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High Performance GeTe Thermoelectrics in both Rhombohedral and Cubic Phases Juan Li, Xinyue Zhang, Xiao Wang, Zhonglin Bu, Liangtao Zheng, Binqiang Zhou, Fen Xiong, Yue Chen, and Yanzhong Pei J. Am. Chem. Soc., Just Accepted Manuscript • DOI: 10.1021/jacs.8b09147 • Publication Date (Web): 25 Oct 2018 Downloaded from http://pubs.acs.org on October 26, 2018
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Journal of the American Chemical Society
High Performance GeTe Thermoelectrics in both Rhombohedral and Cubic Phases Juan Li, Xinyue Zhang, Xiao Wang, Zhonglin Bu, Liangtao Zheng, Binqiang Zhou, Fen Xiong, Yue Chen and Yanzhong Pei1, * 1Interdisciplinary Materials Research Center, School of Materials Science and Engineering, Tongji Univ., Shanghai 201804, China. 2Department of Mechanical Engineering, The University of Hong Kong, Pokfulam Road, Hong Kong SAR, China. *Email:
[email protected] (YP)
Abstract: GeTe experiences phase transition between cubic and rhombohedral through the distortion along [111] direction. Cubic GeTe shares the similarity of a two-valence-band structure (high-energy L and low-energy bands) with other cubic IV-VI semiconductors such as PbTe, SnTe and PbSe, and all show a high thermoelectric performance due to a high band degeneracy. Very recently, the two valence bands were found to switch in energy in rhombohedral GeTe and to be split due to the symmetry-breaking of the crystal structure. This enables the overall band degeneracy to be manipulated either by the control of symmetry-induced degeneracy or by the design of energy-aligned orbital degeneracy. Here, we show Sb-doping for optimizing carrier concentration and manipulating the degree of rhombohedral lattice distortion to maximize the band degeneracy and then electronic performance. In addition, Sb-doping significantly promotes the solubility of PbTe, enhancing the scattering of phonons by Ge/Pb substitutional defects for minimizing the lattice thermal conductivity. This successfully realizes a superior thermoelectric figure of merit, zT of >2 in both rhombohedral and cubic GeTe, demonstrating these alloys as top candidates for thermoelectric applications at T2 in both low-temperature rhombohedral and high-temperature cubic phases, which clearly demonstrates GeTe as a top candidate for efficient thermoelectric power generation applications below 800 K. Results and discussion
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600 0
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Sb-doping 10
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at.% Pb
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Ge0.9Pb0.1Te
20m
Ge0.85Pb0.15Te
e
d
with 4% Sb
20m
Ge0.81Pb0.15Sb0.04Te
20m
Ge0.56Pb0.4Sb0.04Te
Figure 1. Pseudo binary phase diagram of GeTe-PbTe69 with an rough illustration of the increase in PbTe solubility due to Sb-doping (a). Back scattering SEM images for GeTe-PbTe system without (b and c) and with (d and e) Sb-doping, indicating the solubility of PbTe (white spots in c) increases from ~10% to >40% due to 4% Sb-doping and the existence of Ge-precipitates (black domains in b, d and e) in all samples.
Details on synthesis, characterization and measurements of the materials can be found in the supplementary. The room temperature powder X-ray diffraction patterns for all samples are all shown in Figure S1, all the diffraction peaks can be indexed to the rhombohedral structure of GeTe with trace amount of Ge but no PbTe impurity phase is observed. Rietveld refinements are carried out based on the powder X-ray diffraction data to estimate the lattice parameters and inter-axial angles (Fig. 2). Taking Ge0.78Pb0.2Sb0.02Te and Ge0.78Pb0.2Sb0.02Te (Figure S2) for example, more details on the refinement and structural parameters for these samples are given in Table S1and Table S2. In order to further characterize the phase composition, scanning electron microscope (SEM) and energy dispersive spectroscopy (EDS) analyses are carried out (Figure. 1 and S3). When the nominal PbTe concentration is 15% in GeTe, exceeding the solubility (~10%, Figure 1a), PbTe secondary phase is observed as shown in Figure 1c and S3a. However, when doped with 2% Sb the solubility of ACS Paragon Plus Environment
a
xPb (%)
88.8
=0 x Pb
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=0 x Pb
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1
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ySb (%)
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Ge0.85-yPb0.15SbyTe, this work Ge0.8-yPb0.2SbyTe, this work
100
Two-band model, this work
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Ge1-xPbxTe,this work Ge0.96-xPbxSb0.04Te, this work
.15
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xPb+ySb (%)
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25
60 40
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1020
=0 x Pb 0
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xPb (%)
300 K 0
50
88.2 0
c S (V/K)
(deg.) (deg.)
a (Å) a (Å)
10 15 20 25 30 35 40
0
10 15 20 25 30 35 40
Te Sb y
5
88.3
xPb=0.1
6.04
5
Te Sb y
xPb=0.15
1
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Ge0.9-yPb0.1SbyTe, this work
0
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xPb=0.2
6.08
88.6
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xPb (%)
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10 15 20 25 30 35 40
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Ge1-x-yPbxSbyTe, 300 K
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8
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It is found that the energy of mixing decreases from 45.6 meV to 41.1 meV due to Sb-doping in this composition. This means that Sb-doping tends to decrease the formation energy of the alloy, resulting in an increase in the solubility of PbTe in GeTe. It should be noted that all the materials come with trace amount of Ge having similar concentration and distribution (Figure 1 and S3), which is a common case for GeTe 65, 70. This work focuses on materials with 10%, 15% and 20% PbTe alloying with optimized hole concentrations, which all show a peak zT greater than 2 but the origins are different.
nH 1020 cm-3
.
(Figure 3a and 3b). A similar saturation in nH is observed in GeTe alloys without Sb-doping when the PbTe concentration exceeds 10%, which further confirms a limited PbTe solubility of ~10% with the absence of Sb-doping and agrees well with the XRD and SEM results. The decreased hole concentration with the increase of Sb-doping indicates the successful substitution of Ge by Sb for releasing electrons, which is consistent with literature results42, 46, 72. Importantly, alloying and doping nicely enable a board range of carrier concentration (nH) to be achieved, which ensures an optimal nH to be located for maximizing the electronic performance. In addition, such a board carrier concentration enables a detailed comparison on the transport properties to literatures46, 65, 67-68. Figure 3c and 3d show the room temperature Hall carrier concentration dependent Seebeck coefficient (c) and hall mobility (d) for Ge1-x-yPbxSbyTe (x=0.1, 0.15, 0.2), which indicate a negligible modification on band structure due to alloying/doping since the scattering of charge carriers is dominated by acoustic phonons for all samples including pristine GeTe26-27, 41 (Figure S4).
H (cm2/V-s)
PbTe quickly increases to be >20% (Fig. S3b), and 4% Sb-doping leads to a Pb-doping of >40% (Figure 1e and S3c). This indicates that a Sb-doping of 40% (Figure 1a), enabling a systematical investigation on thermoelectric properties of GeTe-based alloys in a broad composition range. To investigate the effect of Sb-doping on the miscibility of GeTe and PbTe, DFT calculations on the energy of mixing for Ge1-x-yPbxSbyTe alloy with y=41% and x= 3.7% are carried out, according to the following equation:
.8 Ge 0
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nH 1020 cm-3
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Figure 2. PbTe-alloying (a and b) and Sb-doping (c and d) dependent lattice parameters (a and c) and rhombohedral angle (b and d) for Ge1-x-yPbxSbyTe alloys at room temperature, with a comparison to literature results62-63, 71, the solid lines are guide to the eye.
-3
1021
nH (cm )
1020
-3
nH (cm )
1021
Figure 3. Composition dependent Hall carrier concentration (a and b), as well as Hall carrier concentration dependent Seebeck coefficient (c) and Hall mobility (d) for Ge1-x-yPbxSbyTe alloys at room temperature, with a comparison to literature results for GeTe alloys41.
a
b
c
The composition dependent lattice parameters and the rhombohedral angle for Ge1-x-yPbxSbyTe alloys with and without Sb-doping are shown in Figure 2a and Figure 2b, respectively. The lattice parameters and interaxial angle show a saturation when x=0.1 for Sb-free samples but continue increasing linearly when Figure 4. Effective band structures of Ge1-xPbxTe alloys, where a 4% Sb-doping is applied. Once fixing the PbTe concentration at 3×3×3 supercell of rhombohedral GeTe is constructed with 5 or 11 of 27 10%, 15% and 20%, varying Sb-doping concentration leads to an Ge atoms be substituted by Pb to simulate PbTe-alloying concentrations increase in both lattice parameters and rhombohedral angle of 19% or 41%, respectively. (Figure 2c and 2d). The main difference between PbTe-alloying To further verify the influence of PbTe-alloying in GeTe, and Sb-doping, relies on the factors that the former dominates the DFT calculation on band structure (Figure 4) is carried out lattice expansion while the later largely pushes the interaxial angle considering alloying concentrations of 19% and 41%, respectively. to approach to 90 degrees (a cubic lattice) when x≤20%. It is seen that Pb-alloying has an insignificant effect on the Being consistent with the linear change in lattice parameters, valence band structure of α-GeTe. It should be noted that a small the room temperature hall carrier concentration (nH) decreases band gap observed at a high Pb concentration (~41%) is believed with increasing PbTe-alloying and Sb-doping concentrations ACS Paragon Plus Environment
Journal of the American Chemical Society 2.0 Ge1-x-yPbxSbyTe
2.0 1.5 1.0 0.5
min 0
5
10 15 20 25 30 35 40
xPb (%)
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3000
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Figure 5. Composition dependent lattice thermal conductivity (a) and sound velocity (b) for Ge1-x-yPbxSbyTe alloys at room temperature, with and without 4% Sb doping.
The detailed temperature dependent Seebeck coefficient, resistivity, thermal conductivity and its lattice thermal component, as well as the thermoelectric figure of merit for Ge1-x-yPbxSbyTe alloys with x=0.10, 0.15, 0.2 are respectively shown in Figure S5, S6 and S7. It is seen that majority of the samples studied here shows a degenerated semiconducting behavior, particularly at T600 K, a few samples with a low carrier concentration (nH25% PbTe alloying at room temperature. Such a low L is approaching the amorphous limit of GeTe according to the Cahill model73-74. In addition, L for samples with and without Sb doping, can be well understood by the Debye-Callaway model75 (solid curves in Figure 5a, details are given in the supplementary), taking into account the changes in sound velocities due to PbTe-alloying. The decrease in sound velocity (Figure 5b) due to alloying suggests a bond softening 57-58, which also contributes to the L-reduction observed (Figure 5a), and the solids lines in Figure 5b are guide to the eye. The optimization in carrier concentration and the reduction in lattice thermal conductivity due to Sb-doping and PbTe-alloying, definitely contribute to an enhancement in thermoelectric figure of merit (zT) in these GeTe-based materials as shown in Figure 6a. Indeed, a high zT of>2 can be guaranteed in both rhombohedral and cubic GeTe with 10~20% PbTe-alloying once the carrier concentration is optimized (Figure S5-S7). A further increase in PbTe-alloying leads to no further improvements in zT in this work.
Energy
b
Sound velocity m/s
a 3.0
0.0
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Ge1-x-yPbxSbyTe, 300 K
L w/m-k
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60
to be related to the unfolding technique, in which only atomic positions are allowed to be relaxed (DFT computational details can be found in Supplementary).
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500
600
T (K) C
700
800
C
Symmetry degree
L4 6 12
6 Z L 3 Rhom.
Near Cubic
Cubic
Figure 6. Temperature dependent thermoelectric figure of merit for Ge1-x-yPbxSbyTe alloys (a), demonstrating their excellent thermoelectric performance in both rhombohedral and cubic phases. Schematic of band structure evaluation for GeTe versus its rhombohedral angle, as well as the illustration of symmetry breaking leading to a better convergence of split bands, a reduced lattice thermal conductivity and an enhanced thermoelectric performance (b).
To understand the high zT achieved from the aspect of band structure, the lower effective masses for both L and bands in cubic GeTe as compared to those of cubic IV-VI semiconductors41, 55, 76, could explain the high thermoelectric performance at 800K (cubic phase). Surprisingly, rhombohedral GeTe actually shows an even higher thermoelectric performance than that of cubic one. This is due to the better convergence of split valence bands in rhombohedral but close to cubic phase. In more details, rhombohedral can be approximated as a directionally distorted cubic lattice along the [111] direction. This results in the interaxial angle decreasing from right to acute. And the degree of rhombohedral angle deviating from 90 can be used as a measure of the degree of rhombohedral distortion. As can be seen from Figure 2, the change in the degree of rhombohedral distortion is dominated by Sb-doping for Ge1-x-yPbxSbyTe alloys when x≤20%, leading the crystal structure to be closer to cubic in GeTe with higher Sb-doping concentrations. Once the cubic lattice reduces to rhombohedral, the original 4 valleys of L band of split into 3 at L and 1 at Z valleys, whereas the original 12 valleys of Σ band split into 6 along Σ and 6 along η valleys41, 77-78. Moreover, the dominant transporting valence band quickly changes from L band in cubic phase to band in rhombohedral phase 41. This indicates that the rhombohedral angle plays an critical role on the valence band structure of GeTe, which has been confirmed by band structure calculations49. Comparing to the case of Bi-doping49, Sb-doping in this work leads to a similar valence band convergence through the control of the cubic-to-rhombohedral symmetry breaking (the rhombohedral angle), which results in a comparable zT -enhancement in the low-T rhombohedral phase. In addition, Sb-doping in this work promotes the solubility of PbTe, ensuring a well-reduced lattice thermal conductivity for realizing a high zT in the high-T cubic ACS Paragon Plus Environment
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phase as well. The above-mentioned 4 in total split valence bands (L3, Z1, Σ6 and η6) in rhombohedral GeTe, largely diversifies the arrangement in energy for a probable higher overall valley degeneracy as illustrated in Figure 6b. This leads to a belief that a better band convergence takes the responsibility for the higher zT in rhombohedral phase than that in cubic phase (Figure 6a). In this work, the degree of rhombohedral distortion can be continuously controlled by Sb-doping and PbTe-alloying (Figure 2), and the band structure mostly favoring thermoelectric performance happens in a rhombohedral phase but close to cubic. Therefore, it can be seen (Figure S5-S7) that material with a smaller concentration of PbTe-alloying requires a higher Sb-doping to optimize the carrier concentration, which leads to a weaker rhombohedral distortion. Quantitatively, when PbTe concentration increases from 10%, 15% to 20%, the required Sb-doping respectively decreases from about 4%, 3% to 2% for optimizing the carrier concentration. This indicates that a high zT in rhombohedral GeTe is expected to have a less PbTe-alloying, while a high zT in cubic GeTe requires more (Figure 6a). Moreover, the high thermoelectric performance in materials shown in Figure 6a is found to be reproducible according to repeated measurements on the same sample (or repeated ones) with a few thermal cycles (Figure S10). This is further supported by the nearly unchanged XRD patterns (Figure S11) on the samples before and after these thermal cycling. Phase transition in GeTe usually leads to a deflection of zT curve. Since Sb-doping dominates the increase of rhombohedral angle toward right angle (Fig. 2b) while the required concentration of Sb-doping for maximizing zT decreases with increasing PbTe-alloying (Fig. 6a), phase transition is found to occur at a lower temperature in materials with a higher Sb-doping concentration (Fig. S12), although PbTe-alloying should increase the phase transition temperature26. The temperature enabling the maximum zT increases with increasing PbTe-alloying, which leads the optimal carrier concentration (n*) for the x=0.1 samples to be higher than that of x=0.15 and x=0.2. This can be understood because n* is strongly temperature dependent via n*~ (m*T)1.5, where m* as the density-of-state mass. Therefore, the decrease in zT with increasing temperature after phase transition in the samples with x=0.1 can be attributed to the bipolar effect (Fig. S5a and S5b) induced by the low carrier concentration. Summary This work demonstrates GeTe alloys as truly top candidates for thermoelectric applications in both rhombohedral phases, where the crystal structures can be well controlled by alloying and doping processes. In addition to the significantly increased PbTe solubility induced by Sb-doping, which sufficiently reduces the lattice thermal conductivity to approach the amorphous limit, the resulting modifications in crystal structure leads to an even higher degeneracy of band valleys in rhombohedral phase for a high thermoelectric performance. Since many thermoelectric materials79-81 enables similar crystal structure modifications, the mechanism of symmetry-breaking for an even higher band degeneracy as illustrated here, could open new possibilities for realizing high thermoelectric performance in low-symmetry materials. Supporting Information. Materials and method, detailed XRD
properties, and the Debye-Callaway model. 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), Fundamental Research Funds for Science and Technology Innovation Plan of Shanghai (18JC1414600), the Fok Ying Tung Education Foundation (Grant No. 20170072210001) and “Shu Guang” Project Supported by Shanghai Municipal Education Commission and Shanghai Education Development Foundation. FX 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
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TOC
15
1.0
x=
0.
1
x
. =0
0.
1.5
2
Ge1-x-yPbxSbyTe
x=
2.0
zT
C
Energy
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60
Journal of the American Chemical Society
0.5
C
C
Symmetry degree
L4 6 12
6 Z L 3
0.0 300
Rhom.
400
500
600
T (K)
Near Cubic
700
ACS Paragon Plus Environment
Cubic
800
