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Electronic structure calculation of bulk and monolayer MoS
_{2} has been performed using plane wave pseudopotential method based on density functional theory. The indirect band gap in the bulk MoS
_{2} was found to be 0.9 eV, whereas in the monolayer-MoS
_{2} the band gap of 1.57 eV was found to be direct one. The calculated physical parameters of monolayer MoS
_{2} are found to be very close to the bulk MoS
_{2} and compare well with available experimental and other theoretical results. The calculated density of states (DOS) may help explain this change in the nature of band gap in bulk and in monolayer MoS
_{2}. A further variation in band gap has been observed in MoS
_{2} monolayer on applying biaxial strain.

Layered transition-metal di-chalcogenides (LTMDCs) have been extensively reviewed in the recent past [_{2} is a typical example of LTMDC family of materials which attracts investigation because of its distinctive industrial applications, ranging from use as a lubricant [_{2} is a semiconductor with an indirect band gap of about 1.23 eV while its monolayer has a direct energy gap of 1.8 eV [_{2} in the recent years. Upon thinning from the bulk [_{2} undergoes an interesting transition. Recently, a monolayer MoS_{2}-based field effect transistor (FET) with HfO_{2} as gate insulator has been successfully implemented [_{2} a very promising candidate for next generation FET and as optoelectronic devices [_{2}.

Theoretically, there are various possibilities of energy gap manipulation in MoS_{2}. By reducing the layer thickness from bulk to monolayer, the indirect band gap energies in the bulk are shifted relative to the direct band gap in the monolayer limit [_{2} nanoparticles with direct band gaps as well as metallic di-chalcogenides nanowires with promising catalytic and thermoelectric properties [

The properties of transition metal di-chalcogenides (TMDs) not only can be tuned by varying number of layers, but also can be modified by application of external field or strain engineering. Studies [_{2} modifies the band gap energy and the carrier effective mass. Moreover, at strains larger than 1% the lowest lying band gap changes from direct to indirect [_{2} could be used to increase carrier mobility of MoS_{2}, to create tunable photonic devices and solar cells [_{2} [_{2} can sustain strains greater than 11% [_{2} by close examination of temperature dependent indirect excitation emission peaks has been explored. A study on elastic constants and electronic structures of two-dimensional monolayer MoS_{2} under elastic strain using first principle calculations has been made [_{2} undergoes a descent trend with the increase in strain. They observed a direct to indirect transition at strain of 0.01 and semiconductor to metal transition at strain of 0.10.

With the goal of understanding the electronic properties of bulk and monolayer MoS_{2} and strain engineering, we carried out ab initio calculations of bulk and monolayer MoS_{2} using gradient corrected exchange-correlation functional in DFT framework and observed a transition from indirect to direct band gap. However if this band gap can be tuned such that a semiconductor with a lower band gap or a semiconductor to metal transition can be achieved with the application of strain, then a wide range of tunable nano device can be fabricated. In the present work, therefore we study the effects of mechanical strains on the electronic properties of monolayer of MoS_{2}. Our results suggest a way of band gap engineering in MoS_{2}.

The calculations were performed using self consistent plane wave pseudopotential total energy method based on density functional technique as implemented in Quantum Espresso code [^{−9} eV reached. We used wave function- and charge-density cut-offs of 70 Ryd and 300 Ryd, respectively. First, we obtained lattice constants a and c by the process of total energy minimization. Optimized structure (coordinates) was used to perform self consistent calculations with a Monkhorst-Pack [_{2}. We used _{2}, we created 15 Å vacuum along Z axis to isolate it and to prevent any interaction between the layers. The cohesive energy per atom of bulk MoS_{2} was calculated as E_{coh} = E(MoS_{2}) − E(Mo) − 2E(S), where E(MoS_{2}) is the total energy of the unit cell of Molybdenum disulphide, E(Mo) is the energy of Mo atom and E(S) is the energy of S atom. The cohesive energies per atom of monolayer MoS_{2} was also calculated accordingly. A uniform tensile strain ranging from 0 to 10% were applied on monolayer MoS_{2} to study the change in behavior of its band gap.

Molybdenum disulphide has a hexagonal structure consisting of S-Mo-S layers as shown in _{2} has two such layers and Mo atoms of one layer are directly above the sulphur atoms of the other layer and vice versa while monolayer MoS_{2} has a single S-Mo-S layer. We have calculated the structural parameters of bulk and monolayer MoS_{2} using GGA as shown in _{2} have been compared with experimental data while the results of monolayer are compared with some other theoretical results. We find excellent agreements as can be seen in _{2} are nearly identical to the structural parameters calculated for bulk MoS_{2}.

The electronic band structure of bulk MoS_{2} and corresponding density of states are shown in _{ }

(a) (b)

(c)

_{2}; (b) Top view of bulk and monolayer MoS_{2}; and (c) Side view of mono layer MoS_{2}. The Mo-atoms are denoted by gray and S-atoms by pale yellow balls. _{ }

Properties | Bulk-MoS_{2} | Monolayer MoS_{2} |
---|---|---|

Lattice constant (a) [angstrom] | 3.19 (present calculation) 3.16 (Ref [ | 3.195 3.20 (Ref [ |

c/a ratio | 3.86 (present calculation) 3.89 (Ref [ | |

Cohesive energy (eV/atom) | 4.960 | 4.979 |

below Fermi energy. A comparative band structure of MoS_{2} bulk and its monolayer and bilayer are shown in _{2}. The bands around the band gap are relatively flat, as expected from the d-character of electron states at these energies.

For bulk MoS_{2} the valence band maximum is at high-symmetric Γ-point and conduction band minima is in between Γ- and K-points, revealing indirect band semiconductor as can be seen in _{2}, we observe that the band edge near Γ point has been shifted up by around 0.7 eV. In case of monolayer, at Λ and Σ point the band edge shifted up in such a way that the conduction band minima occurs at K-point. For monolayer the valence band maxima and conduction band minima are both at high-symmetric K-point revealing direct band gap semiconductor as can be seen in _{2} to its monolayer. A PDOS comparison of bulk and mono layer MoS_{2} (as shown in the _{z2} and degenerate states d_{xy} and d_{x}_{2-y2}. The states d_{x}_{2-y2} and d_{xy} are degenerate in case of bulk while little bit separating in monolayer. The calculated and measured band gap for mono layer MoS_{2} and bulk are shown in

To study the effect of strain on the electronic properties of monolayer MoS_{2}, we first relaxed the atomic position and obtained the optimized geometry. We apply the uniform strain (ε) to the monolayer MoS_{2} in the range 0.0 - 0.10. The strained atomic structure is achieved by enlarging the hexagonal lattice a_{0} with an increment of εa_{o}. Similarly the atomic structure is fully optimized and the band structure is calculated. As for strained structure of MoS_{2}, the band gap versus strain is shown in the

Bulk MoS_{2} | Monolayer MoS_{2} | |
---|---|---|

Present calculation | 0.89 | 1.57 |

Experimental value | 1.23 (Ref [ | 1.80 (Ref [ |

Theoretical results | 0.7 (Ref [ | 1.55 (Ref [ |

While the strain reaches 0.06, the indirect band gap vanishes. We observe a cross over in the figure. Upon ε = 0.0, the monolayer MoS_{2} shows a behavior of semiconductor with direct gap, at ε = 0.005 it has direct (at K) and indirect (Γ-K) band gap of almost equal amount. These results are interesting. Not only the band gap of monolayer MoS_{2} can be tuned by uniform strain, but also direct to indirect and semiconductor to metal transitions are controlled.

Very recently, in a paper by Das et al. [_{2} and ZnO has been theoretically studied. They have found such transition in MoS_{2} to occur at strain 0.83%, close to our calculated value of 0.5%.

In summary, we studied the structural and electronic properties of MoS_{2} using plane wave pseudopotential method under GGA scheme based DFT calculations. Electronic band structure and density of states calculation show many similarities between monolayer-MoS_{2} and bulk-MoS_{2} except the nature of the band gap which is found direct for monolayer-MoS_{2} as compared to indirect for bulk-MoS_{2}. This observation is consistent with the theoretical prediction of indirect to direct band gap transition in going from bulk to monolayer. Such behavior, arising from d-orbital related interaction in MoS_{2}, may also arise in other layered transition metal di-chalcoge- nides. A further variation in band gap has been observed in MoS_{2} monolayer on applying strain. It points out a new direction of band engineering, hence such capability can lead to engineering novel behaviors and holds promise for new applications.

Part of the calculations was performed on High-Performance cluster computer of SNBNCBS, Kolkata for which authors are thankful. SA acknowledges valuable discussion with T.P. Kaloni. This work was initiated at S.N. Bose National Centre, when one of us (SA) was a visiting scientist under the Extended Visitors Linkage Programme (EVLP), which is gratefully acknowledged.