The electronic structure and optical properties of Mn and B, C, N co-doped MoS2 monolayers

The electronic structure and optical properties of Mn and B, C, N co-doped molybdenum disulfide (MoS2) monolayers have been investigated through first-principles calculations. It is shown that the MoS2 monolayer reflects magnetism with a magnetic moment of 0.87 μB when co-doped with Mn-C. However, the systems co-doped with Mn-B and Mn-N atoms exhibit semiconducting behavior and their energy bandgaps are 1.03 and 0.81 eV, respectively. The bandgaps of the co-doped systems are smaller than those of the corresponding pristine forms, due to effective charge compensation between Mn and B (N) atoms. The optical properties of Mn-B (C, N) co-doped systems all reflect the redshift phenomenon. The absorption edge of the pure molybdenum disulfide monolayer is 0.8 eV, while the absorption edges of the Mn-B, Mn-C, and Mn-N co-doped systems become 0.45, 0.5, and 0 eV, respectively. As a potential material, MoS2 is widely used in many fields such as the production of optoelectronic devices, military devices, and civil devices.


Background
Layered transition metal dichalcogenides (TMD) belong to a well-defined chemical and structural family characterized by strong covalent intralayer bonding and weak van der Waals interactions between adjacent layers [1,2]. Transition metal oxides and sulfides have always been an interesting subject in experimental and theoretical works [3][4][5][6][7][8][9] due to their important role in lithium-ion batteries (LIB) [10], flexible electronic devices [11], photoluminescence [12], valleytronics [13,14], and field-effect transistors. Molybdenum disulfide (MoS 2 ) monolayer contains hexagonal planes of Mo atoms lying between two hexagonal planes of S atoms, forming a sheet of S-Mo-S. Each Mo atom bonds with six neighboring S atoms through covalent bonds.
Cheng et al. [15] have found that the formation energy of substitutional doping is formidably large in graphene, rendering doping in this 2D material a challenging issue. It has been proved that a very thin MoS 2 owns a good property of lubrication. It is mainly because the binding energy between S atoms and metal materials is so strong that MoS 2 has a great adsorbability on the metal surface. MoS 2 can also be used as a kind of desulfurization catalyst [16,17] for crude oil in the industry, indeed preventing the phenomenon of sulfur poisoning. Due to its good chemical stability, thermal stability, specific surface area, and high surface activity, MoS 2 can be a utility material. Though its optical and electronic properties [18][19][20][21][22][23][24] have been discussed, MoS 2 still has limitations in improving the optical property for the production of photodetectors in the industry. Doping in MoS 2 [25][26][27], as a typical 2D material, attracts more attention. Through a series of calculations, Mn doping and B (C, N) doping can improve the characters of MoS 2 [24,25]. In order to get more ideal characters of MoS 2 , we calculated three structures including Mn-B, Mn-C, and Mn-N co-doped MoS 2 monolayers in this paper. The MoS 2 monolayer co-doped with Mn-C reflects magnetism. However, the systems co-doped with Mn and B (N) atoms exhibit semiconducting behavior with bandgaps smaller than those of the corresponding primitive state. Mn-B (C, N) co-doping all make the optical absorption edges generate the redshift phenomenon for the MoS 2 monolayer, which results in the enhancement of absorption for infrared light in the MoS 2 monolayer. The redshift degree of the Mn-N co-doped system is the largest. This result may open a new route to MoS 2 in optical device applications.

Methods
In this paper, we will discuss three co-doped structures: Mn-B, Mn-C, and Mn-N co-doped MoS 2 monolayers, as shown in Figure 1. All of the computations are performed using the spin-polarized density functional theory with an all-electron linearized augmented plane wave method, as implemented in the WIEN2K simulation package [28], in order to investigate the electronic and optical properties of the MoS 2 monolayer. The cutoff energy is 300 eV, and the muffin tin radius of Mo, S, Mn, B, C, and N is 1.45, 1.04, 1.40, 0.85, 0.70, and 0.65 Å, respectively. A generalized gradient approximation [29] is used to treat the exchange correlation potential, and relativistic effects are taken into account. In order to get comprehensive results about the Mn-3d orbit, the GGA + U method is also used. The 4 × 4 × 1 supercell of MoS 2 with a = b =12.66 Å [30,31] is adopted through all the calculations, and the 2D MoS 2 are located in the x-y plane with periodic boundary conditions and are modeled in a supercell with a vacuum space of at least 20 Å in the z-axis in order to avoid interactions between adjacent sheets. The Brillouin zone (BZ) is represented by a set of 6 × 6 × 1 k-points [32] for geometry optimization and for static total energy calculations. Structural relaxation is done until the forces on each atom are smaller than 10 −2 eV/Å.

Results and discussion
Formation energy and crystal structure The relative stability of the doped structure is determined from the formation energy and relates to the realization in experiments. Through co-doping, the formation energy can be calculated by the following general equation, which is inferred from some experiences of other semiconductor materials in any form [33][34][35][36]: represent the total energy of the primitive MoS 2 monolayer and the total energy doped with impurities, respectively. n i >0 means the number of atoms which are doped into the system, while n i <0 means the number of atoms which are replaced from the MoS 2 monolayer. E i represents the energy of the single atom. The smaller the value of the formation energy, the greater the stability of the structure. The formation energy under the circumstances of Mn and B, C, N co-doped MoS 2 monolayers is 7.42, 7.03, and 7.56 eV, respectively. Obviously, the case of the Mn-C co-doped system obtains the most stable state.
Due to the sandwich structure of MoS 2 , we put our point to the buckled height between two S atom planes (h), the length of Mo-S (d), and the S-Mo-S bond angle (θ) which are 3.16 Å, 2.42 Å, and 81.65°, respectively. As is known, Figure 1 Optimized geometric structures of the MoS 2 monolayer from the top view (a) and side view (b). The blue, yellow, and purple balls are Mo, S, and Mn atoms, respectively. B or C atom substitutes for the S atom at site A, and N atom replaces the S atom located at site B. the order of radius for nonmetallic atoms is N > C > B. Table 1 shows us that, with the increase of the radius, θ (S-Mo-S) becomes smaller and also the bond length between Mn and S becomes longer and d (Mo-X) becomes shorter. The buckled height h (S-S) under the circumstance of codoping is smaller than that of the primitive state.

Density of states
In Figure 2, we further present the total density of states (DOS) of all structures. Although the pure MoS 2 monolayer is a nonmagnetic semiconductor, the Mn doping results in magnetic states with spin-up and spin-down branches being unequally occupied. The result well agrees with ref. [26]. This phenomenon is due to the Mn and C atoms sharing pairs of electrons. Meanwhile, the interaction between electric charges is reinforced and the polarization phenomenon generated. Consequently, the role of Mn-3d upon the conduction band around the Fermi level is reinforced.
To better understand the effect between different orbits, we demonstrate the partial density of states as shown in Figure 3. In order to realize the effect of the Mn-3d orbit deeply, the GGA + U method is used. The results show us that the orbital coupling between C-2 s, C-2p and Mn-3d becomes stronger as U increases. And the electronic transition between B-2p, C-2 s, C-2p, N-2 s and Mn-3d becomes more active. Above all, the role of Mn-3d enhanced. Considering the Coulomb repulsion between the electrons, the results become convincing.

Energy bandgap
The primitive MoS 2 monolayer has a direct bandgap of 1.85 eV which is consistent with ref. [3]. The band Table 1 The crystal structure of the co-doped MoS 2 monolayers The symbols h, d, and θ are the buckled height, bond length, and bond angle, respectively (X = B, C, N).   Figure 4; Mn-B and Mn-N codoping make the energy bandgap become smaller than before, where the bandgaps are 1.03 and 0.81 eV, respectively. And the Mo 15 MnNS 31 transforms into an indirect semiconductor. Unsurprisingly, the Mn-B (N) co-doping cannot transform the spin state of the material, which makes the system stay in a nonmagnetic state. It is due to the effective charge compensation between Mn or B (N) atoms. But the Mn-C co-doped system reflects spin polarization and the magnetic moment is 0.87 μB. The generation of the magnetic moment is mainly because Mn provides one more electron than the Mo atom; when C substitutes for the S atom, it needs more electrons to make the 2p orbit saturated. In Figure 4c,d, a series of impurity bands appear around the Fermi level which results in the reinforcement of the light absorption and expands the absorbed region. These strong local lines come from the orbital hybridization between C-2 s, C-2p and Mn-3d, Mn-4 s, Mo-5 s, which provide more electronic states in energy space per unit. For Figure 4a  In Figure 5b, the absorption edge of the pure molybdenum disulfide monolayer is 0.8 eV, corresponding to the electrons which transfer from the conduction band to the valence band partially, which is in very good agreement with the experimental value [7]. The codoped structures all reflect the redshift phenomenon, and the absorption edges of the Mn-B, Mn-C, and Mn-N systems become 0.45, 0.5, and 0 eV, respectively. And the value of absorption peaks decreased simultaneously. The redshift phenomenon shows us that the co-doped systems have better optical gas sensing property. Although the number of absorption peaks decreased, the energy range increased, which indicates that the wavelength range for the absorption became wider. In the high-energy region, the absorption of Mo 15 MnBS 31 , Mo 15 MnCS 31 , and Mo 15 MnNS 31 is so little such that the MoS 2 monolayer has high transmittance in the visible light region under these circumstances. These findings indicate that the pure MoS 2 is more suitable to make a near-ultraviolet (6.0~6.5, 6.8~7.0, and 8.5~9.5 eV) photodetector than the MoS 2 monolayer co-doped with Mo-B (C, N). But Mo 15 MnCS 31 is the most suitable to make a near-ultraviolet (3.3~5.8 eV) photodetector. The Mn-B co-doped MoS 2 monolayer is more suitable to make an infrared photodetector.

Conclusions
According to our calculation, the electronic structure and optical properties of Mn and B, C, N co-doped MoS 2 monolayers have been investigated through firstprinciples. As is shown, the MoS 2 monolayer co-doped with Mn-C reflects magnetism and the magnetic moment is 0.87 μB. It is due to the Mn providing one more electron than the Mo atom; when C substitutes for the S atom, it needs more electrons to make the 2p orbit saturated. However, the co-doped systems with Mn and B (N) atoms exhibit semiconducting behavior with bandgaps smaller than those of the corresponding pristine state because of the effective charge compensation between Mn and B (N) atoms. And the energy bandgaps are 1.03 and 0.81 eV, respectively. Mn-B (C, N) co-doping all make the optical absorption edges generate the redshift phenomenon for the MoS 2 monolayer, which results in the enhancement of the MoS 2 monolayer absorbing infrared light. The absorption edge of the pure molybdenum disulfide monolayer is 0.8 eV, where the absorption edges of Mn-B, Mn-C, and Mn-N co-doped systems become 0.45, 0.5, and 0 eV, respectively. Mo 15 MnCS 31 is easier to achieve in the experiments than other structures. As a potential material, it is necessary to realize the tunable bandgap in the MoS 2 monolayer by surface adsorption. Furthermore, our research will progress towards quantum transport simulation and tunneling transistors like silicene [39,40].