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Titanium trisulfide (TiS3) monolayer as a potential thermoelectric material: first-principles based Boltzmann transport study Jie Zhang, Xiao-Lin Liu, Yanwei Wen, Lu Shi, Rong Chen, Huijun Liu, and Bin Shan ACS Appl. Mater. Interfaces, Just Accepted Manuscript • DOI: 10.1021/acsami.6b14134 • Publication Date (Web): 05 Jan 2017 Downloaded from http://pubs.acs.org on January 6, 2017

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ACS Applied Materials & Interfaces

Titanium trisulfide (TiS3) monolayer as a potential thermoelectric material: first-principles based Boltzmann transport study Jie Zhang1, Xiaolin Liu1, Yanwei Wen1, Lu Shi1, Rong Chen2, Huijun Liu3, Bin Shan1,* 1

State Key Laboratory of Material Processing and Die and Mould Technology and

School of Materials Science and Engineering, Huazhong University of Science and Technology, Wuhan 430074, China 2

State Key Laboratory of Digital Manufacturing Equipment and Technology and

School of Mechanical Science and Engineering, Huazhong University of Science and Technology, Wuhan 430074, China 3

Key Laboratory of Artificial Micro- and Nano-Structures of Ministry of Education and School of Physics and Technology, Wuhan University, Wuhan 430072, China

Abstract: Good electronic transport capacity and low lattice thermal conductivity are beneficial for thermoelectric applications. In this study, the potential use as thermoelectric material for the recently synthesized two-dimensional TiS3 monolayer is explored by applying first-principles method combined with Boltzmann transport theory. Our work demonstrates that carrier transport in TiS3 sheet is orientation dependent, caused by the difference of charge density distribution at band edges. Due to a variety of Ti-S bonds with longer lengths, we find TiS3 monolayer show much lower thermal conductivity compared with that of transition metal dichalcogenides such as MoS2. Combined with high power factor along y direction, a considerable n-type ZT value (3.1) can be achieved at moderate carrier concentration, suggesting TiS3 monolayer as a good candidate for thermoelectric applications.

Keywords: transition metal trichalcogenide (TMTC), TiS3 monolayer, carrier mobility, *

thermal

conductivity,

thermoelectric

performance,

first-principles

Author to whom correspondence should be addressed. Electronic mail: [email protected]. 1

ACS Paragon Plus Environment


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calculations, Boltzmann transport equation

1. Introduction The global energy crisis and environmental impact of fossil fuels have led to substantial efforts in developing sustainable energy sources. Thermoelectric devices that are capable of converting heat into electricity and vice versa thus have attracted considerable interest from the scientific community. The performance of a thermoelectric material is described by the dimensionless figure of merit:

ZT = S 2σ T / (κ e + κ L ) .

(1)

Where S is the Seebeck coefficient, σ is the electrical conductivity, T is the temperature, and κ e and κ L are electronic and lattice thermal conductivities, respectively. In order to increase the ZT value of a bulk thermoelectric material, one effective strategy is to enhance the power factor (PF= S 2σ ) by modulation doping and band engineering,1,2,3 the other approach is to reduce the lattice thermal conductivity through the formation of nano-precipitates and all-scale hierarchical architectures.4,5,6 In particular, the seminal work of Hicks et al.7,8 and subsequent experiments9,10,11 have shown that low-dimensional structures could maintain high power factor and low thermal conductivity at the same time. As semiconductors with thickness dependent band gap and high carrier mobility, atomic-layer transition metal dichalcogenides (TMDCs) have attracted growing interest for applications in field-effect transistors (FET) and optoelectronic devices. 12 , 13 , 14 , 15 , 16 In addition, these low-dimensional TMDCs have also been explored as potential thermoelectric materials due to the advantage of flexibility, low cost and minimal environmental impact compared with conventional thermoelectric materials such as Bi2Te3 and PbTe. For example, by using lithium intercalation and filtration technique, Wang et al. synthesized the restacked MoS2 thin-film. It is found that the maximum electrical conductivity and Seebeck coefficient could reach 17.5 S/cm and 93.5 µV/K, respectively.17 Yoshida et al. studied the effect of electric field on the thermopower of ultrathin WSe2 single crystal. They figured out that the power 2


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factor in both the hole and electron side can be optimized and the maximum values are one-order larger than those obtained by changing chemical composition.18 On the theoretical side, with the help of first-principles calculations and semiclassical Boltzmann transport theory, Kumar et al. concluded that the thermoelectric performance of WSe2 is superior to MoSe2 and a peak ZT value of about 0.8 is reached at 1200 K.19 Huang et al. studied the thermoelectric properties of MX2 (M=Mo, W; X=S, Se) monolayers by a ballistic transport approach under linear response regime. They predicted that the ZT of these materials are generally low, among which, p-type MoS2 monolayer shows the highest peak value at room temperature. 20 Although the above works show that TMDCs could be potential thermoelectric materials, the low efficiency is still the main obstacle for their wide application in energy conversion devices. Recently, a new class of 2D layered materials, namely, transition metal trichalcogenide monolayers MX3 (M=Ti, Zr, Hf; X=S, Se, Te), have been successfully prepared.21,22,23,24 Among them, it is found that TiS3 monolayer possesses a direct band gap and much higher carrier mobility,25,26 which are desirable for thermoelectric applications. Moreover, a more complex atomic configuration compared with TMDCs implies that it would own a relatively lower thermal conductivity. For its further applications as thermoelectric material, it is of importance to evaluate the thermoelectric performance of such monolayer. In this work, using first-principles calculations and Boltzmann transport theory, we give a comprehensive study on the electronic and phonon transport properties of TiS3 monolayer. We show that the single-layer structure exhibit a ZT value of 3.1 at room temperature, suggesting that good thermoelectric performance can be achieved in material constituted by light transition metal titanium and sulfur atoms.

2. Methodology Our theoretical calculations are performed within the first-principles plane-wave pseudopotential formulation27,28,29 as implemented in the Vienna Ab-initio Simulation Package (VASP). 30 The generalized gradient approximation (GGA) with the Perdew-Burke-Ernzerhof (PBE)31 exchange-correlation functional is used. The cutoff 3



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energy for the plane wave basis is set to be 500 eV. In the ionic relaxation and charge density calculation, Monkhorst-Pack k-mesh32 of 13×9×5 and 7×10×1 are employed for bulk and monolayer TiS3, respectively. For the optimization of bulk crystal structure, van der Waals (vdW) interaction is explicitly included. A vacuum thickness larger than 14 Å is adopted along the direction normal to the atomic plane so that the interaction between the neighboring monolayers can be neglected. The convergence threshold is set as 1 meV for total energy and 0.01 eV/Å for atomic force. In order to give accurate electronic transport coefficients, we calculate the band structure of TiS3 system by using the hybrid density functional in the form of Heyd-Scuseria-Ernzerhof (HSE06).33 Within the Boltzmann transport theory in the relaxation time approximation,34 the Seebeck coefficient ( S ) and electrical conductivity ( σ ) are expressed as:

S=

ek B

σ

 ∂f 0 

∫ d ε  − ∂ε Ξ (ε )

ε −µ k BT

,

(2)

 ∂f 0  Ξ ( ε ) ,  ∂ε 

σ = e2 ∫ dε  − where f 0 =

1 e

( ε − µ )/ k BT

+1

(3)

is the equilibrium Fermi function, k B is the Boltzmann

constant, and µ is the chemical potential, which can be obtained by integrating the density of states (DOS) from the desired chemical potential to the Fermi level. In this v v approach, the so-called transport distribution function Ξ(ε ) = ∑ vkv vkvτ kv can be v k

v calculated based on the band structures. Here vkv and τ kv are the group velocity and v relaxation time at state k , respectively. For the calculation of electronic thermal

conductivity, we apply the Wiedemann-Franz law κ e = Lσ T , where L =2.45×10‒8 WΩK‒2 is the Lorenz number. In the phonon calculations, harmonic phonon properties are studied using finite displacement method performed in Phonopy package. 35 The lattice thermal conductivity can be estimated by using iterative self-consistent method for solving the phonon Boltzmann transport equation as implemented in the ShengBTE code.36,37,38 4


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A 4×5×1 supercell with Γ point and 3×4×1 supercell with 3×3×1 k-mesh are adopted for the calculations of second- and third-order interatomic force constants (IFCs), respectively. In order to get convergent thermal transport parameters, the interactions up to the eighth nearest neighbors are considered for the anharmonic one.

3. Results and discussion To confirm the validity of our method, we first study the structure and electronic properties of bulk TiS3. As can be seen from Figure 1(a), TiS3 crystallizes in a layered structure with the space group p21m. The neighboring atomic planes composed by the 1D chains of triangular TiS3 unit are held together by van der Waals forces. Table S1 (Supporting information) lists the structural parameters for bulk TiS3 obtained by using different computational framework. It is found that DFT-D2

39

and

optB86b-vdW40 functionals give the best results.41 Besides, we further find that the band structures based on the lattice constants calculated by the two methods are almost the same. Unless otherwise specified, we will use optB86b-vdW functional to take into account the vdW interactions in the following sections. Figure 2(a) shows the band structure of bulk TiS3 by using HSE06. One can see that TiS3 is an indirect semiconductor, with the valence band maximum (VBM) and conduction band minimum (CBM) located at Γ and Z points, respectively. The band gap obtained is 1.09 eV, which is in good agreement with the previous theoretical and experimental works.25,42,43 The calculations show that our approach is reliable for this system, which is the precondition to accurately predict the transport coefficients. In the following, we will apply the same method to deal with the TiS3 monolayer. Due to weak vdW force between the atomic planes, TiS3 single layer can be obtained by mechanical cleavage or liquid-phase exfoliation.21,25 Its corresponding crystal structure is shown in Figure 1(b) and 1(c). Within the monolayer, the outer and inner sulfur atoms are inequivalent and are defined as S1 and S2, respectively. The optimized lattice constants are a=5.03 Å and b=3.42 Å, which are larger than its analogue MoS2 single-layer (a=b=3.19 Å). The Ti-S1 bond marked by d1 has a length of 2.50 Å, while the bond length of Ti-S2 cross and along the atomic plane direction 5



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are different, which are represented by d2=2.47 Å and d3=2.67 Å, respectively. Besides, the two outer S1 atoms are covalently bonded with a length of 2.04 Å. Note that there is only a uniform Mo-S bond (2.41 Å) in MoS2. The more complex atomic configuration of TiS3 monolayer suggest that it would exhibit lower lattice thermal conductivity, as will be discussed in the following. Figure 2(b) shows that TiS3 sheet is a direct semiconductor with both VBM and CBM located at Γ point. The calculated band gap is 1.16 eV, which is slightly larger than its bulk counterpart, indicating that there is a finite quantum confinement effect in this system.44,45 In order to understand the origin of the VBM and CBM states, we also plot the orbital-decomposed band structures in Figure 2(b)-(d). One can see that VBM is derived from the hybridization between the p orbitals of S2 and d orbitals of Ti, whereas the CBM is mainly contributed by the Ti d states. As S1 has almost no contribution to the band edge states, it is reasonable to expect that the carrier type and concentration of the system can be modulated by substitution at the S1 sites without significant changes in the shape of band extrema, which is beneficial for thermoelectric applications. Based on the calculated band structure, we estimate the electronic transport coefficients within the Boltzmann transport theory. In this approach, the electrical conductivity is calculated with respect to carrier relaxation time ( τ ), which is obtained by τ =

µ m* e

, where µ and m* are carrier mobility and effective mass,

respectively. For two-dimensional system, µ

can be determined by using

deformation potential (DP) theory on the basis of effective mass approximation:46,47

µ=

2eh3C , 3k BTm*2 E12

where the elastic modulus C is defined as C =

(4)

∂2 E , the deformation S0 ∂(∂l / l0 )2

potential constant E1 = ∆E / (∆l / l ) , in which ∆E is the variation of band edge position (VBM and CBM) with the lattice dilation of ∆l / l . The energies of band extremum are calculated with respect to a common vacuum level. Other parameters in 6


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the above formulae are total energy E and area S0 of the system. Table 1 lists the calculated mobility and relaxation time of TiS3 monolayer at room temperature. One can see that hole mobility and relaxation time along the x direction are higher than those along the y direction, while it is reversed for the case of electron. To understand this phenomenon, we plot the charge density of band edges in Figure S1 (Supporting information). It can be clearly seen that the charge density of VBM shows spatial continuity along the x direction, indicating a sizable hole mobility along this direction. However, the charge density of CBM has a continuous distribution along y direction, which means electron transport is favorable in this direction. Moreover, we find that y-direction electron mobility has an order of 104 cm2V−1s−1, which is much higher than that of MoS2 monolayer (in the range of 60 ~ 200 cm2V−1s−1)12,48 and has potential use in thermoelectric applications. In Figure 3, we plot the calculated room temperature electronic transport coefficients along x and y directions as a function of carrier concentration ( n ) from 1011 to 1014 cm−2. We see that both the p-type and n-type Seebeck coefficient along two directions are almost identical to each other in the carrier concentration range considered. Besides, the absolute values of Seebeck coefficient increase with decreasing carrier concentration, which coincides with the relation: S ∝ (1/ n )

2/3 49

.

On the other hand, due to the direction dependence of carrier relaxation time, the electrical conductivity exhibits strong anisotropy. With the increase of carrier concentration, σ shows a reversed behavior with Seebeck coefficient, implying a compromise must be taken to maximize the PF, as indicated in Fig. 3(c). Since the Seebeck coefficient is normally isotropic as mentioned, we can see from the figure that the highest PF appears in the direction where the electrical conductivity is the largest. We next discuss the thermal transport properties of TiS3 monolayer. Figure 4(a) displays the phonon dispersion relation of this structure. It is found that the phonon dispersion is asymmetric along the Γ-X and Γ-Y directions. Based on the formula

7



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v=

∂w , the acoustic phonon group velocities near Γ point are calculated and listed in ∂q

Table 2. For comparison, we also present corresponding results of MoS2 monolayer. One see that the group velocity is different for that along x and y directions, which means that the thermal transport of TiS3 monolayer will exhibit orientation dependence. Besides, a smaller acoustic phonon velocity compared with that of MoS2 suggest that a lower lattice thermal conductivity in TiS3 monolayer. Figure 4(b) shows the partial phonon DOS of TiS3 monolayer, we find there is a strong hybridization between the Ti and S1 atoms in the frequency region 0 ~ 5 THz. Since the heat is mainly carried by low frequency phonons, we can conclude that heat transport along Ti-S1 bond is the key thermal transfer mechanism in TiS3 monolayer, as will be discussed later. Figure 4(c) plots the calculated lattice thermal conductivity κ L of the TiS3 layer as a function of temperature in the range from 200 to 800 K. For two-dimensional system, the calculated κ L depends on the selection of layer thickness. In our study, we apply the interlayer separation of the bulk TiS3 (8.72 Å). One can find that the lattice thermal conductivity decreases with increasing temperatures, implying the thermal transport is determined by the Umklapp process. It should be noted that the room temperature κ L are 17.9 and 10.2 W/mK along the y and x directions, respectively, which are much lower than that of MoS2 sheet50,51,52 and suggest that TiS3 monolayer could have favorable thermoelectric performance. In order to understand the reason that thermal transport along the Ti-S1 bond dominates in TiS3 monolayer, we have plotted the phonon group velocity and relaxation time of different modes in Figure 5(a) and (b). One can clearly see in the range of 0 ~ 5 THz, the phonon group velocity and relaxation time are much larger than those of high frequency phonons. As a result, the room temperature accumulative thermal conductivity occupies a lot in this frequency region, as shown in Fig. 5(c). It should be noted that the low frequency phonon DOS are mainly contributed by the hybridization between Ti and S1 atoms as mentioned above, which indicates that thermal carry on Ti-S1 bond is the main heat transfer mechanism in TiS3 monolayer. 8


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Such a behavior is consistent with the fact that the bond length of Ti-S1 is much smaller than that of Ti-S2 along the planar direction. On the other hand, the longer bond for Ti-S1 and Ti-S2 is also the reason for the lower lattice thermal conductivity of TiS3 sheet than its analogue MoS2 monolayer. Figure 6 shows the percentage contribution of different phonon modes to the total lattice thermal conductivity. We can see that along the x direction, three acoustic phonons dominate the thermal transport in TiS3 monolayer. For example, almost 85% of the total thermal conductivity are contributed by acoustic phonons in the temperature range considered. However, it is not the case along the y direction, where the contributions from the optical phonons are quite large. Similar behavior has also been found in phosphorene and can be attributed to the hybridization of low frequency optical phonons with the acoustic phonons (see Fig. 4(a)).53 Note that the thermal conductivity from optical phonons slowly increase with the temperature, which may be due to the fact that more high frequency phonons are stimulated at high temperatures.54 With all the transport coefficients obtained, we can now evaluate the thermoelectric performance of TiS3 monolayer. Figure 7 shows the room temperature ZT values as a function of carrier concentration. For p-type system, the highest ZT of 0.68 can be achieved along the x direction at the concentration of 2.4×1012 cm‒2. However, the optimal ZT is very small along the y direction due to the relatively large lattice thermal conductivity. Moreover, the ZT value of n-type system can reach as high as 3.1 when the carrier concentration is 7.2×1011 cm‒2. Our calculations suggest that TiS3 monolayer can be a promising thermoelectric material by properly adjusting the carrier concentration.

4. Summary We have investigated the electronic, phonon and thermoelectric properties of TiS3 monolayer by first-principles calculations and Boltzmann theory. It is found that the band gap changes little when reducing the dimension of bulk TiS3, which is much different from other two-dimensional materials such as MoS2 and phosphorene. Since the contribution of S1 atom to the band edges is negligible, substitution at S1 site can 9



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be used to adjust the carrier concentration of the system. We find that the anisotropic electronic transport of TiS3 monolayer is due to the difference of charge density distribution at the band extrema. On the other hand, TiS3 sheet possesses much lower thermal conductivity than its analogue MoS2 single-layer, which is consistent with its relatively complex atomic configuration. At a moderate carrier concentration, TiS3 monolayer possesses superior thermoelectric performance with a maximum room temperature ZT value of 3.1, suggesting that n-type system can be a very promising thermoelectric material.

10


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Supporting Information Structural parameters of bulk TiS3 obtained by using different computational framework and charge density of VBM and CBM of TiS3 monolayer.

Acknowledgement This work is supported by the National Basic Research Program of China (2013CB934800), National Natural Science Foundation of China (51572097, 51575217), and the Hubei Province Funds for Distinguished Young scientists (2014CFA018 and 2015CFA034). Rong Chen acknowledges the Thousand Young Talents Plan, the Recruitment Program of Global Experts. The calculations are done at the Texas Advanced Computing Center (TACC) at The University of Texas at Austin (http://www.tacc.utexas.edu).

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Table 1. The deformation potential constant E1, elastic modulus C, effective mass m*, carrier mobility µ and relaxation time τ of TiS3 monolayer at room temperature. Direction

carriers

E1 (eV)

C (N/m)

µ (×103

*

m (m0)

2

−1 −1

τ (10−13s)

cm V s ) hole

3.16

84.41

0.30

1.33

2.27

electron

1.08

84.41

1.51

0.45

3.87

hole

−3.99

134.83

1.02

0.12

0.67

electron

0.81

134.83

0.38

20.21

43.66

x

y

Table 2. The group velocity of acoustic phonons (out-of-plane acoustic (ZA), transverse acoustic (TA), longitudinal acoustic (LA)) near Γ point for TiS3 monolayer along x and y directions. The result of MoS2 single-layer is also listed for comparison. direction

ZA (km/s)

TA (km/s)

LA (km/s)

x

0.88

3.01

5.43

y

1.11

2.31

6.16

1.40

3.96

6.47

TiS3 MoS2

12


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Figure 1. The ball-and-stick model of (a) bulk TiS3, (b) and (c) are side-view and top-view of TiS3 monolayer, respectively. The coordinate axes (x, y, z) and structural parameters (d0, d1, d2, d3) are indicated.

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Figure 2. (a) Calculated band structure of bulk TiS3, and the orbital-decomposed band structure of TiS3 monolayer: (b) the d orbits of Ti (red), (c) the p orbits of S2 (green), (d) the p orbits of S1 (blue). The fermi level is set to 0 eV.

14


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Figure 3. The room temperature electronic transport coefficients: (a) absolute values of Seebeck coefficient, (b) electrical conductivity, (c) power factor of TiS3 monolayer as a function of carrier concentration from 1011 to 1014 cm−2.

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Figure 4. (a) The phonon dispersion relations and (b) partial phonon DOS of TiS3 monolayer, (c) is the calculated lattice thermal conductivity as a function of temperature along x and y directions.

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Figure 5. The extracted (a) group velocity and (b) relaxation time of different phonon modes for TiS3 monolayer as a function of frequency, (c) is the variation of accumulative lattice thermal conductivity with respect to cutoff frequency at room temperature.

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Figure 6. Percentage contribution of different phonon branches to lattice thermal conductivity of TiS3 monolayer along (a) x and (b) y directions as a function of temperature.

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Figure 7. The calculated (a) p-type and (b) n-type ZT values of TiS3 monolayer as a function of carrier concentration along x and y directions at 300 K.

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Titanium Trisulfide Monolayer as a Potential ... - ACS Publications

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