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First principles study for band engineering of MoS2 monolayer with Mn doping
Solid State Communications 309 (2020) 113844
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Communication
First principles study for band engineering of MoS2 monolayer with Mn doping Xiaoping Han a, Noureddine Amrane a, Zongsheng Zhang b, Maamar Benkraouda a, * a b
Department of Physics, United Arab Emirates University, Al-Ain, P.O.Box 15551, United Arab Emirates School of Energy and Power Engineering, North University of China, Taiyuan, 030051, China
A R T I C L E I N F O
A B S T R A C T
Communicated by Y.E. Lozovik
The electronic properties of MoS2 monolayer with various levels of Mn incorporation are investigated using the Heyd-Scuseria-Enrzerhof hybrid functional. Four Mn doping concentrations are considered: 2.78%, 6.25%, 11% and 25%. Results show that, with the increasing Mn doping, the Mn-induced intermediate band (IB) ranges from the localized to dispersive states, effectively acting as a stepping stone to help relay valence electrons to the conduction band. Simultaneously, the IB divides the band gap into narrower subgaps, inducing significant bandgap reduction. The combined effects of the IB widening and the band-gap narrowing engineer the band structure to extend the optical absorption of MoS2 monolayer into the long-wavelength region of solar irradiance. Detailed formation-energy calculations reveal a high favorability for Mn to substitute Mo in MoS2 monolayer under the Mo-poor condition. This work provides a fundamental guidance for broadening the functional applications of MoS2 monolayer in photocatalysis, photovoltaic cells and other photonic devices.
Keywords: A. MoS2 monolayer D. Electronic properties E. first-principles calculation E. Hybrid functional
1. Introduction Molybdenum disulfide, MoS2, is a layered transition metal dichal cogenide semiconductor [1] that has attracted considerable interest in connection with its catalytic and electronic properties [2–9]. Its layered structure has a graphene-like hexagonal arrangement of Mo and S atoms, which stack together to form S–Mo–S sandwiches coordinated in a triangular prismatic fashion. Many important properties and functions have been reported in MoS2, such as magnetism in MoS2 nanosheets attributed to the presence of magnetic edge states [10–13], irradiation in MoS2 attributed to a combination of point defects and edge states [14], single crystals attributed to zigzag edges at grain boundaries [15]. As a result, MoS2 has been become one of important materials required for devices like field-effect transistor [16,17], logic circuits [18], and pho totransistors [19], thus attracting considerable interest in extensively investigating MoS2 both experimentally and theoretically. The recent attentions regarding MoS2-based materials focus on the atomically thin layers of MoS2 for electronics, which can be readily yielded through exfoliating [20]. Especially, of particular interest is the MoS2 monolayer in that it is semiconducting [21–23] and direct in band gap [24] (while the bulk MoS2 has an indirect gap). This has made the MoS2 monolayer become a promising candidate for optoelectronic
application, such as photodetectors [19,25], photovoltaics [26–28], and light emitters [29]. However, its band gap is 1.83–1.98 eV [30,31], still having room to be further reduced for broadening practical applications. To achieve it, some works have been done to investigate the effect of dopants on the electronic properties of MoS2 monolayer. Feng et al. [32] reported that Se substitution for S in MoS2 monolayer induced the band gap to reduce by 7%. The similar phenomenon was observed in Ni and Co substitutions for Mo [33], which shifted down the conduction band to narrow the band gap of MoS2 monolayer. In another two studies, Re [34] and Nb [34,35] doping was found to introduce shallow levels into MoS2 monolayer, beneficial to light harvesting. Additionally, the doping using non-metal (H, B, C, N, F) [36] and transition-metal (Cr, V, Mn, Fe, Co) [36–38] was reported to engineer the band structure towards the di rection for widening optoelectronic applications. However, these dop ants are insufficient to effectively extend the optical absorption of MoS2 monolayer into the long-wavelength regions of solar irradiance. With respect to other transition metals, Mn demonstrates a potential as a substitutional dopant in MoS2 monolayer, as this has been shown to provide insight into applications to electronic and spintronic devices. Cheng et al. [37] proposed a two-dimensional diluted magnetic semi conductor using Mn to dope into MoS2 monolayer. The similar results have been found in other two works [38,39]. Another work [40]
* Corresponding author. E-mail addresses: [email protected] (X. Han), [email protected] (N. Amrane), [email protected] (Z. Zhang), [email protected] (M. Benkraouda). https://doi.org/10.1016/j.ssc.2020.113844 Received 13 June 2019; Received in revised form 5 February 2020; Accepted 8 February 2020 Available online 10 February 2020 0038-1098/© 2020 Elsevier Ltd. All rights reserved.
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Solid State Communications 309 (2020) 113844
Fig. 1. (a) Unit cell of MoS2. (b) Side view and (c) top view of 4 � 4 supercell of MoS2 monolayer. Mo and S atoms are represented by purple and yellow spheres, respectively. Fig. 2. Phonon dispersion for a 6 � 6 supercell of MoS2 monolayer with a Mn substitution.
reported the ferromagnetism in MoS2 monolayer with three levels of Mn doping concentrations (4%, 8% and 12%). Apparently, these studies mainly focused on the magnetic properties, and little has been done to investigate the mechanism for engineering the band structure and modulating the electronic properties of MoS2 monolayer, so as to widen its applications. In actual applications, it is necessary to develop a doping strategy to extend its optical absorption of MoS2 monolayer to the long-wavelength regions of solar irradiance. At the present work, the electronic properties of MoS2 monolayer with various concentrations of Mn doping have been studied using the Heyd-Scuseria-Enrzerhof hybrid functional. Results show that the low-concentration Mn doping induces a localized intermediate band (IB), ineffective in acting as a stepping stone to relay the valence electrons to the conduction band. In contrast, the dispersive IB induced by the increased Mn incorporation is helpful to not only offer sufficient capacity for a large number of electrons but also effectively narrow the band gap, significantly enhancing the optical absorption of MoS2 monolayer in the long-wavelength range.
of 500 eV is used in all calculations. All structures are geometrically relaxed until the total force on each ion was reduced to be less than 0.01 eV/Å. All investigations of Mn-doped MoS2 monolayer are conducted on the basis of the theoretically obtained equilibrium lattice parameters of pure MoS2 monolayer (a ¼ b ¼ 3.18 Å), which is within 1% of its experimental values (a ¼ b ¼ 3.16 Å) [47]. It is worth especially stressing that taking the spin orbit coupling (SOC) into account does not cause the evident splitting of electronic bands for either pure or Mn-doped MoS2 monolayer: the conduction band and gap states (for the doped cases) slightly shift downward. This allows one to conduct a reliable study on the electronic properties of Mn-doped MoS2 monolayer even without including the SOC. 3. Results and discussions First, we examine the case with a low doping concentration, where a Mo atom is replaced by a Mn atom from a 6 � 6 supercell of MoS2 monolayer, corresponding to a doping concentration of 2.78%. The substitutional Mn is found to pull the surrounding atoms closer, and the lattice structure near Mn is slightly distorted. In order to confirm the thermodynamic stability, we calculate the phonon frequency, as shown as Fig. 2. It is clear from the figure that all branches of the phonon spectrum are positive, indicative of the dynamic stability of such a Mndoped structure of MoS2 monolayer. Actually, the same phenomenon has been observed in the subsequent structures of MoS2 monolayer with increased Mn contents (6.25%, 11.1% and 25%), also implying their thermodynamic stabilities. Fig. 3(a) shows the total density of states (DOS) of the optimized structure, where a narrow isolated band appears within the band gap. The detailed analyses of partial density of states (PDOS) have been made and shown in Fig. 3(b–d). Apparently, this gap band is mainly attributed to the 3d state of the substitutional Mn ion, with some hybridization with the 3p states of the six S ions nearest neighboring to Mn ion (as marked by red spots in Fig. 4(a)) and the 4d states of the six Mo ions neighboring to Mn ion (as marked by blue spots in Fig. 4(a)). To better characterize this impurity state, we map the charge density difference between pure and Mn-doped MoS2 monolayer. This can be done by subtracting the charge density of the structure with Mn substitution from that of pure MoS2 monolayer, as shown in Fig. 4 (b). It is obvious that the most portion of charge density difference is localized around the Mn atom, with some contributions from the S and Mo atoms surrounding the Mn atom. This is in line with the PDOS chart shown in Fig. 3, where the isolated state is predominantly owing to Mn 3d state. Furthermore, we calculate the planar average charge density difference along the x direction using the equation
2. Method The bulk MoS2 has a layered 2H prototype structure with the space group of P63mmc, where two hexagonal planes of S atoms are separated by a plane of Mo atoms, as shown in Fig. 1(a). The MoS2 monolayer has a P6 m2 space group, with Mo atoms having a trigonal prismatic coordi nation with S atoms. Its side and top views are shown in Fig. 1(b) and (c). To investigate the effect of various concentrations of Mn doping, we use a Mn atom to substitute a Mo atom in 6 � 6, 4 � 4, 3 � 3 and 2 � 2 supercells of MoS2 monolayer, corresponding to 2.78%, 6.25%, 11.1% and 25% of Mn doping, respectively. A vacuum region of 13 Å normal to the monolayer is used to separate periodic images. All the calculations of Mn-doped monolayers are performed using the Vienna Ab initio Simu lation Package (VASP) [41,42], with the ionic potentials including the effect of core electrons being described by the projector augmented wave (PAW) method [43,44]. The plane-wave basis is generated with valence configurations of Mo-4d55s2, S-3s23p4, and Mn-3d54s2. The Heyd-Scuseria-Enrzerhof (HSE) hybrid method [45] is used to consider the nonlocal effect in the exchange-correlation (XC) functionals, where the exchange potential is separated into a long-range and short-range parts, and 25% Hartree-Fock (HF) exchange is mixed with the Perdew-Burke-Ernzerhof (PBE) functional [46] only in the short-range part and the long-range part of the exchange potential is described by PBE functional alone. The Brillouin zone integration is performed on well-converged Gamma-centered k-point grid. Extensive tests are car ried out to ensure convergence with respect to the number of k-points and energy cutoff. For the k-point integration, we use 2 � 2 � 1, 3 � 3 � 1, 4 � 4 � 1 and 6 � 6 � 1 meshes for 6 � 6, 4 � 4, 3 � 3 and 2 � 2 supercells of MoS2 monolayer, respectively. A plane-wave energy cutoff
ΔρðxÞ ¼ ρðxÞMoS2 :Mn 2
ρðxÞMoS2
ρðxÞMn ;
(1)
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Solid State Communications 309 (2020) 113844
Fig. 3. (a) Total DOS of a 6 � 6 supercell of MoS2 monolayer with a Mn substitution for Mo. (b) PDOS of the 3d state of Mn atom. (c) PDOS of the 3p states of six S atoms surrounding Mn atom (atoms S1 – S6 as marked in Fig. 4(a)). (d) PDOS of the 4d state of six Mo atoms surrounding Mn atom (atoms Mo1 – Mo6 as marked in Fig. 4(a)). The dot-dashed lines at energy zero represent the Fermi level. Fig. 4. (a) Schematic for a 6 � 6 supercell of MoS2 monolayer with a Mn substitution for Mo. Here the Mn, Mo and S atoms are represented using green, purple and yellow spheres, respectively. The six S atoms (S1 – S6) and six Mo atoms (Mo1 – Mo6) sur rounding the Mn substitution are marked using red and blue spots, respectively. Note: each red spot marks two S atoms in two S layers. (b) Mn-induced charge densities in the MoS2 monolayer. Light blue and yellow isosurfaces represent positive and negative spin densities (�0.021 e/Å3), respectively.
This indicates that the excess electrons brought by Mn substitution mainly concentrate on the area surrounding the dopant. Examining Fig. 3(a), one can see the Mn-induced narrow gap state, or an intermediate band (IB), is at 0.9 eV above the valence band maximum (VBM). Apparently, the appearance of this IB divides the forbidden gap of the host phase into two narrower (lower and upper) subgaps, which makes it possible for the valence electrons to be energetically pumped up to the conduction band (CB) using the IB as a stepping stone. Namely, the electrons from the VB do not need to directly jump from the valence band (VB) to CB through across the original forbidden gap, and instead they can jump across the lower subgap (0.9 eV) to the IB first, followed by the subsequent jump across the upper subgap (0.72 eV) to the CB. Undoubtedly, such jumps are energetically favorable. However, this IB is very localized, which is associated with a very low mobility. We calculate the electron and hole mobilities of this IB using the expression [48–50]
Fig. 5. The planar average charge density difference along the x direction. The location of Mn substitution is at zero.
where ρðxÞMoS2 :Mn , ρðxÞMoS2 and ρðxÞMn are the planar average charge densities of pure and Mn-doped monolayer MoS2, and Mn atom along the x direction, respectively. The calculated results are shown in Fig. 5, where the negative values of ΔρðxÞ represent the charge accumulation.
μ¼
3
2eℏ3 C2D 3kB Tjm* j2 Ed2
;
(2)
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Solid State Communications 309 (2020) 113844
overlaps with the VB and CB. In addition, the electron calculated mobility is more than 500 cm2/V. Therefore, 25% Mn doping signifi cantly enhances the optical absorption of MoS2 monolayer. Also, we examine the effect of substitutional Mn on the optical properties. The optical absorption spectra from virgin and substitu tionally doped MoS2 monolayers have been calculated and shown in Fig. 7. It is obvious that, in the cases of 11.1% and 25% doping con centrations, the energy gap reduction causes red-shift in the absorption edge in Region A, and the IB induces the secondary optical absorption hillocks within Region B, and the lower sub-gap gives rise to the tail absorption in Region C. This is consistent with the results of electronic structure calculations (Fig. 6). Therefore, the high Mn doping yields the combined effects of the gap narrowing and the IB widening, which contributes to the significantly enhanced optical absorption and makes the doped materials effective optical absorbers in the long-wavelength regions of the solar radiation. Further, we assess the thermodynamic stability of Mn-doped MoS2 monolayer on the basis of the formation energy of Mn in MoS2 mono layer, which can be calculated using the following equation:
Table 1 The calculated deformation potential constant Ed (eV), elastic modulus C2D (N/ m), and the effective mass m* (m0) and carrier mobility μ (cm2/Vs) of the in termediate band in Fig. 3(a) as well. Electron Hole
Ed
C2D
m*
μ
12.13 6.67
147.3 147.3
4.32 10.38
0.75 0.43
where the parameters e, ħ, kB, and T are electronic charge, reduced Planck constant, Boltzmann constant, and temperature (here 300K is used), respectively. The term C2D is the elastic modulus defined as C2D ¼ ½∂2 E =∂δ2 �=S0 , where E is the total energy, δ is the applied uniaxial strain, and S0 is the area of the optimized 2D system. The term m* is the
effective mass, which can be given as m* ¼ ℏ2 ð∂2 E=∂k2 Þ 1 . Here k is the magnitude of the wave-vector in momentum space. The term Ed repre sents the deformation potential constant of the valence band minimum for hole or conduction band maximum for electron along the transport direction, defined by Ed ¼ ΔE=ðΔS =S0 Þ. Here ΔE is the energy shift of the band edge, and ΔS is the deformation of S0 (up to 0.5%). Table 1 shows the calculated values of deformation potential constants, elastic moduli, and the effective masses and carrier mobilities of the IB. The very low mobilities (0.75 and 0.43 cm2/V for electron and hole mobilities) limit the role of the IB as a stepping stone, with the pinned electrons from the valence band to be readily annihilated via recombination with holes on the valence band. Therefore, 2.78% Mn doping hardly has positive effect on improving the optical absorption of MoS2 monolayer. To elaborate the effect of Mn concentration, we have investigated the MoS2 monolayer with increased Mn contents (6.25%, 11.1% and 25%), and their total DOSs are shown in Fig. 6. It is evident that the IB broadens with the Mn content. With 6.25% Mn, four states appear with the band gap, as shown in Fig. 6(a). Although each state is strongly localized, they nearly mix together, just with very small gaps. This makes the electron jump between these gap states very easily achieved. It is clear from Fig. 6(a) that the appearance of these four gap states yields a lower subgap (0.3 eV) and an upper subgap (0.4 eV) below and above them, making it much easier for electrons to jump from the VB to IB and then from the IB to CB. Accordingly, with 6.25% Mn doping, the optical absorption of MoS2 monolayer has been remarkably enhanced. When Mn content is increased to 11.1%, the IB continues to become dispersive (see Fig. 6(b)). The calculated electron mobility is 210 cm2/V, which is sufficient to make the IB efficiently relay the electrons from the VB to CB and prevent the electron-hole recombination. Therefore, the IB will effectively act as a stepping stone to relay valence electrons into the CB under the illumination of low energy photons, thus promoting effective optical absorption of low energy photons. More interestingly, the widening of IB causes the lower and upper subgaps to be remarkably narrowed (the lower subgap is less than 0.3 eV and the upper one is less than 0.2 eV), and they are easily overcome when the valence electrons jump into the IB. Further increase in Mn concentration to 25% drives the IB to become much more dispersive (Fig. 6(c)), and the IB almost
ΔEf ¼ EðMoS2 : MnÞ þ EðMoÞ
EðMnÞ
EðMoS2 Þ;
(3)
where E(MoS2:Mn) and E(MoS2) are the total energies of the supercells with and without Mn substitution, while E(Mo) and E(Mn) are the atomic total energies of Mo and Mn, respectively. The calculated for mation energies for 2.78%, 6.25%, 11.1% and 25% of Mn doping are 0.16, 0.24, 0.31 and 0.39 eV, respectively. Evidently, the formation energy of Mn increases with its doping concentration, but their small positive values would be readily surmountable, demonstrating that it is highly favorable to form Mn substitution in MoS2 monolayer. Further more, the effect of different chemical environments (e.g., Mo-rich and Mo-poor conditions) on the formation energy of Mn doping has been
Fig. 7. Calculated optical absorption spectra from pure MoS2 monolayer and doped systems with four Mn concentrations.
Fig. 6. Total DOSs for MoS2 monolayer with (a) 6.25%, (b) 11.1%, and (c) 25% of Mn incorporation. 4
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Solid State Communications 309 (2020) 113844
Fig. 8. (a) Mo and S chemical potential ΔμMo and ΔμS between Mo-poor and Mo-rich limits. (b) Formation energies for four Mn doping concentrations in MoS2 monolayer between Mo-poor and Mo-rich conditions.
investigated using the expression [51], ΔEf ¼ EðMoS2 : MnÞ þ μMo
μMn
EðMoS2 Þ
4. Conclusions (4)
MoS2 monolayer with various levels of Mn incorporation has been investigated using the Heyd-Scuseria-Enrzerhof hybrid functional. Re sults show that, with the increasing concentration of Mn dopant, the Mninduced intermediate band ranges from the localized to dispersive states, thus effectively engineering the band structure of MoS2 mono layer to extend its optical absorption into the long-wavelength region of solar irradiance. Detailed thermodynamic analyses reveal that it is highly favorable for Mn to substitute Mo in MoS2 monolayer under Mopoor conditions. This work provides a fundamental guidance for broadening the functional applications of MoS2 monolayer, making it attractive for a wide range of photonic applications, such as optical absorbers in photovoltaic cells, and active materials for photo detectors and light emission diodes.
Here the chemical potential μMo ¼ EðMoÞ þ ΔμMo , where the extra neous chemical potential ΔμMo is subject to its surrounding conditions. Concretely, ΔμMo is limited by the constraints: ΔμMo � 0 and ΔμMo þ 2ΔμS ¼ Ef ðMoS2 Þ, where Ef ðMoS2 Þ refers to the formation energy of MoS2 (the calculated Ef ðMoS2 Þ using the HSE is 2.48 eV, agreeing excellently with the experimental value of 2.44 eV [52]). Under the Mo-rich or S-poor condition, ΔμMo will be 0 eV, thus ΔμS ¼ 12Ef ðMoS2 Þ ¼ 1:24 eV. Under the Mo-poor or S-rich condition, ΔμS will be 0 eV, thus ΔμMo ¼ Ef ðMoS2 Þ ¼ 2:48 eV. Fig. 8(a) illustrates ΔμMo and ΔμS between the Mo-rich and Mo-poor limits. Similarly, the extraneous chemical potential of Mn ΔμMn can be obtained from the constraint ΔμMn þ ΔμS ¼ Ef ðMnSÞ, i.e., ΔμMn ¼ Ef ðMnSÞ ΔμS , where Ef ðMnSÞ refers to the for mation energy of MnS (here the NaCl-structure MnS is used). Its HSE-calculated formation energy is 2.08 eV, being in excellent agreement with the experimental value of 2.21 eV [53]. Based on the above ΔμS , ΔμMn under Mo-rich and Mo-poor conditions can be calcu lated to be 0.84 and 2.08 eV, respectively. Fig. 8(b) shows the calculated formation energies for 2.78%, 6.25%, 11.1% and 25% of Mn substitutions in MoS2 monolayer between Mo-poor and Mo-rich limits. Apparently, the Mo-poor condition encourages the formation of Mn substitution while the Mo-rich chemical potential is energetically infe rior due to the high formation energy. Under the Mo-poor condition each concentration of Mn doping has a negative formation energy, revealing that Mn substitution is highly favorable to form in MoS2 monolayer. Overall, the present work makes clear of the change in electronic properties of MoS2 monolayer with doping concentration, which helps develop a doping strategy to extend its optical absorption to long wavelength regions of solar irradiance. With a low doping concentra tion, the induced localized gap state depresses its role as a stepping stone, with the pinned electrons which are readily annihilated through recombining with holes. In contrast, the dispersive intermediate band induced by the high Mn doping is helpful to provide adequate density of states and carrier mobility, which enhances the electron-hole separation and lowers the probability for carrier recombination. Moreover, the appearance of the wide intermediate band allows to realize multiwavelength absorption of solar light. Accordingly, the outcome of this work offers great promise for practical applications of MoS2 monolayer in photocatalysis and photovoltaics as well as spintronic devices.
Acknowledgement We acknowledge grants from United Arab Emirates University Pro gram for Advanced Research (Grant Nos: 31S109, 31R146, 31R109Research Center-ECEER-9-2016). Partial financial support is provided by North University of China through the Key R&D Plans of Shanxi Province (Grant No. 201803D421084). References [1] A.D. Yoffe, Chem. Soc. Rev. 5 (1976) 51. [2] L.S. Byskov, J.K. Norskov, B.S. Clausen, H. Topsøe, J. Catal. 187 (1999) 109. [3] P. Raybaud, J. Hafner, G. Kresse, S. Kasztelan, H. Toulhoat, J. Catal. 189 (2000) 129. [4] M. Sun, A.E. Nelson, J. Adjaye, J. Catal. 233 (2005) 411. [5] N.M. Galea, E.S. Kadantsev, T. Ziegler, J. Phys. Chem. C 113 (2009) 193. [6] A. Vojvodic, B. Hinnemann, J.K. Norskov, Phys. Rev. B 80 (2009), 125416. [7] T. Li, G. Galli, J. Phys. Chem. C 111 (2007) 16192. [8] E. Gourmelon, O. Lignier, H. Hadouda, G. Couturier, J.C. Bernede, J. Tedd, J. Pouzed, J. Salardenne, Sol. Energy Mater. Sol. Cells 46 (1997) 115. [9] M. Thomalla, H. Tributsch, J. Phys. Chem. B 110 (2006) 12167. [10] Y. Li, Z. Zhou, S. Zhang, Z. Chen, J. Am. Chem. Soc. 130 (2008) 16729. [11] A.R. Botello-Mendez, F. Lopez-Urıas, M. Terrones, H. Terrones, Nanotechnology 20 (2009), 325703. [12] C. Ataca, S. Ciraci, J. Phys. Chem. C 115 (2011) 13303. [13] J. Zhang, J.M. Soon, K.P. Loh, J. Yin, M.B. Sullivian, P. Wu, Nano Lett. 7 (2007) 2370. [14] S. Mathew, K. Gopinadhan, T.K. Chan, X.J. Yu, D. Zhan, L. Cao, A. Rusydi, M.B. H. Breese, S. Dhar, Z.X. Shen, Appl. Phys. Lett. 101 (2012), 102103. [15] S. Tongay, S.S. Varnoosfaderani, B.R. Appleton, J. Wu, A.F. Hebard, Appl. Phys. Lett. 101 (2012), 123105. [16] A. Ayari, E. Cobas, O. Ogundadegbe, M.S. Fuhrer, J. Appl. Phys. 101 (2007), 014507. [17] B. Radisavljevic, A. Radenovic, J. Brivio, V. Giacometti, A. Kis, Nat. Nanotechnol. 6 (2011) 147.
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Solid State Communications journal homepage: http://www.elsevier.com/locate/ssc
Communication
First principles study for band engineering of MoS2 monolayer with Mn doping Xiaoping Han a, Noureddine Amrane a, Zongsheng Zhang b, Maamar Benkraouda a, * a b
Department of Physics, United Arab Emirates University, Al-Ain, P.O.Box 15551, United Arab Emirates School of Energy and Power Engineering, North University of China, Taiyuan, 030051, China
A R T I C L E I N F O
A B S T R A C T
Communicated by Y.E. Lozovik
The electronic properties of MoS2 monolayer with various levels of Mn incorporation are investigated using the Heyd-Scuseria-Enrzerhof hybrid functional. Four Mn doping concentrations are considered: 2.78%, 6.25%, 11% and 25%. Results show that, with the increasing Mn doping, the Mn-induced intermediate band (IB) ranges from the localized to dispersive states, effectively acting as a stepping stone to help relay valence electrons to the conduction band. Simultaneously, the IB divides the band gap into narrower subgaps, inducing significant bandgap reduction. The combined effects of the IB widening and the band-gap narrowing engineer the band structure to extend the optical absorption of MoS2 monolayer into the long-wavelength region of solar irradiance. Detailed formation-energy calculations reveal a high favorability for Mn to substitute Mo in MoS2 monolayer under the Mo-poor condition. This work provides a fundamental guidance for broadening the functional applications of MoS2 monolayer in photocatalysis, photovoltaic cells and other photonic devices.
Keywords: A. MoS2 monolayer D. Electronic properties E. first-principles calculation E. Hybrid functional
1. Introduction Molybdenum disulfide, MoS2, is a layered transition metal dichal cogenide semiconductor [1] that has attracted considerable interest in connection with its catalytic and electronic properties [2–9]. Its layered structure has a graphene-like hexagonal arrangement of Mo and S atoms, which stack together to form S–Mo–S sandwiches coordinated in a triangular prismatic fashion. Many important properties and functions have been reported in MoS2, such as magnetism in MoS2 nanosheets attributed to the presence of magnetic edge states [10–13], irradiation in MoS2 attributed to a combination of point defects and edge states [14], single crystals attributed to zigzag edges at grain boundaries [15]. As a result, MoS2 has been become one of important materials required for devices like field-effect transistor [16,17], logic circuits [18], and pho totransistors [19], thus attracting considerable interest in extensively investigating MoS2 both experimentally and theoretically. The recent attentions regarding MoS2-based materials focus on the atomically thin layers of MoS2 for electronics, which can be readily yielded through exfoliating [20]. Especially, of particular interest is the MoS2 monolayer in that it is semiconducting [21–23] and direct in band gap [24] (while the bulk MoS2 has an indirect gap). This has made the MoS2 monolayer become a promising candidate for optoelectronic
application, such as photodetectors [19,25], photovoltaics [26–28], and light emitters [29]. However, its band gap is 1.83–1.98 eV [30,31], still having room to be further reduced for broadening practical applications. To achieve it, some works have been done to investigate the effect of dopants on the electronic properties of MoS2 monolayer. Feng et al. [32] reported that Se substitution for S in MoS2 monolayer induced the band gap to reduce by 7%. The similar phenomenon was observed in Ni and Co substitutions for Mo [33], which shifted down the conduction band to narrow the band gap of MoS2 monolayer. In another two studies, Re [34] and Nb [34,35] doping was found to introduce shallow levels into MoS2 monolayer, beneficial to light harvesting. Additionally, the doping using non-metal (H, B, C, N, F) [36] and transition-metal (Cr, V, Mn, Fe, Co) [36–38] was reported to engineer the band structure towards the di rection for widening optoelectronic applications. However, these dop ants are insufficient to effectively extend the optical absorption of MoS2 monolayer into the long-wavelength regions of solar irradiance. With respect to other transition metals, Mn demonstrates a potential as a substitutional dopant in MoS2 monolayer, as this has been shown to provide insight into applications to electronic and spintronic devices. Cheng et al. [37] proposed a two-dimensional diluted magnetic semi conductor using Mn to dope into MoS2 monolayer. The similar results have been found in other two works [38,39]. Another work [40]
* Corresponding author. E-mail addresses: [email protected] (X. Han), [email protected] (N. Amrane), [email protected] (Z. Zhang), [email protected] (M. Benkraouda). https://doi.org/10.1016/j.ssc.2020.113844 Received 13 June 2019; Received in revised form 5 February 2020; Accepted 8 February 2020 Available online 10 February 2020 0038-1098/© 2020 Elsevier Ltd. All rights reserved.
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Fig. 1. (a) Unit cell of MoS2. (b) Side view and (c) top view of 4 � 4 supercell of MoS2 monolayer. Mo and S atoms are represented by purple and yellow spheres, respectively. Fig. 2. Phonon dispersion for a 6 � 6 supercell of MoS2 monolayer with a Mn substitution.
reported the ferromagnetism in MoS2 monolayer with three levels of Mn doping concentrations (4%, 8% and 12%). Apparently, these studies mainly focused on the magnetic properties, and little has been done to investigate the mechanism for engineering the band structure and modulating the electronic properties of MoS2 monolayer, so as to widen its applications. In actual applications, it is necessary to develop a doping strategy to extend its optical absorption of MoS2 monolayer to the long-wavelength regions of solar irradiance. At the present work, the electronic properties of MoS2 monolayer with various concentrations of Mn doping have been studied using the Heyd-Scuseria-Enrzerhof hybrid functional. Results show that the low-concentration Mn doping induces a localized intermediate band (IB), ineffective in acting as a stepping stone to relay the valence electrons to the conduction band. In contrast, the dispersive IB induced by the increased Mn incorporation is helpful to not only offer sufficient capacity for a large number of electrons but also effectively narrow the band gap, significantly enhancing the optical absorption of MoS2 monolayer in the long-wavelength range.
of 500 eV is used in all calculations. All structures are geometrically relaxed until the total force on each ion was reduced to be less than 0.01 eV/Å. All investigations of Mn-doped MoS2 monolayer are conducted on the basis of the theoretically obtained equilibrium lattice parameters of pure MoS2 monolayer (a ¼ b ¼ 3.18 Å), which is within 1% of its experimental values (a ¼ b ¼ 3.16 Å) [47]. It is worth especially stressing that taking the spin orbit coupling (SOC) into account does not cause the evident splitting of electronic bands for either pure or Mn-doped MoS2 monolayer: the conduction band and gap states (for the doped cases) slightly shift downward. This allows one to conduct a reliable study on the electronic properties of Mn-doped MoS2 monolayer even without including the SOC. 3. Results and discussions First, we examine the case with a low doping concentration, where a Mo atom is replaced by a Mn atom from a 6 � 6 supercell of MoS2 monolayer, corresponding to a doping concentration of 2.78%. The substitutional Mn is found to pull the surrounding atoms closer, and the lattice structure near Mn is slightly distorted. In order to confirm the thermodynamic stability, we calculate the phonon frequency, as shown as Fig. 2. It is clear from the figure that all branches of the phonon spectrum are positive, indicative of the dynamic stability of such a Mndoped structure of MoS2 monolayer. Actually, the same phenomenon has been observed in the subsequent structures of MoS2 monolayer with increased Mn contents (6.25%, 11.1% and 25%), also implying their thermodynamic stabilities. Fig. 3(a) shows the total density of states (DOS) of the optimized structure, where a narrow isolated band appears within the band gap. The detailed analyses of partial density of states (PDOS) have been made and shown in Fig. 3(b–d). Apparently, this gap band is mainly attributed to the 3d state of the substitutional Mn ion, with some hybridization with the 3p states of the six S ions nearest neighboring to Mn ion (as marked by red spots in Fig. 4(a)) and the 4d states of the six Mo ions neighboring to Mn ion (as marked by blue spots in Fig. 4(a)). To better characterize this impurity state, we map the charge density difference between pure and Mn-doped MoS2 monolayer. This can be done by subtracting the charge density of the structure with Mn substitution from that of pure MoS2 monolayer, as shown in Fig. 4 (b). It is obvious that the most portion of charge density difference is localized around the Mn atom, with some contributions from the S and Mo atoms surrounding the Mn atom. This is in line with the PDOS chart shown in Fig. 3, where the isolated state is predominantly owing to Mn 3d state. Furthermore, we calculate the planar average charge density difference along the x direction using the equation
2. Method The bulk MoS2 has a layered 2H prototype structure with the space group of P63mmc, where two hexagonal planes of S atoms are separated by a plane of Mo atoms, as shown in Fig. 1(a). The MoS2 monolayer has a P6 m2 space group, with Mo atoms having a trigonal prismatic coordi nation with S atoms. Its side and top views are shown in Fig. 1(b) and (c). To investigate the effect of various concentrations of Mn doping, we use a Mn atom to substitute a Mo atom in 6 � 6, 4 � 4, 3 � 3 and 2 � 2 supercells of MoS2 monolayer, corresponding to 2.78%, 6.25%, 11.1% and 25% of Mn doping, respectively. A vacuum region of 13 Å normal to the monolayer is used to separate periodic images. All the calculations of Mn-doped monolayers are performed using the Vienna Ab initio Simu lation Package (VASP) [41,42], with the ionic potentials including the effect of core electrons being described by the projector augmented wave (PAW) method [43,44]. The plane-wave basis is generated with valence configurations of Mo-4d55s2, S-3s23p4, and Mn-3d54s2. The Heyd-Scuseria-Enrzerhof (HSE) hybrid method [45] is used to consider the nonlocal effect in the exchange-correlation (XC) functionals, where the exchange potential is separated into a long-range and short-range parts, and 25% Hartree-Fock (HF) exchange is mixed with the Perdew-Burke-Ernzerhof (PBE) functional [46] only in the short-range part and the long-range part of the exchange potential is described by PBE functional alone. The Brillouin zone integration is performed on well-converged Gamma-centered k-point grid. Extensive tests are car ried out to ensure convergence with respect to the number of k-points and energy cutoff. For the k-point integration, we use 2 � 2 � 1, 3 � 3 � 1, 4 � 4 � 1 and 6 � 6 � 1 meshes for 6 � 6, 4 � 4, 3 � 3 and 2 � 2 supercells of MoS2 monolayer, respectively. A plane-wave energy cutoff
ΔρðxÞ ¼ ρðxÞMoS2 :Mn 2
ρðxÞMoS2
ρðxÞMn ;
(1)
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Fig. 3. (a) Total DOS of a 6 � 6 supercell of MoS2 monolayer with a Mn substitution for Mo. (b) PDOS of the 3d state of Mn atom. (c) PDOS of the 3p states of six S atoms surrounding Mn atom (atoms S1 – S6 as marked in Fig. 4(a)). (d) PDOS of the 4d state of six Mo atoms surrounding Mn atom (atoms Mo1 – Mo6 as marked in Fig. 4(a)). The dot-dashed lines at energy zero represent the Fermi level. Fig. 4. (a) Schematic for a 6 � 6 supercell of MoS2 monolayer with a Mn substitution for Mo. Here the Mn, Mo and S atoms are represented using green, purple and yellow spheres, respectively. The six S atoms (S1 – S6) and six Mo atoms (Mo1 – Mo6) sur rounding the Mn substitution are marked using red and blue spots, respectively. Note: each red spot marks two S atoms in two S layers. (b) Mn-induced charge densities in the MoS2 monolayer. Light blue and yellow isosurfaces represent positive and negative spin densities (�0.021 e/Å3), respectively.
This indicates that the excess electrons brought by Mn substitution mainly concentrate on the area surrounding the dopant. Examining Fig. 3(a), one can see the Mn-induced narrow gap state, or an intermediate band (IB), is at 0.9 eV above the valence band maximum (VBM). Apparently, the appearance of this IB divides the forbidden gap of the host phase into two narrower (lower and upper) subgaps, which makes it possible for the valence electrons to be energetically pumped up to the conduction band (CB) using the IB as a stepping stone. Namely, the electrons from the VB do not need to directly jump from the valence band (VB) to CB through across the original forbidden gap, and instead they can jump across the lower subgap (0.9 eV) to the IB first, followed by the subsequent jump across the upper subgap (0.72 eV) to the CB. Undoubtedly, such jumps are energetically favorable. However, this IB is very localized, which is associated with a very low mobility. We calculate the electron and hole mobilities of this IB using the expression [48–50]
Fig. 5. The planar average charge density difference along the x direction. The location of Mn substitution is at zero.
where ρðxÞMoS2 :Mn , ρðxÞMoS2 and ρðxÞMn are the planar average charge densities of pure and Mn-doped monolayer MoS2, and Mn atom along the x direction, respectively. The calculated results are shown in Fig. 5, where the negative values of ΔρðxÞ represent the charge accumulation.
μ¼
3
2eℏ3 C2D 3kB Tjm* j2 Ed2
;
(2)
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overlaps with the VB and CB. In addition, the electron calculated mobility is more than 500 cm2/V. Therefore, 25% Mn doping signifi cantly enhances the optical absorption of MoS2 monolayer. Also, we examine the effect of substitutional Mn on the optical properties. The optical absorption spectra from virgin and substitu tionally doped MoS2 monolayers have been calculated and shown in Fig. 7. It is obvious that, in the cases of 11.1% and 25% doping con centrations, the energy gap reduction causes red-shift in the absorption edge in Region A, and the IB induces the secondary optical absorption hillocks within Region B, and the lower sub-gap gives rise to the tail absorption in Region C. This is consistent with the results of electronic structure calculations (Fig. 6). Therefore, the high Mn doping yields the combined effects of the gap narrowing and the IB widening, which contributes to the significantly enhanced optical absorption and makes the doped materials effective optical absorbers in the long-wavelength regions of the solar radiation. Further, we assess the thermodynamic stability of Mn-doped MoS2 monolayer on the basis of the formation energy of Mn in MoS2 mono layer, which can be calculated using the following equation:
Table 1 The calculated deformation potential constant Ed (eV), elastic modulus C2D (N/ m), and the effective mass m* (m0) and carrier mobility μ (cm2/Vs) of the in termediate band in Fig. 3(a) as well. Electron Hole
Ed
C2D
m*
μ
12.13 6.67
147.3 147.3
4.32 10.38
0.75 0.43
where the parameters e, ħ, kB, and T are electronic charge, reduced Planck constant, Boltzmann constant, and temperature (here 300K is used), respectively. The term C2D is the elastic modulus defined as C2D ¼ ½∂2 E =∂δ2 �=S0 , where E is the total energy, δ is the applied uniaxial strain, and S0 is the area of the optimized 2D system. The term m* is the
effective mass, which can be given as m* ¼ ℏ2 ð∂2 E=∂k2 Þ 1 . Here k is the magnitude of the wave-vector in momentum space. The term Ed repre sents the deformation potential constant of the valence band minimum for hole or conduction band maximum for electron along the transport direction, defined by Ed ¼ ΔE=ðΔS =S0 Þ. Here ΔE is the energy shift of the band edge, and ΔS is the deformation of S0 (up to 0.5%). Table 1 shows the calculated values of deformation potential constants, elastic moduli, and the effective masses and carrier mobilities of the IB. The very low mobilities (0.75 and 0.43 cm2/V for electron and hole mobilities) limit the role of the IB as a stepping stone, with the pinned electrons from the valence band to be readily annihilated via recombination with holes on the valence band. Therefore, 2.78% Mn doping hardly has positive effect on improving the optical absorption of MoS2 monolayer. To elaborate the effect of Mn concentration, we have investigated the MoS2 monolayer with increased Mn contents (6.25%, 11.1% and 25%), and their total DOSs are shown in Fig. 6. It is evident that the IB broadens with the Mn content. With 6.25% Mn, four states appear with the band gap, as shown in Fig. 6(a). Although each state is strongly localized, they nearly mix together, just with very small gaps. This makes the electron jump between these gap states very easily achieved. It is clear from Fig. 6(a) that the appearance of these four gap states yields a lower subgap (0.3 eV) and an upper subgap (0.4 eV) below and above them, making it much easier for electrons to jump from the VB to IB and then from the IB to CB. Accordingly, with 6.25% Mn doping, the optical absorption of MoS2 monolayer has been remarkably enhanced. When Mn content is increased to 11.1%, the IB continues to become dispersive (see Fig. 6(b)). The calculated electron mobility is 210 cm2/V, which is sufficient to make the IB efficiently relay the electrons from the VB to CB and prevent the electron-hole recombination. Therefore, the IB will effectively act as a stepping stone to relay valence electrons into the CB under the illumination of low energy photons, thus promoting effective optical absorption of low energy photons. More interestingly, the widening of IB causes the lower and upper subgaps to be remarkably narrowed (the lower subgap is less than 0.3 eV and the upper one is less than 0.2 eV), and they are easily overcome when the valence electrons jump into the IB. Further increase in Mn concentration to 25% drives the IB to become much more dispersive (Fig. 6(c)), and the IB almost
ΔEf ¼ EðMoS2 : MnÞ þ EðMoÞ
EðMnÞ
EðMoS2 Þ;
(3)
where E(MoS2:Mn) and E(MoS2) are the total energies of the supercells with and without Mn substitution, while E(Mo) and E(Mn) are the atomic total energies of Mo and Mn, respectively. The calculated for mation energies for 2.78%, 6.25%, 11.1% and 25% of Mn doping are 0.16, 0.24, 0.31 and 0.39 eV, respectively. Evidently, the formation energy of Mn increases with its doping concentration, but their small positive values would be readily surmountable, demonstrating that it is highly favorable to form Mn substitution in MoS2 monolayer. Further more, the effect of different chemical environments (e.g., Mo-rich and Mo-poor conditions) on the formation energy of Mn doping has been
Fig. 7. Calculated optical absorption spectra from pure MoS2 monolayer and doped systems with four Mn concentrations.
Fig. 6. Total DOSs for MoS2 monolayer with (a) 6.25%, (b) 11.1%, and (c) 25% of Mn incorporation. 4
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Fig. 8. (a) Mo and S chemical potential ΔμMo and ΔμS between Mo-poor and Mo-rich limits. (b) Formation energies for four Mn doping concentrations in MoS2 monolayer between Mo-poor and Mo-rich conditions.
investigated using the expression [51], ΔEf ¼ EðMoS2 : MnÞ þ μMo
μMn
EðMoS2 Þ
4. Conclusions (4)
MoS2 monolayer with various levels of Mn incorporation has been investigated using the Heyd-Scuseria-Enrzerhof hybrid functional. Re sults show that, with the increasing concentration of Mn dopant, the Mninduced intermediate band ranges from the localized to dispersive states, thus effectively engineering the band structure of MoS2 mono layer to extend its optical absorption into the long-wavelength region of solar irradiance. Detailed thermodynamic analyses reveal that it is highly favorable for Mn to substitute Mo in MoS2 monolayer under Mopoor conditions. This work provides a fundamental guidance for broadening the functional applications of MoS2 monolayer, making it attractive for a wide range of photonic applications, such as optical absorbers in photovoltaic cells, and active materials for photo detectors and light emission diodes.
Here the chemical potential μMo ¼ EðMoÞ þ ΔμMo , where the extra neous chemical potential ΔμMo is subject to its surrounding conditions. Concretely, ΔμMo is limited by the constraints: ΔμMo � 0 and ΔμMo þ 2ΔμS ¼ Ef ðMoS2 Þ, where Ef ðMoS2 Þ refers to the formation energy of MoS2 (the calculated Ef ðMoS2 Þ using the HSE is 2.48 eV, agreeing excellently with the experimental value of 2.44 eV [52]). Under the Mo-rich or S-poor condition, ΔμMo will be 0 eV, thus ΔμS ¼ 12Ef ðMoS2 Þ ¼ 1:24 eV. Under the Mo-poor or S-rich condition, ΔμS will be 0 eV, thus ΔμMo ¼ Ef ðMoS2 Þ ¼ 2:48 eV. Fig. 8(a) illustrates ΔμMo and ΔμS between the Mo-rich and Mo-poor limits. Similarly, the extraneous chemical potential of Mn ΔμMn can be obtained from the constraint ΔμMn þ ΔμS ¼ Ef ðMnSÞ, i.e., ΔμMn ¼ Ef ðMnSÞ ΔμS , where Ef ðMnSÞ refers to the for mation energy of MnS (here the NaCl-structure MnS is used). Its HSE-calculated formation energy is 2.08 eV, being in excellent agreement with the experimental value of 2.21 eV [53]. Based on the above ΔμS , ΔμMn under Mo-rich and Mo-poor conditions can be calcu lated to be 0.84 and 2.08 eV, respectively. Fig. 8(b) shows the calculated formation energies for 2.78%, 6.25%, 11.1% and 25% of Mn substitutions in MoS2 monolayer between Mo-poor and Mo-rich limits. Apparently, the Mo-poor condition encourages the formation of Mn substitution while the Mo-rich chemical potential is energetically infe rior due to the high formation energy. Under the Mo-poor condition each concentration of Mn doping has a negative formation energy, revealing that Mn substitution is highly favorable to form in MoS2 monolayer. Overall, the present work makes clear of the change in electronic properties of MoS2 monolayer with doping concentration, which helps develop a doping strategy to extend its optical absorption to long wavelength regions of solar irradiance. With a low doping concentra tion, the induced localized gap state depresses its role as a stepping stone, with the pinned electrons which are readily annihilated through recombining with holes. In contrast, the dispersive intermediate band induced by the high Mn doping is helpful to provide adequate density of states and carrier mobility, which enhances the electron-hole separation and lowers the probability for carrier recombination. Moreover, the appearance of the wide intermediate band allows to realize multiwavelength absorption of solar light. Accordingly, the outcome of this work offers great promise for practical applications of MoS2 monolayer in photocatalysis and photovoltaics as well as spintronic devices.
Acknowledgement We acknowledge grants from United Arab Emirates University Pro gram for Advanced Research (Grant Nos: 31S109, 31R146, 31R109Research Center-ECEER-9-2016). Partial financial support is provided by North University of China through the Key R&D Plans of Shanxi Province (Grant No. 201803D421084). References [1] A.D. Yoffe, Chem. Soc. Rev. 5 (1976) 51. [2] L.S. Byskov, J.K. Norskov, B.S. Clausen, H. Topsøe, J. Catal. 187 (1999) 109. [3] P. Raybaud, J. Hafner, G. Kresse, S. Kasztelan, H. Toulhoat, J. Catal. 189 (2000) 129. [4] M. Sun, A.E. Nelson, J. Adjaye, J. Catal. 233 (2005) 411. [5] N.M. Galea, E.S. Kadantsev, T. Ziegler, J. Phys. Chem. C 113 (2009) 193. [6] A. Vojvodic, B. Hinnemann, J.K. Norskov, Phys. Rev. B 80 (2009), 125416. [7] T. Li, G. Galli, J. Phys. Chem. C 111 (2007) 16192. [8] E. Gourmelon, O. Lignier, H. Hadouda, G. Couturier, J.C. Bernede, J. Tedd, J. Pouzed, J. Salardenne, Sol. Energy Mater. Sol. Cells 46 (1997) 115. [9] M. Thomalla, H. Tributsch, J. Phys. Chem. B 110 (2006) 12167. [10] Y. Li, Z. Zhou, S. Zhang, Z. Chen, J. Am. Chem. Soc. 130 (2008) 16729. [11] A.R. Botello-Mendez, F. Lopez-Urıas, M. Terrones, H. Terrones, Nanotechnology 20 (2009), 325703. [12] C. Ataca, S. Ciraci, J. Phys. Chem. C 115 (2011) 13303. [13] J. Zhang, J.M. Soon, K.P. Loh, J. Yin, M.B. Sullivian, P. Wu, Nano Lett. 7 (2007) 2370. [14] S. Mathew, K. Gopinadhan, T.K. Chan, X.J. Yu, D. Zhan, L. Cao, A. Rusydi, M.B. H. Breese, S. Dhar, Z.X. Shen, Appl. Phys. Lett. 101 (2012), 102103. [15] S. Tongay, S.S. Varnoosfaderani, B.R. Appleton, J. Wu, A.F. Hebard, Appl. Phys. Lett. 101 (2012), 123105. [16] A. Ayari, E. Cobas, O. Ogundadegbe, M.S. Fuhrer, J. Appl. Phys. 101 (2007), 014507. [17] B. Radisavljevic, A. Radenovic, J. Brivio, V. Giacometti, A. Kis, Nat. Nanotechnol. 6 (2011) 147.
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