The first-principles study on Mo-doped monolayer ReS2

Based on the first-principles calculations, the electronic structure and optical properties of the Mo-doped monolayer rhenium disulfide (ReS2) model are calculated, and the system stability, bond length, charge difference density, band structure, photoabsorption coefficient, system stability, and reflectivity are analyzed. The calculation results show that doping changes the structural stability of the system, which gradually decreases with an increasing concentration of doping. The calculation of band structure and density of states indicated that the band gap value of the system decreases continuously to 0 with increasing doping concentration, while the average charge population of atoms at doping sites keeps increasing with the better electron-losing ability of atoms. Compared with the intrinsic monolayer ReS2, the peak of systemic reflectivity at different doping concentrations has corresponding degrees of redshift in a certain wavelength range, as demonstrated by the optical properties.


Introduction
Two-dimensional transition metal sulfides (TMDs) have been known since 1960. More than 40 kinds of TMD materials and their basic properties were conducted as early as 1969 [1][2][3], with the most topical materials in Group VI, MoS 2 and WS 2 , being the most prevalent [4,5]. Recently, rhenium disulfide (ReS 2 ) semiconductor materials in Group VII have attracted widespread attention because of their undeniable enormous application potential. Rhenium disulfide (ReS 2 ) consists of three atomic layers, S-Re-S, in which Re and S covalently bond together, and has unique structural, optoelectronic, and chemical properties that have led to subsequent studies of various properties of rhenium disulfide [6][7][8][9][10][11][12][13][14].
In the design and application of nano-devices, the tunability of the band gap is essential for materials. Rhenium disulfide, which exhibits semiconducting transition metal properties, cannot be effectively used in micro-and nanodevices yet. Thus, its modification has become a research hotspot. There have been many researchers to modulate the intrinsic properties of rhenium disulfide such as band gap, transport characteristics, and magnetic properties by adsorption, stretching, and straining [15][16][17][18]. Rhenium disulfide has no transition from direct to indirect band gap, making it unique among semiconductor transition metal dihalides, while atomic substitutional doping becomes a new feasible strategy due to its effective modulation for band gap. Meantime, transition metal sulfides have received increasing attention as electrochemical energy storage and electrode conversion materials for lithiumion batteries and hydrogen evolution reactions, and so on. However, most of them show a low electrical conductivity, which significantly limits their electrochemical performance. Therefore, metal heteroatom doping can be used for modulating the electronic structure, which is an effective strategy to solve this problem.
Deniz et al. [19] studied the structural, electronic, and magnetic properties of substitutionally doped ReS 2 monolayers at either the S or Re site systematically via first-principles density functional calculations, confirming that Mo, Nb, Ti, and V atoms can be easily incorporated in a single layer of ReS 2 as substitutional impurities. This particular phenomenon aroused an interest in the field, and the substitutional doping of rhenium disulfide was also conducted through experiments. Zheng and the co-workers [20] investigated the optical properties of Au-doped ReS 2 using piezoreflectance (PzR) measurements. They characterized the polarization property and identified the origin of the excitonic transitions as well. Obodo et al. [21] proved that a ferro-or a non-magnetic ground state constructure could be obtained by choosing dopant ions in ReS 2 and ReSe 2 monolayers with the method of quantum mechanical calculations. Liang et al. [22] prepared   [26] synthesized polycrystalline thin films of Mo-doped rhenium disulfide alloys via aerosol-assisted chemical vapor deposition (AACVD) and found that the interlayer spacing increased and the vibrational modes of ReS2 destructed with increasing Mo content in the ReS 2 substrate. Qin et al. [27] constructed a supercell model of ReS 2 to study the band gap variation at two different doping concentrations using first-principles software. Nevertheless, the above studies are merely limited to the structure, strain, and band gap changes at different concentrations, and the effect of different concentrations of Mo atomic doping on the electronic structure and optical properties of rhenium disulfide remains to be investigated, among which whether the band structure can achieve zero band gap remains to be explored. Herein, we systematically calculated the system, electronic structure, and optical properties of substitutional Mo-doped monolayer rhenium disulfide, which compared with pure rhenium disulfide system. Furthermore, the evolution in band gap, electronic structure, and optical properties of doped ReS 2 system was discussed. It is expected that our studies will provide some references in the application of semiconductor devices.

Methods
The calculation module used in this work was Cambridge Sequential Total Energy Package (CASTEP) in Material Studio 8.0, which optimizes and simulates monolayer rhenium disulfide under different conditions based on first-principles [28]. For the exchange-correlation energy, the Perdew-Burke-Ernzerhof (PBE) functional within generalized-gradient approximation (GGA) was utilized [29][30][31][32].
In reciprocal lattice, the first Brillouin Zone (K-points) was divided into 7 × 7 × 1 Monkhorst-Pack grid for batch calculation with the plane wave cutoff energy of 400 eV to ensure favorable convergence during the calculation. The following thresholds were used for convergence of the structure: energy iteration convergence accuracy of 1.0 × 10 −6 eV/atom for individual atoms; internal stress convergence value of 0.05 GPa; interatomic interaction forces less than 0.01 eV/Å; and displacement of atoms less than 0.001 Å during geometry optimization.
The following thresholds were used for the convergence of structure: energy iteration convergence accuracy of 1.0 × 10 −6 eV/atom for individual atom; internal stress convergence of 0.05 GPa; the interaction force convergence between atoms less than 0.01 eV/Å; and displacement of atoms less than 0.001 Å during geometry optimization.
A 4 × 4 × 1 supercell model of rhenium disulfide constructed using MS is shown in Fig. 1a, for a single cell of rhenium disulfide with total 3 atoms. Figure 1b-d show the supercell models with the number of Mo atoms substitutionally doped at one, two, and three, respectively.

Stability of doping system
We calculated the formation energy and binding energy of doped ReS2 system in order to investigate the structural stability. The formation energy is defined as shown in Eq. (1) [33]: where E tot [X] and E tot ReS 2 are the total energy after doping and without doping, respectively. When ni > 0, it is defined as the number of atoms doped into the system, while ni < 0 means the number of atoms removed from the system. E form is the system formation energy, where a negative value indicates a stable structure, and a positive value indicates that the structure exists but requires energy to maintain it. The formation energy is calculated as 1.4116 eV, 2.3871 eV, and 3.8252 eV for Mo atom doping concentrations of 1, 2, and 3, respectively, indicating that the structure after Mo atom substitution doping still needs the energy to maintain and increases with the doping concentration. Compared with the intrinsic monolayer rhenium disulfide, the more atoms are doped, the greater the effect on the formation energy.

Crystalline structure
The intrinsic electronic properties of monolayer rhenium disulfide were simulated using MS (Material studio). The structure of rhenium disulfide was optimized with the optimized lattice parameters of a = 6.52 Å and b = 6.42 Å, which are in agreement with the experimental data (a = 6.51 Å and b = 6.41 Å [34], a = 6.51 Å and b = 6.41 Å [35]). The The bond length of the rhenium disulfide system will be inevitably affected by doping with Mo atoms. And its distribution of rhenium disulfide structure was discussed by numbering the atoms of the rhenium disulfide model as shown in Fig. 2. It is found that the bond length with the surrounding atoms was distorted owing to doping with Mo atoms and changed at different sites.
The bond lengths of the Mo atoms substitutionally doped at different concentrations with the surrounding S atoms with the farthest distance are 2.55646 Å, 2.58808 Å, and 2.60870 Å, with the relative changes of 2.06%, 3.32%, and 4.14%, respectively, corresponding to one, two, and three Mo atoms doped, respectively, as observed in Table 1 which presents the structure parameters of pure ReS 2 and system optimized by substitutional Mo doping at different concentrations. It is demonstrated that the bond length and the corresponding amount of change gradually increase as more number of doped atoms, as a result of the more intense energy transfer, and the bond length change may be also relative to the band gap change to some extent.

Influence of substitutional Mo doping on rhenium disulfide
The electronic properties of the intrinsic rhenium disulfide and Mo-doped rhenium disulfide systems were calculated using CASTEP, and the first Brillouin zone used was the closed path G(0,0,0) → M(0,0.500,0) → K(0.333,0.333,0) → G(0,0,0). Figure 3 shows the energy band structure for intrinsic monolayer rhenium disulfide, where the rightmost shows density of states regarded as the projection of the energy band structure. As shown in the figure, the intrinsic monolayer rhenium disulfide is a direct band gap semiconductor with a band gap value of 1.489 eV, which is closer to the 1.440 eV in the literature [37] with the error of only 3.4%, while the band gap value of the intrinsic monolayer rhenium disulfide is also in keeping with the results in the reference [38]. It is seen that the peak density of states of intrinsic monolayer rhenium disulfide located at − 4 eV, and the DOS curve exhibited a trough trend at the Fermi energy level with a value of 0 which corresponds to the band gap of the band structure. The density of states structure of rhenium disulfide also demonstrated several energy levels in the curve other than the Fermi level also close to 0, which proves that the energy band structure of rhenium disulfide possesses a large modification space and is more suitable for application in energy band engineering. As can be seen from Figs. 4 and 5, the band gap decreases from 1.489 eV to 1.321 eV when one Mo atom doped and continues to 0.559 eV when the number of atoms increases to two, which corresponds to a medium band gap semiconductor. When the doped atoms rise to three, the band gap decreases continuously, even eventually reaching 0 eV, corresponding to a zero gap semiconductor which makes it a material with metallicity. In the range of our current study, the band gap reduces with an increasing number of single Mo atoms doped, meaning that the minimum energy required for valence electron to guide band declines. When doped two or three atoms, the band gap value goes down more significantly with a more obvious decline of band gap, and the minimum energy required for valence electron to guide band falls down more deeply. The density of states plotted for different numbers of doped atoms shows that the density of states of the system varies slightly with the number of doped atoms, and its range where the number of electronic states near the Fermi plane is 0 shrinks with an increasing number of doped atoms, corresponding to the energy band structure.
In order to study the charge distribution and electron transfer, the charge density difference and Mulliken charge population of substitutional Mo-doped ReS2 system were calculated in this paper. The charge density difference of substitutional Mo-doped ReS 2 system is shown in Fig. 6, and the charge population of Mo atoms and surrounding Re atoms under the effect of substitutional Mo doping are listed in Table 2 Figure 6 shows the systematic charge density difference with a different number of doped atoms, where the purple part indicates the distribution. It is seen that the distribution of charge density difference in the system with a different number of doped atoms is relatively uniform, in which the charge mainly concentrated on the bonds between Re-S and Mo-S. It can be inferred that charge transfer occurred between Re and S as well as Mo and S, which is especially manifest between the doped Mo atoms and their nearby S atoms. When the monolayer of intrinsic rhenium disulfide is doped with Mo atoms in place, the value of charge accumulation in the bonding region between the doped Mo atoms and S atoms disperses, and the electronegativity strengthens with an increasing number of doped atoms. In contrast, the charge accumulates more dramatically in the area between Re atoms and S atoms near the Mo atoms, with a mainly weakened electronegativity. Associated with Mulliken charge population, it can be observed that the charge population of doped Mo atoms increases to a varying degree compared to that of original Re sites in the intrinsic rhenium disulfide system. In other words, when doped with one atom, the charge population of Mo1 (formerly Re10) goes up from 0.16 to 0.38, even more than two times, with an atomic loss of 0.22 e. When doped with two atoms, the charge population of Mo1 increases from 0.16 to 0.32, and that of Mo2 (formerly Re7) also increases from 0.16 to 0.32 in comparison with the intrinsic ReS2 system. Furthermore,

Influence of substitutional Mo doping on optical property of rhenium disulfide
To study the effect of different concentrations of Mo doping on the optical property of the monolayer rhenium disulfide system, the curves of systematic absorption coefficient and reflectivity were plotted, as shown in Figs. 7 and 8. Meanwhile, the locations (wavelength) of the highest reflection peak and absorption peak, as well as their characteristic values in the Mo-doped monolayer rhenium disulfide system, are listed in Table 3 and Table 4. It can be seen that the light starts to reflect in all doped systems at a wavelength of 63 nm from Fig. 7a and b. The original system shows a reflection peak at a wavelength of about 188.64 nm with the value of 0.354 cm −1 from Fig. 7a-b and Table 3. The increase in the number of doped atoms causes redshift of the highest reflection peak to different degrees with respect to the original ReS 2 system. Moreover, the light is not absorbed in the Mo-doped ReS 2 system with the wavelength range from 0 to 64 nm, while it starts to be absorbed when the wavelength reaches 64 nm, as illustrated in Fig. 8a Table 4.

Conclusions
In summary, the system of ReS 2 doped with Mo atoms is calculated by means of density functional theory and its formation energy, and bond lengths are analyzed relatively to investigate the effect of Mo doping on the stability of Res 2 .
The results indicate an increase of formation energy and a decrease of bonding energy for ReS 2 when more Mo atoms doped. Namely, the stability shows a negative correlation with the number of doped atoms. The influence of doping on electronic structure is concluded by studying the bond The analysis of charge density difference and charge population demonstrates that the charge transfer occurs on the bonds Re-S and Mo-S. The charge accumulation in the bonding region between the doped Mo atoms and S atoms disperses, and the electronegativity strengthens with an increasing number of doped atoms. The charge population of doped Mo atoms increases to a varying degree compared to that of original Re sites in the intrinsic rhenium disulfide system, and the average charge population of the atoms at the three doping positions has been increasing with the increase of Mo atoms doped. It is can be seen by studying the optical property that the increase in the number of doped atoms causes redshift of the highest reflection peak to different degrees with respect to the original ReS 2 system. The results above show that substitutional Mo doping is less sensitive to the systematic optical property but more to the band gap value and the degree of charge transfer.
Author contribution All authors contributed to the study conception and design. Material preparation, conceptualization, translation, and methodology were performed by He Li, Ying Wang, GuiLi Liu, Lin Wei, and Duo Wang. The first draft of the manuscript was written by He Li, and all authors commented on previous versions of the manuscript. All authors read and approved the final manuscript.