#
Recent Advancement on the Optical Properties of Two-Dimensional Molybdenum Disulfide (MoS_{2}) Thin Films

^{*}

## Abstract

**:**

_{2}) has gained increasing attention due to its promising optical, electronic, and optoelectronic properties. Of particular interest is the indirect to direct band-gap transition from bulk and few-layered structures to mono-layered MoS

_{2}, respectively. In this review, the study of these properties is summarized. The use of Raman and Photoluminescence (PL) spectroscopy of MoS

_{2}has become a reliable technique for differentiating the number of molecular layers in 2D MoS

_{2}.

## 1. Introduction

_{2}, MoSe

_{2}, WS

_{2}, WSe

_{2}, and their 2D oxides [3].

^{6}·cm

^{2}·V

^{−1}·S

^{−1}at 2 K [5]. For this reason attempts have been made to use graphene to develop a new ultrathin electrical conductor [6]. Although graphene nanoribbons (GNRs) exhibit a small band-gap due to edge effects, field-effect transistors (FETs) and optoelectronic devices based on GNRs still suffer from a relatively low current on/off ratio (just exceeding 10

^{4}) [7]. Although structurally similar to graphene thin layers of h-BN (boron nitride nanosheets, BNNSs [8,9]) and their nanotubular structures (boron nitride nanotubes, BNNTs [10,11,12,13]) have a 6 eV band-gap, and are therefore not interesting as a material for FETs. In contrast, TMDCs have band-gaps of approximately 1–2 eV [14,15]. Furthermore, FETs made from molybdenum disulfide (MoS

_{2}) have a field-effect mobility of at least 200 cm

^{2}·V

^{−1}·S

^{−1}[16], and high on/off switch ratios of up to 10

^{10}at room temperature [17]. Although bulk TMDCs have been studied for decades [14,15,18], atomically thick 2D layers of TMDCs have just started to gain attention in the past three years, as indicated by a significant increase in the number of published articles as summarized in Figure 1.

**Figure 1.**The number of papers published with a title containing or a topic pertaining to molybdenum disulfide (MoS

_{2}).

_{2}is a prospective 2D material for photovoltaic and optoelectronic applications. Therefore, this article will focus on reviewing the optical properties of MoS

_{2}as a representative TMDC. In Section 2, the crystal structure of MoS

_{2}will be described. This is followed by a discussion of the electronic band structure of MoS

_{2}, which will prepare readers for the associated optical properties to be discussed in Section 4 (Raman scattering and IR absorption) and Section 5 (resonance Raman scattering).

## 2. Crystal Structure

_{2}) belongs to a class of TMDC materials with a formula MX

_{2}, where M is a transition metal element of group IV (Ti, Zr, Hf), group V (V, Nb, Ta), or group VI (Mo, W), and X is a chalcogen (S, Se, Te). These materials form layered structures of the form X–M–X, with the chalcogen atoms in two hexagonal planes separated by a plane of transition metal atoms. For example, MoS

_{2}has a layered structure of covalently bonded S–Mo–S, which is bonded to adjacent layers by weak van der Waals (vdW) interactions between neighboring S–S layers. As shown in Figure 2a, the S and Mo atom layers are hexagonal in structure and each Mo atom is located at the center of a trigonal prism created by six S atoms [19]. Such a tri-layer sandwich structure is considered as a monolayer of MoS

_{2,}and is stacked in three possible configurations, with weak vdW S–S bonds as shown in Figure 2b, to form multilayer MoS

_{2}.

**Figure 2.**(

**a**) Hexagonal structure of S and Mo layers; (

**b**) Side view schematic illustration of the 1T/2H/3R type structures of MoS

_{2}; (

**c**) indicates the number of layers in a repeat unit.

_{2}to form a bulk crystal of different polytypes, which vary by stacking order and atom coordination. As shown in Figure 2b, there are three known common MoS

_{2}structures. The 2H and 3R structures both occur in nature, and have trigonal prismatic coordination [20]. The 3R type has rhombohedra symmetry with three S-Mo-S units. The 2H-MoS

_{2}has hexagonal symmetry with two S–Mo–S units per primitive cell. The 1T type is a metastable structure discovered in the 1990s [21,22]. It has octahedral coordination with tetragonal symmetry. It has only one S–Mo–S as a repeat cell. Both the 1T and 3R types are metastable, and they can change to the 2H-MoS

_{2}structure through heating [23,24]. All of the bulk MoS

_{2}crystals discussed hereafter are of the 2H-MoS

_{2}structure.

## 3. Electronic Band Structure: Optical and Optoelectronic Properties

**Figure 3.**Band structure of different layers of MoS

_{2}[36]. Reprinted figure with permission from [Kuc, A.; Zibouche, N.; et al. Influence of quantum confinement on the electronic structure of the transition metal sulfide TS

_{2}. Phys. Rev. B

**2011**, 83, 245213] Copyright (2011) by the American Physical Society.

_{2}has been of particular interest. As shown in Figure 3, bulk MoS

_{2}is an indirect band gap semiconductor with a band gap of 1.2 eV, which originates from the top of the valence band situated at the Γ point to the bottom of the conduction band halfway between the Γ and K points. It should be noted that there is a direct band gap situated at the bulk MoS

_{2}K point. As the number of layers decreases, the fundamental indirect band-gap (from the Γ point to halfway between the Γ point and the K point) increases due to the quantum confinement effect. In the case of monolayer MoS

_{2}, it becomes larger than the direct band-gap located at the K-point, which has been changed by less than 0.1 eV as the number of layers was reduced. In the monolayer limit, MoS

_{2}changes from a bulk indirect band-gap semiconductor to a 2D direct band-gap semiconductor. The indirect band-gap of bulk MoS

_{2}(1.2 eV) is supplanted by the direct band-gap (1.9 eV) at the monolayer MoS

_{2}K-point, as shown in Figure 3.

_{2}and other TMDCs [53,54,55]. The out-of-plane effective mass for electrons and holes around the K point is far exceeded by the free electron and hole mass (m

_{0}). Whereas the hole effective mass around the Γ point is estimated to be 0.4 m

_{0}, and the electron effective mass of the conduction band minimum along the Γ-K direction is only 0.6m

_{0}[46]. Therefore, the decrease of thickness to monolayer leads to significant quantum confinement. To explain this result, Mak et al. applied a zone-folding scheme to describe the electronic band structure of ultrathin MoS

_{2}film [46]. As shown in Figure 4a, the allowed electronic state’s wave vector (out-of-plane momentum k) for monolayer MoS

_{2}can directly occur in the A-H direction. By increasing the MoS

_{2}thickness, the out-of-plane momentum k will approach the Γ-K direction (Figure 4b). In this case the top of the conduction band and the bottom of the valence band occur at the Γ point and along the Γ-K direction. The d orbitals’ contribution to the band structure of MoS

_{2}has been of particular research interest [25,28,32,33,42,56]. The 2H-MoS

_{2}with trigonal prismatic coordination has a filled ${d}_{{z}^{2}}$ valence band that overlaps the filled sp orbitals of the S atoms. The conduction band is derived from the degenerate ${d}_{{x}^{2}-{y}^{2}}$ and ${d}_{x}$ orbitals that overlap the empty anti-bonding sp orbitals of the S atoms. Based on density of state (DOS) data [34,35,36,37,39], the valence and conduction bands near the Γ point were found to be a linear combination of d orbitals of the Mo atoms and p

_{z}orbitals of the S atoms. At the K point, the valence and conduction band states are primarily composed of the d orbitals of the Mo atoms, which are located in the middle of the S–Mo–S unit. Compared to the Mo atoms, the S atoms have strong interlayer coupling; their electron state energy depends on layer thickness, and leads to a direct band-gap structure at the K point when the layer thickness decreases.

**Figure 4.**(

**a**) Simplified electronic band structure of bulk MoS

_{2}[46]. Reprinted figure with permission from [Mak, K.F.; Lee, C.; James, H.; Jie, S.; Heinz, T.F. Atomically Thin MoS

_{2}: A New Direct-Gap Semiconductor. Phys. Rev. Lett.

**2010**, Phys. Rev. Lett. 105.136805] Copyright (2010) by the American Physical Society. (

**b**) Brillouin zone and special point of the hexagonal lattice system (MoS

_{2}) [57].

_{2}, especially for monolayer MoS

_{2}[24,46,47,49], as shown in Figure 5. This phenomenon allows the possibility of using MoS

_{2}for optoelectronic applications [58].

_{2}. The corresponding absorption peaks can be identified as shown in Figure 5b. Both of them correspond to A and B exciton transitions in the direct band-gap structure [14,18,59]. A clear indirect to direct band structure transition between bilayer and monolayer MoS

_{2}can be best seen from the photocurrent spectra shown in Figure 5c. The direct band-gap energies of E

_{A}and E

_{B}, as measured by different methods, are summarized in Table 1. Initially, the research was in agreement that the A and B exciton transitions occur at the Γ point [60,61,62]. There was some disagreement from M. R. Khan and G. J. Goldsmith’s work in 1983, which put the A and B exciton transition at the A point of the Brillouin Zone [63]. However, further calculations have shown that the A and B exciton transitions at the K point [30,32,64,65,66]. The A and B exciton energy difference is due to the d–d transitions from the filled d

_{x}orbital to the degenerated d

_{xy}and d

_{x}

^{2}

_{-y}

^{2}orbitals, which split by spin-orbit coupling [62,67].

**Figure 5.**(

**a**) Photoluminescence spectra from monolayer to bulk MoS

_{2}[47]. Reprinted figure with permission from [Splendiani, A.; Sun, L.; Zhang, Y.; Li, T.; Kim, J.; Chim, C.-Y.; Galli, G.; Wang, F. Emerging photoluminescence in monolayer MoS

_{2}. Nano Lett.

**2010**, 10, 1271–1275] Copyright (2010) by the American Chemical Society. (

**b**) Absorption spectra of ultrathin film MoS

_{2}from 1.3 nm to 7.6 nm. Inset figure shows the A exciton energy with film thickness [24]. Reprinted figure with permission from [Eda, G.; Yamaguchi, H.; Voiry, D.; Fujita, T.; Chen, M.; Chhowalla, M. Photoluminescence from chemically exfoliated MoS

_{2}. Nano Lett.

**2011**, 11, 5111–5116.] Copyright (2011) by the American Chemical Society. (

**c**) Photoconductivity spectra of monolayer and bilayer MoS

_{2}[46]. Reprinted figure with permission from [Mak, K.F.; Lee, C.; James, H.; Jie, S.; Heinz, T.F. Atomically Thin MoS

_{2}: A New Direct-Gap Semiconductor. Phys. Rev. Lett.

**2010**, Phys. Rev. Lett. 105.136805] Copyright (2010) by the American Physical Society.

_{2}is expected to have strong excitonic effects, which will affect the optical properties. One of the commonly used calculation methods is the GW plus Bethe–Salpeter equation (GW-BSE), which computes quasiparticle band structure and optical response, including electron–electron/hole interactions. Although the previously reported experimental and theoretical band gap for MoS

_{2}is around 1.9 eV, recent calculations based on the GW method for monolayer MoS

_{2}have shown that the quasiparticle band-gap is larger. However, the calculated results vary widely between 2.2 and 2.8 eV [37,66,68,69,70,71,72]. Currently there is no experimental proof for the larger quasiparticle band-gap in MoS

_{2}, although evidence was recently demonstrated for WS

_{2}[73].

**Table 1.**There is a wide range of published values of direct band-gap energy E

_{A1}and E

_{B1}measured at different temperatures.

1.929 ± 0.005 | 2.136 ±.008 |

1.845 ± 0.008 | 2.053 ± 0.01 |

1.88 | 2.06 |

1.9255 | 2.137 |

1.92 | 2.124 |

1.9449 | 2.1376 |

1.90 | 2.10 |

1.91 | 2.11 |

1.82 | 1.95 |

1.78 | 1.96 |

1.88 | 2.03 |

1.85 | 1.98 |

## 4. Lattice Dynamic: Raman Scattering and IR Absorption

_{2}that correspond to the phonon modes that contribute to Raman scattering and IR absorption. As was illustrated in Figure 2, MoS

_{2}consists of two hexagonal planes of S atoms and an intercalated hexagonal plane of Mo atoms. The symmetry point group of the S atoms is C

_{3v}, while the symmetry of the Mo atoms is point group D

_{3h}. Furthermore, the irreducible representations of C

_{3v}and D

_{3h}are related to factor group D

_{6h}[80]. Therefore, MoS

_{2}with even numbers of layers or bulk crystal have a symmetry similar to the D

_{6h}point group, and systems with odd numbers of layers (including monolayer crystals) have D

_{3h}space group symmetry (without inversion symmetry) [38].

_{2}Raman spectroscopy studies, A

_{1g}, E

_{2g}

^{1}, E

_{2g}

^{2}, and E

_{1g}. As shown in Figure 6, the A

_{1g}mode is due to the out-of-plane vibration among the S atoms as viewed along the [100] direction. The other three Raman active modes are due to in-plane vibrations, illustrated in Figure 6. Among the four Raman-active modes the A

_{1g}and E

_{2g}

^{1}modes near 400 cm

^{−1}are readily observable. The E

_{1g}mode and E

_{2g}

^{2}mode usually cannot be detected by conventional Raman Scattering measurements.

**Table 2.**Relevant phonon irreducible symmetry representations of S atoms (C

_{3v}), Mo atoms (D

_{3h}), and bulk 2H-MoS

_{2}point group D

_{6h}. This table is compiled from the work of T. J. Weiting et al. [80], A.M. Sanchez et al. [38], and T. Livneh et al. [84]. Some vibration frequency data were measured by [85,86].

C_{3v}(S) | D_{3h}(Mo) | D_{6h}(MoS_{2}(Γ)) | Transformation Properties | Activity | Vibration Direction | Atoms Involved | Frequency(cm^{−1}) |
---|---|---|---|---|---|---|---|

A_{1} | A_{1}’ | A_{1g} | (α_{xx} + α_{yy},α_{zz}) | Raman | Out | S | 409 |

A_{2}’ | B_{1u} | - | Inactive | Out | S | 403 | |

A_{2} | A_{1}’’ | B_{2g}^{1} | - | Inactive | Out | Mo + S | 475 |

B_{2g}^{2} | - | Inactive | Out | Mo + S | 56 | ||

A_{2}’’ | A_{2u}^{1} | T_{z} | IR(E)$\parallel \text{c}$ | Out | Mo + S | 470 | |

A_{2u}^{2} | T_{z} | Acoustic | Out | Mo + S | - | ||

E | E’ | E_{2g}^{1} | (α_{xx} - α_{yy},α_{zz}) | Raman | In | Mo + S | 383 |

E_{1u}^{1} | (T_{x},T_{y}) | IR(E)$\perp \text{c}$ | In | Mo + S | 384 | ||

E_{2g}^{2} | (α_{xx} - α_{yy},α_{zz}) | Raman | In | Mo + S | 34 | ||

E_{1u}^{2} | (T_{x},T_{y}) | Acoustic | In | Mo + S | - | ||

E’’ | E_{1g} | (α_{yz},α_{zx}) | Raman | In | S | 286 | |

E_{2u} | - | Inactive | In | S | 297 |

_{1g}mode is due to the laser polarization chosen and random crystal direction of different MoS

_{2}samples [86]. For example, the E

_{1g}mode is forbidden for s-polarized laser light incident on the MoS

_{2}crystal surface (the E field is perpendicular to the c-axis of MoS

_{2}) [85]. In 1970, J. L. Verbel and T. J. Wieting studied the E

_{1g}mode, and predicted that it would be located around 519 cm

^{−1}[83]. However, after correcting for the polarization effect in 1971 they discovered the very weak line at 287 cm

^{−1}[80]. This was confirmed by J. M. Chen and C. S. Wang using back scattering geometry [87,88], which placed the E

_{1g}mode at 286 cm

^{−1}. This E

_{1g}mode has been shown to be more intense than the other three first-order Raman active modes, which are activated with the use of a p-polarized laser. Conversely, the E

_{1g}mode intensity is much weaker with the use of an s-polarized laser [85].

_{2g}

^{2}mode is due to the vibrational interaction of adjacent rigid layers within the MoS

_{2}crystal. For this reason it is difficult to observe the E

_{2g}

^{2}peak at low wavenumber, because of the presence of strong Rayleigh scattering. The corresponding Raman scattering peak for the E

_{2g}

^{2}mode is located at 33.7($\pm $1) cm

^{−1}and was first experimentally observed by J. L. Verbel, T. J. Wieting, and P. R. Reed by use of a triple Raman spectrometer [89].

_{1g}, E

_{2g}

^{1}, E

_{2g}

^{2}, and E

_{1g}) there are four degeneracy lattice modes—E

_{2u}, E

_{1u}

^{1}, B

_{1u}, and B

_{2g}

^{2}—that are Raman inactive. Among these, E

_{1u}

^{1}and A

_{2u}

^{1}are IR active modes [83].

**Figure 7.**(

**a**) Raman spectrum for different thicknesses of MoS

_{2}. (

**b**) Frequencies of A

_{1g}and E

_{2g}

^{1}modes against layer thickness [82]. Reprinted figure with permission from [Lee, C.; Yan, H.; Brus, L.E.; Heinz, T.F.; Hone, J.; Ryu, S. Anomalous lattice vibrations of single- and few-layer MoS

_{2}. ACS Nano

**2010**, 4, 2695–2700] Copyright (2010) by the American Chemical Society.

_{2g}

^{1}and A

_{1g}modes, as shown in Figure 7a. To explain the vibrational modes of E

_{2g}

^{1}and A

_{1g}, many classical models have been introduced. For example, Bromley used a Born–Von model in the nearest neighbor approximation in an attempt to explain this observation [90]. On the other hand, T. J. Wieting and J. L. Verble found that the classical dielectric oscillator model fits well with the infrared reflectivity and Raman scattering data [80]. This model fits well because the interlayer force is about 100 times smaller than the intralayer force [89], and therefore one only needs to consider the interatomic forces within a single layer. Furthermore, because of the small effective charge, the coulomb force is negligible [80]. However, C. Lee et al. found that these two modes exhibited abnormal film thickness dependence, as shown in Figure 7 [81]. For instance, as shown in Figure 7b, when the film thickness is increased the frequency of the E

_{2g}

^{1}mode decreases (red shifts) while the A

_{1g}increases (blue shifts). This width-dependent frequency shift means that the E

_{2g}

^{1}and A

_{1g}frequency are better for identifying ultrathin MoS

_{2}thickness than either peak intensity or width for no more than four layers [91]. This result is consistent with optical microscope, atomic force microscopy (AFM), and photoluminescence measurements [47,81,91]. Based on various published sources, we have summarized in Table 3 the E

_{2g}

^{1}and A

_{1g}mode frequencies detected from bulk and thin layers of MoS

_{2}by various laser wavelengths.

_{2g}

^{1}and A

_{1g}modes’ frequency on the layer thickness of MoS

_{2}can be explained using the van der Waals force model. As the number of layers is increased, the restoring force between inter-layer S–S bonds will enhance, which fits the observed trend of the out-of-plane A

_{1g}mode frequency increasing. However, the E

_{2g}

^{1}peak shows a red-shift as the number of layers is increased, which suggests that the classical model for coupled harmonic oscillators is inadequate and there is an additional interlayer interaction. One reason for the inadequacy of the classical model is that it only considers weak interlayer interaction. However, the properties of the MoS

_{2}layers might be different from those on the surface of bulk MoS

_{2}. This is consistent with surface phenomenon measurements investigated by P. A. Bertrand, who reported the surface phonon dispersion of MoS

_{2}as measured by high resolution electron-energy-loss spectroscopy (HREELS). It was found that the peak energy of the A

_{1g}optical mode for thin layers is 3.1($\pm $0.2) meV lower than the related bulk phonon [92].

Laser (nm) | E_{2g}^{1} Mode Frequency (cm^{−1}) | A_{1g} Mode Frequency (cm^{−1}) | |||||||||
---|---|---|---|---|---|---|---|---|---|---|---|

1 L | 2 L | 3 L | 4 L | bulk | 1 L | 2 L | 3 L | 4 L | bulk | ||

325 | 384.2 | 382.8 | 382.8 | 382.7 | 382.5 | 404.9 | 405.5 | 406.3 | 407 | 407.8 | |

488 | 384.7 | 383.3 | 383.2 | 382.9 | 383 | 402.8 | 405.5 | 406.5 | 407.4 | 408 | |

514.5^{#} | 384.3 | 383.2 | 382.7 | 382.3 | 382 | 403 | 404.8 | 405.8 | 406.7 | 407.8 | |

514.5* | 386.1 | 383.1 | - | 383.7 | 383.3 | 404.7 | 406.8 | - | 408 | 408.6 | |

532 | 384.7 | 382.5 | 382.4 | 382.4 | 383 | 402.7 | 404.9 | 405.7 | 406.7 | 407.8 | |

632.8 | 385 | 383.8 | 383.3 | 382.9 | 381.5 | 403.8 | 404.8 | 405 | 406 | 406.6 | |

632.8* | 386.4 | 383.1 | - | 383.3 | 382.8 | 405 | 406.2 | - | 407.3 | 408.3 |

_{2g}

^{1}peak with the increase in layer thickness is due to the fact that thinner MoS

_{2}has a shorter intra-layer S–Mo–S distance. In 1977, B. J. Mrstik et al. found surface reconstruction in MoS

_{2}by the use of low-energy electron diffraction (LEED). These LEED measurements showed that the topmost intra-layer space between S–Mo–S atoms of thin MoS

_{2}contracts up to 5% compared to that in bulk planes [94]. These results show that layer stacking effects change the intralayer structure. Moreover, A. M. Sanchez and L. Wertz introduced long-range Coulomb interlayer interactions into models of multilayer MoS

_{2}to explain the E

_{2g}

^{1}anomalous red-shift when the thickness is increased [38]. It was previously introduced to explain the vibrational mode of β-GaSe by T. J. Wieting et al. [95]. From these models it is apparent that the interlayer force changes in two ways when moving from monolayer to bulk samples. The short-range term of the force slightly increases because of the enhanced restoring interaction between adjacent layers. The long-range term of the force will decrease, because the layers extend over the effective charge, which leads to Coulombic screening [96]. However, this effect mainly happens between the Mo atoms. From Figure 6 the E

_{2g}

^{1}mode involves the in-plane vibration of Mo atoms. Consequently, the considerable decrease in the Coulombic, long-range interaction between the Mo atoms overcompensates for the slight increase of the short-range weak interlayer interaction. On the other hand, the A

_{1g}mode is not influenced by the Coulomb potential screening, because the A

_{1g}mode only involves out-of-plane vibration of the S atoms.

## 5. Resonant Raman Scattering

_{1g}mode combines with a weak longitudinal acoustic phonon mode at the M point of the Brillouin zone (LA(M)) corroborating inelastic neutron scattering data from Wakabayashi et al. [97].

_{2}using 676.4 nm (1.83 eV), 647.1 nm (1.92 eV), and 530.9 nm (2.34 eV) excitation lasers whose energy is either near or just out of the edge of the MoS

_{2}absorption region [86]. Typically resonance Raman Scattering is excited by use of a He-Ne 632.8 nm (1.96 eV) laser whose energy is between two absorption bands A (~1.9 eV) and B (~2.1 eV), and falls in the region of electronic transition. The resonance Raman spectra show that multiple modes are shifted from the first-order Raman frequencies, which suggests that the electronic transitions are strongly coupled with phonon modes. There are several reports of this resonant Raman scattering phenomenon in MoS

_{2}[78,79,86,91,93,98,99,100]. All of these studies are in general agreement on the attribution of the peaks observed in the resonant Raman scattering spectrum, which suggests coupling between vibrational modes and longitudinal acoustic phonon modes.

**Table 4.**The phonon frequency of Raman-active and LA modes at different points of the Brillouin zone.

Phonon Frequency (cm^{−1}) | ||||
---|---|---|---|---|

Γ[80,85,86] | M[97] | M[84] | K[84] | |

409 | 397 | 412 | 408 | |

E_{2g}^{1} | 383 | 373 | 370 | 345 |

E_{1g} | 287 | 294 | 330 | 336 |

309 | ||||

E_{2g}^{2} | 34 | - | 233(LA) | 241(LA) |

160(ZA) | 192(ZA) | |||

LA | - | 234 | 235 | 241 |

_{1g}, E

_{2g}

^{1}, and A

_{1g}modes in the Γ-M (from center to the [100] plane (shown in Figure 4b)) direction is relatively small [97]. From the measurement of resonance Raman spectra in Table 4, the line of the A

_{1g}(M) mode almost corresponds to the calculated value of A

_{1g}(Γ) (409 cm

^{−1}) mode. Similarly, the estimated value of the E

_{2g}

^{1}(M) mode is a little smaller than the calculated value of the E

_{2g}

^{1}(Γ) (383 cm

^{−1}) mode, which is consistent with Coulombic force theory [38]. However, as shown in Table 4, the energy of the E

_{2g}

^{2}rigid layer mode at the M points increases considerably in the Γ–M direction due to the aforementioned longitudinal acoustic mode LA (M) interaction [97]. The phonon dispersion has three acoustic modes, whose frequencies linearly depend on the wave-vector. They play an important role in the resonance Raman spectrum of MoS

_{2}. The longitudinal acoustic (LA), and transverse acoustic (TA) modes are due to in-plane vibration. They both have a linear dispersion and higher energy than the out-of-plane acoustic (ZA) mode [38]. The dispersion of the LA, TA, and ZA modes flatten at the border of the Brillouin zone near the high-symmetry M point. Even though it is hard to observe in bulk MoS

_{2}as shown in Figure 8, this LA (M) mode has been observed in MoS

_{2}nanoparticles [79], MoS

_{2}monolayer [101], few layers [93], and their aqueous suspension [21]. Hence the peak at ~230 cm

^{−1}is related to the structural defect-induced scattering in MoS

_{2}[93]. Lack of this feature may confirm relatively good crystal quality for the natural MoS

_{2}sample [102].

^{−1}and 700 cm

^{−1}can be seen in Figure 8. One of the most pronounced peaks is the multi-modeband at 466 cm

^{−1}. Generally it is attributed to the 2LA (M) mode at ~450 cm

^{−1}[78,79,86], and the normally IR-active A

_{2u}(Γ) phonon mode near 466 cm

^{−1}[97]. In addition, K. Golasa et al. proposed a new phonon mode XA around 180 cm

^{−1}[100]. They suggested that the high energy component of the 466 cm

^{−1}peak is rather due to a combined mode E

_{1g}(M) + XA (M), even if the E

_{1g}is forbidden by back scattering geometry. Similarly, the E

_{1g}+ LA (M) mode at 528 cm

^{−1}has been observed in many different samples. Contrary to previous studies [79,86,91,93,101,103], which simply assign the peak at ~645 cm

^{−1}as A

_{1g}(M) + LA (M), K. Golasa et al. [100,104] suggest it is composed of two components: the high-wavenumber part is due to the E

_{1g}+ 2XA (M) modes and the low-wavenumber one, which is marked as “S” in Figure 8, is the real A

_{1g}(M) + LA (M) process. In this way, G. L. Frey’s description of the 641 cm

^{−1}peak shift to low-energy in MoS

_{2}nanoparticles can be explained [98].

_{2g}

^{1}and A

_{1g}in Figure 8. Three additional bands marked “a,” “b,” and “c” are in the vicinity of the E

_{2g}

^{1}and A

_{1g}peaks [78,93,98,100,104]. The “a” band is at ~395 cm

^{−1}, which is not shown in Figure 8 but has been observed by Sekine et al., Livneh et al., and Golasa et al. [78,98,104]. The mode labeled “b” at 420 cm

^{−1}is attributed to a two-phonon Raman scattering process ${\omega}_{b}={\omega}_{QA}+{\omega}_{TO}$. It involves the successive emission of a dispersive longitudinal quasi-acoustic (QA) phonon and a dispersionless transverse optical (TO) phonon. The QA phonon belongs to the Δ

_{2}branch along the c axis (ending in the B

_{2g}

^{2}inactive mode at the Γ point). The TO phonon has a finite vector near the Γ point (with E

_{2u}

^{1}symmetry) of the Δ

_{6}branch along the c axis [97]. Using this, Livneh explains the ~5 cm

^{−1}difference in the “b” mode between the Stokes and anti-Stokes Raman spectra [98]. Therefore, the band denoted as “c” at ~ 377 cm

^{−1}corresponds to this TO phonon. However, unlike the IR spectrum result [80], the “c” band was directly considered to be the E

_{1u}

^{2}mode in Sekine’s measurement [78]. P. N. Ghosh et al.’s calculation based on the vdW interlayer model also obtained E

_{1u}

^{2}at 2 cm

^{−1}lower than the E

_{2g}

^{1}mode [105], but they suggest the probability of long-range Coulombic interaction. Finally, A. M. Sanchez et al. made ab initio calculations considering long-range Coulombic interaction, which showed that the E

_{1u}

^{2}mode is 3 cm

^{−1}higher than E

_{2g}

^{1}mode [38]. The IR-active mode E

_{1u}

^{2}can be experimentally observed at the high wavenumber side of the E

_{2g}

^{1}mode from the resonant Raman scattering in Livneh’s work [98]. Another Raman-inactive mode, B

_{1u}, which is the Davydov pair of A

_{1g}modes, is also observed at the low-wavenumber side of the A

_{1g}band [78,93,98].

_{2}thicknesses from monolayer to bulk are shown in Figure 8. One of the most significant differences is that almost all the resonance peaks are broadened and the relative intensity change as a result of thickness decreases, as was previously reported [91]. The change in the shape and location of the resonance modes at ~ 465 cm

^{−1}and 643 cm

^{−1}have been explained in detail by K. Golasa et al. [100,104]. In addition, the resonance Raman modes higher than 500 cm

^{−1}are hardly observed in the spectrum of monolayer MoS

_{2}. There are several possible reasons for this result. The most reasonable possibility is that the long-range acoustic modes in monolayer MoS

_{2}are strongly affected by interactions with the substrate [99,104]. In the bulk case, only a relatively tiny amount of atoms in the whole sample directly interact with the substrate, and the substrate therefore has little impact on the lattice vibrations. Under resonance conditions, the modification of acoustic modes by the substrate causes the suppression of most multi-phonon processes.

**Figure 8.**Resonant Raman spectra of different thickness MoS

_{2}using 632.8 nm laser in room temperature [93]. Reprinted figure with permission from [Chakraborty, B.; Matte, H.S.S.R.; Sood, A.K.; Rao, C.N.R. Layer-dependent resonant Raman scattering of a few layer MoS

_{2}. J. Raman Spectrosc.

**2013**, 44, 92–96.] Copyright (2013) by John Wiley and Sons.

^{−1}seems to still be present in monolayer MoS

_{2}at room temperature [93,101,104]. However, there is no quasi-acoustical mode present in the monolayer limit, thus the behavior contradicts its assignment to the combined process involving the quasi-acoustic phonons. Therefore, mode “b” should not be present in the monolayer MoS

_{2}spectrum at all. Based on the data from K. Golasa, the peak “b” at ~420 cm

^{−1}clearly disappears from the spectrum in the monolayer MoS

_{2}at 4.2 K. This observation also seems to suggest that a new model is needed to explain the apparent presence of the mode “b” at ~420 cm

^{−1}.

- Difference process: $\text{I}\propto \text{n}\left(1,\text{T}\right)\times \left[\text{n}\left(2,\text{T}\right)+1\right]$
- Combination process: $\text{I}\propto \left[\text{n}\left(1,\text{T}\right)+1\right]\times \left[\text{n}\left(2,\text{T}\right)+1\right]$,

_{i}[85]. Based on these absorption and excitation processes for phonons, they tentatively identify two low frequency peaks at 150 cm

^{−1}and 188 cm

^{−1}and three high frequency peaks at 567 cm

^{−1}, 750 cm

^{−1}, and 816 cm

^{−1}.

## 6. Conclusions

_{2}layers. Although these properties have been studied for bulk MoS

_{2}since the 1960s, the discovery of graphene has led to more interest in the investigation of these properties for 2D thin films of MoS

_{2}. Since the discovery of the relationship between Raman and photoluminescence (PL) spectra with the film thickness of MoS

_{2}in 2010, these optical spectra have become reliable and popular signals for the identification of mono- or few-layered MoS

_{2}structures.

## Acknowledgements

## Conflicts of Interest

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## Share and Cite

**MDPI and ACS Style**

Ye, M.; Winslow, D.; Zhang, D.; Pandey, R.; Yap, Y.K.
Recent Advancement on the Optical Properties of Two-Dimensional Molybdenum Disulfide (MoS_{2}) Thin Films. *Photonics* **2015**, *2*, 288-307.
https://doi.org/10.3390/photonics2010288

**AMA Style**

Ye M, Winslow D, Zhang D, Pandey R, Yap YK.
Recent Advancement on the Optical Properties of Two-Dimensional Molybdenum Disulfide (MoS_{2}) Thin Films. *Photonics*. 2015; 2(1):288-307.
https://doi.org/10.3390/photonics2010288

**Chicago/Turabian Style**

Ye, Mingxiao, Dustin Winslow, Dongyan Zhang, Ravindra Pandey, and Yoke Khin Yap.
2015. "Recent Advancement on the Optical Properties of Two-Dimensional Molybdenum Disulfide (MoS_{2}) Thin Films" *Photonics* 2, no. 1: 288-307.
https://doi.org/10.3390/photonics2010288