Reducing Lattice Thermal Conductivity of the Thermoelectric SnSeMonolayer: Role of Phonon−Electron CouplingYajing Sun, Zhigang Shuai, and Dong Wang*

MOE Key Laboratory of Organic Opto Electronics and Molecular Engineering, Department of Chemistry, Tsinghua University,Beijing 100084, PR China

*S Supporting Information

ABSTRACT: SnSe-based materials possess ultrahigh thermoelectric effi-ciency and show great potential in next-generation thermoelectric devices.The excellent thermoelectric performance of SnSe has been attributed to itsultralow lattice thermal conductivity. In addition to phonon−phononinteractions, grain boundary, and defect and impurity scatterings, phonon−electron coupling also plays a part in the lattice thermal transport of dopedmaterials, yet it is often overlooked. In this work, we investigated the effect ofphonon−electron coupling on the lattice thermal conductivity of thethermoelectric SnSe monolayer. We found that the lattice thermalconductivity decreased by as much as 30% when the carrier density exceeded1013 cm−2 (equivalent to carrier concentration of ∼1020 cm−3), showing thesignificant suppression effect. Such level of carrier concentration is oftenrequired for thermoelectric conversion, so the contribution of phonon−electron coupling to the reduction for lattice thermal conductivity is as muchas other scattering mechanisms and needs to be accounted for engineering phonon transport of thermoelectric materials.

1. INTRODUCTION

In crystalline materials, lattice vibrations will destroy theperiodic potential in which the electrons move and seriouslyimpede the electrical transport. According to the solid-statetheory, interactions between electrons and phonons constitutethe main scattering mechanism in charge transport.1,2

However, effect of such interactions on phonon transportproperties, such as the lattice thermal conductivity, is oftenoverlooked. It was well believed that the electron−phononinteractions can be safely neglected when phonon transportproperties are cared for because charge carrier concentrationsin semiconductors or insulators are extremely low.3 However,the performance of semiconductor-based electronic devices isoften improved by increasing the carrier concentration.4−6

Nowadays, the carrier concentration of electronic materials canbe manipulated to the level as high as 1021 cm−3 in bulk and1014 cm−2 in two-dimensional systems via various dopingmethods.7−11 Meanwhile, experiments also show that thermalconductivities of some materials, such as thermoelectricclathrate and La3Te4−zMz (M = Sb, Bi), vary significantlywith the doping level.12−14 The thermal conductivity of dopedmaterials usually decreases with the increasing carrierconcentration, which has been attributed to the introductionof new phonon scattering pathways via phonon−electroncoupling (PEC). Recently, comprehensive theoretical studiesof the effect of PEC on the lattice thermal conductivity havebeen conducted for single-crystal silicon and bulk SiC andSiGe.3,15−17 It was found that suppression on phonontransport due to the PEC effect can be significant. With the

increase of carrier concentration, the phonon−electronscattering is becoming a scattering mechanism as importantas the phonon−phonon scattering in the phonon transport. Atthe carrier concentration as high as ∼1020 cm−3, the latticethermal conductivity was reduced by more than 40% in theabovementioned materials. In a word, to account for the PEC-induced scattering is essential when the accurate prediction oflattice thermal conductivity is needed, especially in dopedsingle-crystalline thermoelectric materials. In polycrystallinematerials, grain boundary and defect scatterings are alsoimportant. In this work, we will address the PEC effect in two-dimensional materials, which is rarely studied.In addition to the traditional substitution strategy used in

bulk materials, many effective and convenient approaches ofdoping can be applied to low-dimensional materials, whichinclude surface charge transfer, intercalation, and field-effectmodulation.11 As far as we know, the only research targetingthe PEC effect on the phonon transport of low-dimensionalmaterials, deals with silicon nanostructure, in which bothboundary and phonon−electron scattering mechanisms werestudied.18 However, the rates of scattering in the nanostructurewere not explicitly calculated, instead, they were assumed thesame values as in the bulk silicon. As we know, because of theirunique electronic structure and phonon dispersions arisingfrom the quantum confinement effect, low-dimensional

Received: March 12, 2019Revised: April 17, 2019Published: April 18, 2019

Article

pubs.acs.org/JPCCCite This: J. Phys. Chem. C 2019, 123, 12001−12006

© 2019 American Chemical Society 12001 DOI: 10.1021/acs.jpcc.9b02344J. Phys. Chem. C 2019, 123, 12001−12006

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materials often exhibit charge and thermal transport featuresquite different from their bulk counterpart.19−22 Therefore,evaluating the PEC effect on the lattice thermal conductivity oflow-dimensional materials is essential for the accurateprediction of their thermal transport properties.SnSe is emerging as a high-performance thermoelectric

material due to its ultralow lattice thermal conductivity.23

Though controversies on the intrinsic thermal conductivity ofSnSe single crystals exist,24 the SnSe-based material isbecoming a promising candidate for thermoelectric conversion.SnSe possesses a layered structure, and fabrication ofmultilayer and monolayer nanosheets as well as their electricaltransport and thermoelectric properties has been reported.25,26

In this work, by performing first-principles computation ofPEC in the thermoelectric SnSe monolayer, we found that thephonon scattering due to PEC cannot be neglected in two-dimensional systems, as it has been previously disclosed in bulksystems, especially at high carrier concentrations. The PEC-induced suppression of thermal conductivity increases with thecarrier concentration. When the carrier density reaches 1013

cm−2 (equivalent to carrier concentration of ∼1020 cm−3), thelattice thermal conductivity can be reduced by as much as 30%.According to our calculation, the reduction of lattice thermalconductivity due to PEC is more dramatic in the SnSemonolayer than bulk. Our study points out that in the dopingoptimization of thermoelectric materials, the lattice thermalconductivity is no longer a constant and it decreases withincreasing doping level due to the PEC effect, which is actuallybeneficial to achieve high thermoelectric efficiency.

2. METHOD

The structural optimization and electronic band structurecalculation were performed based on the density functionaltheory implemented in Quantum Espresso package with theexchange−correlation functional of Perdew−Burke−Ernzer-hof.27 The density functional perturbation theory (DFPT) wasthen employed to calculate the phonon properties and theelectron−phonon coupling matrix elements. The latticethermal conductivity can be determined by solving the phononBoltzmann transport equation via

∫∑κ υ τ= c qds

n

qq s q s q s

3

,2

, ,(1)

where n is the number of atoms in the unit cell, υq,s, cq,s, and τq,sare, respectively, the phonon group velocity, heat capacity, andphonon lifetime of the sth phonon mode with wave vector q. Inour calculation, the overall phonon lifetime is obtained byapplying Matthiessen’s rule to both phonon−phonon scatter-ing mechanism arising from anharmonic lattice vibrations andPEC scattering mechanism1

τ τ τ= +1 1 1

q s q s q s, ,PP

,PEC

(2)

The phonon−phonon scattering was calculated by theShengBTE package in the approximation of three-phononscattering.28 The second-order and third-order interatomicforce constants were calculated using the 5 × 5 supercell. Fromthese, we could obtain the scattering matrix elements Vss′s″

± .According to Fermi’s golden rule, phonon−phonon scatteringrates Γss′s″

± can be written as

π δ ω ω ωωω ω

Γ = − ℏ ′ − ″′ + ″ +

± ′ − ″′ ″

| |′ ″±

′ ″±n n

n nV

4 1( )

ss s ss s2

lmoonoo

|}oo~oo

(3)

In doped systems, the phonon lifetimes due to PECscattering can be written as

∑τ

π

δ ε ε ω

= −ℏ

| | × −

× − − ℏ

+

+

g k q f f1 2

( , ) ( )

( )

q s mn kmn s nk mk q

nk mk q qs

,PEC

,,

2

(4)

where gmn,s(k,q) = ⟨ψmk+q|∂V|ψnk⟩ is the electron−phononcoupling matrix element. In order to simplify the calculation,the electron−phonon matrix elements on the dense grid werederived with the help of Wannier interpolation as implementedin the EPW code.29 The electronic band energy, phononenergy, and electron−phonon matrix elements were firstcalculated on coarse k- and q-meshes of 5 × 5, respectively,and then interpolated to a fine grid of 400 × 400.

3. RESULTS AND DISCUSSION3.1. Geometry and Electronic Band Structure. SnSe

crystallizes in two phases, the Pnma phase below 750 K and theCmcm phase above. In this work, we choose the low-temperature Pnma phase for our first-principles calculation.The monolayer of SnSe could be stripped easily from its bulkbecause of the weak interlayer van der Waals interactions.30

The optimized structure of the SnSe monolayer is shown inFigure 1a. Each Sn atom is covalently bonded to three nearest

Se atoms, forming a wrinkled structure. The orthogonal latticeis similar to that of puckered phosphorene and arsenene, withthe optimized lattice parameters of 4.19 and 4.46 Å along thetwo orthogonal directions, respectively. Because the latticeparameters and atomic structures in the two directions areclose to each other, the transport anisotropy of the SnSemonolayer is not as significant as it is in phosphorene andarsenene.Figure 1b shows the electronic band structure and density of

states. The SnSe monolayer is a semiconductor with anindirect band gap of 0.65 eV, which is larger than the bulk oneof 0.48 eV because of the lack of interlayer van der Waalsinteractions. The band gap enlargement has been also observedin other materials with layered structures, such as in transition-metal chalcogenides.31 By analyzing the density of states, wesee that the valence band (VB) maximum is composed mainlyof the Se element and the conduction band (CB) minimum is

Figure 1. (a) Top and side views of the Pnma phase of the SnSemonolayer. (b) Electronic band structure and density of states of theSnSe monolayer.

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composed of the Sn atom. The charge separation of VB andCB is caused by the electronegativity difference of Se and Snatoms, with Se (p4) being the electron acceptor and Sn (p2)being the electron donor.3.2. Phonon−Phonon Scattering. We calculated the

phonon dispersion under the harmonic approximation and thethree-phonon scattering rate using the third-order forceconstants of the SnSe monolayer. From the phonon dispersionplot (Figure 2), no obvious phonon band gap (acoustic−

optical gap) was observed, which may result in much strongerphonon−phonon scattering than other high thermal con-ductivity materials like cubic III−V compounds or puckeredphosphorene. As shown in Figure 3, the three-phononscattering rates range from 10−3 to 10 ps−1, which are about2 orders of magnitude larger than those in the III−Vcompound boron arsenide,32 leading to the ultralow thermalconductivity in the SnSe monolayer.In addition, from the distribution of phonon density of

states, in the low-frequency region, Sn atoms contributedominantly, while the high frequency phonons arise mainlyfrom Se atoms. This is because of the larger mass of Sn atomsthan Se. The phonon frequencies of SnSe are lower than otherlight-weight materials, so the phonon group velocities (υq,s =∂ωq,s/∂q) are also smaller. The phonon group velocities fallinto the range of 1−2 km/s. This is another reason for the lowthermal conductivity of SnSe. As mentioned before, the similarstructure along the two perpendicular directions leads to theisotropic phonon dispersion and phonon group velocities. Thepredicted room-temperature thermal conductivity of thepristine SnSe monolayer is 5.58 and 5.01 W m−1 K−1 alongb and c directions, respectively. To obtain the thermal

conductivity of the monolayer, an effective thickness of 5.79Å is taken, which is half of the out-of-plane lattice parameter ain bulk SnSe. Figure 3c shows the accumulation of latticethermal conductivity with the phonon mean free path. It canbe seen that the phonon modes with the intrinsic mean freepath of 0.5−10 nm contribute mostly to the lattice thermalconductivity of the SnSe monolayer.

3.3. Phonon−Electron Coupling. It is well-known thatthe electron−phonon coupling is essential to the chargetransport. The charge carrier will be scattered from one state toanother by absorbing or emitting a phonon, so its lifetime andmean free path are shortened. In the electron−phononscattering process, the phonon lifetime and mean free pathwill also be further shortened if the charge carrierconcentration is high. High-performance thermoelectricmaterials are often doped to increase the electrical con-ductivity, with the carrier concentration on the order of 1020

cm−3. It has been pointed out that at such level of carrierconcentration, the thermoelectric figure of merit could also beimproved in both n- and p-doped situations by the reductionof lattice thermal conductivity.4,6 In two-dimensions, the roleof PEC in the phonon transport is not yet clarified. Wecalculated the PEC scattering rates in both n- and p-dopedSnSe monolayers with the carrier density of up to 1013 cm−2,and the result is shown in Figure 4. First, we find that at thecarrier density of 1013 cm−2, the rate of phonon−electronscattering is almost on the same order of magnitude as that ofphonon−phonon scattering. Especially in the low-frequencyregion, the electron−phonon scattering rate even exceeds thephonon−phonon scattering rate, making PEC the leadingphonon scattering pathway for the heat resistance. In both n-and p-doped cases, the phonon−electron scattering rates spana wide range between 10−3 and 1 ps−1. Second, we find that thePEC scattering rate in the case of electron doping is higherthan that in the hole doping. To figure out the reason, we recallthe band structure of the SnSe monolayer. As can be seen fromFigure 1, there exist two energy valleys in the CB and twoenergy peaks in the VB along the high symmetry directions,and they are located near the X-point (X′) and the Y-point(Y′), respectively. We find that the energy difference betweenthe two CB valleys is only 0.17 eV, which is much smaller thanthat between the two VB peaks, 0.37 eV. Because the phonon−electron scattering process needs to obey the conservation ofboth energy and momentum, the intervalley scattering ofelectrons (CB) is much easier than that of holes (VB). Theabove analysis can be further verified by the scattering ratesdecomposed as a function of both phonon frequency and

Figure 2. Phonon dispersion and phonon density of states of the SnSemonolayer.

Figure 3. (a) Three-phonon scattering rates and (b) phonon group velocities of acoustic (ZA, TA, and LA) and optical modes as a function of thephonon frequency. (c) Accumulative lattice thermal conductivity at 300 K and respective phonon mode contribution decomposed with the phononmean free path.

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phonon wave vector (Figure S1). It shows that in the regime ofmedium-to-large wave vectors, the scattering rate of electronsis high while that of holes is low. The overall scattering ratedue to PEC in the n-doped monolayer of SnSe is obviouslyhigher than that in p-doped one. Different from intravalleyscatterings, intervalley scatterings are always mediated byphonon branches with medium-to-large wave vectors. In thelarge wave vector region, many intervalley scatter paths areforbidden in the p-doping situation, leading to extremely smallscattering rates. Therefore, the main reason for the low PECscattering rate in the p-doped SnSe is the larger energydifference between the two energy tops of VB, whichsuppresses the intervalley scattering.The lattice thermal conductivity of the SnSe monolayer at

300 K, which varies with the carrier concentration, is shown inFigure 5a. At low carrier densities (<108 cm−2), the scatteringeffect due to PEC in both n- and p-doped systems is not

obvious as compared to the phonon−phonon scattering.However, with the increase of carrier density, the effectgradually demonstrates. As the carrier density exceeds 1012

cm−2, the PEC scattering starts to suppress the lattice thermalconductivity significantly. When the carrier density reaches1013 cm−2, the lattice thermal conductivity can be reduced bymore than 30%. It shows that the PEC effect cannot beneglected for the accurate prediction of lattice thermalconductivity in two-dimensional materials at relatively highcarrier densities, and to discern the critical carrier densityabove which PEC is not negligible, we introduce a parametercalled the effective electron distance. We assume that chargecarriers (electrons or holes) in the doped two-dimensionalsystem are distributed evenly in the plane and the averagedistance between two adjacent carriers is defined as theeffective electron distance. At low carrier densities, the effectivedistance is large, which means that the average distancebetween two neighboring electrons is large. If this effectivedistance is longer than the intrinsic phonon mean free pathsthat have the largest contribution to the total thermalconductivity (2−10 nm for the SnSe monolayer as shownabove in Figure 3c), the phonon transport will not besignificantly hindered by PEC. However, with the increase ofcarrier density, the effective distance between charge carriersdecreases. In this case, one can imagine that the phonon willencounter and collide with the electron before it is scattered byother phonons. Therefore, if the effective electron distance isless than 10 nm, amounting to the carrier density of more than1012 cm−2, we have to account for the effect of PEC on thethermal transport. At this carrier density, the phonon scatteringcontributed by PEC is as much as 10%. The similar rule ofthumb can also be applied to the bulk SnSe single crystal(Supporting Information Figure S3). Compared to the bulksystem, the phonon mean free path in the monolayer is evenlonger, which indicates that the thermal conductivity in thedoped SnSe monolayer is more prone to PEC. In a previousstudy of PEC effect on the phonon transport in the siliconnanostructure, it was concluded that the lattice thermalconductivity reduction due to PEC is not significant even atthe carrier concentration as high as 1021 cm−3.3 The reasoncould be that in the nanostructure, the boundary scattering isthe dominating scattering mechanism. As we show in thisstudy, the PEC scattering plays an important role in thethermal transport of two-dimensional materials when the

Figure 4. PEC scattering rates at (a) electron (pink dots) and (b)hole (blue dots) concentration of 1013 cm−2 as compared with three-phonon scattering rates (black dots).

Figure 5. (a) Normalized lattice thermal conductivity as a function of the carrier density at 300 K. κph−ph represents the lattice thermal conductivityarising from only phonon−phonon interaction. (b) Lattice thermal conductivity changing with the temperature at the hole and electron densityboth of 2 × 1013 cm−2.

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carrier concentration reaches a level often seen in thermo-electric materials.We have also explored the temperature dependence of

lattice thermal conductivity with and without the inclusion ofPEC scattering. From Figure 5b, we can see that the latticethermal conductivity of single-layered SnSe is inverselyproportional to the temperature when only phonon−phononscattering is considered. After the electron−phonon scatteringis taken into account, the lattice thermal conductivity decreasesmore rapidly and deviates from the inversely proportionaldependence on the temperature.

4. CONCLUSIONSBased on the DFPT and Wannier interpolation method, westudied the effect of PEC on the lattice thermal conductivity ofthe thermoelectric SnSe monolayer. As in bulk materials, wefound that PEC plays a significant role in the lattice thermalconduction of two-dimensional materials at high carrierconcentrations. Specifically, when the carrier density reaches1013 cm−2, equivalent to the carrier concentration of ∼1020cm−3, the lattice thermal conductivity will be reduced by morethan 30%, which could further enhance the thermoelectricefficiency of materials. The effective charge distance, which canbe easily derived from the carrier concentration, was proposedto gauge the importance of PEC in the lattice thermaltransport. When this effective charge distance is reduced to avalue comparable to the intrinsic phonon mean free paths,which contribute mostly to the heat conduction of undopedmaterials, the PEC effect on the lattice thermal conductivitycannot be ignored. Because of the quantum confinement effect,the lattice thermal transport is more sensitive to PEC in low-dimensional SnSe than its bulk.

■ ASSOCIATED CONTENT*S Supporting InformationThe Supporting Information is available free of charge on theACS Publications website at DOI: 10.1021/acs.jpcc.9b02344.

PEC scattering rates as a function of phonon frequencyand wave vector in monolayer SnSe and PEC effect inthe SnSe single crystal (PDF)

■ AUTHOR INFORMATIONCorresponding Author*E-mail: dong913@tsinghua.edu.cn.ORCIDYajing Sun: 0000-0003-2807-9382Zhigang Shuai: 0000-0003-3867-2331Dong Wang: 0000-0002-0594-0515NotesThe authors declare no competing financial interest.

■ ACKNOWLEDGMENTSThis work is supported by the National Natural ScienceFoundation of China (grant no. 21673123) and the Ministry ofScience and Technology of China (grant nos. 2015CB655002and 2017YFA020451). Computational resources are providedby the Tsinghua Supercomputing Center.

■ REFERENCES(1) Ziman, J. M. Electrons and Phonons: The Theory of TransportPhenomena in Solids; Clarendon Press: Oxford, 1960.

(2) Xi, J.; Wang, D.; Yi, Y.; Shuai, Z. Electron-Phonon Couplingsand Carrier Mobility in Graphynes Sheet Calculated Using theWannier-Interpolation Approach. J. Chem. Phys. 2014, 141, 034704.(3) Liao, B.; Qiu, B.; Zhou, J.; Huberman, S.; Esfarjani, K.; Chen, G.Significant Reduction of Lattice Thermal Conductivity by theElectron-Phonon Interaction in Silicon with High Carrier Concen-trations: A First-Principles Study. Phys. Rev. Lett. 2015, 114, 115901.(4) Duong, A. T.; Nguyen, V. Q.; Duvjir, G.; Duong, V. T.; Kwon,S.; Song, J. Y.; Lee, J. K.; Lee, J. E.; Park, S.; Min, T.; et al. AchievingZt=2.2 with Bi-Doped N-Type Snse Single Crystals. Nat. Commun.2016, 7, 13713.(5) Zhao, L.-D.; Tan, G.; Hao, S.; He, J.; Pei, Y.; Chi, H.; Wang, H.;Gong, S.; Xu, H.; Dravid, V. P.; et al. Ultrahigh Power Factor andThermoelectric Performance in Hole-Doped Single-Crystal Snse.Science 2016, 351, 141−144.(6) Chen, C.-L.; Wang, H.; Chen, Y.-Y.; Day, T.; Snyder, G. J.Thermoelectric Properties of P-Type Polycrystalline Snse Doped withAg. J. Mater. Chem. A 2014, 2, 11171−11176.(7) Korkosz, R. J.; Chasapis, T. C.; Lo, S.-h.; Doak, J. W.; Kim, Y. J.;Wu, C.-I.; Hatzikraniotis, E.; Hogan, T. P.; Seidman, D. N.;Wolverton, C.; et al. High Zt in P-Type (Pbte)1-2x(Pbse)X(Pbs)XThermoelectric Materials. J. Am. Chem. Soc. 2014, 136, 3225−3237.(8) Zhang, Q.; Chere, E. K.; McEnaney, K.; Yao, M.; Cao, F.; Ni, Y.;Chen, S.; Opeil, C.; Chen, G.; Ren, Z. Enhancement of Thermo-electric Performance of N-Type Pbse by Cr Doping with OptimizedCarrier Concentration. Adv. Energy Mater. 2015, 5, 1401977.(9) Hippalgaonkar, K.; Wang, Y.; Ye, Y.; Qiu, D.; Zhu, H.; Wang, Y.;Moore, J.; Louie, S. G.; Zhang, X. High Thermoelectric Power Factorin Two-Dimensional Crystals Ofmos2. Phys. Rev. B 2017, 95, 115407.(10) Liu, C.; Xiong, Y.; Huang, Y.; Tan, X.; Li, L.; Xu, D.; Lin, Y.-H.;Nan, C.-W. Fevsb-Based Amorphous Films with Ultra-Low ThermalConductivity and High Zt: A Potential Material for ThermoelectricGenerators. J. Mater. Chem. A 2018, 6, 11435−11445.(11) Luo, P.; Zhuge, F.; Zhang, Q.; Chen, Y.; Lv, L.; Huang, Y.; Li,H.; Zhai, T. Doping Engineering and Functionalization of Two-Dimensional Metal Chalcogenides. Nanoscale Horiz. 2019, 4, 26−51.(12) Bentien, A.; Christensen, M.; Bryan, J. D.; Sanchez, A.;Paschen, S.; Steglich, F.; Stucky, G. D.; Iversen, B. B. ThermalConductivity of Thermoelectric Clathrates. Phys. Rev. B: Condens.Matter Mater. Phys. 2004, 69, 045107.(13) Bentien, A.; Johnsen, S.; Iversen, B. B. Strong Phonon ChargeCarrier Coupling in Thermoelectric Clathrates. Phys. Rev. B: Condens.Matter Mater. Phys. 2006, 73, 094301.(14) May, A. F.; Flage-Larsen, E.; Snyder, G. J. Electron and PhononScattering in the High-Temperature Thermoelectricla3te4−Zmz-(M=Sb,Bi). Phys. Rev. B: Condens. Matter Mater. Phys. 2010, 81,125205.(15) Wang, T.; Gui, Z.; Janotti, A.; Ni, C.; Karandikar, P. StrongEffect of Electron-Phonon Interaction on the Lattice ThermalConductivity in 3c-Sic. Phys. Rev. Mater. 2017, 1, 034601.(16) Fan, D. D.; Liu, H. J.; Cheng, L.; Liang, J. H.; Jiang, P. H. Afirst-principles study of the effects of electron-phonon coupling on thethermoelectric properties: a case study of the SiGe compound. J.Mater. Chem. A 2018, 6, 12125−12131.(17) Cheng, L.; Yan, Q.-B.; Hu, M. The Role of Phonon-Phononand Electron-Phonon Scattering in Thermal Transport in Pdcoo2.Phys. Chem. Chem. Phys. 2017, 19, 21714−21721.(18) Fu, B.; Tang, G.; Li, Y. Electron-Phonon Scattering Effect onthe Lattice Thermal Conductivity of Silicon Nanostructures. Phys.Chem. Chem. Phys. 2017, 19, 28517−28526.(19) Novoselov, K. S.; Geim, A. K.; Morozov, S. V.; Jiang, D.;Zhang, Y.; Dubonos, S. V.; Grigorieva, I. V.; Firsov, A. A. ElectricField Effect in Atomically Thin Carbon Films. Science 2004, 306,666−669.(20) Lindsay, L.; Broido, D. A.; Mingo, N. Flexural Phonons andThermal Transport in Graphene. Phys. Rev. B: Condens. Matter Mater.Phys. 2010, 82, 115427.

The Journal of Physical Chemistry C Article

DOI: 10.1021/acs.jpcc.9b02344J. Phys. Chem. C 2019, 123, 12001−12006

12005

(21) Venkatasubramanian, R.; Siivola, E.; Colpitts, T.; O’Quinn, B.Thin-film thermoelectric devices with high room-temperature figuresof merit. Nature 2001, 413, 597−602.(22) Qin, G.; Zhang, X.; Yue, S.-Y.; Qin, Z.; Wang, H.; Han, Y.; Hu,M. Resonant Bonding Driven Giant Phonon Anharmonicity and LowThermal Conductivity of Phosphorene. Phys. Rev. B 2016, 94,165445.(23) Zhao, L.-D.; Lo, S.-H.; Zhang, Y.; Sun, H.; Tan, G.; Uher, C.;Wolverton, C.; Dravid, V. P.; Kanatzidis, M. G. Ultralow ThermalConductivity and High Thermoelectric Figure of Merit in SnseCrystals. Nature 2014, 508, 373−377.(24) Wei, P.-C.; Bhattacharya, S.; He, J.; Neeleshwar, S.; Podila, R.;Chen, Y. Y.; Rao, A. M. The Intrinsic Thermal Conductivity of Snse.Nature 2016, 539, E1−E2.(25) Jiang, J.; Wong, C. P. Y.; Zou, J.; Li, S.; Wang, Q.; Chen, J.; Qi,D.; Wang, H.; Eda, G.; Chua, D. H. C.; et al. Two-Step Fabrication ofSingle-Layer Rectangular Snse Flakes. 2D Mater. 2017, 4, 021026.(26) Ju, H.; Kim, J. Chemically Exfoliated Snse Nanosheets andThe i r Sn s e/Po l y (3 , 4 -E th y l en ed i o x y t h i ophene ) :Po l y -(Styrenesulfonate) Composite Films for Polymer Based Thermo-electric Applications. ACS Nano 2016, 10, 5730−5739.(27) Giannozzi, P.; Baroni, S.; Bonini, N.; Calandra, M.; Car, R.;Cavazzoni, C.; Ceresoli, D.; Chiarotti, G. L.; Cococcioni, M.; Dabo,I.; et al. Quantum Espresso: A Modular and Open-Source SoftwareProject for Quantum Simulations of Materials. J. Phys. Condens. Matter2009, 21, 395502.(28) Li, W.; Carrete, J.; Katcho, N. A.; Mingo, N. Shengbte: A Solverof the Boltzmann Transport Equation for Phonons. Comput. Phys.Commun. 2014, 185, 1747−1758.(29) Noffsinger, J.; Giustino, F.; Malone, B. D.; Park, C.-H.; Louie,S. G.; Cohen, M. L. EPW: A program for calculating the electron-phonon coupling using maximally localized Wannier functions.Comput. Phys. Commun. 2010, 181, 2140−2148.(30) Chang, C.; Tan, G.; He, J.; Kanatzidis, M. G.; Zhao, L.-D. TheThermoelectric Properties of Snse Continue to Surprise: Extraordi-nary Electron and Phonon Transport. Chem. Mater. 2018, 30, 7355−7367.(31) Radisavljevic, B.; Radenovic, A.; Brivio, J.; Giacometti, V.; Kis,A. Single-Layer Mos2 Transistors. Nat. Nanotechnol. 2011, 6, 147−150.(32) Lindsay, L.; Broido, D. A.; Reinecke, T. L. First-PrinciplesDetermination of Ultrahigh Thermal Conductivity of Boron Arsenide:A Competitor for Diamond? Phys. Rev. Lett. 2013, 111, 025901.

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DOI: 10.1021/acs.jpcc.9b02344J. Phys. Chem. C 2019, 123, 12001−12006

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