High Thermoelectric Performance in Two-Dimensional Janus Monolayer Material WS-X (X = Se and Te)

In the present work, Janus monolayers WSSe and WSTe are investigated by combining first-principles calculations and semiclassical Boltzmann transport theory. Janus WSSe and WSTe monolayers show a direct band gap of 1.72 and 1.84 eV at K-points, respectively. These layered materials have an extraordinary Seebeck coefficient and electrical conductivity. This combination of high Seebeck coefficient and high electrical conductivity leads to a significantly large power factor. In addition, the lattice thermal conductivity in the Janus monolayer is found to be relatively very low as compared to the WS2 monolayer. This leads to a high figure of merit (ZT) value of 2.56 at higher temperatures for the Janus WSTe monolayer. We propose that the Janus WSTe monolayer could be used as a potential thermoelectric material due to its high thermoelectric performance. The result suggests that the Janus monolayer is a better candidate for excellent thermoelectric conversion.


■ INTRODUCTION
The world's energy demand is rapidly increasing due to factors like considerable growth in population, industrialization, development in technology, etc. Until recently, these energy needs were being fulfilled with fossil fuels and other nonrenewable resources; 1 however, the massive consumption of such resources led to the unavailability of them. The burning process generates energy with waste heat, exhaust gases, pollution, and other harmful effects on the environment. 2,3 The renewable resources have a small contribution in fulfilling these energy needs. The total replacement of fossil fuels is not possible at present. 4 Hence, improved energy efficiency and reduced energy demand are the expected solutions to this problem. 5 Thermoelectric materials have the ability to convert electricity from heat by the Seebeck effect, and they are also able to produce a cooling effect by the Peltier effect. 6 Lightweight, cost-effective, and efficient thermoelectric materials can help in generating electric energy from waste heat. Development and identification of such materials with high thermoelectric conversion performance have remained a big challenge since the discovery of the thermoelectric concept. 7,8 The ability of thermoelectric conversion of thermoelectric material is summarized by the thermoelectric figure of merit (ZT), which is expressed as ZT = S 2 σT/κ, where S, σ, and κ represent the Seebeck coefficient, electrical conductivity, and thermal conductivity, respectively. 9−11 The thermal conductivity of the material is expressed as κ = κ l + κ e. The thermal conductivity (k) involves lattice thermal conductivity (κ l ) due to lattice vibrations and electronic contributions (κ e ) due to electronic motion. 10,11 The best thermoelectric performance measured until now has ZT values ranging from 2.5 to 2.8. 11−14 The new material (a thin layer of iron, vanadium, tungsten, and aluminum applied to a silicon crystal) developed by the scientists of TU Wien has shown that the high efficiency ZT value lies between 5 and 6. 15 The new derivatives of two-dimensional (2D) materials, Janus 2D materials, have attracted considerable research attention due to their distinct properties. Their properties are quite different compared to the traditional 2D materials. 16 The Janus 2D material possesses unique properties due to its mirror asymmetry in the structure. 16,17 The Janus transition metal dichalcogenides (TMDs) belong to an important class of materials due to their structure, stability, electronic properties, and other properties. 16 In 2013, the dynamical stability of MoSSe, WSSe, WSTe, and WSeTe was proved through a theoretical investigation by Cheng et al. 18 Various methods, such as micromechanical exfoliation, liquid exfoliation, chemical vapor deposition (CVD), and hydrothermal synthesis, are used for the experimental synthesis of 2D materials. Janus 2D materials do not exist in nature. However, the Janus MoSSe monolayer from MoS 2 was first successfully synthesized through CVD by Li and co-workers in 2017. 16 The Janus monolayer MoSSe was also experimentally synthesized from MoSe 2 in 2017. 19 Among these previously reported materials, MoSSe provides a foundation for theoretical and experimental investigations on other Janus type materials. 17 Recent theoretical studies suggest that the Janus monolayer has promising applications in various fields such as gas sensing, 20 optoelectronics, 21 photocatalysts, 22,23 spintronics, and valleytronics. 18,24,25 In addition, Gu and Yang found that the lattice thermal conductivity can be significantly reduced by the minimization of the frequency gap. 26 It can also be reduced by changing its stoichiometry. 27,28 Low lattice thermal conductivity can effectively increase the ZT.
Motivated by these exciting properties of the Janus monolayer, we have systematically investigated the structural properties, electronic properties, lattice thermal conductivity, and thermoelectric behavior of the Janus 2D material WS-X (where X = Se and Te). The structure of WSSe and WSTe can be prepared by the replacement of one S atom with Se and Te in the molecule of WS 2 . 27,29,30. We have also reported a comparative study with its traditional disulfide form WS 2 . To effectively simulate their thermoelectric behavior, the Seebeck coefficient, electric conductivity, thermal conductivity, and ZT have been determined as a function of temperature. The results of this study show the enhancement in thermoelectric performance from WS 2 toward WSSe and WSTe.

■ COMPUTATIONAL METHODS
In this work, first-principles simulations are performed using Vienna Ab initio Simulation Package (VASP) software. 31,32 The densityfunctional theory calculations are performed by the generalized gradient approximation method with the Perdew−Burke−Ernzerhof (PBE) exchange-correlation (XC) functional. 33 For the monolayer WS-X system (X = S, Se, and Te), a projected augmented wave (PAW) with a default energy of 500 eV was used to describe the core and valence electron interactions. 34 We also have the Heyd− Scuseria−Ernzerhof (HSE06) functional to obtain accurate electronic properties. For hybrid functional HSE06, we have used the exchangecorrelation energy functional HSE06 with a mixing parameter (α) of 25% and a screening parameter of 0.2 Å −1 . The thick vacuum of order 25 Å is inserted to prevent interactions between periodic layers along the normal direction (z-direction). 35 The Monkhorst pack meshes of (19 × 19 × 1) are used for the k-point sampling. 36 For these materials, the optimized structures are achieved by the conjugate gradient (CG) method within a converge criterion of 10 −3 eV/Å for Hellmann−Feynman forces and 10 −8 eV/cell for energy. In order to check dynamic stability, the phonon dispersions for these materials are calculated through the density functional perturbation theory (DPFT) method by creating supercells of 5 × 5 × 1 and using a kpoint mesh of 3 × 3 × 1. 37 Lattice thermal conductivity of these materials are determined by a relaxation time approximation (RTA) method through a Phono3py code. 38 The second-order force constants (for harmonic phonons) for the 4 × 4 × 1 sized supercells of these materials and the third-order force (an-harmonic force constants) for the 3 × 3 × 1 sized supercells of these materials are computed by the finite-displacement method using a k-point mesh of for the 3 × 3 × 1 sized supercells of these materials. 37 To calculate the lattice thermal conductivity, a q-mesh of 19 × 19 × 1 is used for sampling. The alternative 24 × 24 × 1 q mesh did not have a relevant effect on our conclusions. The deformation potential (DP) theory developed by Bardeen and Shockley is employed to calculate carriers' mobility. 39 The semiclassical Boltzmann theory, Boltzmann transport , and RTA methods have been employed to calculate the Seebeck coefficient and transport properties of these materials through the BoltzTrap2 code. 40,41 We have used constant relaxation time approximation with t = 10 −14 s for thermal and electrical conductivity calculations. Ab initio molecular dynamics (AIMD) simulations 31,42 were performed in the canonical ensemble (fixed particle number, volume, and temperature, NVT) with a time step of 2 fs by keeping the temperature fixed at 1200 K to check the thermal stability. Vesta software was used for visualization of materials. 43 ■ RESULTS AND DISCUSSIONS Structural Properties of WS 2 , WSSe, and WSTe. The optimized stable structures of the monolayer WS 2 and the Janus monolayer WSSe and WSTe are shown in Figure 1. These materials have hexagonal lattice symmetry in 2D space.
Here, each unit cell of these material contains three atoms (one atom of W, one atom of S, and one atom of X = S, Se, or Te). Each tungsten (W) atom has four coordinates (4 W−X bonds; X = S, Se, and Te). While sulfur (S), selenium (Se), and tellurium (Te) atoms have two coordinates (2 W−X bonds; X = S, Se, or Te) in the structures. The optimized WS 2 monolayer has lattice parameters a = 3.191 Å and b = 3.191 Å in x and y directions, respectively, as shown in Table 1. This value is agreed with previously reported values. 44  vacuum of 25 Å is also present in the z-direction to prevent interactions between adjacent layers. The Janus monolayer structure for this two-dimensional WS 2 monolayer can be achieved by the replacement of any one S atom with Se atom or Te atom in its structure. After optimization of the predicated Janus materials WSSe and WSTe, the WSSe has lattice constants a = 3.258 Å, and b = 3.258 Å in x and y directions, respectively, and the WSTe has lattice constants a = 3.370 Å and b = 3.370 Å (see Table 1). This optimized lattice parameter is very close to previous investigations. 27 Both materials, WSSe and WSTe, have a hexagonal lattice arrangement in 2D space. There are two W− S bonds having a bond length of 2.42 Å, whereas the Janus monolayer WSSe has one W−S bond of 2.55 Å and another W−Se bond of 2.43 Å. In addition, Janus WSTe has one W−S bond of 2.44 Å and a W−Te bond of 2.73 Å as presented in Table 1. The W−S bonding is relatively weaker than that in the Janus TMDs, WSSe and WSTe. The W−Te bond in Janus WSTe is weaker than any other bonding among these materials. To check the dynamical stability of this monolayer, we have computed the phonon band structure as shown in Figure S1 (see Supporting Information). From the phonon band structures, we can see that there is no negative frequency. It means that the Janus monolayer is a dynamically stable structure. From ab initio molecular dynamics (AIMD) calculations, all these monolayers at 1200 K show thermal stability, which is shown in Figure S2 (see Supporting Information).
Electronic Properties of Monolayer WS 2 and Janus WSSe and WSTe. To study the electronic properties of the 2D single materials WS 2 , WSSe, and WSTe, the PBE band structure and the hybrid band structure were computed along the symmetry path Γ-M-K-Γ. Here, Figure 2(a,c, and e) shows the PBE bandstructure of monolayers WS 2 , WSSe, and WSTe. The calculated band gap of WS 2 is 1.84 eV, which is of direct nature. This value of the direct band gap for the monolayer WS 2 is very close to the experimental value of the band gap in the previous investigation. 46 −50 Similarly, the calculated directgaps of WSSe and WSTe are 1.72 and 1.23 eV, which are also agreed with earlier reported values. 51 The band gaps for the HSE06 functional (see Figure S3 in Supporting Information) are 2.15 eV for WSSe, which is very close to the previously reported values 2.07 and 1.71 eV for WSTe, which also agrees with the pristine value 1.56 eV. 30,52 The Janus TMD monolayers WSSe and WSTe have a semiconductor nature as presented in Table 2.
For a better analysis of the electronic structure, the projected density of states (PDOS) for two-dimensional materials WS 2 , WSSe, and WSTe is determined as shown in Figure 2(b,d, and f). For these materials, the d-orbital of the W atom provides the main contribution to the formation of conduction bands. It also provides the main contribution in the valence band near the Fermi levels of these materials. The p-orbital of the S atom also provides small contributions over conduction bands. Similarly, p-orbitals of S, Se, and Te have contributed to the conduction band of WSSe and WSTe. The s-orbitals of W, S, Se, and Te have negligible contribution information of conduction and valence bands. Far from the Fermi level, the p-orbitals of S, Se, and Te have a more massive contribution in the valence band of Janus WSSe and WSTe. In the WS 2 monolayer, this contribution has been provided by only the S atom. This indicates the stable replacement of the S atom by the Se and Te atom in Janus WSSe and WSTe, respectively.
Another significant contribution of d-orbitals of the W atom is found in the valence band of all of these materials. At many places, the d-orbitals of the W atom are overlapped with porbitals of S, Se, and Te atoms in the valence band far from the Fermi level. The flat band lines in these suggest a large effective mass for them, and the Seebeck coefficient directly depends on the effective mass (m*). 53 According to that, the monolayers WS 2 , Janus WSSe, and WSTe have higher values of the Seebeck coefficient.
Carrier Mobility and Relaxation Time. Using the DP theory based on the effective mass of carriers presented by Bardeen and Shockley, the carrier mobility can be determined by the following expression: 2 where μ is carrier mobility, C is elastic modulus in the strain direction, m* is the effective mass of the carrier, k b is the Boltzmann constant, and E 1 is the DP. Here, the effective mass m*  Figure 3(a,b) shows the plot of electron mobility and hole mobility. The electronic mobility of WS 2 is slightly bigger than WSSe and WSTe. The effective masses of carriers in WSTe are slightly more than WS 2 and WSTe as presented in Table 3. For WS 2 and WSSe, the hole's effective mass is slightly larger than that of the electron in the case of WSTe as shown in Table 3, whereas the hole mobility of WSSe is slightly larger than WS 2 and WSTe. The curve of carries' mobility has shown a parabolic decrease with temperature. In addition, the values of carrier mobilities at room temperature for Janus materials are presented in Table 3. In these materials, the relaxation time of the electron and can be calculated through the formula τ = μ * m e . Therefore, the curve of relaxation time is also a parabolic function of temperature. The relaxation time of electronic collision is decreased with an increase in the temperature. The relaxation time of the carrier is the same for the WS 2 monolayer and its Janus materials. Figure 3(c,d) shows the relaxation time of electrons and holes. Thermoelectric Properties of Janus Monolayer Materials. The Seebeck coefficient, electric conductivity, thermal conductivity, and ZT are calculated as a function of temperature with a constant relaxation time (τ = 10 −14 s) for the monolayer WS 2 and the Janus monolayers WSSe and WSTe. Figure 4(a) shows the computed Seebeck coefficients of the material at a temperature range from 300to 1200 K. Initially, the Seebeck coefficient of a pure monolayer WS 2 has a slightly higher value than both Janus monolayers at 300 K (see Table 4). For the materials WS 2 , WSSe, and WSTe, the Seebeck effect decreases as a parabolic function of temperature. In the Janus monolayers WSSe and WSTe, the value of Seebeck coefficients decreases more slowly than the pure monolayer WS 2 . The value of Janus WSSe Seebeck coefficients exceeds the values of WS 2 near 400 K. Similarly, the curve of the Seebeck coefficient of WSTe crosses at a higher temperature at 800 K. At higher temperatures, both Janus materials WSSe and WSTe have shown more Seebeck effect. Figure 4(b) shows the electrical conductivity of materials. The Janus monolayer WSTe has low electric conductivity than the monolayer WS 2 and the Janus monolayer WSSe in the whole temperature range. The electric conductivity of all materials increases with temperature, but the electric conductivity of WSTe increases much slower than WS 2 and WSSe. For higher temperatures, WS 2 and WSSe have almost the same value. At low temperatures, the electric conductivity of WSSe shows a slightly higher value.
Thermal conductivities of the monolayer WS 2 and the JTMD monolayers WSSe and WSTe are shown in Figure 4(d− f). The monolayer WS 2 has higher thermal conductivity than the JTMD monolayers WSSe and WSTe. It is observed that the WSTe has ultralow thermal conductivity because both the electronic part and lattice contribution are very low; whereas, for the WS 2 and WSSe, the lattice thermal conductivity is very high in comparison to the electronic thermal conductivity. Therefore, they too have a high thermal conductivity in comparison to WSTe. WSTe has ultralow thermal conductivity. Its value is almost 150 times smaller than that of WS 2 and 100 times smaller than that of WSSe near room temperature. The thermal conductivity of the Janus WSTe monolayer is relatively very low as compared to other 2D materials. 54−56 The ultralow value of thermal conductivity plays a significant role in the enhancement of the high ZT. Graphene has a high thermoelectric power factor (S 2 σ), but it has a very low ZT value of 0.55 × 10 −3 at room temperature due to its ultrahigh thermal conductivity. 57 Graphene oxide is a potential 2D thermoelectric material with a ZT value of 0.05− 0.75 due to its thermopower factor of 127−287 μV K −1 (4−22 times of the graphene value) and very low lattice thermal conductivity of 15−22% of the graphene value. 58 Therefore, lattice thermal conductivity plays an important role in the thermoelectric ZT.
The calculated ZT values for these materials are shown in Figure 4(c). WS 2 and WSSe have low ZT values in the whole temperature range because both these materials have high thermal conductivity. The monolayer WS 2 and the Janus monolayer WSSe report a ZT value of 0.006 and 0.012. Here, it is observed that the replacement of one S atom by a Se atom optimizes the ZT value. Predicated WSTe shows high thermoelectric conversion performance with a high ZT value. Initially, its ZT value is 0.75 at 300 K (near room temperature) as shown in Table 4. Its ZT increases with temperature. At higher temperatures (near 600 K temperature), it becomes constant with temperature. It shows ZT = 2.56 at a higher temperature (1200 K) as shown in Table 4. The single layers of GaS, GaSe, and GaTe have ZT values of 0.89, 0.90, and 0.85 at room temperature, respectively, and decrease with the increase in temperature. 59 The single-layer MoS 2 has reported ZT values of 0.04, 0.07, and 0.11 at 300 K, 400 K, and 500 K, respectively. 60 The ZT of 0.52, 0.59, and 0.25 at room temperature are found in AlS, AlSe, and AlTe monolayers under moderate conditions. 61 The anisotropic materials PdS 2 , PdSe 2, and PdTe 2 show larger thermoelectric conversion performance with ZT values of 0.85, 1.18, and 2.42, respectively, compared to the commercial thermoelectric material Bi 2 S 3 (ZT = 0.80). 55