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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

= (S2σ/к)T, where S, σ, к and T are the Seebeck coefficient, electrical conductivity,

total thermal conductivity (a sum of electronic кele and lattice кlat thermal

conductivity), and absolute temperature, respectively. Therefore, high thermoelectric

performance requires both a high power factor (S2σ) 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 723-973K 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

300-773K temperature range results in an expected maximum conversion efficiency

of almost 17%.

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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 SnSe7 coordination polyhedra with three short and four very long

Sn-Se bonds and a lone pair (5s2) 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.

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Figure 2. SnSe crystal structure (gray Sn atoms and red Se atoms) along (a) a axis, (b) highly

distorted SnSe7 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 4 × 1019

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 5 × 1019

cm-3

. Interestingly, the electronic valence bands of SnSe are much

more complex than PbTe, and the Fermi level of SnSe even approaches the 4th

, 5th

and

6th

valence bands when the doping levels in the material are as high as 5 × 1020

cm−3

,

Figures 3 (b)-(d).

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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 5 × 1017

cm−3

, 5 × 1019

cm−3

, 2 ×

1020

cm−3

, and 5 × 1020

cm−3

, respectively. (b-c) are the Fermi surfaces of SnSe (Pnma) at 5 ×

1019

cm−3

, 2 × 1020

cm−3

and 5 × 1020

cm−3

, respectively.3

3. Electrical transport properties

When undoped the carrier concentration does not exceed ∼1017

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 ∼1017

cm-3

to ~ 1019

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 Bi2-xSbxTe3 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 300-500K (Biswas et al., Nature 489 (2012) 414).

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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

4 × 1019

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 4 × 1019

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 (RH) is consistent with multi-valley transport as it

shows a continuous increase with temperature in the range 10-773K (inset of Figure 5

(d)). A single band transport would have produced a temperature-constant Hall

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coefficient. The values of RH 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/kB) of

ln[RH(T)-RH(0)]/RH(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 kBT 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[RH(T)-RH(0)]/RH(0) as a function of 1/T, inset shows the Hall

coefficient for hole-doped SnSe.3

5. 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,

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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 0.25-0.28 W m-1

K-1

.2 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 axis2 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 SnSe2 and hole-doped SnSe.

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The intriguing question is what gives rise to the ultralow thermal conductivity of SnSe?

The 5s2 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

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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 5s2 lone pair of electrons in

Sn2+

to stereochemically express itself, is at the root of this property. This situation

creates expanded coordination polyhedra around the Sn2+

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

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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 ZTmax of 2.0 at 773K, Figure 9 (a). The ZTmax is

large over the entire working temperature range of 300-773K and likely also below

300K. The material also projects a large so-called average or device ZTdev, which

actually determines the overall thermoelectric conversion efficiency () of a device.

In fact, SnSe has the highest device ZT of ~1.34 (ZTdev) from 300-773K known

among thermoelectric materials. The projected theoretical conversion efficiency of

hole-doped SnSe for Tc =300K and Th = 773K is 17 %, Figure 9 (b).

Figure 9. (a) ZT values for SnSe crystals; (b) The calculated efficiency as a function of hot

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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 300-773K 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. 51571007.

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, E-mail:

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 2009. 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 2011. 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

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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=(S2σ/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.

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Fig. (a) thermoelectric power generation model, (b) thermoelectric cooling model, (c)

the space probe and thermoelectric generators

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

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Fig. Photo of first page of the published paper