Nanoscale

PAPER

Cite this: Nanoscale, 2019, 11, 19923

Received 4th June 2019,Accepted 7th September 2019

DOI: 10.1039/c9nr04726c

rsc.li/nanoscale

Monolayer SnP3: an excellent p-typethermoelectric material†

Xue-Liang Zhu,a,b,c Peng-Fei Liu, c,d Junrong Zhang,c,d Ping Zhang,e

Wu-Xing Zhou,a,f Guofeng Xie *a,b,f and Bao-Tian Wang *c,d

Monolayer SnP3 is a novel two-dimensional (2D) semiconductor material with high carrier mobility and

large optical absorption coefficient, implying its potential applications in the photovoltaic and thermo-

electric (TE) fields. Herein, we report on the TE properties of monolayer SnP3 utilizing first principles

density functional theory (DFT) together with semiclassical Boltzmann transport theory. Results indicate

that it exhibits a low lattice thermal conductivity of ∼4.97 W m−1 K−1 at room temperature, mainly originat-

ing from its small average acoustic group velocity (∼1.18 km s−1), large Grüneisen parameters (∼7.09),strong dipole–dipole interactions, and strong phonon–phonon scattering. A large in-plane charge trans-

fer is observed, which results in a non-ignorable bipolar effect on the lattice thermal conductivity. The

exhibited mixed mode between in-plane and out-of-plane vibrations enhances the complexity of the

phonon phase space, which enhances the possibility of phonon scattering processes and results in sup-

pression of thermal conductivity. A highly twofold degeneracy appearing at the K point gives a high

Seebeck coefficient. Our calculated figure of merit (ZT ) for optimal p-type doping at 500 K can approach

3.46 along the armchair direction, which is better than the theoretical value of 1.94 reported in the well-

known TE material SnSe. Our studies here shed light on monolayer SnP3 in use as a TE material and

supply insights to further optimize the TE properties in similar systems.

1. Introduction

Along with the development of human society, a huge demandin energy has followed. Thus, techniques and materials inrelation to producing and converting energy are important.With the depletion of fossil energy resources, which give riseto many problems such as air pollution and the greenhouseeffect, exploiting renewable energy resources as well as relatedmaterials is urgently in demand. In particular, TE materialsthat could directly and reversibly convert waste heat and elec-trical power have attracted much attention.1,2 Generally, the

conversion efficiency of a TE material can be well quantifiedby ZT3

ZT ¼ S2σTκ

; ð1Þ

where S, T, σ, and κ are the Seebeck coefficient, absolute temp-erature, electric conductivity, and total thermal conductivity,respectively. The total thermal conductivity is the sum of thelattice thermal conductivity κl, unipolar electronic thermalconductivity κe and the bipolar thermal conductivity κb. Forcommercial applications of a TE material, its ZT value shouldbe greater than 1.0. Normally, a good TE material shouldexhibit both low thermal conductivity and a high Seebeckcoefficient.4 Although it is very difficult to regulate the trans-port coefficients independently because of their strong inter-action, TE performance has been improved time and timeagain by new concepts or mechanisms. Several commonapproaches to enhance ZT are mainly devoted to optimizingthe electrical transport property by band structureengineering,5,6 and/or suppressing the material’s heat conduc-tivity ability via low-dimensional technologies7–9 and phononiccrystal patterning.10,11

Since the experimental acquisition of graphene by themechanical cleavage method in 2004,12 2D materials have

†Electronic supplementary information (ESI) available. See DOI: 10.1039/C9NR04726C

aSchool of Materials Science and Engineering, Hunan University of Science and

Technology, 411201 Xiangtan, China. E-mail: gfxie@xtu.edu.cnbSchool of Physics and Optoelectronics, Xiangtan University, Hunan 411105,

P. R. ChinacInstitute of High Energy Physics, Chinese Academy of Sciences (CAS),

Beijing 100049, China. E-mail: wangbt@ihep.ac.cndDongguan Neutron Science Center, Dongguan 523803, ChinaeInstitute of Applied Physics and Computational Mathematics, Beijing 100088, ChinafHunan Provincial Key Lab of Advanced Materials for New Energy Storage and

Conversion, 411201 Xiangtan, China

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become the hottest topic in the scientific community due totheir wonderful optical, thermal, electronic, and mechanicalproperties.13–15 Various 2D materials, such as silicene,16

phosphorene,17,18 borophene,19 and a series of layered tran-sition metal dichalcogenides,20–22 have been predicted theor-etically and/or synthesized experimentally. Monolayer semi-conducting materials with a narrow band gap have been sys-tematically studied in recent years due to their favourable com-bination of electrical and thermal transport properties, whichcan lead to a significantly large figure-of-merit.23–27 Forexample, by employing first-principles methods Huang et al.found that the unique crystal structure and electronic pro-perties of Mg3Sb2 monolayer can result in a low lattice thermalconductivity and high power factor,28 and consequently a highZT (>2 at 600 K) for the n-type sample.

Very recently, a 2D layered material, SnP3, which can beextracted from its bulk structure by using mechanical exfolia-tion approaches, has been theoretically proposed by Sunet al.29 Note that the layered bulk SnP3 has been synthesizedsince 1970 experimentally and exhibits metallic properties.30 Itis reported that the monolayer SnP3 possesses an indirectband gap (∼0.82 eV) with high electron mobility of 228 cm2

V−1 s−1.31 Meanwhile, its excellent electrical properties, largeoptical absorption coefficient (∼106 cm−1) and tunable bandgap offer diverse perspectives for applications in Na-ion bat-teries, nanophotonics, and photovoltaic solar cells.32 Based onthese intrinsic properties, it probably has a good TE perform-ance. In this paper, we systematically study the TE propertiesof monolayer SnP3 by using first-principles calculations and aBoltzmann transport approach. We find that it shows a goodcombination of electrical and thermal transport properties.Detailed analyses of the phonon spectra, lattice vibrationmode, Born effective charge, phonon velocity, and Grüneisenparameters are provided to explain its good macroscopic pro-perties. The maximum ZT value of 3.46 can be achieved by theoptimal p-type doping at 500 K. These results indicate thatSnP3 exhibits an extraordinary TE response and could be anideal material for TE applications.

2. Computational methods

In this paper, first-principles calculations were carried outbased on DFT as implemented in the Vienna ab initio simu-lation package (VASP).33 The generalized gradient approxi-mation (GGA)34 in the Perdew–Burke–Ernzerhof (PBE)35 formfor the exchange–correlation functional was used. Thevalence electrons included Sn: s2p2 and P: s2p3. The cutoffenergy of the plane wave was set as 500 eV on a 7 × 7 × 1Monkhorst–Pack k-mesh. To avoid interlayer interactions, thelength of the unit cell of 20 Å was used along the z direction.The van der Waals (vdW) interactions were corrected by usingthe DFT approach.36 The geometric structure was fullyrelaxed until the residual forces on atoms were less than 0.01eV Å−1. The criterion of convergence for total energy was setas 10–6 eV Å−1. To obtain a more accurate band gap, the

Heyd–Scuseria–Ernzerhof (HSE06)37 screened hybrid func-tional was employed.

The phonon transport properties were evaluated by theBoltzmann transport equation as implemented in ShengBTEcode.38 The harmonic second-order interaction force constants(2nd IFCs) were obtained by the VASP and Phonopy packages39

using a 3 × 3 × 1 supercell with a 3 × 3 × 1 k-mesh. The anhar-monic third-order IFCs (3rd IFCs) were obtained using thesame supercells with the finite-difference method.40

Interactions including the sixth-nearest-neighbor atoms wereconsidered for the 3rd IFCs. Here, the convergence of theκl with respect to the k-grids was carefully tested. A dense35 × 35 × 1 k-mesh was used for the calculation of the latticethermal conductivity (see Fig. S1, ESI†).

On the basis of Boltzmann transport theory and the rigidband approach, the electronic transport properties wereacquired, implemented in the BoltzTraP code.41 The constantrelaxation time was used in the calculation of TE transportparameters, which was calculated from the deformation poten-tial theory. This approximation was valid because the relax-ation time does not vary strongly within the energy scaleof kBT.

42 This method has accurately predicted TE propertiesof many materials.43 In order to obtain an accurateFourier interpolation of the Kohn–Sham eigenvalues, a dense45 × 45 × 1 k-mesh was used in the Brillouin zone (BZ).

3. Results and discussion3.1. Atomic and electronic structures

Monolayer SnP3 crystallizes in a hexagonal lattice with spacegroup P3̄m1 (164) as shown in Fig. 1. The optimized latticeparameter a equals 7.37 Å, which is consistent with the pre-vious report.32 This structure has a puckered configurationalong the zigzag direction, analogous to that of blue phosphor-ene. Interestingly, it looks like a graphene type honeycombfrom the top view.12 Compared with bulk SnP3,

44 the plicatedconfiguration of monolayer SnP3 is more conspicuous, result-ing in strong lattice vibrations.

In Fig. 1(d), we present the electronic band structuresobtained from the PBE as well as the HSE06 hybrid functionalpotentials. It can be seen that the two approaches exhibit ana-logous band structures. Our calculations show that monolayerSnP3 is a semiconductor with the valence band maximum(VBM) and conduction band minimum (CBM) locating at theK and Γ points, respectively. Based on the PBE functional, thecalculated band gap is 0.53 eV. The more accurate band gap of0.82 eV obtained from HSE06 is between that of the monolayerGeP3 (0.55 eV)45 and InP3 (1.14 eV).46 A twofold degeneracycould be observed at the K point. This kind of band degener-acy has been verified to be critical for achieving high ZT47 andcan be realized through proper band engineering.48 Suchintrinsic twofold degeneracy mainly appears in the valenceband (VB) along the Γ–K direction (zigzag) and primarilyoriginates from the p-orbitals. This gives rise to outstandingp-type electronic properties along the zigzag direction.49

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Interestingly, this degenerated electronic state is relatively flatat the VB edge, which is beneficial for good Seebeck coeffi-cients and has been verified in many materials.50 Severalsharp peaks in the electronic density of states (DOSs) areobserved at the VB, a signal of a dramatic increase in Seebeckcoefficients. Thus, an intrinsic VB degeneracy and a peakyDOS appear together in the monolayer SnP3. These featuresare good electronic characteristics for high-performance TEdevices.

Based on DFT calculations, the Born effective charge anddielectric constant could be obtained, as shown in Table 1.It is noted that the dielectric constant of in-plane (xx andyy direction) is much higher than that of out-of-plane (zzdirection), which is a characteristic behavior for all 2Dlayered materials. The calculated Born effective charge isZ*Sn;xx ¼ Z*

Sn;yy ¼ 2:27; Z*Sn;zz ¼ 0:37. We find that the charge

transfer in the xx and yy directions is 6 times larger than thatalong the zz direction, which indicates that the dipole–dipoleinteractions have markable anisotropy in the in-plane and out-of-plane directions. Here, we present the corresponding para-

meters of MoS2.51,52 The dielectric constants of MoS2 are

slightly higher than that of SnP3 in the in-plane direction,while the dielectric constants are almost equal along thezz direction. Additionally, we can also see clearly that the Borneffective charge of SnP3 is much larger than that of MoS2,which implies that SnP3 has a stronger dipole–dipole inter-action than MoS2. A recent report indicates that the strongdipole–dipole interaction is beneficial to the stability of acous-tic vibrations and leads to the low thermal conductivity.51

3.2. Electrical transport properties

The electronic properties can be characterized on the basis ofcarrier mobilities for monolayer SnP3, along both the armchairand zigzag directions. We calculate them using the defor-mation potential (DP) theory.53 The formula of carrier mobilityin 2D systems can be written as follows:54,55

μ2D ¼ eℏ3C2D

κBTm*m*dE1

2 ; ð2Þ

where m*, m*d, kB, E1 and C2D are the effective mass, average

effective mass (m*d ¼

ffiffiffiffiffiffiffiffiffiffiffiffim*

xm*y

q, x and y are armchair and zigzag

directions), the Boltzmann constant, the DP constant and the2D elastic constants, respectively. The calculated effectivemass, carrier mobility and scattering time (τ = μm*/e) areshown in Table 2. Clearly, the mobilities of the electrons arehighly isotropic, while the mobilities of the holes are stronglyanisotropic, agreeing with the previous theoretical report.29

Noticeably, it shows a high hole mobility (703.47 cm2 V−1 s−1)along the armchair direction at room temperature, which ismuch higher than that of MoS2 (∼200.52 cm2 V−1 s−1).55 Thehigh mobility in monolayer SnP3 is associated with the idealband gap, which is beneficial to its electrical transport.

The Seebeck coefficients S, electrical conductivity σ, andelectronic thermal conductivity κe are indispensable for evalu-ating the TE performance of materials. Here, using theBoltzmann transport theory based on the rigid band approach,we systematically research these electronic transport coeffi-cients. The negative and positive chemical potentials μ corres-pond to p- and n-type doping, respectively. The transportcoefficients as functions of T and μ can be defined by41

SαβðT ; μÞ ¼ 1eTVσαβðT ; μÞ

ðΣαβðεÞðε� μÞ � @fμðT ; εÞ

@ε

� �dε; ð3Þ

σαβðT ; μÞ ¼ 1V

ðΣαβðεÞ � @fμðT ; εÞ

@ε

� �dε; ð4Þ

Table 1 The Born effective charge (Z*) and dielectric constant (ε)

Type Atom Z*xx ¼ Z*

yy Z*zz εxx εzz

SnP3 Sn 2.27 0.37 4.14 1.27P −0.75 −0.12

MoS2 Mo 1.34 0.14 4.58 1.26S −0.67 −0.07

Fig. 1 Top (a) and side (b) views of the atomic structure of monolayerSnP3. (c) A top view of its primitive cell and the corresponding first BZwith high-symmetry points. (d) The electronic band structures calcu-lated by using PBE (dashed blue lines) and HSE06 hybrid functionalpotentials (solid red lines). (e) Total and partial DOSs.

Table 2 DP constant E1, elastic constant C2D, effective mass m*, carriermobility μ, and scattering time τ for electrons and holes along the zigzagand armchair directions in monolayer SnP3 at 300 K

DirectionCarrierstype

E1(eV)

C2D

(N m−1)m*(m0)

μ(cm2 V−1 s−1)

τ(ps)

Zigzag Electron 1.87 31.72 0.98 201.67 0.11Hole 1.08 31.72 1.67 302.73 0.28

Armchair Electron 1.81 31.16 0.97 215.85 0.12Hole 1.02 31.16 0.79 703.47 0.31

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where α and β are Cartesian indices, Σαβ(ε) is the transport dis-tribution function, and V is the volume of the unit cell. Asshown in Fig. 1(b), the distance between the top-Sn andbottom-Sn of monolayer SnP3 is 2.82 Å, and the van der Waalsradius of Sn is 2.25 Å.56 Therefore in our calculationsthe effective thickness of monolayer SnP3 heff = 2.25 × 2 + 2.82 =7.32 Å is chosen to convert the conductance of monolayer SnP3to conductivity. It should be pointed out that the results of thethermoelectric figure of merit ZT is independent of the choiceof heff because we use the same effective thickness for bothelectrical and phonon transport property calculations. As

shown in Fig. 2, the monolayer SnP3 exhibits relatively largevalues of the Seebeck coefficients. Obviously, the Seebeckcoefficient for p-type doping is visibly higher than that of then-type due to the larger μ and degenerate VBs. At room temp-erature, the maximum Seebeck coefficients along the armchairand zigzag directions can reach to 907 and 900 μV K−1,respectively. The temperature-dependent decreasing behaviorof the Seebeck coefficients is slowing down with increasingtemperature. This phenomenon is typical for TE materials. Atlow chemical potentials, we can see that the Seebeck coeffi-cients appear as peaks due to the sharp energy dependence of

Fig. 2 (a) and (b) Seebeck coefficients, (c) and (d) electrical conductivity with respect to the scattering time, (e) and (f ) electronic thermal conduc-tivity, and (g) and (h) power factor with respect to the scattering time at different temperatures along the armchair (left panels) and zigzag (rightpanels) directions as functions of the chemical potential.

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the total DOS, i.e., large ∂n(ε)/∂ε, as shown in Fig. 1. Actually,the Seebeck coefficients and the electronic DOS have the fol-lowing Mott relation57

S ¼ π2kB2T3e

1ndnðεÞdε

þ 1μ

dnðεÞdε

� �ε¼μ

: ð5Þ

The formula implies that the Seebeck coefficient can befurther improved by regulating the carrier concentration.

Fig. 2(c) and (d) show the electrical conductivity σ/τ as afunction of chemical potential. One can see that the σ/τ ofmonolayer SnP3 exhibits an evidently anisotropic behavior.The σ/τ along the zigzag direction is obviously larger than thatalong the armchair direction. In addition, we can also findthat the p-type doping has larger σ/τ than that of the n-typeones. Meanwhile, the slopes of the σ/τ around the VBM andCBM are flattened with increasing temperature because theelectrons obey the Fermi–Dirac distribution. As shown inFig. 2(e) and (f), the κe of monolayer SnP3 can be defined bysolving the Wiedemann–Franz law58

κe ¼ LσT ; ð6Þ

where L is the Lorenz number. To provide accurate calcu-lation of the TE performance, here we use electron trans-port modeling, and calculate the Lorenz numbers by

L ¼ 1:5þ exp � Sj j116

� �,59,60 based on the Seebeck coefficients.

The Lorenz numbers are presented in Fig. S2.† Similar to theσ/τ, the κe/τ is highly anisotropic as well. The large electricaltransport coefficients along the zigzag direction may lead tohigh TE values along it. Based on the Seebeck coefficients andthe electrical conductivity, we calculate the power factor withrespect to the scattering time as shown in Fig. 2(g) and (h).No matter what kinds of directions, the S2σ/τ of the p-typeis always higher than that of the n-type, which implies it canbe categorized as a p-type TE material.

Based on the Boltzmann transport equation, the calculatedSeebeck coefficients and electrical conductivities are the sumof the contributions from both the majority and minority car-riers, which already include the bipolar effect.61 However, thebipolar part of the thermal conductivity needs to be additivelyconsidered in the case of a small band gap and high tempera-ture,62 which is given by κb = σpσn(Sp − Sn)

2T/(σp + σn). In thenext section, we discuss the bipolar effect on the thermal con-ductivity and TE performance of monolayer SnP3.

3.3. Phonon transport properties

The phonon dispersions as well as the partial atomic phonondensity of states (PhDOSs) of monolayer SnP3 are shown inFig. 3. The phonon dispersion curves with their colorweighted by the contributions of Sn and P atoms are calcu-lated to guarantee the optimized structure locating at theminimum on the potential energy surface. No imaginary fre-quency is observed, indicating the dynamical stability ofmonolayer SnP3 at ambient pressure. The maximum fre-quency of the optical mode can approach 13.08 THz, com-parable to those of MoS2 (14.83 THz)63 and phosphorene(13.35 THz).64 Similar to the well-known TE material SnSe,65

the lowest optical mode frequency of monolayer SnP3 is1.91 THz, which is a sign for good TE performance. In thelow-frequency region, we find that the partial PhDOSs ofSn and P atoms are evenly distributed, which further provesits stable nature. Note that the relatively flat phonon dis-persion curves and spiculate PhDOS are responsible for smallphonon velocities and low thermal conductivities.

The vibration modes can be carefully analyzed by investi-gating the atomic motions for each mode of the phonon spec-trum, especially near/at the high symmetry points. Here, sometypical lattice vibrations of monolayer SnP3 near/at the Γ pointare presented in Fig. 3(c). One can see that the vibrations ofthe acoustic phonon branches are strictly along the in-plane(TA and LA) or out-of-plane (ZA), which belong to an intrinsic

Fig. 3 (a) Phonon dispersion and (b) total and partial phonon density of states (PhDOS) of monolayer SnP3. (c) The corresponding vibrational modesof the acoustic phonon branches (ZA, TA, and LA) and the lowest optical branch (Opt1) near and at the Γ point.

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vibration property. Interestingly, disordered off phase phononvibrations are observed for the lowest optical branch. One ofthe Sn atoms moves in-plane in the opposite direction to theother, while the P atoms vibrate out-of-plane. These in-planeand out-of-plane mixed mode vibrations will significantly sup-press phonon thermal transport via phonon–phonon scatter-ing and give rise to the low thermal conductivity.66

The expression for the thermal conductivity of a phonon inthe i direction, which is obtained by solving the Boltzmanntransport equation under the relaxation time, is given as:67

κl;i ¼Xλ

Xq

cphυg;i2ðq; λÞτðq; λÞ: ð7Þ

The summation is over all phonon modes with wave vector qand dispersion branch λ, cph is the mode volumetric specificheat, υg,i (q,λ) is the i component of the group velocity vector,and τ (q,λ) is the relaxation time of the phonon mode withwave vector q and dispersion branch λ. The κl values of mono-layer SnP3, at temperatures from 300 to 800 K, are presented inFig. 4(a). Obviously, the κl exhibits temperature dependence

and is proportional to 1/T, due to inherent enhancement inphonon–phonon scattering with respect to the temperature.This is a common behavior demonstrated in some classical TEmaterials.68–70 It is demonstrated in the inset of Fig. 4(a) thatthe bipolar thermal conductivity increases exponentially withincreasing temperature. The values of bipolar thermal con-ductivity κb reach ∼0.1 W m−1 K−1 at 700 K, which areclearly smaller than the values of lattice thermal conductivity∼2 W m−1 K−1. Therefore, the influence of bipolar thermalconductivity on the thermoelectric performance is non-appreciable in the temperature range concerned (300 K ≤ T ≤700 K). However, at higher temperature (T > 700 K), becausethe bipolar thermal conductivity increases sharply withincreasing temperature, and the lattice thermal conductivityobeys T−1, the effect of bipolar thermal conductivity becomesnon-negligible. Unlike its electrical transport properties, the κlof monolayer SnP3 exhibits weak anisotropy. As shown inFig. 4(a), the κl values at room temperature are calculated to be4.97 and 5.41 W m−1 K−1 along the armchair and zigzag direc-tions, which are much lower than that of stanene (11.9 W m−1

Fig. 4 (a) Calculated lattice thermal conductivity with respect to temperature for monolayer SnP3. (b) Phonon group velocity, (c) Grüneisen para-meters, and (d) phonon relaxation time with respect to frequency for monolayer SnP3. The inset of (a) is the bipolar thermal conductivity. The insetsof (b) and (c) are the phonon group velocity and Grüneisen parameters of the three acoustic modes along the Γ–M–K–Γ high-symmetry lines. Theinset of (d) is the total three phonon scattering phase space.

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K−1)71 and phosphorene (78 W m−1 K−1).72 Such low κl impliesthat it might be a promising candidate for TE applications.

The phonon velocity is a closely related physical parameterfor the thermal transportation. Using our calculated phonondispersion, it can be calculated by

υλ;q ¼ @ωλ;q

@q; ð8Þ

where ωλ,q is the phonon frequency, and is plotted in Fig. 4(b).We find that the phonon velocities for TA and LA branches atthe Γ point are 2.53, and 4.04 km s−1, respectively. Comparedwith the bulk phosphorene,64 monolayer SnP3 possesses lowerphonon group velocities, due to the flat phonon dispersionsand low cutoff frequency. Additionally, it is evident that thegroup velocities have small differences along the Γ–M (arm-chair) and Γ–K (zigzag) high-symmetry directions, shown inthe inset in Fig. 4(b), further demonstrating the weak an-isotropy of the κl. To obtain more insights for the phonontransport properties, the Grüneisen parameters γ and phononrelaxation time of each phonon branch are introduced, as

shown in Fig. 4(c) and (d). The γ can qualitatively analyze theanharmonic interactions. It can be obtained according to

γλ;q ¼ � Vωλ;q

@ωλ;q

@V: ð9Þ

Generally, large |γ| indicates that it has a strong phonon–phonon anharmonic scattering73 and is responsible for low κl,especially under high temperature. Obviously, a large γ ofabout −7 for ZA can be observed, implying strong anharmoni-city. The large γ mainly exists in the low-frequency region,which greatly suppresses the thermal transport and leads tolow κl. In general, for materials containing lone-pair electrons,the nonbonding electrons will interact with the valence elec-trons of the adjacent neighboring atoms, causing increasedanharmonicity at limited temperature. This is the commonorigin for high Grüneisen parameters.74,75 The negative valuesof the γ indicate that this material may have the property ofnegative thermal expansion. The phonon relaxation time canbe acquired by the summation of various scattering pro-cesses.76 From Fig. 4(d), we find that the phonon relaxation

Fig. 5 ZT with respect to chemical potential and carrier concentration for monolayer SnP3 along the (a) and (c) armchair and (b) and (d) zigzagdirections.

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time of the LA mode is the longest, then the TA and ZA modes,and then the optical modes. Compared with the bulk phos-phorene and stanene, monolayer SnP3 exhibits a shorterphonon relaxation time, which is also a significant drivenforce for its low κl. The three phonon scattering phase space(P3) can further provide insight into the phonon relaxationtime and is shown in the inset of Fig. 4(d). We can see clearlythat the monolayer SnP3 has a larger P3 in the whole frequencyregion than that of the bulk phosphorene.77 This fact indicatesthat it possesses a large P3 allowing phonon–phonon scatter-ing and will hinder the thermal transport.

3.4. Thermoelectric figure of merit

By combining the phonon and electron transport coefficients,we calculate the ZT of monolayer SnP3 and plot it in Fig. 5. Theelectronic scattering time τ is obtained by the DP theory asshown in Table 2. Similar to SnSe2,

78 an anisotropic TEresponse is observed in monolayer SnP3. One can see that theZT of the p-type doping is obviously superior to that of then-type doping, which can be attributed to the difference in thecarrier mobility in electrons and holes. No matter what type ofdoping, the ZT of monolayer SnP3 along the zigzag direction isalways larger than that along the armchair direction, whichoriginates mainly from the different electronic relaxationtimes. We find that the thermal stability of monolayer SnP3can be retained at 700 K by performing ab initio moleculardynamic (AIMD) simulations (see Fig. S3, ESI†). Therefore, weonly consider the value of ZT below 700 K. As shown in Fig. 5,the ZT at 500 K can approach 3.46 and 2.97 along the armchairand zigzag directions, which are much larger than that ofphosphorene (0.7).79 The carrier concentration dependent ZTvalues ranging from 300 K to 700 K are shown in Fig. 5(c) and(d). The corresponding concentration of maximum ZT (500 K)for n-type (p-type) monolayer SnP3 is around 1 × 1013 cm−2 to2 × 1013 cm−2 along the armchair and zigzag directions. Thisorder of carrier concentrations has been realized experi-mentally in 2D MoS2.

80 Overall, our results show that themonolayer SnP3 is a hopeful candidate for TE applications.

4. Conclusion

In summary, we studied the TE properties of monolayer SnP3through using DFT and Boltzmann transport equation. Resultsindicate that monolayer SnP3 possesses intrinsically low heattransport ability. Its small phonon group velocity, largeGrüneisen parameters, and short phonon relaxation timegreatly suppress the phonon transport and lead to low κl of4.97 and 5.41 W m−1 K−1 at room temperature along the arm-chair and zigzag directions, respectively. Unlike the isotopicthermal transport property, the electrical transport exhibits anobvious anisotropic behavior. Highly degenerate VB, peakyDOS, high hole mobility (703.47 cm2 V−1 s−1) and largeSeebeck coefficients (907 μV K−1) are observed. The ZT at 500 Kunder p-type doping can approach 3.46 along the armchairdirection. Collectively, these results demonstrate the great

advantages of monolayer SnP3 for converting heat energy withhigh efficiency at moderate temperatures ranging from 300 Kto 500 K.

Conflicts of interest

There are no conflicts to declare.

Acknowledgements

The calculations were performed at the Supercomputer Centrein the China Spallation Neutron Source. This work was finan-cially supported by National Natural Science Foundation ofChina (NSFC) (Grant No. 11874145) and the PhD Start-upFund of Natural Science Foundation of Guangdong Province,China, (No. 2018A0303100013).

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