Optical and thermoelectric properties of new Janus ZnMN2 (M = Ge, Sn, Si and N = S, Se, Te) monolayers: a first-principles study

Thermoelectric materials have received great interest because they directly tap into the vast reserves of currently underused thermal energy, in an environmentally friendly manner. In this work, we investigated the electronic, optical and thermoelectric properties of novel ZnMN2 (M = Ge, Sn, Si and N = S, Se, Te) monolayers by performing density functional theory calculations. The dynamic and thermal stabilities of ZnMN2 (M = Ge, Sn, Si and N = S, Se, Te) monolayers were confirmed by their phonon band structures and ab initio molecular dynamics (AIMD) simulations, which showed that all the studied monolayers are stable. Calculated electronic band structures showed that ZnSiTe2, ZnGeSe2, and ZnSnTe2 have a direct band gap, while the remaining monolayers have an indirect band gap. Optical properties in terms of the imaginary part of the dielectric function have also been investigated, which showed that all the first excitonic peaks lie in the visible region. Transport coefficients, such as the Seebeck coefficient (S), electrical conductivity (σ) and power factor (PF) were calculated using the Boltzmann theory and plotted against chemical potential. The results demonstrated that the peak values of the p-type region for the PF are greater than those of the n-type region. Notably, ZnSiTe2 exhibits a large PF due to its smaller Seebeck coefficient and higher electrical conductivity compared to ZnSnS2, indicating that it is a promising candidate for thermoelectric applications. Our findings reveal that ZnMN2 (M = Ge, Sn, Si and N = S, Se, Te) monolayers open up new possibilities for optoelectronics and thermoelectric device applications.


I. Introduction
A shortage of energy is currently predicted to be a great challenge in the near future for our society. 1It is expected that the world's energy demands will rise by up to 60% by 2030. 1 Currently, about 80% of the world's energy is generated by heat engines using fossil fuels as an energy source, which has a big drawback of carbon dioxide emission. 1Due to this increasing demand for clean energy, researchers are trying to develop renewable energy sources to resolve energy issues and also to avoid environmental pollution. 2,3Recently, solar cells, winddriven generators, thermoelectric devices and fuel cells have attracted tremendous attention.2][13] The efficiency of thermoelectric materials depends on the Seebeck coefficient (S), electrical conductivity (s), total conductivity (K) and absolute temperature (T).For efficient thermoelectric materials, the electrical conductivity (s) and Seebeck coefficient (S) is high and the thermal conductivity is low. 14,15ince the discovery of single-layer graphene in 2004, 16 research interest in the eld of 2D materials has grown explosively in just a few years.Recently, thanks to developments in synthesis techniques and theoretical simulation, a variety of 2D materials have been theoretically predicted and successfully fabricated, such as hexagonal boron nitride (h-BN), 17 transitionmetal dichalcogenides (TMDCs), 18 group-III metal chalcogenides, 20 group-IV and -VI metal monochalcogenides, such as SiO, SiS, GeS and SnS, 21 and carbide and nitride semiconductors. 22ately, a novel class of 2D materials named Janus transitionmetal dichalcogenides (JTMDCs) has attracted attention from researchers due to the distinct properties that the materials obtain from their parent transition-metal dichalcogenide monolayers.Lu and co-workers 23 conrmed the successful fabrication of JTMDCs by using chemical vapor deposition (CVD).Recently, a group of novel 2D Janus group-III monochalcogenides with the general formula ZnXY 2 (X = Si, Ge, Sn and Y = S, Se, Te) and constructed according to their isoelectronic mutation has been investigated, and refers to group-III monochalcogenides, 24 which have been attracting much interest due to their higher piezoelectricity, direct bandgaps and large effective mass difference, making them good candidates for applications in optoelectronics, photocatalysis, exible nanodevices and electromechanical systems. 24ue to their appealing mechanical and electronic properties, 2D materials with layered structures have attracted tremendous attention as efficient thermoelectric materials.6][27] In addition, Guo et al. 28 reported that the n-type Janus ZrSSe monolayer has excellent thermoelectric performance, which was better than that of a ZrS 2 monolayer.According to Bera et al., the HfSSe monolayer was dynamically stable, and gradual increases and decreases in the bandgap were observed with changes in the applied biaxial strain.They also suggested that, due to the SOC effect, the HfSSe monolayer has a higher power factor than the HfSe 2 monolayer but lower than that of the HfS 2 monolayer. 29These 2D materials exhibit fascinating properties, such as a large potential, when they are used in the fabrication of highperformance thermoelectric devices.

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Although interesting research results for both experimental and theoretical prediction of thermoelectric properties have been calculated, a comprehensive study of ZnMN 2 (M = Si, Ge, Sn and N = S, Se, Te) monolayers is still missing.So, here in this paper, we investigated the structural, optoelectronic and thermoelectric properties of ZnMN 2 (M = Si, Ge, Sn and N = S, Se, Te) monolayers using density functional theory, which is based on rst-principles calculations.

II. Computational details
These calculations are based on density functional theory (DFT) techniques and approaches using PWSCF code. 30In the rst Brillouin zone (BZ), a G-point-centered 12 × 12 × 1 Monkhorst-Pack k-point grid is used with a kinetic energy 450 eV.To avoid the interactions between adjacent layers of atoms, a vacuum layer with thickness of 25 Å is considered.Forces and energies are converged to 10 −3 eV Å and 10 −6 eV, respectively.The exchange-correlation functional is a key component that accounts for the electron-electron interactions in a system, so we used the GGA approximation. 31,32,37Boltzmann semiclassical theory 33 is used to calculate the electrical transport properties, like the Seebeck coefficient (S), electrical conductivities (s), thermal conductivities (k) and power factor (PF), using the BoltzTraP soware package.This is primarily designed for studying the thermoelectric and electronic transport properties of materials, such as electrical conductivity, the Seebeck coefficient, and the electronic density of states.Boltz-TraP uses the Boltzmann transport theory and the constant relaxation time approximation. 33The following equations can be used to express all of these parameters: and the power factor (PF) is In the equations above, e is the charge on the elementary charge carrier, 3 is the energy, K B is the Boltzmann constant, s k is the relaxation time, f 0 is the Fermi distribution function, m denotes the chemical potential, and v k is the group velocity.

III. Results and discussion
Optimized lattice constants of ZnSiS 2 , ZnSiSe 2 , ZnSiTe 2 , ZnGeS 2 , ZnGeSe 2 , ZnGeTi 2 , ZnSnS 2 , ZnSnSe 2 and ZnSnTi 2 monolayers are listed in Table 1 and are in agreement with previously reported work. 19The geometrical structure of the ZnMN 2 monolayer consists of four sublayers with two middle layers of Zn and M (M = Si, Ge, Sn), and two outer layers of N (N = S, Se, Te).The monolayer has a hexagonal structure and is held together by covalent bonds, as presented in Fig. 1, where the gray spheres represent the Zn atoms, the yellow spheres represent Si, Ge, or Sn, and the blue spheres represent different chalcogen atoms. 34,35One can easily observe that the bond lengths for the bonds containing S atoms are shorter than those containing Se and Te atoms due the difference in electron affinities of S, Se, and Te atoms.The calculated lattice constants, bond lengths and band gaps of the various ZnMN 2 monolayers are given in Table 1.
To investigate the dynamic stability of ZnMN 2 (M = Ge, Sn, Si and N = S, Se, Te) monolayers, phonon band spectra were   monolayers can be experimentally synthesized in the laboratory.Furthermore, we investigated the thermal stability of these monolayers using ab initio molecular dynamics calculations.
The results are presented in Fig. 3, conrm that there is no bond

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breaking at room temperature (300 K) to the system, hence these systems are stable at room temperature. 36,39he band structure and band gap values are very sensitive to the choice of exchange correlation function, therefore, we considered both PBE and HSE06 functionals for our calculations.The calculated electronic band structures of ZnMN 2 (M = Si, Ge, Sn; N = S, Se, Te) using the PBE 37,38 functionals are shown in Fig. 4. One can see from the calculated electronic band structures that all the monolayers are semiconducting with a narrow band gap, and are therefore suitable for thermoelectric applications.One can also observe that ZnGeS 2 , ZnGeSe 2 and ZnSnTe 2 have a direct band gap with the CBM and VBM lying at the G-point, while the remaining monolayers have an indirect band gap with the VBM and CBM at the Gand M-G-points,   2 and are in good agreement with previous available data. 19or further verication of the various atomic states of the monolayers, we computed the partial density of states (PDOS) of ZnXY 2 monolayers, which are depicted in Fig. 5.The contributions of different states of the atoms are shown by different colors.From the PDOS of the ZnSiS 2 , ZnSiSe 2 and ZnSiTe 2 monolayers, it can be clearly seen that in the VBM the major contribution is due to the Te-p z atom, whereas the CBM is generated by the S, Se and Te-p z atoms.In the second row which shows results for the ZnGeS 2 , ZnGeSe 2 and ZnGeTe 2 monolayers, the VBM and CBM are due to the Ge and chalcogen p z atoms, respectively.While in the third row, which shows results for ZnSnS 2 , ZnSnSe 2 and ZnSnTe 2 monolayers, the VBM and CBM are from the Sn-p z and chalcogen p z states.In all these monolayers, some little contributions are also present due to Zn atoms.High mobility may be favored by this type of partially ionic nature with cross-gap hybridization. 40he absorption spectra of systems are measured to investigate the optical properties of materials.They allow the dielectric function 3 2 (u) 46 to be determined, therefore absorption spectra are a fundamental tool for understanding the interaction of electromagnetic radiation with matter.The imaginary part of the dielectric function 3 2 (u) was calculated for the different monolayers and the results are shown in Fig. 6.Exciton peaks can clearly be seen for ZnSiS 2 (0.96 eV), ZnSiSe 2 (0.72 eV), ZnSiTe 2 (0.662 eV), ZnGeS 2 (0.61 eV), ZnGeSe 2 (0.661 eV), ZnGeTe 2 (0.64 eV), ZnSnS 2 (0.52 eV), ZnSnSe 2 (0.63 eV) and ZnSnTe 2 (0.67 eV).These values indicate strong modications in the positions of excitons from the S atom to the Te atom, suggesting that this is promising for controlling the excitonphonon interactions or coupling at the nanoscale, and for applications in thermal imaging sensors in the future. 47ased on the Boltzmann theory, 41 we calculated transport coefficients such as the Seebeck coefficient, electrical conductivity, and power factor against chemical potential.The Seebeck coefficient is a quantied measurement of convinced voltage, 42 and the Seebeck coefficient of a material represents the magnitude of the thermoelectric voltage induced by a temperature difference across the material. 45The Seebeck coefficient at (a) 300 K and (b) 800 K for ZnSiS 2 (black), ZnSiSe 2 (red) and ZnSiTe 2 (green) is presented in Fig. 7 plotted against the chemical potential, and the Seebeck coefficient values for the ntype doped region are given in Table 2 and those for the p-type doped region are given in Table 3.The Seebeck coefficient results for ZnGeS 2 , ZnGeSe 2 and ZnGeTe 2 are shown in Fig. 8,

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and the values for the n-type doped region are given in Table 2 and those for the p-type doped region are given in Table 3.The Seebeck coefficient results for ZnSnS 2 , ZnSnSe 2 and ZnSnTe 2 are shown in Fig. 9, and the values for the n-type doped region are given in Table 2 and those for the p-type doped region are given in Table 3. From our calculations, it is clear that ZnSnSe 2 has a greater value in both the n-type and p-type regions at 300 K and 800 K.According to the preceding discussion, ZnXY 2 monolayers are p-type materials, and raising the temperature reduces the Seebeck coefficient, which makes these materials ideal for thermoelectric device applications, and similar results are also reported in ref.  2 and  3, respectively, for 300 K and 800 K. Our results show that ZnSiTe 2 had a larger value in both the n-type and p-type regions at 300 K and 800 K.According to the preceding discussions, ZnMN 2 monolayers are p-type materials, and raising the temperature reduces the Seebeck coefficient.To measure the thermoelectric power of a material, the power factor (PF) is one of the best parameters to describe the efficiency of that material with the general formula PF = sS 2 , where S represents the Seebeck coefficient and s is the electrical conductivity of the material.The calculated values of the power factor at 300 K and 800 K are shown in Fig. 7 for monolayers of ZnSiS 2 , ZnSiSe 2 , and ZnSiTe 2 , Fig. 8 for monolayers of ZnGeS 2 , ZnGeSe 2 , and ZnGeTe 2 , and Fig. 9 for monolayers of ZnSnS 2 , ZnSnSe 2 and ZnSnTe 2 .The values are given in Tables 2 and 3.It is obvious from Fig. 7(e, f), 8(e, f) and 9(e, f) that the peak values of the PF at both 300 K and 800 K in the p-type region are greater than in the n-type region.Furthermore, it can be seen that ZnSnS 2 has a large PF at 300 K and 800 K because of its smaller Seebeck coefficient and higher electrical conductivity than ZnSiTe 2 , making it a promising candidate for thermoelectric applications. 48

IV. Conclusions
Using DFT, the structural, electronic, optical and thermoelectric properties of novel 2D Janus ZnMN 2 (M = Si, Ge, Sn and N = S, Se, and Te) monolayers constructed according to their isoelectronic mutation have been investigated.Moreover, a direct band Furthermore, values for the imaginary part of the dielectric function were calculated, which indicated strong modications in the positions of excitons from the S atom to the Te atom, suggesting that this is promising for controlling the excitonphonon interactions.Finally, we investigated the thermoelectric properties, including the Seebeck coefficient (S), electrical conductivity (s), and power factor (PF), at temperatures of 300 K and 800 K, based on Boltzmann theory.The results conrmed that the peak values of the PF at 300 K and 800 K in the n-type region are greater than in the p-type region.Furthermore, it can be seen that ZnSiTe 2 has a large PF at 300 K and 800 K because of its smaller Seebeck coefficient and higher electrical conductivity than ZnSnS 2 , making it a promising candidate for thermoelectric applications.

Fig. 1
Fig. 1 Top (a) and side (b) views of ZnMN 2 (M = Si, Ge and Sn and N = S, Se and Te) monolayers.

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2024 The Author(s).Published by the Royal Society of Chemistry Nanoscale Adv., 2024, 6, 680-689 | 683 Paper Nanoscale Advances calculated using the phonopy code, as shown in Fig. 2.There are four atoms in each primitive unit cell, therefore, each phonon band dispersion is composed of three acoustic zero-frequency modes and 12 optical branches.It is clear from Fig. 2 that all phonon modes have positive eigenfrequencies at the G-point of the Brillouin zone, indicating that ZnMN 2 (M = Ge, Sn, Si and N = S, Se, Te) monolayers are dynamically stable, which conrms that ZnMN 2 (M = Ge, Sn, Si and N = S, Se, Te)

43 and 44 .
The electrical conductivity (s) of the materials is due to the holes and electrons in the semiconductors, and values of the electrical conductivity were calculated and plotted against m for the ZnMN 2 (M = Si, Sn and Ge and N = S, Se and Te) monolayers.For good thermoelectric materials, we need high s values.The calculated values for s for both n-type and p-type doped regions are given in Tables

Table 1
Calculated lattice constant (A), bond length (d) and band gap (E g ) values of ZnMN 2 (M = Si, Ge and Sn and N = S, Se and Te) monolayers