## Heat conversion gets a power boost

Thermoelectric materials convert waste heat into electricity, but often achieve high conversion efficiencies only at high temperatures. Zhao *et al.* tackle this problem by introducing small amounts of sodium to the thermoelectric SnSe (see the Perspective by Behnia). This boosts the power factor, allowing the material to generate more energy while maintaining good conversion efficiency. The effect holds across a wide temperature range, which is attractive for developing new applications.

## Abstract

Thermoelectric technology, harvesting electric power directly from heat, is a promising environmentally friendly means of energy savings and power generation. The thermoelectric efficiency is determined by the device dimensionless figure of merit *ZT*_{dev}, and optimizing this efficiency requires maximizing *ZT* values over a broad temperature range. Here, we report a record high *ZT*_{dev} ∼1.34, with *ZT* ranging from 0.7 to 2.0 at 300 to 773 kelvin, realized in hole-doped tin selenide (SnSe) crystals. The exceptional performance arises from the ultrahigh power factor, which comes from a high electrical conductivity and a strongly enhanced Seebeck coefficient enabled by the contribution of multiple electronic valence bands present in SnSe. SnSe is a robust thermoelectric candidate for energy conversion applications in the low and moderate temperature range.

With more than 60% of the world’s produced energy being lost as waste heat in the low and moderate temperature range, a compelling need exists for high-performance thermoelectric materials that can directly convert this heat to electrical power (*1*–*5*). The thermoelectric conversion efficiency is characterized by the temperature-dependent quantity *ZT* = *S*^{2}σ*T*/κ, where *S* is the Seebeck coefficient, σ is the electrical conductivity, κ is the total thermal conductivity, *T* is the temperature, and the product (*S*^{2}σ) is the power factor (*PF*). The conversion efficiency of heat to electricity for a large number of potential applications requires enhancing *ZT* over a wide range of temperatures. However, many previous advances have focused on improving the maximum *ZT* (*ZT*_{max}) as a function of temperature (*6*–*16*). Many such improvements in *ZT*_{max} came from strategies such as hierarchical architecturing, band structure engineering, and intrinsically low thermal conductivity, which enabled huge reductions in lattice thermal conductivity (e.g., nanostructuring) (*6*–*8*). Materials that incorporate one or more of these strategies include the systems AgPb_{m}SbTe_{m+2} (LAST) (*6*, *8*), PbTe-SrTe (*9*), NaPb_{m}SbTe_{m+2} (SALT) (*10*), PbTe-Tl (*11*), PbTe-PbSe (*12*), Mg_{2}(Si,Sn) (*13*), MgAgSb (*14*), PbSe-CdS (*15*), and triple filled Skutterudites (*16*). Many of these thermoelectrics are heavy-metal–based materials, which include rare-earth metals and elements with low abundance. Therefore, developing thermoelectrics requires not only a high maximum *ZT*, but a high *ZT* value over a wide range of temperatures, and materials made from relatively nontoxic and more earth-abundant elements.

A surprising choice for a promising thermoelectric candidate is SnSe single crystal, because its two-dimensional (2D) anisotropic and low-symmetry crystal structure would not have been expected to exhibit high carrier mobility (*17*). Recently, we showed that SnSe exhibits one of the lowest lattice thermal conductivities known for crystalline materials (<0.4 W m^{−1 }K^{−1} at 923 K) (*18*) and without any doping exhibits record high *ZT*s along the *b* and *c* crystallographic directions at 723 to 973 K (fig. S1). Unlike the facile doping behavior of Pb-based rock-salt chalcogenides (*5*, *19*), doping SnSe is challenging because of the layered anisotropic structure, where each SnSe layer is two atoms thin, and the locally distorted bonding around the Sn and Se atoms. Here, we demonstrate successful hole doping in single crystals of SnSe using sodium as an effective acceptor and find a vast increase in *ZT* from 0.1 (undoped) to 0.7 (doped) along the *b* axis at 300 K while obtaining the *ZT*_{max} of 2.0 at 773 K (Fig. 1A). The hole-doped SnSe (*b* axis) outperforms most of current state-of-the-art p-type materials at 300 to 773 K (*9*, *10*, *14*, *18*, *20*, *21*) (Fig. 1B). The high *PF* and *ZT* give the highest device *ZT* (*ZT*_{dev}) from 300 to 773 K known in the field of thermoelectric materials of ~1.34. The *ZT*_{dev} over the entire working temperature range is important, as it determines the thermoelectric conversion efficiency (η). The thermoelectric efficiency of a material between a hot temperature *T*_{h} and cold side temperature *T*_{c} can be calculated from the Seebeck coefficient, electrical conductivity, and thermal conductivity as a function of *T* (*22*)

The *ZT*_{dev} of hole-doped SnSe is much higher than that of typical high-performance thermoelectrics (*9*, *18*, *23*) from 300 to 773 K (Fig. 1C). Although the extremely low thermal conductivity enables the high *ZT* of undoped SnSe crystals from 723 to 973 K, we attribute the large *ZT*_{dev} enhancement in hole-doped SnSe to the enormous boost in *PF* in the temperature range from 300 to 773 K. The projected conversion efficiency of hole-doped SnSe for *T*_{c} = 300 K and *T*_{h} = 773 K is ∼ 16.7%, which is higher than that of other high-performance thermoelectrics (*9*, *18*, *23*) (Fig. 1D).

The origins of the high performance come from various different contributions. We increased the electrical conductivity of SnSe from ∼ 12 S cm^{−1} to > 1500 S cm^{−1} (Fig. 2A) by hole doping the material, changing the temperature dependence from semiconductor-like to metal-like. With rising temperature, the electrical conductivity of hole-doped SnSe (*b* axis) decreases from 1486 S cm^{−1} at 300 K to 148 S cm^{−1} at 773 K. We estimated the carrier density at 300 K using Hall data as ∼4 × 10^{19} cm^{−3}. The Seebeck coefficient is ∼+160 μV K^{−1} at 300 K, close to that of commercial Bi_{2-}* _{x}*Sb

*Te*

_{x}_{3}with similar hole concentrations (

*24*), and increases to ∼+300 μV K

^{−1}at 773 K. The combination of increased electrical conductivity and high Seebeck coefficient results in a

*PF*of ∼40 μW cm

^{−1 }K

^{−2}for hole-doped SnSe (

*b*axis) at 300 K (Fig. 2C). This value rivals that of optimized p-type Bi

_{2-}

*Sb*

_{x}*Te*

_{x}_{3}along its

*ab*crystallographic plane direction (

*24*). The

*PF*s remain at a high value of ∼14 μW cm

^{−1 }K

^{−2}around 773 K for hole-doped SnSe (

*b*axis), which is twice as high as the value of ∼6.4 μW cm

^{−1 }K

^{−2}at 773 K for the undoped SnSe (

*b*axis) (Fig. 2C, inset). Therefore, the main contribution to the huge enhancement of

*ZT*from 300 to 773 K is the superior

*PF*afforded by doping.

The total thermal conductivity (κ_{tot}) of hole-doped SnSe is low and shows a decreasing trend with rising temperature (Fig. 2D). κ_{tot} of hole-doped SnSe (*b* axis) decreases from ∼1.65 W m^{−1 }K^{−1} at 300 K to ∼0.55 W m^{−1 }K^{−1} at 773 K. The lattice thermal conductivity (κ_{lat}) of hole-doped SnSe is as low as that of undoped SnSe. We previously explained this low thermal conductivity in terms of density functional theory (DFT)–calculated large Grüneisen parameters of SnSe caused by strong anharmonic bonding (*18*). This anharmonicity has recently been experimentally confirmed by inelastic neutron scattering measurements (*25*). The κ_{lat} values of hole-doped SnSe are still as low as that (0.2 to 0.3 W m^{−1 }K^{−1}) of undoped SnSe at 773 K (fig. S2D). We note that the intrinsically low thermal conductivity of SnSe is sensitive to the stoichiometric ratio (*26*) and the sample processing conditions (*27*). A recent neutron powder diffraction analysis demonstrated a nearly ideal stoichiometry and an exceptionally high anharmonicity of the chemical bonds of SnSe and reported an ultralow thermal conductivity value close to 0.1 W m^{−1 }K^{−1} at room temperature for polycrystalline SnSe (*26*). By strictly eliminating exposure to the atmosphere during sample preparation, Zhang *et al*. (*27*) observed lattice thermal conductivities of polycrystalline SnSe as low as those of the SnSe single crystals (*18*).

The *PF*s achieved in hole-doped SnSe are much higher than those in the rock-salt lead and tin chalcogenides (*19*, *28*–*30*), especially in the 300 to 500 K range. These high *PF*s derive from the much larger Seebeck coefficient, because the electrical conductivity of hole-doped SnSe (*b* axis) is comparable to those of rock-salt chalcogenides. To obtain insight into the enhanced Seebeck coefficients and PFs, we plotted (similar to a Pisarenko plot) the room-temperature Seebeck coefficients of rock-salt chalcogenides with similar carrier density of ∼4 × 10^{19} cm^{−3} (Fig. 3A). The Seebeck coefficient for hole-doped SnSe at ∼+160 μV K^{−1} is clearly much higher than ∼+70 μV K^{−1} for PbTe (*19*), ∼ +60 μV K^{−1} for PbSe (*28*), ∼+50 μV K^{−1} for PbS (*29*), and ∼+25 μV K^{−1} for SnTe (*30*).

For heavily hole-doped PbTe and PbSe, the Fermi level is pushed downward toward the heavy valence band (*19*), enhancing the Seebeck coefficient because of the contribution of this second valence band to transport. This enhancement, however, only appears at high temperatures, as the extra contribution of the heavy valence band requires a carrier density of (~4 to 5) × 10^{19} cm^{−3} and (1 to 2) × 10^{20} cm^{−3} at 300 K because the energy difference between the two valence bands in PbTe (0.15 eV) (*15*) and PbSe (0.25 eV) (*19*) decreases at high temperatures. The energy difference for PbS and SnTe between the two bands is even larger (>0.3 eV) (*29*, *30*), resulting in decreasing Seebeck coefficients from PbTe, to PbSe, to PbS, to SnTe (Fig. 3A). We observed a much larger Seebeck coefficient of ∼+160 μV K^{−1} (at 300 K) for the hole-doped SnSe than expected from a single-band contribution (∼+30 μV K^{−1}), which is well supported by the Pisarenko plot (Fig. 3B). The large Seebeck coefficient suggests the contribution of more than one valence band. This conclusion is supported by Hall data and DFT calculations of the band structure.

The Hall coefficient (*R*_{H}) is consistent with multivalley transport, as it shows a continuous increase with temperature in the range 10 to 773 K (fig. S3A). 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 is in effect already at very low temperatures; i.e., the energy difference between the competing valence bands is much lower than in other chalcogenide materials. To estimate the energy gap (Δ*E*) between the first two bands, we used a well-developed model for a typical two-band compound to analyze the Hall data. In this model, the temperature-dependent *R*_{H} (*T*) can be expressed as (*19*) (2)where *R*_{H} (0) represents the Hall coefficient at 0 K; μ_{1}, μ_{2}, and *m*_{1}, *m*_{2} denote the carrier mobilities and density-of-states (DOS) effective masses of the first and the second valence band, respectively; *k*_{B} is the Boltzmann constant; and Δ*E* is the energy separation between the two valence band maxima. The slope (–Δ*E*/*k*_{B}) of ln[*R*_{H}(*T*) – *R*_{H}(0)]/*R*_{H}(0) versus 1/*T* yields Δ*E* ∼ 0.02 eV at 0 K, assuming that Δ*E* varies linearly with temperature (fig. S4). This energy gap between the first two valence bands of SnSe is much smaller than that in PbTe, PbSe, PbS, and SnTe (*19*, *28*–*31*). The Δ*E* ∼ 0.02 eV value is comparable to *k*_{B}*T* at room temperature, suggesting that the valence bands are nearly equal in energy. This near-degeneracy is consistent with the much higher Seebeck coefficients and *PF*s observed at room temperature. As the temperature increases, the carriers are thermally distributed over several bands of similar energy, resulting in the enhanced Seebeck coefficient of ∼+160 μV K^{−1} at 300 K.

We analyzed the electronic structure and thermoelectric properties of hole-doped SnSe using DFT calculations of the low-temperature *Pnma* phase (Fig. 3C). The DFT valence band maximum (VBM) lies in the Γ-*Z* direction (band 1 in Fig. 3C), but another valence band is located just below the VBM (band 2). 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, consistent with the very small value experimentally estimated above (0.02 eV). We found this slight energy difference between calculation and experiment to be reasonable given the approximations underlying the DFT calculations. Such a small energy gap is easily crossed by the Fermi level as the hole doping approaches (∼4 to 5) × 10^{19} 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 than the 0.15 eV between the first and the second valence bands of PbTe, in which the heavy hole band contribution becomes considerable as the carrier density exceeds ∼(4 to 5) × 10^{19} cm^{−3} (*19*, *31*). Interestingly, the electronic valence bands of SnSe are much more complex than those of PbTe, and the Fermi level of SnSe even approaches the fourth, fifth, and sixth valence bands for doping levels as high as 5 × 10^{20} cm^{−3} (Fig. 3C). Another illustration of the complex band structure is shown in the Fermi surface, which has multiple types of pockets (or valleys) coming from the numerous valence bands, all within a small energy window (Fig. 3, C to F). The multitude of valence band maxima is a distinctive feature of SnSe and is absent in the rock-salt chalcogenides.

The SnSe effective masses at each valence-band extremum are also anisotropic, in agreement with previous calculations (*32*). Because of the 2D nature of the material, the effective mass has a larger value along the *k _{x}* direction (

*a*axis) than along either of the in-plane directions

*k*and

_{y}*k*(

_{z}*b*and

*c*axes). For the first valence maximum along Γ-

*Z*, the effective masses are

*m*

_{kx}* = 0.76

*m*

_{0},

*m*

_{ky}* = 0.33

*m*

_{0}, and

*m*

_{kz}* = 0.14

*m*

_{0}. For the second maximum along Γ-

*Z*, the

*m*

_{kx}* = 2.49

*m*

_{0},

*m*

_{ky}* = 0.18

*m*

_{0}, and

*m*

_{kz}* = 0.19

*m*

_{0}are heavier than for the first band. These heavy holes play an important role in enhancing the Seebeck coefficients. We also performed Seebeck coefficient calculations as a function of hole concentration at 300 K using both a single-band model and a calculation that includes multivalley effects (

*33*). We calculated the Seebeck coefficients by taking into account multiple valleys (considering all bands within ±2 eV of the Fermi level) and using a single parabolic band model with three different effective masses:

*m*

_{d}* = 0.47

*m*

_{0},

*m*

_{d}* = 0.75

*m*

_{0}, and

*m*

_{d}*= 1.20

*m*

_{0}(Fig. 3B). The Seebeck coefficient calculated with the full, multivalley DFT band structure is +168 μV K

^{−1}at 4 × 10

^{19}cm

^{−3}, which is very close to the experimentally observed value for this carrier concentration, +160 μV K

^{−1}. In contrast, using a single-band model, we cannot reproduce the experimental Seebeck coefficient, even with a range of possible effective masses: A single-band model with our calculated DOS effective mass (0.47

*m*

_{0}) from the first VBM yields a Seebeck coefficient of only +84 μV K

^{−1}at 4 × 10

^{19}cm

^{−3}. An estimated effective mass of 0.75

*m*

_{0}, obtained by fitting experimental Seebeck coefficients in polycrystalline SnSe (

*34*,

*35*), gives a single-band model Seebeck coefficient of ∼+110 μV K

^{−1}at 4 × 10

^{19}cm

^{−3}. The effective mass

*m*

_{d}* = 1.20

*m*

_{0}is an extreme value that we obtained by fitting the single-band Seebeck coefficients at extremely low concentrations (e.g., <1 × 10

^{17}cm

^{−3}) to the full multivalley calculated Seebeck coefficients. Even with this very heavy effective mass, the Seebeck coefficients (Fig. 3B, black dashed line) are still lower than those of the multivalley model at higher hole concentrations. We cannot explain the observed Seebeck coefficient enhancements with a single-band model, even with a wide range of possible effective masses. In SnSe, the experimental Seebeck coefficients exhibit isotropic values (Fig. 2B) along all three crystallographic directions. The electrical conductivity values, however, along these directions are different and reflect the respective mobilities, with the highest being along the

*b*and

*c*axes, in agreement with the calculated lighter effective masses along these axes. The distinctive crystal structure of SnSe, therefore, plays a key role in the exceptional electronic band structure characteristics that result in an ultrahigh

*PF*and

*ZT*. The 2D sheets in SnSe have strong, accordion-like corrugation and are well separated from one another, with long intersheet Sn···Se bonding interactions of ~3.5 Å (Fig. 4). Longer Sn-Se bonding interactions of ~3.3 Å are also present along the corrugation direction (

*c*axis). Along the

*c*and

*b*directions, the Sn-Se bonding is shorter, at 3.3 and 2.8 Å, respectively. As a result, the width of the valence bands along these in-plane directions is wider (and the effective hole masses lower) than along the

*a*direction (lower carrier mobilities and larger effective hole masses).

We demonstrate that hole doping SnSe pushes its Fermi level deep into the band structure, activating multiple valence band maxima that lie close together in energy, enabling enhanced Seebeck coefficients and power factors (*PF*s). Therefore, the unique electronic band structure of SnSe is key to the high power factor and thermoelectric performance of the doped samples over a wide temperature plateau, from 300 to 773 K. The high conversion efficiency improves the prospects of realizing very efficient thermoelectric devices with hole-doped SnSe crystals as a p-type leg.

## Supplementary Materials

www.sciencemag.org/content/351/6269/141/suppl/DC1

Materials and Methods

Supplementary Text

Figs. S1 to S13

## References and Notes

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**Acknowledgments:**This work was supported in part by the U.S. Department of Energy, Office of Science and Office of Basic Energy Sciences, under award DE-SC0014520 (G.T., H.C., V.P.D., S.H., C.W., and M.G.K.); and S3TEC-EFRC grant DE-SC0001299 (G.J.S.). This work was also supported by the “Zhuoyue” Program from Beihang University and the Recruitment Program for Young Professionals and the National Natural Science Foundation of China under grant 51571007 (L.-D.Z., Y.P., S.G., and H.X.). and by the Science, Technology and Innovation Commission of Shenzhen Municipality under grant no. ZDSYS20141118160434515 and Guangdong Science and Technology Fund under grant no. 2015A030308001 (J.H.).The synthesis, characterization, transport measurements, and DFT calculations were supported by DE-SC0014520. The validation measurements were supported by DE-SC0001299. Measurements at University of Michigan (C.U.) were supported by Energy Frontier Research Centers (EFRC) grant DE-SC0001054 All data in the main text and the supplementary materials are available online at www.sciencemag.org.