, 0.08, 0.10, and 0.12). The electrical conductivity for SnSe0.97I0.03
23 (dotted line), SnSe0.97Br0.03
26 (dashed line), and single crystal SnSe17 (solid line) is included for comparison. The polycrystals were measured parallel to the hot pressing direction. The single crystal was measured along the b axis. d) Optical absorption spectra of SnSe1–
Br (x = 0, 0.06, 0.08, 0.10, and 0.12). The inset shows the calculated band gap of the samples.
Figure 2
Temperature dependence of a) Hall coefficient and b) Hall mobility for SnSe1–
Br (x = 0, 0.06, 0.08, 0.10, and 0.12).
Temperature dependence of a) electrical conductivity b) Seebeck coefficient, and c) power factor for SnSe1–
Br (x = 0, 0.06, 0.08, 0.10, and 0.12). The electrical conductivity for SnSe0.97I0.03
23 (dotted line), SnSe0.97Br0.03
26 (dashed line), and single crystal SnSe17 (solid line) is included for comparison. The polycrystals were measured parallel to the hot pressing direction. The single crystal was measured along the b axis. d) Optical absorption spectra of SnSe1–
Br (x = 0, 0.06, 0.08, 0.10, and 0.12). The inset shows the calculated band gap of the samples.Temperature dependence of a) Hall coefficient and b) Hall mobility for SnSe1–
Br (x = 0, 0.06, 0.08, 0.10, and 0.12).To clearly demonstrate the electronic transport properties of undoped and Br‐dopedpolycrystalline SnSe, the room temperature Hall carrier concentration and Hall carrier mobility together with real composition and density of all the samples are listed in Table
. The relative density of all the samples is higher than 90% although the evaporation of Sn and Se during melting and hot pressing. With increasing content of Br, the room temperature Hall electron concentration increased to ≈1.3 × 1019 cm−3, higher than those of I‐doped (higher solubility of Br in SnSe than I in SnSe) and less Br‐dopedSnSe, suggesting the successful doping of Br. The carrier mobility decreased when Br was doped. Compared with the carrier mobility ≈250 cm2 V−1 s−1 of the single crystals along the b axis,17 the mobility of all the polycrystals is very low because of the scattering by the variety of defects in the crystal structure. Many factors, such as off‐stoichiometry, density (amount of holes), and microstructural features, etc. all together affect the carrier mobility, making the change of the carrier mobility for Br‐dopedSnSe complex. But with the increased carrier concentration, the electrical conductivity of heavy Br‐dopedSnSe is comparable to that of single crystal SnSe (see Figure 1a). We also investigated the temperature dependence of a) Hall coefficient and b) Hall mobility for SnSe1–
Br (x = 0, 0.06, 0.08, 0.10, and 0.12) and presented in Figure 2. With increasing content of Br, the absolute value of Hall coefficient decreased in the whole temperature range. The bipolar temperature increased after Br doping. The temperature dependence of Hall mobility (Figure 2b) shows an ionization impurity scattering at lower temperature for both undoped (T < 460 K) and heavy Br‐dopedSnSe (T < 600 K).
Table 1
Room temperature real composition, density, Hall carrier concentration (n
H), and carrier mobility (µ
H) for SnSe1–
Br samples measured along the hot pressing direction
Nominal Comp.
Real Comp.
Density [g cm−3]
nH [1018 cm−3]
µH [cm2 V−1 s−1]
SnSe
SnSe1.03
5.76
0.16
14.5
SnSe0.94Br0.06
SnSe0.96Br0.05
5.62
7.2
1.2
SnSe0.92Br0.08
SnSe0.91Br0.07
5.63
8.8
3.4
SnSe0.90Br0.10
SnSe0.87Br0.073
5.70
9.3
6.2
SnSe0.88Br0.12
SnSe0.82Br0.08
5.57
13.4
5.4
SnSe0.97I0.0323
SnSe0.88I0.03
5.81
0.046
–
SnSe0.97Br0.0326
–
5.80
1.8
0.6
SnSe (the b axis)17
–
–
0.3
250
Room temperature real composition, density, Hall carrier concentration (n
H), and carrier mobility (µ
H) for SnSe1–
Br samples measured along the hot pressing directionFigure
presents the temperature dependence of a) the thermal diffusivity, and b) total thermal conductivity of heavy Br‐doped SnSe1–
Br (x = 0, 0.06, 0.08, 0.1, and 0.12) in comparison with the reported data on n‐type SnSe0.8I0.03S0.1
23 (dotted line) and less Br‐doped SnSe0.97Br0.03
26 (dash line) measured parallel to the hot pressing direction. In a conservative way, considering that Br has a little higher atomic mass than Se, C
p of SnSe was used for the calculation of the total thermal conductivity for all the SnSe1–
Br samples. It should be mentioned that the total thermal conductivity (κ) is the sum of the electronic thermal conductivity (κe = LσT, where L is the Lorenz number) and lattice thermal conductivity (κL). The contribution of electronic thermal conductivity could be negligible due to the low electrical conductivity (<3000 S m−1) shown in Figure 1a. Therefore, the lattice thermal conductivity is almost the same as the total thermal conductivity. As the thermal conductivity depends on many factors such as density, off‐stoichiometry, and slightly different preferential orientation, etc., the room temperature thermal conductivity of Br‐doped samples looks random. With increasing temperature, the total thermal conductivity of all the samples decreased. The lowest room temperature thermal conductivity is ≈0.63 W m−1 K−1 for SnSe0.94Br0.06, lower than 0.72 W m−1 K−1 for SnSe0.87I0.03S0.1, and the lowest thermal conductivity is ≈0.25 W m−1 K−1 at 773 K for SnSe0.92Br0.08, lower than ≈0.30 W m−1 K−1 for SnSe0.87I0.03S0.1 and ≈0.32 W m−1 K−1 for SnSe0.97Br0.03. This low thermal conductivity (at 773 K) is comparable to the results for single crystals measured along the a axis (e.g., 0.23 W m−1 K−1 for undoped SnSe and 0.27 W m−1 K−1 for Na‐dopedSnSe).17, 29 With increasing content of Br, the thermal conductivity at 773 K decreased. The suppression of the bipolar effect (Figure 2a) possibly contributes to the decreased bipolar thermal conductivity at thigh temperature. Certainly, the low thermal conductivity of Br‐doped samples is also related to the defect scattering (we will discuss below). When Br is higher than 10 atm%, the thermal conductivity increased, which is maybe due to the doping limit confirmed by E
g data. In our previous study, lower thermal conductivity was achieved in 10 atm% SnS alloyed SnSe0.97I0.03 due to increased point defects,23 while heavy concentration of Br substituting Se in SnSe shows better effect in reducing the thermal conductivity.
Figure 3
Temperature dependence of a) thermal diffusivity and b) total thermal conductivity for SnSe1–
Br (x = 0, 0.06, 0.08, 0.1, and 0.12) measured parallel to the hot pressing direction compared with reported data on SnSe0.8I0.03S0.1
23 (dotted line) and SnSe0.97Br0.03
26 (dashed line).
Temperature dependence of a) thermal diffusivity and b) total thermal conductivity for SnSe1–
Br (x = 0, 0.06, 0.08, 0.1, and 0.12) measured parallel to the hot pressing direction compared with reported data on SnSe0.8I0.03S0.1
23 (dotted line) and SnSe0.97Br0.03
26 (dashed line).The intrinsically ultralow thermal conductivity of SnSe comes from the layered structure and strong anharmonicity of the chemical bonding.30 To further investigate the underlying mechanisms of the low thermal conductivity, we conducted a detailed microstructure investigation using high‐resolution transmission electron microscopy (HRTEM) and high‐angle annular‐dark‐field scanning transmission electron microscopy (HAADF‐STEM). The low‐magnification transmission electron microscopy (TEM) image in Figure
a shows a lamellar microstructure of SnSe0.9Br0.1 sample, which is consistent with layered crystal structure. Figure 4b,c shows HAADF‐STEM images viewed along [010] and [011] zone axes, respectively. The corresponding selected area electron diffraction (SAED) patterns inset in the upper left of the images. Since the contrast of HAADF‐STEM images is roughly proportional to Z1.7, where Z is the atomic number, the atomic column appeared bigger and brighter for Sn atoms (Z = 50) and smaller and darker for Se atoms (Z = 34) shown in Figure 4b. Along the [011] direction, the atomic columns of Sn and Se overlapped (see Figure 4c). Due to the similar atomic radii between Se and Br, a well integrality of lattice structure was achieved in spite of the substitution of Se with heavy content of Br, which is good for the electronic transport. The dashed rectangles represent the unit cell shown in Figure 4b,c. The two atom‐thick slabs marked by dashed rectangle were corrugated, forming a zigzag‐like Sn‐Se chains along the [001] direction. Some lattice distortions and defects were observed in the SnSe0.9Br0.1 sample. Figure 4d shows a [100] HRTEM image with contrast fluctuations. From the enlarged view inserted in the upper right, we can see the fluctuations clearly which is due to the composition fluctuations caused by Br doping. In Figure 4e, the spacing of the (400) planes in some areas as marked by the dashed line has a slight change. This lattice distortion is responsible for the intensity streaking along the [100]* direction in the corresponding fast Fourier transforms (FFTs) (see inset of Figure 4e). Figure 4f is a [021] image of SnSe0.9Br0.1, where the variety of images contrast induced by the dislocations is remarkable. In order to distinctly show the structure of the dislocation core, the filtering processing for Figure 4f was performed. From the filtered image shown in right part of Figure 4f, the inserted half planes parallel to (012) plane are clearly shown, which could significantly enhance the high frequency phonon scattering and contribute to the decreased high‐temperature thermal conductivity in Br‐dopedSnSe samples.
Figure 4
Microstructures of SnSe0.9Br0.1 sample. a) Low‐magnification TEM image shows the layered structure of the sample. HAADF‐STEM images of SnSe0.9Br0.1 viewed along b) [010] and c) [011]. The top‐left inset is the respective SAED pattern. The overlays show Se atoms in blue and Sn atoms in red. A single unit cell is marked by the dashed rectangle. d) A [100] HRTEM image with contrast fluctuations. e) HRTEM image shows the lattice distortion along the [100]* direction. The inset is corresponding FFTs. f) Many edge dislocations, and the extra half planes marked by ⊥ in magnified filtered image of the circular left area.
Microstructures of SnSe0.9Br0.1 sample. a) Low‐magnification TEM image shows the layered structure of the sample. HAADF‐STEM images of SnSe0.9Br0.1 viewed along b) [010] and c) [011]. The top‐left inset is the respective SAED pattern. The overlays show Se atoms in blue and Sn atoms in red. A single unit cell is marked by the dashed rectangle. d) A [100] HRTEM image with contrast fluctuations. e) HRTEM image shows the lattice distortion along the [100]* direction. The inset is corresponding FFTs. f) Many edge dislocations, and the extra half planes marked by ⊥ in magnified filtered image of the circular left area.Figure
a shows the temperature dependence of ZT for the SnSe1–
Br (x = 0, 0.06, 0.08, 0.10, and 0.12) samples. Due to the decreased thermal conductivity and increased electrical properties, the peak ZT increased with increasing Br content. The highest ZT value of ≈1.3 at 773 K was obtained in 10 atm% Br‐dopedSnSe, which is significantly higher compared to the undoped SnSe (ZT ≈0.3 at 773 K) sample and also higher than the previously reported maximum ZT of I‐doped (ZT ≈0.8 at 773 K),23 and less Br‐doped (ZT ≈1.1 at 773 K) n‐type SnSe.26 To further clarify the anisotropy of SnSe, the TE properties perpendicular to the hot pressing direction were also measured and presented in Figure S3 in the Supporting Information. Due to the comparable power factor but higher thermal conductivity, the ZT value perpendicular to the hot pressing direction is much lower than that parallel to the hot pressing direction. We also present the average ZTs between 300 and 773 K for undoped SnSe and 10 atm% Br‐dopedSnSe compared with reported optimum data of SnSe0.97I0.03,23 SnSe0.97Br0.03,26 and single crystal SnSe,17 shown in Figure 5b. The average ZT of 10 atm% Br‐dopedSnSe (≈0.35) is relatively higher than undoped SnSe (≈0.07), even close to that of single crystal SnSe (≈0.37) along the b axis.17
Figure 5
a) Temperature dependence of ZT for SnSe1–
Br (x = 0, 0.06, 0.08, 0.10, and 0.12) measured parallel to the hot pressing direction compared with reported data on SnSe0.97I0.03
23 (dotted line) and SnSe0.97Br0.03
26 (dashed line). b) Comparison of average ZT between 300 and 773 K for undoped SnSe (this work, green), 10 atm% Br‐doped SnSe (this work, purple), single crystal SnSe17 (the b axis, pink), SnSe0.97I0.03
23 (red), and SnSe0.97Br0.03
26 (blue).
a) Temperature dependence of ZT for SnSe1–
Br (x = 0, 0.06, 0.08, 0.10, and 0.12) measured parallel to the hot pressing direction compared with reported data on SnSe0.97I0.03
23 (dotted line) and SnSe0.97Br0.03
26 (dashed line). b) Comparison of average ZT between 300 and 773 K for undoped SnSe (this work, green), 10 atm% Br‐dopedSnSe (this work, purple), single crystal SnSe17 (the b axis, pink), SnSe0.97I0.03
23 (red), and SnSe0.97Br0.03
26 (blue).
Conclusions
In summary, we demonstrated an enhanced figure‐of‐merit in n‐type polycrystalline SnSe through a synergistic approach of optimizing the carrier optimization and effectively scattering the phonons by heavy bromine doping. With increasing doping concentration of Br, the room temperature Hall carrier concentration increased from 1.6 × 1017 cm−3 (p‐type) in undoped SnSe to 1.3 × 1019 cm−3 (n‐type) in SnSe0.88Br0.12, contributing to an increased electrical conductivity and power factor. The composition fluctuation and edge dislocations effectively scattered the short‐to‐medium wavelength phonons, resulting in the decreased thermal conductivity. With enhanced electrical properties and low thermal conductivity, a highest ZT value of ≈1.3 at 773 K was achieved in SnSe0.9Br0.1 along the hot pressing direction.
Experimental Section
Synthesis: Stoichiometric SnSe1–
Br (x = 0, 0.06, 0.08, 0.10, and 0.12) were prepared by melting, ball milling, and hot pressing. The raw materials (≈13 g, Sn shot (99.8%, Alfa Aesar), Se shot (99.999%, Australian Elements) and SnBr2 powder (99.2%, Alfa Aesar)) were sealed into the double evacuated quartz tubes and slowly heated up to 1193 K at a rate of 100 K h−1 and kept at that temperature for 6 h, then slowly cooled at the same rate to 873 K and kept for 50 h, finally slowly cooled to room temperature. The obtained ingots were cleaned and sealed into a stainless steel jar inside an argon filled glove box and ball milled by a high energy ball mill SPEX 8000D (SPEX SamplePrep) for 2 min. The powder was loaded into the graphite die and hot pressed at 873 K for 7 min using alternating current press (ac‐HP) under an axial pressure of 50 MPa, producing a cylinder‐shaped sample with ≈12.7 mm in diameter and ≈15 mm in height. All the samples were cut from two directions (parallel and perpendicular to the hot pressing direction) and measured along both directions.Characterizations: X‐ray diffraction spectra analysis was conducted on a Rigaku D/max 2500 PC instrument with Cu Kα (λ = 1.5418 Å) radiation and a scanning rate of 8 ° min−1 from two directions of the anisotropic samples. No obvious second phase was found when x ≤ 0.12 (see Figure S1a,b in the Supporting Information). The microstructures were investigated by a scanning electron microscope (SEM, Hitachi S4700) and a spherical aberration‐corrected (Cs‐corrected) electron microscope (JEM‐ARM200F). The chemical composition was analyzed by an energy‐dispersive X‐ray spectrometer attached to SEM. Room temperature optical diffuse reflectance spectra of the powders were detected on a UV‐3600 UV–vis–NIR spectrophotometer system. The band gaps were calculated using the Kubelka–Munk function. The Seebeck coefficient (S) and electrical resistivity (ρ) were simultaneously measured using a commercial system (CTA‐3) from room temperature to 773 K to avoid the effect of structural transition. Temperature‐dependent Hall coefficient (R
H) was measured using the van der Pauw technique under a reversible magnetic field of 1.5 T. Hall carrier concentration (n
H) and Hall mobility (µ
H) were calculated via n
H = 1/(eR
H) and µ
H = R
H/ρ, respectively. The thermal conductivity (κ) was calculated by κ = DαC, where D is volumetric density determined by the Archimedes method, α is thermal diffusivity measured using a laser flash technique (Netzsch LFA457), and C
p is specific heat capacity taken from previous data.17 Due to the anisotropy of SnSe, both the electrical and thermal transport properties were measured along and perpendicular to the hot pressing direction. The uncertainty for the electrical conductivity is 3%, the Seebeck coefficient 5%, the thermal conductivity 7% (comprising uncertainties of 4% for the thermal diffusivity, 5% for the specific heat, and 3% for the density), so the combined uncertainty for the power factor is 10% and that for ZT value is 12%. In order to increase the readability of the curves, error bars for TE data were not shown in the figures.
Conflict of Interest
The authors declare no conflict of interest.SupplementaryClick here for additional data file.
Authors: Mogens Christensen; Asger B Abrahamsen; Niels B Christensen; Fanni Juranyi; Niels H Andersen; Kim Lefmann; Jakob Andreasson; Christian R H Bahl; Bo B Iversen Journal: Nat Mater Date: 2008-08-31 Impact factor: 43.841