Ab initio prediction of semiconductivity in a novel two-dimensional Sb2X3 (X= S, Se, Te) monolayers with orthorhombic structure

\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\hbox {Sb}_2\hbox {S}_3$$\end{document}Sb2S3 and \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\hbox {Sb}_2\hbox {Se}_3$$\end{document}Sb2Se3 are well-known layered bulk structures with weak van der Waals interactions. In this work we explore the atomic lattice, dynamical stability, electronic and optical properties of \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\hbox {Sb}_2\hbox {S}_3$$\end{document}Sb2S3, \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\hbox {Sb}_2\hbox {Se}_3$$\end{document}Sb2Se3 and \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\hbox {Sb}_2\hbox {Te}_3$$\end{document}Sb2Te3 monolayers using the density functional theory simulations. Molecular dynamics and phonon dispersion results show the desirable thermal and dynamical stability of studied nanosheets. On the basis of HSE06 and PBE/GGA functionals, we show that all the considered novel monolayers are semiconductors. Using the HSE06 functional the electronic bandgap of \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\hbox {Sb}_2\hbox {S}_3$$\end{document}Sb2S3, \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\hbox {Sb}_2\hbox {Se}_3$$\end{document}Sb2Se3 and \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\hbox {Sb}_2\hbox {Te}_3$$\end{document}Sb2Te3 monolayers are predicted to be 2.15, 1.35 and 1.37 eV, respectively. Optical simulations show that the first absorption coefficient peak for \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\hbox {Sb}_2\hbox {S}_3$$\end{document}Sb2S3, \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\hbox {Sb}_2\hbox {Se}_3$$\end{document}Sb2Se3 and \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\hbox {Sb}_2\hbox {Te}_3$$\end{document}Sb2Te3 monolayers along in-plane polarization is suitable for the absorption of the visible and IR range of light. Interestingly, optically anisotropic character along planar directions can be desirable for polarization-sensitive photodetectors. Furthermore, we systematically investigate the electrical transport properties with combined first-principles and Boltzmann transport theory calculations. At optimal doping concentration, we found the considerable larger power factor values of 2.69, 4.91, and 5.45 for hole-doped \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\hbox {Sb}_{{2}}\hbox {S}_{{3}}$$\end{document}Sb2S3, \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\hbox {Sb}_{{2}}\hbox {Se}_{{3}}$$\end{document}Sb2Se3, and \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\hbox {Sb}_{{2}}\hbox {Te}_{{3}}$$\end{document}Sb2Te3, respectively. This study highlights the bright prospect for the application of \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\hbox {Sb}_2\hbox {S}_3$$\end{document}Sb2S3, \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\hbox {Sb}_2\hbox {Se}_3$$\end{document}Sb2Se3 and \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\hbox {Sb}_2\hbox {Te}_3$$\end{document}Sb2Te3 nanosheets in novel electronic, optical and energy conversion systems.


Method
The density-functional theory (DFT) calculations in this work are performed using the plane-wave basis projector augmented wave (PAW) method along with generalized gradient approximation (GGA) with Perdew-Burke-Ernzerhof(PBE) 84,85 functional as implemented in the Vienna ab-initio Simulation Package (VASP) 86,87 . Moreover, for the band structure calculations spin-orbit-coupling (SOC) was included on top of GGA and Heyd-Scuseria-Ernzerhof (HSE06) 88 screened-nonlocal-exchange functional of the generalized Kohn-Sham scheme, respectively for more accurate band gap calculations. The kinetic energy cut-off of 500 eV was set for plane-wave expansion and the energy was minimized structures are obtained until variation in the energies fall below 10 −8 eV. Van der Waals (vdW) correction proposed by Grimme to describe the long-range vdW interactions 89 . Charge transfers analysis is accomplished using the Bader technique 90 . To get optimized structures, total Hellmann-Feynman forces were reduced to 10 −7 eV/Å. 21 × 21× 1 Ŵ centered k-point sampling was used or the primitive unit cells by using Monkhorst-Pack 91 . In this work, the phonon dispersion relations are acquired using machine-learning interatomic potentials on the basis of moment tensor potentials (MTPs) 92 . The training sets are prepared by conducting ab-initio molecular dynamics (AIMD) simulations over 4 × 2× 1 supercells with 2 × 2× 1 k-point grids and a time step of 1 fs. AIMD simulations are carried out at 50 and 600 K, each for 800 time steps and half of the full trajectories are selected to create the training sets. MTPs were then passively fitted using the methodology explained in the previous works 93 www.nature.com/scientificreports/ relations and harmonic force constants over 4 × 12× 1 supercells using the trained MTPs for the interatomic force calculations 93,94 . The optical properties, such as imaginary and real parts of dielectric tensor (Im(ε ) and Re(ε)), absorption coefficient ( α ), reflectivity (R) Random phase approximation (RPA) ? method on the basis of screened hybrid Heyd-Scuseria-Ernzerhof functional (HSE06) 88 was employed to study optical properties using the VASP 86,87 . The optical properties were evaluated using a dense k-point grid of 18 × 8× 1 Ŵ-centered Monkhorst-Pack 91 . For more details about calculations of optical properties see supporting information. The electrical transport coefficients, such as electrical conductivity ( σ ), Seebeck coefficient (S), and electronic thermal conductivity ( κ e ) are calculated using the Boltzmann transport equation as implemented in the Boltztrap2 code 96 under the constant relaxation time and rigid band approximations.

Structural properties
The geometrical atomic structures of Sb 2 X 3 (X = S, Se, Te) monolayers in the different views are depicted in Fig. 1a. The primitive unit cell of the Sb 2 X 3 monolayers is indicated by red rectangular and is formed by 10 atoms with space group Pmcn. In the crystal structure of Sb 2 X 3 , each Sb atom is encompassed by six X (X = S, Se, Te) atoms and each X atom is encompassed by four Sb atoms. Notice that the vectors − → a = − → b are the translational unit cell vectors. The calculated lattice parameters of a ( b ) in the Sb 2 S 3 , Sb 2 Se 3 and Sb 2 Te 3 monolayers are equal to 3.86 ( where ρ tot , ρ X and ρ Sb show charge densities of the Sb 2 X 3 and isolated atoms, respectively. It is clear that Sb atoms are positively charged and surrounded by negatively charged S, Se or Te atoms. Each S, Se and Te atom labeled X1(X2) (see Fig. 1b), gains about 0.75e (0.82e), 0.59e (0.64e) and 0.36e (0.37e) from the adjacent Sb atoms in Cohesive energy, which is defined as the energy required to separate condensed material into isolated free atoms, is one of the most important physical parameters in quantifying the energetic stability of materials. The cohesive energy per atom is calculated using the following equation: where E X and E Sb represent the energies of isolated single X (S, Se and Te) and Sb atoms, n tot is the total number of atoms in unit cell. E tot represents the total energy of the Sb 2 X 3 monolayer. The cohesive energy of Sb 2 S 3 and Sb 2 Se 3 are found to be -7.94 and -7.36 eV/atom, respectively. While the cohesive energy of Sb 2 Te 3 is -6.81 eV/ atom. These finding indicates that the formation of Sb 2 S 3 is more favorable than the others. The results of Ab initio molecular dynamics (AIMD) simulation for the studied monolayers at room temperature are shown in Fig. 1c. The snapshots of top and side views of the structures after 5 ps are illustrated in Fig. 1d. Analysis of the AIMD trajectories also shows that the structure could stay intact at 500 K with very stable energy and temperature profiles, proving the thermal stability of the Sb 2 X 3 monolayer.
Apparently, phonon branches are free from any imaginary frequencies indicating the dynamical stability of the structures. The more negative values for cohesive energies suggest that the energetically more stable monolayer, and the structures represent more stability when the atoms get lighter. The dynamical stability of single-layers of Sb 2 X 3 is verified by calculating their phonon band dispersions through the whole BZ which are presented in Fig. 2a The electrostatic potential for the Sb 2 X 3 monolayers is shown in Fig. 2d. Notice that the electrostatic potential of studied monolayers are flat in the vacuum region. The work function was calculated using the following = E vacuum − E F , where E vacuum is the energy of the vacuum which is extracted from the electrostatic potential, and E F is the Fermi energy. The calculated work function of the studied monolayers are 5.17 ( Sb 2 S 3 ), 4.94 ( Sb 2 Se 3 ) and 4.53 eV ( Sb 2 Te 3 ). We found that the work function is decreases as the electronegativity of X (X = S, Se and Te) atom decreases.

Electronic properties
The electronic band structure of Sb 2 X 3 monolayers are shown in Fig. 3a. Our results show that, Sb 2 S 3 is an indirect semiconductor with a band gap of 1.22 eV within PBE functional. Notice that the valance band minimum (VBM) is located at the Ŵ point, while the conduction band maximum (CBM) is located along the Ŵ -S points. Similar Sb 2 S 3 , Sb 2 Se 3 and Sb 2 Te 3 exhibit semiconducting characteristics with indirect band gap of 0.96 eV and 0.86 eV, respectively. Notice that, we can see that both the VBM and CBM of these monolayers are located along the Ŵ and Y points, respectively. The electronic band structure of Sb 2 X 3 monolayers with considering spin orbital coupling (SOC) are shown in Fig. S1a-c in the supplementary information (SI). With considering of SOC effect, the band gaps of the Sb 2 S 3 , Sb 2 Se 3 and Sb 2 Te 3 monolayers decrease to 0.95, 0.75 and 0.45 eV, respectively. The charge densities of the VBM and CBM orbitals are shown in the inset (see inset in Fig. 3a). It is clear that energy bands around the Fermi-level are formed mainly by X atoms. Since these monolayers are semiconductor, the HSE06 functional was also used to study the electronic band structures, shown in Fig. 3. It is clear that the HSE06 results are consistent with PBE/GGA for the type of indirect semiconducting band gap in these systems. Based on the acquired band structure by HSE06 method, the indirect band gap of Sb 2 S 3 , Sb 2 Se 3 and Sb 2 Te 3 was estimated to be 2.15, 1.35 and 1.37 eV, respectively. The band gap value of Sb 2 Te 3 is still larger than that reported in Ref. 97 . The nature of such difference is due to the underestimation of traditional DFT method. Therefore, our calculations methods are reliable. In order to explain the origin of the electronic states, the DOS and the PDOS are shown in Fig. 3b,c, respectively. It is clearly seen that the semiconducting character of Sb 2 S 3 comes from S and Te atoms, while Sb atoms does now show any contribution. From DOS and PDOS, it is clearly seen that the VBM are composed of the p z and p x,y orbitals states of S atom, while the CBM comes from p z and p x,y orbitals of S and Sb atoms. We found that the VBM of Sb 2 Se 3 and Sb 2 Te 3 originates from Se/Te-p x,y orbitals, while the CBM consists of Se/Te-p z and Sb-p z orbital states. Table 1. Structural and electronic parameters of Sb 2 X 3 (X = S, Se, Te) monolayers as shown in Fig. 1b, including lattice constants a, b ; the bond lengths between Sb-X atoms d 1,2,3,4 ; the bond angles between X-Sb-X atoms θ 1,2,3 ; the thickness defined by the difference between the largest and smallest z coordinates of X atoms (t); the cohesive energy per atom, (E coh ) ; the charge transfer (�Q) between atoms Sb and X 1 ( X 2 ) atoms are shown inside (outside) parentheses as shown in Fig. 1b; the work function (�). The band gap (E g ) of PBE and HSE06 are shown outside and inside parentheses, respectively.

Optical properties
Now we discuss the optical responses of this novel 2D system using the RPA+ HSE06. The depolarization effect of 2D materials along out-of-plane direnction is strong 98 , hence we only report the optical properties for in-plane polarizations ( E x and E y ). Due to the asymmetric lattice along the x-and y-directions the optical properties are aisotropic for light polarizations along these axes and hence the optical properties along both directions are reported. Fig. 4a illustrates the imaginary and real parts of the dielectric function of these 2D systems along the in-plane directions. It can be seen that the Im(ε ) along x-and y-axes starts with a gap confirming the semiconducting properties for optical spectra along these directions for these novel 2D systems. The first peak of  www.nature.com/scientificreports/ Im(ε ) occurs at 2.39, 2.16 and 1.67 eV for the Sb 2 S 3 , Sb 2 Se 3 and Sb 2 Te 3 monolayers, respectively, along x-axis while it appears at 1.74, 1.36 and 1.10 eV along y-axis. These results indicate that the first peaks of Im(ε ) for all monolayer systems are in visible and IR range of light along talong x-and y-axes. These results also indicate that by increasing atomic number of X element in Sb 2 X 3 monolayers, the first Im(ε ) peak slightly shifts to lower energies (red shift). The static dielectric constants (the values of Re(ε ) at zero energy) for Sb 2 Te 3 monolayer along E x were calculated to be 4.0, 6.4 and 9.1, respectively, while the corresponding values for E y are 3.9, 5.5 and 7.8. The plasma frequencies which define by the roots of Re(ε ) with x = 0 line 99,100 were calculated for these 2D monolayers. The values of first plasma frequencies along x-axis are 4.27, 3.51 and 2.65 eV for Sb 2 S 3 , Sb 2 Se 3 and Sb 2 Te 3 monolayers, respectively, while the corresponding values for the same systems along E y are 4.8, 4.45 and 2.98 eV. The absorption coefficient α for all studied 2D systems along in-plane polarization are shown in Fig. 4b,c. The first absorption peaks for the Sb 2 S 3 , Sb 2 Se 3 and Sb 2 Te 3 monolayers along E x are in the visible range of light and occur at energy of 2.39, 2.18 and 1.77 eV, respectively. The corresponding values of the first absorption peaks along y-axis locate at energy of 1.98, 2.13 and 1.14 eV for the same monolayers. These results show the first absorption peaks of Sb 2 S 3 and Sb 2 Se 3 monolayers for E y are in visible range of light while it occur at IR range for Sb 2 Te 3 monolayer. According to our optical results, these 2D systems have potential applications in optoelectronic devices in the visible and IR spectral range. Fig. 4b illustrates the absorption coefficient as a function of wavelength for the Sb 2 X 3 monolayers for the in-plane polarizations in the UV-vis range (350-700 nm) of light. It is obvious that the absorption coefficients for these 2D materials are high ( ∼ 10 5 cm −1 ) to be used in optical devices 101 . Interestingly, optically anisotropic character of these systems along x-and y-axes is highly desirable for the design of polarization-sensitive photodetectors 102 .

Thermoelectric properties
The Seebeck coefficients as a function of carrier concentration for Sb 2 X 3 monolayers are presented in Fig. 5a,b. Large Seebeck coefficients are found for the p-type doping in these monolayers due to the flat valence band which increases the density of states near the Fermi level. Monolayer Sb 2 S 3 achieves higher Seebeck coefficient values of 530 µVK −1 , 483 µVK −1 at 300 K along the x and y directions, respectively. The variation in electrical conductivity ( σ/τ ) and the electronic thermal conductivity ( κ e /τ ) with respect to carrier concentration are plotted in Fig. 5c-f. The σ/τ and κ e /τ of n-type are larger than that of the p-type one at the same doping level because of the dispersive conduction bands which lower the effective mass. The σ/τ and κ e /τ follow the Wiedemann-Franz law. The σ/τ exhibits anisotropic behavior where the σ/τ value along the x-direction is higher than that alone the y-direction because of the dispersive band nature along Ŵ -X than Ŵ -Y direction. The power-factor (PF) ( S 2 σ/τ ) Figure 4. (a) Imaginary and real parts of the dielectric function as a function of photon energy of the Sb 2 S 3 , Sb 2 Se 3 and Sb 2 Te 3 monolayers for the in-plane polarizations ( E x and E y ), predicted using the RPA + HSE06 approach. Absorption coefficient as a function of (b) wavelength and (c) energy for the Sb 2 X 3 monolayers for the in-plane polarizations ( E x and E y ) in the UV-vis range of light, predicted using the RPA + HSE06 approach.

Conclusion
In summary, we introduced Sb 2 X 3 (X = S, Se, and Te) monolayers as novel, dynamically and thermally stable 2D indirect gap semiconductors. Using the HSE06 method the band gaps of Sb 2 S 3 , Sb 2 Se 3 and Sb 2 Te 3 monolayers are predicted to be 2.15, 1.35 and 1.37 eV, respectively, appealing for applications in nanoelectronics. Optical calculations indicate that the first absorption peaks of these novel nanosheets along in-plane polarization are located in IR and visible range of light, suggesting its prospect for applications in optoelectronics. Moreover, the in-plane optical anisotropy of these novel 2D materials is highly desirable for the design of polarization-sensitive photodetectors. We also show that Sb 2 X 3 monoalyers can be used for thermoelectric application because of their larger power factors, the power factor for the hole-doped Sb 2 Te 3 can reach 5.45 ( 10 11 Wm −1 K −2 s −1 ). Our results confirm the stability and highlights the outstanding prospect for the application of Sb 2 X 3 nanosheets in novel electronic, optical and energy conversion systems. www.nature.com/scientificreports/