SnSe: a remarkable new thermoelectric material

Transcription

1 SnSe: a remarkable new thermoelectric material A radioisotope thermoelectric generator (RTG) is an electrical generator that uses an array of thermocouples to convert the heat released by the decay of a suitable radioactive material into electricity by the Seebeck effect. This generator has no moving parts. RTGs have been used as power sources in satellites and space probes etc, Figure 1 (a). The first radioisotope power units were developed in the late 1950s and early 1960s by the US and Soviet space programmes. The United States has used radioisotope power units on 27 missions, from a Navy navigation satellite launched in 1961 to the Mars Curiosity rover in 2011, Figure 1 (b) shows the RTG used in the Apollo 12, Figures 1 (c)-(e) show the RTGs in the movie of < The Martian>. Thermoelectric efficiency depends on the figure of merit, ZT. There is no theoretical upper limit to ZT, and as ZT approaches infinity, the thermoelectric efficiency approaches the Carnot limit. In the past two decades we have witnessed a surge in interest to develop alternative renewable energy technologies. The ZT is defined as ZT = (S 2 σ/к)t, where S, σ, к and T are the Seebeck coefficient, electrical conductivity, total thermal conductivity (a sum of electronic к ele and lattice к lat thermal conductivity), and absolute temperature, respectively. Therefore, high thermoelectric performance requires both a high power factor (S 2 σ) and a low thermal conductivity (к). Although it is quite difficult to control the above parameters independently due to their complex interrelationships, thermoelectric performance records have been broken continuously in the past decade, thanks to the development of new concepts and/or mechanisms. 1 Recently, SnSe surprised the scientific community as a new promising thermoelectric material, exhibiting one of the lowest lattice thermal conductivities known for crystalline materials (< 0.4 Wm -1 K -1 at 923K) and without even any doping achieving high ZTs > 2.3 at K along the b- and c- crystallographic directions. Hole doping leads to a remarkable enhancement in both electrical conductivity and the Seebeck coefficient, rationalizing the impressive performance. High ZT over K temperature range results in an expected maximum conversion efficiency of almost 17%. 1

2 Figure 1. Radioisotope thermoelectric generators (RTG) used in (a) deep space probes and (b) Apollo 12; (c) and (d) shows the RTGs in the movie of < The Martian>; (e) the typical RTG. 1. Crystal structure SnSe adopts a simple layered orthorhombic crystal structure at room temperature, which can be derived from a three-dimensional distortion of the NaCl structure. 2 Perspective views of the room temperature SnSe crystal structure along the crystallographic a, b, c axes are shown in Figures 2 (a)-(d). The structure contains highly distorted SnSe 7 coordination polyhedra with three short and four very long Sn-Se bonds and a lone pair (5s 2 ) from the Sn 2+ atoms sterically accommodated in between the four long Sn-Se bonds, see Figure 2 (b). The two-atom-thick SnSe slabs are strongly corrugated creating a zig-zag folded accordion-like projection along the b-axis. 2

3 Figure 2. SnSe crystal structure (gray Sn atoms and red Se atoms) along (a) a axis, (b) highly distorted SnSe 7 coordination polyhedron with three short and four long Sn-Se bonds, SnSe crystal structures along (c) b axis and (d) c axis. 2. Electronic band structure and DOS effective mass As shown in Figure 3 (a), The DFT valence band maximum (VBM) lies in the Γ-Z direction (band 1), but another valence band is located just below the VBM (band 2). 3 A third band also exists with its band maximum along the U-X direction (band 3). The calculation shows a very small energy gap between the first two valence bands in the Γ-Z direction of 0.06 ev. Such a small energy gap is easily crossed by the Fermi level as the hole doping approaches cm -3. In addition, the energy gap between the first and the third band (i.e. maximum of U-X to the maximum Γ-Z) is only 0.13 ev. This value is smaller to the 0.15 ev between the first and the second valence bands of PbTe, in which the heavy hole band contribution is significant as the carrier density exceeds cm -3. Interestingly, the electronic valence bands of SnSe are much more complex than PbTe, and the Fermi level of SnSe even approaches the 4 th, 5 th and 6 th valence bands when the doping levels in the material are as high as cm 3, Figures 3 (b)-(d). 3

4 Figure 3. (a) Electronic band structure of SnSe. The red dotted lines from top to bottom represent the Fermi levels with the carrier concentration of cm 3, cm 3, cm 3, and cm 3, respectively. (b-c) are the Fermi surfaces of SnSe (Pnma) at cm 3, cm 3 and cm 3, respectively Electrical transport properties When undoped the carrier concentration does not exceed cm -3, 2 Figure 4 (a). Hole doping increases the electrical conductivity from 12 S cm 1 to 1500 S cm 1 as the carrier concentration increases from cm -3 to ~ cm 3 at 300K, Figure 4 (b). For the undoped SnSe, the Seebeck coefficients show almost isotropic behavior and are independent of crystallographic direction, Figure 4 (c). For hole-doped SnSe, the Seebeck coefficient is +160 μvk -1 at 300K, and increases to +300 μvk -1 at 773K. After hole doping, however, the combination of vastly increased electrical conductivity and still high Seebeck coefficient results in a large power factor of 40 μwcm -1 K -2 for hole-doped SnSe (b axis) at 300K, Figure 4 (d). The high power factors obtained in hole-doped SnSe rival those of the optimized Bi 2-x Sb x Te 3 materials near room temperature (Poudel et al., Science 320 (2008) 634), and are much higher than those of the high performance hierarchical architectured p-type PbTe-SrTe system in the range of K (Biswas et al., Nature 489 (2012) 414). 4

5 Figure 4. Electrical transport properties for undoped SnSe 2 and hole-doped SnSe 3 : (a) electrical conductivity; (b) carrier concentration; (c) Seebeck coefficients and (d) power factors. 4. Origin of the ultra-high power factor These high power factors derive from the much larger Seebeck coefficient since the electrical conductivity of hole-doped SnSe (b axis) is comparable to those of the rock-salt chalcogenides. As shown in Figure 5 (a), the room temperature Seebeck coefficients of rock-salt chalcogenides plotted with similar carrier concentration of cm -3 offer further insight into the enhanced Seebeck coefficients. The Seebeck coefficient for hole-doped SnSe +160 μvk -1 is clearly much higher than +70 μvk -1 for PbTe, +60 μvk -1 for PbSe, +50 μvk -1 for PbS, and +25 μvk -1 for SnTe. 3 As shown in Figure 5 (b), the Seebeck coefficient calculated with the full, multi-valley DFT band structure is +168 μvk -1 at cm 3, which is very close to the experimentally observed value for this carrier concentration, +160 μvk -1. In contrast, using a single band model gives a much lower Seebeck coefficient and cannot reproduce the experimental values. Therefore, the observed experimental Seebeck coefficient enhancements of hole-doped SnSe can be attributed to the multi band character of the electronic structure, as shown by the schematic diagram of Figure 5 (c). The Hall coefficient (R H ) is consistent with multi-valley transport as it shows a continuous increase with temperature in the range K (inset of Figure 5 (d)). A single band transport would have produced a temperature-constant Hall 5

6 coefficient. The values of R H in hole-doped SnSe are temperature dependent, thus ruling out the single band model of transport. The Hall data imply that the convergence of multiple band maxima of hole-doped SnSe has already happened below room temperature consistent with the notion that the energy difference between the competing valence bands in SnSe is much lower than in PbTe. The energy gap ( E) between the first two bands is estimated using the slope (- E/k B ) of ln[r H (T)-R H (0)]/R H (0) vs. 1/T plot, which yields a E 0.02 ev at 0 K, assuming E varies linearly with temperature, Figure 5 (d). The E 0.02 ev estimate is consistent with the DFT calculation value 0.06 ev, and comparable to k B T at room temperature suggesting the valence bands are nearly equal in energy. This energy gap between the first two valence bands of SnSe is much smaller than that in PbTe (0.15 ev), PbSe (0.25 ev), PbS (0.45 ev) and SnTe (0.35 ev). Figure 5. (a) Room temperature Seebeck coefficients comparisons; (b) calculated Seebeck coefficients as a function of carrier density; (c) schematic diagram showing the multiple valence bands of SnSe; (d) ln[r H (T)-R H (0)]/R H (0) as a function of 1/T, inset shows the Hall coefficient for hole-doped SnSe Intrinsically low thermal conductivity and anharmonic bonding The temperature dependence of total thermal conductivities ( tot ) for undoped and hope doped SnSe are shown in Figure 6 (a). At room temperature, the values of tot for undoped SnSe are ~ 0.46, 0.70 and 0.68 W m -1 K -1 along the a, b and c axis directions, 6

7 respectively. Compared to state-of-the-art thermoelectrics, these thermal conductivity values are exceedingly low and surprisingly they decrease even further with rising temperature. At 773 K they all fall in the range W m -1 K It should be noted that the thermal conductivity of SnSe is intrinsically lower than that of hierarchical architecture p-type PbTe-SrTe system (Biswas et al., Nature 489 (2012) 414), as shown in Figure 6 (b). The low thermal conductivity in single phase SnSe is therefore believed to derive from the very high anharmonicity of its chemical bonds but other factors may also play a role such as non-stoichiometry, defects etc. 2 To more accurately obtain an estimate of the lattice thermal conductivity of hole-doped SnSe, the Lorenz number L has to be calculated based on a multi-band model, as shown in Figure 6 (c). Using more correct Lorenz numbers, one can see that the lattice thermal conductivity of hole-doped SnSe is comparable to, even lower than undoped SnSe, Figure 6 (d). Figure 6. (a) Total thermal conductivities for undoped SnSe 2 and hole-doped SnSe 3 ; (b) The lattice thermal conductivity comparison of SnSe along b axis 2 and hierarchical architectured PbTe-4SrTe-2Na (Biswas et al., Nature 489 (2012) 414); (c) The calculated Lorenz number; (d) The lattice thermal conductivity comparisons of undoped SnSe 2 and hole-doped SnSe. 3 The intriguing question is what gives rise to the ultralow thermal conductivity of SnSe? The 5s 2 lone electron pair of Sn 2+ and its tendency to stereochemically express itself by occupying its own space in the structure and causing a wide range of Sn-Se bond lengths is behind a strong case of extreme bond anharmonicity which causes ultra 7

8 strong phonon scattering. Although all bonding in real materials is anharmonic, the degree of anharmonicity varies strongly from material to material. In general, materials with substantial anharmonic bonding have low thermal conductivities. 2 Ideal perfectly harmonic bonds in one-dimension are schematically illustrated in Figure 7. The force to which an atom is subjected is proportional to its displacement from equilibrium position, and the proportionality constant is called the spring constant or stiffness. In the anharmonic case, the spring stiffness varies with increasing atom displacement, which has pronounced consequences when two phonons run into each other. The presence of the first phonon then changes the spring constant values for the second phonon, which thus runs into a medium with modified elastic properties. High anharmonicity therefore results in enhanced phonon-phonon scattering, which reduces the lattice thermal conductivity. The Grüneisen parameter is used to measure the strength of anharmonicity. The larger is the Grüneisen parameter, the stronger is the anharmonicity and thus phonon scattering. The PbTe system has extraordinary physical and chemical properties favorable for high thermoelectric performance one of which is the large Grüneisen parameter of ~1.45. The large Grüneisen parameter in PbTe can be ascribed to the recent discovery that the Pb atoms are in fact somewhat displaced off the octahedron center in the rock-salt structure and the displacement increases with rising temperature (Bozin et al., Science 330 (2010) 1660). Figure 7. The schematic representations of harmonicity and anharmonicity, anharmonicity is the deviation from the equilibrium position that being harmonicity. What is the atomic level basis for anharmonic bonding in SnSe? In our view the broad range of bond lengths between Sn and Se atoms in the layered accordion-like structure, which is a consequence of the tendency of the 5s 2 lone pair of electrons in Sn 2+ to stereochemically express itself, is at the root of this property. This situation creates expanded coordination polyhedra around the Sn 2+ centers with a mix of weak, medium and strong Sn-Se interactions which can in principle participate in resonance bonding states which can be dynamic especially at high temperatures. The resonant type bonding is schematically shown in Figure 8. This can give rise to a soft 8

9 malleable coordination environment and crystal structure and high anharmonicity. Figure 8. Schematic indicating resonant bonding in SnSe. 6. The maximum and device ZT Doping SnSe with donor and acceptor atoms is not as straightforward as it is with PbTe, PbSe or PbS. It seems that many conventional dopants are rejected from the structure or are accommodated to a very limited degree. We believe this is because of the layered anisotropic structure where each SnSe layer is only two atoms thin and the locally distorted highly covalent bonding around the Sn and Se atoms may destabilize guest atoms with large differences in chemical character. We found that sodium is one of the effective acceptor dopants in SnSe, which cause a two order of magnitude increase in the hole concentration, 3 and a vast increase in ZT from 0.1 to 0.7 along the b axis at 300K while obtaining the ZT max of 2.0 at 773K, Figure 9 (a). The ZT max is large over the entire working temperature range of K and likely also below 300K. The material also projects a large so-called average or device ZT dev, which actually determines the overall thermoelectric conversion efficiency ( ) of a device. In fact, SnSe has the highest device ZT of ~1.34 (ZT dev ) from K known among thermoelectric materials. The projected theoretical conversion efficiency of hole-doped SnSe for T c =300K and T h = 773K is 17 %, Figure 9 (b). Figure 9. (a) ZT values for SnSe crystals; (b) The calculated efficiency as a function of hot 9

10 side temperature (cold side temperature is 300K) of hole-doped SnSe (b axis), 3 undoped SnSe (b axis), 2 PbTe-4SrTe-2Na (Biswas et al., Nature 489 (2012) 414), and PbTe-30PbS-2.5K (Wu et al. Nature Comm.5 (2014) 4515). Summary and Outlook The physics of thermal and charge transport in SnSe is unusual and fascinating. The high thermoelectric performance of SnSe crystals suggests that single phase materials, strongly anharmonic bonding and intrinsically ultralow thermal conductivity are promising candidates for developing high thermoelectric performance. It is remarkable that such an ultralow thermal conductivity can be realized in a simple compound such as SnSe, as it does not have high molecular weight, a complex crystal structure or a large unit cell. It is also remarkable that such an ultra-high power factor can be achieved in a not so narrow bandgap semiconductor of only orthorhombic crystal symmetry. The multiple valence band extrema lying closely in energy is the key to this performance which persists of over a wide temperature plateau from K and perhaps even wider. Hole doping quickly pushes the Fermi level deep into the valence band structure activating several Fermi pockets to produce enhanced Seebeck coefficients and high power factors. The resulting high figure of merit improves the prospects of realizing very efficient thermoelectric devices using hole-doped SnSe crystals as a p-type leg. The discovery of exceptional physical properties in SnSe clearly points to new directions in thermoelectric science in terms of what materials systems might we pursue as superior thermoelectrics. In this context many more materials are yet to be investigated, especially those that share electronic and structural features with SnSe. Acknowledgments This work was supported by the Zhuoyue program of Beihang University, the Recruitment Program for Young Professionals, and NSFC under Grant No We thank Professors M.G. Kanatzidis, H. B. Xu, Y. L. Pei, S. K. Gong, J. G. Snyder, C. Uher, C. Wolverton, V. P. Dravid and J. P. Heremans, for plentiful discussions and fruitful collaborations. Lidong Zhao, professor, school of material science and engineering, Beihang University, zhaolidong@buaa.edu.cn Lidong Zhao received his B.E. and M.E. degrees in Materials Science from the Liaoning Technical University and his Ph.D. degree in Materials Science from the University of Science and Technology Beijing in He was a postdoctoral research fellow in the LEMHE-ICMMO (CNRS-UMR 8182) at the University of Paris-Sud from 2009 to 2011, and a postdoctoral research fellow in the Department of Chemistry at the Northwestern University since He has published nearly 100 SCI-indexed papers including Science, Nature, Nature Commun., Chemical Reviews, J. Am. Chem. Soc., Energy Environ. Sci., Adv. Mater., Adv. Funct. Mater., Adv. Energy 10

11 Mater., PRB, etc. He has 8 granted China patents, and 2 US patents. He is on the editorial advisory board of journals of Materials Science in Semiconductor Processing and Progress in Natural Science: Materials International. He is an American Chemical Society member. References [1] L. D. Zhao, et al., Energy & Environmental Science 7, 251 (2014). [2] L. D. Zhao, et al., Nature 508, 373 (2014). [3] L. D. Zhao, et al., Science 351, 141 (2016). Significance Statistical results show that more than 60% of energy is lost in vain worldwide, most in the form of waste heat. High performance thermoelectric materials that can directly and reversibly convert heat to electrical energy have thus draw growing attentions of governments and research institutes. Thermoelectric system is an environment-friendly energy conversion technology with the advantages of small size, high reliability, no pollutants and feasibility in a wide temperature range. A dimensionless figure of merit (ZT) is defined as a symbol of the thermoelectric performance, ZT=(S 2 σ/к)t. Higher average ZT values projects higher thermoelectric power generation and cooling efficiency. Conceptually, to obtain a high ZT, both Seebeck coefficient (S) and electrical conductivity (σ) must be large, while thermal conductivity (κ) must be minimized so that the temperature difference producing Seebeck coefficient can be maintained. Figure (a) is the power generation model based on the Seebeck effect, where an applied temperature difference drives charge carriers in the material to diffuse from hot side to cold side, resulting in a current flow through the circuit. The Seebeck effect is the thermoelectric power generation model. And in some extreme situations or special occasions, the thermoelectric technology plays an irreplaceable role. The radioisotope thermoelectric generators (RTGs) have long been used as power sources in satellites and space probes, such as Apollo 12, Voyager 1 and Voyager 2, etc. Nowadays, thermoelectric power generation gets increasing application in advanced scientific fields, and the thermal source could be fuels, waste-heat, geothermal energy, solar energy and radioisotope, as shown in Figure 1 (c). Figure (b) is the thermoelectric cooling model based on the Peltier effect, where the heat is absorbed at the upper junction and rejected at the lower junction when a current is made to flow through the circuit, and the upper end is active cooling. Thermoelectric coolers can also be used to cool computer components to keep temperatures within design limits, or to maintain stable functioning when overclocking. For optical fiber communication applications, where the wavelength of a laser or a component is highly dependent on temperature, Peltier coolers are used along with a thermistor in a feedback loop to maintain a constant temperature and thereby stabilize the wavelength of the device. 11

12 Fig. (a) thermoelectric power generation model, (b) thermoelectric cooling model, (c) the space probe and thermoelectric generators 12

13 Fig. Coverpage of Science 351 (2016) in which the paper was published 13

14 Fig. Photo of first page of the published paper 14