LETTERS

Peierls distortion as a route to high thermoelectricperformance in In4Se32d crystalsJong-Soo Rhyee1, Kyu Hyoung Lee1, Sang Mock Lee1, Eunseog Cho1, Sang Il Kim1, Eunsung Lee1, Yong Seung Kwon2,Ji Hoon Shim3 & Gabriel Kotliar4

Thermoelectric energy harvesting—the transformation of waste heatinto useful electricity—is of great interest for energy sustainability.The main obstacle is the low thermoelectric efficiency of materialsfor converting heat to electricity, quantified by the thermoelectricfigure of merit, ZT. The best available n-type materials for use inmid-temperature (500–900 K) thermoelectric generators have arelatively low ZT of 1 or less, and so there is much interest in findingavenues for increasing this figure of merit1. Here we report a binarycrystalline n-type material, In4Se32d, which achieves the ZT value of1.48 at 705 K—very high for a bulk material. Using high-resolutiontransmission electron microscopy, electron diffraction, and first-principles calculations, we demonstrate that this material supportsa charge density wave instability which is responsible for the largeanisotropy observed in the electric and thermal transport. The highZT value is the result of the high Seebeck coefficient and the lowthermal conductivity in the plane of the charge density wave. Ourresults suggest a new direction in the search for high-performancethermoelectric materials, exploiting intrinsic nanostructural bulkproperties induced by charge density waves.

Over the past decade, there has been a renewed focused effort onthermoelectric materials motivated by the increasing societal needs forrenewable energy and by technological advances in nanoscale science.The thermoelectric performance of a given material is characterized bythe materials’ dimensionless figure of merit ZT (ZT 5 S2sT/k, whereZ, S, s, T, and k are respectively a measure of the material’s ther-moelectric properties, Seebeck coefficient, electrical conductivity,absolute temperature, and thermal conductivity), which can beenhanced by following two approaches. The first seeks to minimizethe thermal conductivity by promoting phonon scattering and locali-zation while preserving the itineracy of the electron transport2–6. Thesecond seeks to enhance the power factor S2s through the quantumconfinement effect in reduced dimensionalities7,8.

Recently, a new approach to ultralow thermal conductivity wasexplored. It was suggested that the layered structure of disorderedtwo-dimensional crystalline sheets may have extremely low thermalconductivity9. Based on this, we propose the possible application ofcharge density waves (CDWs) to thermoelectricity. The CDW is alow-dimensional transport phenomenon involving strong electron–phonon coupling10. This strong interaction breaks the translationalsymmetry of lattices. The in-plane lattice distortion by CDWs oflayered structured materials may realize the concept of layered anddisordered crystalline sheets. In spite of the possible low thermal con-ductivity in a CDW system, it is necessary to select one type of carriertransport (electron or hole) to achieve a high power factor, becausemixed carrier transport (electrons and holes) suppresses the Seebeckcoefficient11. In4Se3 provides an interesting realization of a material

with reduced dimensionality, supporting quasi-one-dimensional In-chains12, nanorod structures13, and asymmetric band dispersion14. Thecrystal structure of In4Se3 is shown in Fig. 1. It forms a layered struc-ture of (In3)51 clusters covalently bonded to Se ions in the b–c planesheld together by van der Waals interactions along the a axis. Althoughthe layered crystal structure is similar to the conventional Bi2Te3

compound, the intrinsic properties of the nanorod structure andthe quasi-one-dimensional chains of In4Se3 are different from thoseof Bi2Te3 and similar alloyed compounds. It is a bandgap semi-conductor having a sizable bandgap of 0.5–1.0 eV with anisotropicband dispersions14. To reduce the energy of the bandgap, we employedself doping by Se deficiency, that is, a compound of formula In4Se32d.We successfully grew two Se-deficient In4Se32d crystal ingots; In59Se41

(In4Se2.78, d 5 0.22) and In63Se37 (In4Se2.35, d 5 0.65). From X-raydiffraction of the cross-sectional plane of the grown crystal, we findthat the growth direction contains the a–b plane, whereas the perpen-dicular to the growth direction has two mixed crystalline orientationsof b–c and a–c planes (Supplementary Information); here we denotethe perpendicular to the growth direction as the b–c plane, for con-venience, because electrical conduction is thought to be dominantalong the b–c plane, based on the results of band structure calculationof In4Se32d (d 5 0.25).

Figure 2 shows representative thermoelectric properties ofIn4Se2.35 (d 5 0.65) along the growth direction (a–b plane, squares)and perpendicular to the growth direction (b–c plane, red circles),together with results from theoretical Boltzmann transport calcula-tions. As shown in Fig. 2a, the thermal conductivity k(T) of In4Se2.35

is very low (#1.2 W m21 K21 at 300 K) along the b–c plane, and it

1Materials Research Laboratory, Samsung Advanced Institute of Technology, Yongin 446-712, Korea. 2Department of Physics, Sung Kyun Kwan University, Suwon 440-746, Korea.3Department of Chemistry, Pohang University of Science and Technology, Pohang 790-784, Korea. 4Department of Physics and Astronomy, Rutgers University, Piscataway, NewJersey 08854-8019, USA.

In

Se

a

b

c

Figure 1 | Crystal structure of In4Se3. Perspective view of the a–b plane.Covalently bonded In–Se layers are stacked along the a-axis direction byrelatively strong van der Waals interactions.

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decreases with increasing temperature (0.74 W m21 K21 at 705 K).The thermal conductivities before and after heat treatment (450 uCfor 24 h) are almost identical along the b–c plane (open red circles).

The Seebeck coefficient S(T) and electrical resistivity r(T) arepresented in Fig. 2b and 2c, respectively. Compounds of formulaIn4Se32d (d # 0.65) are n-type materials with negative Seebeck co-efficient. Before heat treatment, In4Se32d (d 5 0.65) exhibits a sharpdip in S near 415 K (a–b plane) and 465 K (b–c plane) which is close tothe bulk melting temperature of the excess indium (Tm < 430 K). Thelow temperature thermal instability can be eliminated by annealingthe sample at 450 uC for 24 h, which gives reproducible data withoutthe transitions, as shown in Fig. 2b (red open circles). The electricalresistivity r(T) before and after heat treatment shows semiconduct-ing behaviour of r(T) (Fig. 2c). Although the low-temperature valuesof S(T) and r(T) are affected by the excess In, the annealing effect isnot significant in the regime which is relevant for thermoelectricity attemperatures higher than Tm.

The dimensionless figure of merit ZT shown in Fig. 2d reaches theremarkably high value of 1.48 for In4Se2.35 (d 5 0.65) at 705 K alongthe b–c plane. In the case of In4Se2.78 (d 5 0.22), ZT reaches 1.1 at thesame temperature (Supplementary Information). The higher ZTvalues of In4Se2.35 (d5 0.65) than those of In4Se2.78 (d5 0.22) aremainly caused by the lowering of thermal conductivity with increas-ing Se deficiency owing to the defect-induced phonon scattering atthe Se-defect sites. The energy recycling efficiency g is calculated fromthe relation1;

g~DT

T h

ffiffiffiffiffiffiffiffiffiffiffiffiffiffi

1zZTp

{1ffiffiffiffiffiffiffiffiffiffiffiffiffiffi

1zZTp

z Tc

Th

where Th (Tc) is the hot(cold)-side temperature and DT/Th is theCarnot efficiency. The efficiency g for waste heat recovery of In4Se2.35

(d 5 0.65) can reach 11.4% when Th is 705 K and the temperaturedifferenceDT 5 300 K. It could generate commercially viable levels ofpower by recycling waste heat in this mid-temperature range. TheHall carrier concentration nHall of the In4Se2.35 (d 5 0.65) crystal forcrystal orientations along the a–b and the b–c planes, determined byHall resistivity measurements, is estimated to be 4 3 1018 cm23 and4 3 1017 cm23 at 300 K, respectively (Fig. 2d inset). The carrier con-centrations for the In4Se32d compounds of d 5 0.22 and d 5 0.65

(7 3 1018 cm23 along the a–b plane for d 5 0.22) are lower thanthe optimum carrier concentration (1019–1020 cm23) for narrowbandgap semiconductors15.

To understand the microscopic origin of the exceptional propertiesof this material, we performed first-principles transport calculationsof In4Se3 using the BoltzTraP program16. Calculations of the angle-averaged transport coefficients, within the rigid band approximation,can account for the experimental trends and confirm the potential ofIn4Se32d as a thermoelectric material. Using a chemical potentialm 5 0.22 eV and a scattering time t 5 2.2 3 10214 s, we obtained anelectron concentration of 1 3 1018 cm23 and a high Seebeck co-efficient (2360mV K21 at 600 K), which is comparable to the observedexperimental value. The calculated temperature-dependent behaviourof S(T) and r(T) can qualitatively reproduce the experimental data, asshown in Fig. 2b and c (blue line and blue triangles). Using a constantvalue of the angle-averaged lattice thermal conductivitykph 5 0.8 W m21 K21, we can account for the temperature dependenceof the power factor and ZT, as shown in the inset of Fig. 2c and Fig. 2d,respectively. Within the rigid band approximation, the carrier densityof those compounds is not yet optimal (Supplementary Information),and therefore ZT could be further increased by optimizing the carrierconcentration by means of chemical substitutions.

High-resolution transmission electron microscopy (HRTEM)images and electron diffraction patterns are presented in Fig. 3.Figure 3a shows the HRTEM image of the a–b plane of theIn4Se2.78 (d 5 0.22) crystal. The Bragg spots of the electron diffrac-tion pattern in the a–b plane (Fig. 3a inset) accompany small super-structure peaks in the chain direction. Quasi-one-dimensional Braggspots and secondary superstructure peaks indicate the lattice distor-tion along the chain direction. Figure 3b shows the HRTEM image ofthe cross-sectional plane of the In4Se2.78 (d5 0.22) crystal ingot.There are several grain boundaries between the stripe and chequer-board patterns with arbitrary orientation: the stripe and chequer-board patterns are considered to be the a–c and b–c planes,respectively. The grains are about 20 nm or less in width. The electrondiffraction pattern of the b–c plane shows a rhomboidal Braggdiffraction pattern with one-dimensional superlattice peaks betweenthe bright Bragg peaks (Fig. 3b inset), indicating the presence of aPeierls instability along the b-axis direction.

a

c

b

d

1.6

1.4

1.5

10

1

0.1

0.01

1.0

0.5

0.0

1.2

1.0

0.8

–300

300 400 500 600 700 300 400 500 600 700

–350

–400

–450

–500

Temperature (K)

Temperature (K)Temperature (K)

Temperature (K)

300

1.5

1.0

0.5

0.0

30020010001016

1017

1018

400 500 600 700S

2 σ (m

W m

–1 K

–2)

σ

a–b plane

b–c plane

a–b planeb–c plane

b–c plane (anneal)

Boltzmann transport

S (µ

V K

–1)

ZT

(W m

–1 K

–1)

κ(Ω

cm

)ρ

n Hal

l (cm

–3)

In4Se3–δ (δ = 0.65)δ δ

Figure 2 | Anisotropic thermoelectric properties, annealing effect, andangle-averaged value of Boltzmann transport calculations for In4Se32d

(d 5 0.65) bulk crystal. Shown are thermoelectric properties along the a–b(squares) and b–c planes (circles). Symbols shown both open and filledindicate measurements before and after heat treatment (450 uC, 24 h),

respectively. Blue triangles and lines indicate the result of the Boltzmanntransport calculations. a, Temperature-dependent thermal conductivities,k(T). b, Seebeck coefficient, S(T). c, Electrical resistivity, r(T), and powerfactor defined by S2s (inset). d, Dimensionless figure-of-merit ZT andeffective carrier concentration, neff (inset).

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The Peierls instability of this material is also suggested by theoreticalconsiderations, once we explicitly include the Se vacancies in thecalculations. We calculated the generalized electron susceptibilityx(q), where q is the momentum vector (ref. 17), from the band struc-ture of In4Se32d (d 5 0.25); x(q) is shown along the X–U symmetryline in Fig. 4b. The sharp peak at the (0, 1/2, 1/16) point can beunderstood from the quasi-one-dimensional Fermi surface nestingin the b–c plane shown in Fig. 4a. It consists of two smooth dia-mond-shaped Fermi surfaces located at the upper and lower zoneboundaries of the first Brillouin zone. There is a well defined com-mensurate nesting vector q (red arrow) defined in the b–c plane whichcan result in a CDW instability once the electron–phonon or electron–electron correlations are incorporated in a calculation going beyondthe local-density approximation. Because of the long range latticemodulation along the c direction, the density wave instability is closelyconnected to the quasi-one-dimensional Peierls instability of thechain-like structure along the b axis of this material.

The electron diffraction pattern shown in Fig. 3b inset is consistentwith this Fermi surface nesting behaviour. The small faint peaksbetween the Bragg spots indicate the doubling superstructure inthe b direction, while the long-range modulation in the c directioncannot be seen, probably owing to the experimental resolution.Lattice distortion along the b axis is clearly visible in the electrondiffraction pattern shown in Fig. 3a inset.

Thermal transport properties shown in Fig. 2 also suggest thepresence of a CDW. We note that the thermal conductivity in theb–c plane is lower than that in the a–b plane in the In4Se2.35 crystal,which is at first sight surprising, as the bonding in the b–c plane isweaker than in the a–b plane. The in-plane (b–c plane) lattice distor-tion driven by the CDW lowers the thermal conductivity. In addition,the Hall carrier concentration is anisotropic with respect to crystalorientations. In usual cases, the carrier density is isotropic withrespect to crystal orientations. However, in this case, the carrierdensity along the b–c plane is lower than that of the a–b plane, whichis caused by the CDW along the b–c plane. Because of the CDW gapopening, the itinerant carrier density is decreased along the b–c plane.These facts, and the S(T) and r(T) shown in Fig. 2b and c, suggest theformation of a CDW at a temperature higher than 705 K.

The theoretical calculations in the rigid band approximation of theIn4Se32d compound cannot however account for the observed aniso-tropy of the transport coefficients (see Supplementary Information fordetails). The rigid band approximation does not take into account theCDW with supercell zone boundaries. The quasi-one-dimensionallattice distortion, and the exotic anisotropic properties of thermaland electrical transport coefficients, together indicate the importantrole of the CDW in achieving a high ZT in the b–c plane. The in-planelattice distortion by CDW lowers thermal conductivity, and theintrinsic nanostructural low dimensionality of this material resultsin the high Seebeck coefficient.

The present thermoelectric investigations of In4Se32d crystalssuggest that bulk low-dimensional layered materials with strongelectron–phonon coupling, such as Peierls or CDW instabilities,are promising candidates for new thermoelectric materials.Compared to other realizations of high-ZT n-type thermoelectricmaterials through nanoscale phase separation18,19, the CDW mecha-nism for high ZT has the advantage of being realized as an intrinsi-cally bulk phenomenon without artificial control of nanoscale phasesegregation. This resulted in an exceptionally high ZT (1.48 at 705 K)in compounds with high chemical stability and good mechanicalproperties that can be combined with well established p-type thermo-electrics (such as skutterudites) to produce highly efficient ther-moelectric power generation modules.

METHODS SUMMARY

The In4Se32d crystal ingots were grown by the Bridgeman method. In and Se were

placed in an evacuated quartz ampoule with an excess of In (5–10 at.%) for Se-

deficiency control. Heat treatment was followed by the melting and crystallizing at

550 uC and 590 uC for d 5 0.65 and 0.22 compounds, respectively, during a week

with a growth rate of 1.5 mm h21. The chemical inhomogeneity was examined by

inductively coupled plasma spectroscopy and electron dispersive spectroscopy

measurements. High-temperature thermal conductivity was obtained by

measurements of sample density rs, thermal diffusivity l (by the laser flash

method), and heat capacity Cp (in an ULVAC system); k 5 rlCp, where heat

capacity Cp was derived from Dulong-Petit fitting at high temperatures

(T $ 300 K). The high-temperature electrical resistivity and Seebeck coefficient

were measured by the four-probe method (in an ULVAC system). The Hall

resistivity rxy measurement was carried out by the five-contact AC-transport

technique, using a physical property measurement system (Quantum Design).

The effective carrier concentration was calculated by the one-band model as the

following relation: neff 5 21/(RHe), where the Hall coefficient RH 5 rxy/H and

e 5 1.602 3 10219 C.

The first-principles calculation was performed by the pseudopotential plane

wave method using the Vienna Ab initio Simulation Package. We adopted the

generalized gradient approximation implemented by Perdew, Burke, and

Ernzerhof for the exchange correlation energy functional with the spin–orbit

interaction. The thermoelectric properties are calculated using the BoltzTraP

program.

Received 22 January; accepted 20 April 2009.

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Z

Z

X XU0 5 10 15 20 25 30

(0,1

/2,1

/16)

(0,1/2,1/16)

a b

c

q

ba

XXU

Γ Γ

Γ Γ

(q)χ

Figure 4 | Fermi surface and generalized electron susceptibility ofIn4Se32d. a, Fermi surface of In4Se32d (d 5 0.25) in the b–c plane (blue andgreen lines). Black square is the first Brillouin zone. Fermi nesting vectorq (red arrow) is defined in the closed Fermi surface. b, Generalized electronsusceptibility x(q) along the X(0, 1/2, 0)–U(0, 1/2, 1/2) symmetry line (top).The x(q) has a singularity at the (0, 1/2, 1/16) point (bottom). The numberson the horizontal axis indicates the calculation mesh along the X–U–Xsymmetry line.

ba

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Supplementary Information is linked to the online version of the paper atwww.nature.com/nature.

Acknowledgements We thank D. Johnson, K. Koumoto and B. I. Min fordiscussions. We also thank H. R. Choi for TEM measurements. J.H.S. wassupported by the WCU programme (KOSEF: R32-2008-000-10180-0).

Author Information Reprints and permissions information is available atwww.nature.com/reprints. Correspondence and requests for materials should beaddressed to S.M.L. (sangmocklee@samsung.com).

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