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. 2022 May 20;2(5):417–422. doi: 10.1021/acsphyschemau.2c00021

Fano-Type Wavelength-Dependent Asymmetric Raman Line Shapes from MoS2 Nanoflakes

Manushree Tanwar †, Love Bansal †, Chanchal Rani †, Sonam Rani ‡, Suchita Kandpal †, Tanushree Ghosh †, Devesh K Pathak †, I Sameera ‡, Ravi Bhatia ‡, Rajesh Kumar †,§,∥,*
PMCID: PMC9955271  PMID: 36855687

Abstract

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Excitation wavelength-dependent Raman spectroscopy has been carried out to study electron–phonon interaction (Fano resonance) in multi-layered bulk 2H–MoS2 nano-flakes. The electron–phonon coupling is proposed to be caused due to interaction between energy of an excitonic quasi-electronic continuum and the discrete one phonon, first-order Raman modes of MoS2. It is proposed that an asymmetrically broadened Raman line shape obtained by 633 nm laser excitation is due to electron–phonon interaction whose electronic continuum is provided by the well-known A and B excitons. Typical wavelength-dependent Raman line shape has been observed, which validates and quantifies the Fano interaction present in the samples. The experimentally obtained Raman scattering data show very good agreement with the theoretical Fano–Raman line-shape functions and help in estimating the coupling strength. Values of the electron–phonon interaction parameter obtained, through line-shape fitting, for the two excitation wavelengths have been compared and shown to have generic Fano-type dependence on the excitation wavelength.

Keywords: electron−phonon interaction, Fano resonance, Raman line shape, MoS2, light−matter interaction, 2-D materials

Introduction

Light–matter interaction in transition metal chalcogenides1 like MoS2, MoSe2,WS2, and WSe2 has been widely explored to make next-generation photonics and optical devices1 by exploring their unique electronic,2−4 optical,5 and spin-valleytronic6 and electrical7 properties. Among these, MoS2 has gained tremendous attention due to its application in light detection,8 light emission,9 solar energy storage,10 field-effect transistors (FETs),11,12 and so forth. To be used in device applications, the material should be well versed with its optical, vibrionic, and electronic properties and their interplay, if any, present, in the material of interest. For example, electron–phonon interaction13 commonly known as Fano resonance, which is a prominent phenomenon affecting lattice thermal conductivity14 and carrier transport15 and governing optical properties of the material, needs to be carefully analyzed in any material prior to its use in devices. U. Fano, for the first time, gave the theoretical explanation of asymmetric line shape based on the superposition principle of quantum mechanics. The effect of Fano resonance is observed in various systems where there is a strong interaction of a discrete state and a degenerate continuum, with its first observation in the atomic system.16 Since its first report in 1961, a variety of systems have been found to exhibit Fano resonance that manifests in different genres like non-linear Fano resonance,17 Fano scattering,18 and so forth, making it a topic worth exploring in different materials including in their nano-regimes. For example, in a two-oscillator system with a driving force when the frequency of the latter is equal to the eigenfrequency of the oscillator, the amplitude of the oscillator grows toward the maximum value. In a weakly coupled oscillator system, there are two resonance frequencies in which the first resonance is characterized using Breit–Wigner resonance, whereas the second frequency is characterized using an asymmetric profile. Fano resonance manifests itself in terms of asymmetric line-shape profiles comprising a dip called the anti-resonance dip or minima and a peak corresponding to the maxima of resonance.

Raman spectroscopy19−24 is a widely used non-destructive tool to study Fano resonance and hence can be employed to study the perturbed electronic–vibrionic properties and their interplay in transition metal dichalcogenides. In bulk materials, Fano resonance takes place due to matching of energy of the electronic continuum provided by free carriers via either heavy doping25,26 or photoexcited carriers,27,28 with the discrete one-phonon energy, causing a constructive and destructive interference.16,29 Such a perturbation is manifested in terms of asymmetric Raman line-shape profiles and is often shifted in terms of its peak position. Another prominent feature of these Raman profiles depicting Fano resonance is the presence of antiresonance (dip) on either the pre-maximum or post-maximum side30 depending on the type of carrier (electron or hole) involved in generating the electronic continuum. To analyze the effect of resonance, parametric Raman line shape analysis is done. The Raman line shape parameters31 to assess the perturbation in line shape include the peak position, full width at half-maximum (fwhm),32 and asymmetry ratio (αR) defined by the ratio of lower half width (ΓL) to higher half width (ΓH), that is, αR = ΓL/ΓH of the observed Raman spectrum.

Raman vibrational modes of 2H–MoS2 include four first-order Raman active modes, namely, E22g, E1g, E12g, and A1g with the Raman line shape centered at approximately 32, 286, 378, and 408 cm–1, respectively, for the bulk phase. The E22g mode involves the interlayer mode caused by the vibration of two rigid layers against each other, and the E1g mode is forbidden in backscattering geometry on the surface perpendicular to the c axis. All the modes, except E22g, involve the intra-layer (S–Mo–S) atomic vibrations.33 The characteristic modes, namely, E12g and A1g have been widely explored due to shift in only the peak position of the symmetric Raman line shape obtained by changing layer thickness.34 The energies of these discrete modes are in the range of a few tens of millielectron volt which may participate in Fano-type interaction if a system possesses an appropriate continuum. Bulk MoS2 is known to have two excitonic energy states corresponding to A and B excitons,3,35,36 separated by a couple of hundred millielectron volt, which may provide the necessary quasi-continuum of states which can enable the Fano coupling with the discrete phonons. Since there is no fundamental restriction which can prohibit the Fano resonance from taking place, it would be interesting to study MoS2-type two-dimensional (2D) systems to explore the presence of Fano interaction using Raman spectroscopy.

The current paper deals with the parametric spectral line shape analysis of the observed asymmetric Raman spectrum obtained from multi-layered MoS2 nanoflakes (MLMNs). The presence of asymmetry in the Raman line shape hints at the presence of electron–phonon interaction which, in this case, is caused by energy resonance between an exciton-mediated electronic continuum of ∼100 meV and discrete one-phonon vibration modes, namely, E12g and A1g. The presence of the excitonic continuum is revealed by a broad photoluminescence (PL) emission. The origin of the electronic continuum has been identified as the energy difference between A and B exciton levels with the indirect band gap of 2H–MoS2, which leads to the exciton-mediated Fano-like interference in bulk MoS2. The presence of Fano resonance has been substantiated by strong wavelength-dependent Raman line-shape parameters. This has been further validated by theoretical line-shape fitting of the observed Raman scattering data using the Fano–Raman line-shape function which not only shows a good fit between the experiment and theoretical line shape but also helps in quantifying the Fano coupling strength. The variation in the wavelength-dependent Raman line-shape parameters, obtained from the line-shape fitting, shows the typical trend observed for systems where Fano-type resonance is present.

Experimental Details

The MoS2 nanoflakes have been synthesized by a facile one-step hydrothermal route.37−40 In a typical synthesis, 1.7 g of ammonium heptamolybdatetetrahydrate [(NH4)6Mo7O24·4H2O] and 3 g of thiourea (CH4N2S) were dissolved in 60 ml of deionized water by continuous stirring for 30 min. Homogeneous and colorless solution was obtained, which was transferred into a 100 mL Teflon-lined stainless-steel autoclave. The autoclave was heated to 220 °C in an oven for a period of 24 h and then cooled down to room temperature. The MoS2nano-flake sample, in the form of a black-colored product, was collected after centrifugation and was washed with deionized water and ethanol several times. At the end, the reaction product was dried using a freeze dryer at −80 °C in vacuum. A NOVA NanoSEM 450 field emission scanning electron microscopy (SEM) instrument and X-ray diffraction (XRD) instrument equipped with Cu Kα (Rigaku Miniflex-II) were employed for structural characterization of MoS2. Raman spectroscopy measurements were carried out using a HORIBA-JobinYovn LABRAM HR spectrometer using 632 and 532 nm excitation using minimum laser power (1 mW).

Results and Discussion

Structural characterization of the prepared MoS2 sample has been carried out using SEM and XRD, whereas information about electronic states has been obtained using the photoluminescence (PL) technique. The hydrothermally prepared MoS2 sample shows a nano-flake-like morphology as can be seen in the SEM images (Figure 1a). A zoomed view at higher magnification (Figure 1b) confirms the formation of flower petal-shaped MLMNs with a petal thickness > 25 nm41 representing multi-layered (bulk) MLMNs. Figure 1c shows the PL spectrum recorded using 532 nm excitation laser, showing the characteristic A and B excitons at 1.9 and 2.1 eV, respectively.15,36 This further indicates the presence of MLMNs in the sample with ∼350 meV broad electronic states. The phase purity and crystallinity of these MLMNs have been confirmed by analyzing the XRD pattern of MLMNs (Figure 1d). The XRD pattern shows diffraction peaks of 2θ values of 14.06, 31.98, 35.36, 43.52, and 57.1° corresponding to (002), (100), (101), (103), and (110) planes, respectively, of MoS2 which is in complete agreement with the standard card (JCPDS file no. 37-1492) confirming the 2H–MoS2 phase. The sharp XRD peaks mean the presence of the crystalline structural phase.

Figure 1.

Figure 1

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(a) SEM micrographs of MoS2 nano-flakes and (b) magnified view showing the nano-petal-type morphology, (c) room-temperature PL spectrum recorded using 532 nm laser excitation, and (d) XRD pattern of MoS2 nano-flakes. Reprinted in part with permission from Solar Energy Materials and Solar Cells2021,236, 111502.2 Copyright 2022 Elsevier.

To understand the vibrational properties of MoS2, Raman spectroscopy has been employed. As discussed above, Raman line shape parameters deliver a wealth of information about the effect of perturbations on physical processes.22,29,42−45 A typical Raman spectrum of Bulk MoS2 consists of two characteristic modes, namely, E12g and A1g, arising due to in-plane and out-of-plane vibration modes,34 wherein the in-plane mode consists of vibration of two S atoms in one direction and a Mo atom in the opposite direction. On the other hand, the out-of-plane mode consists of two S atoms vibrating opposite each other with a stationary Mo atom in between.46 A symmetric Raman spectral line shape can easily represent these Raman modes, and no exception has been reported so far regarding the symmetric nature of the Raman spectrum. It is important here to mention that the Raman line shape, and associated symmetry, is sensitive to any perturbation in the system.47,48 To dig out any possible interaction present at the microscopic level, Raman spectra have been recorded using 633 nm, and Raman line shape parameters have been extracted. Figure 2 shows the spectrum (red curve), recorded using 633 nm excitation, with E12g (378 cm–1) and A1g (404 cm–1) modes having an asymmetry ratio (αR) of 1.4 and 0.7, respectively, estimated using the formula defined above. Raman line shape from bulk MoS249 is symmetric with the two peaks observed around ∼377 and ∼405 cm–1. In other words, the Raman modes (Figure 2) confirm that the sample is multi-layered and thus represented by bulk nature. Moreover, the separation between the E12g and A1g modes is more than 24 cm–1 which is another observation41,50,51 that helps in ascertaining that the Raman spectroscopy sees these MLMNs as if they are in bulk regimes. Since the MLMNs are not limited by the number of layers, the presence of the quantum confinement effect, one of the typical reasons for an asymmetric Raman line shape, can be discounted in the MLMNs samples.

Figure 2.

Figure 2

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Experimentally obtained Raman spectra of MoS2 flakes recorded using 633 and 532 nm laser excitation represented by red and green colors, respectively. The spectra have been recorded in backscattering geometry (inset).

Presence of electron–phonon interaction (Fano effect) is another perturbation that is known to induce asymmetry in an otherwise symmetric Raman line shape.16−18,52,53 As mentioned above, quantum confinement, which might have caused the asymmetry, is absent; Fano interaction could be a likely reason for the Raman line-shape asymmetry as seen in Figure 2. The presence of electron–phonon interaction, if any, also demands the presence of wavelength-dependent change in Raman line-shape parameters to confirm its presence. In an attempt to confirm this, the Raman spectrum from MLMNs has also been recorded from 532 nm excitation (in addition to 633 nm) as shown in Figure 2 (green curve). The E12g and A1g modes recorded with a 532 nm laser also represent asymmetric Raman line shape with αR calculated as 1.2 and 0.8, respectively, which are different from the values obtained for the 633 nm spectrum (red curve, Figure 2). This is an additional observation which suggests the possible Fano interaction in addition to the observed inflated FWHM of 10 and 7 cm–1 for E12g and A1g modes, respectively. A report by Lee54 et al. shows FWHM values for E12g modes as ∼2 cm–1 (independent of layer thickness) and A1g mode as ∼2.5 cm–1 for bulk MoS2 where no Fano interaction is present. In other words, the wavelength-dependent variation in Raman line-shape parameters and inflated Raman line width are a strong indication of the presence of Fano interaction in the MLMNs which has manifested in terms of asymmetry in the Raman line shape (Figure 2). The same has been substantiated by theoretical fitting of the Raman data as discussed below. The theoretical explanation of the wavelength dependence of electron–phonon interaction is explained on the basis of the square of the electron–phonon interaction parameter (q), which represents the ratio of the scattering probability of the discrete state to that of the continuum, that is, q ∝|Rp/Re |, where Rp and Re are the Raman tensor for one-phonon and electronic Raman scattering55 and are given by eqs 1 and 2, respectively.

graphic file with name pg2c00021_m001.jpg 1
graphic file with name pg2c00021_m002.jpg 2

where |0⟩ &|f⟩ represent initial and final states, respectively; ωL is the frequency of scattering radiation, and p is the linear momentum. Therefore, the relation of q with Rp and Re shows the wavelength dependence of electron–phonon interaction.

As mentioned above, the electron–phonon interaction arises due to appropriate matching of energies of the electronic continuum arising by heavy doping,55,56 by photo excitation of carriers,27,28 and so forth, with the discrete one-phonon energy. The resonance of two energies leads to constructive or destructive interference, and the resulting perturbed line shape is characterized by Raman spectral parameters like ωo, FWHM, and αR. In this case, the possible quasi-electronic continuum is provided by exciton energies, and the same can be understood as follows. The room-temperature PL spectrum of MoS2 nano-flakes (Figure 1c) shows two peaks at ∼1.9 and ∼2.2 eV corresponding to A and B excitons, respectively, arising due to transitions at the K point of the Brillouin zone.15,57 It means that the discrete phonon modes can interact with this excitonic quasi-electronic continuum that can manifest itself as asymmetric Raman line shape as observed in Figure 2.

To further validate the presence and quantify the extent of electron–phonon interaction strength, theoretical fitting of experimentally obtained Raman spectra corresponding to E12g and A1g has been done using the Fano–Raman line-shape function52,58 (eq 3) mentioned below

graphic file with name pg2c00021_m003.jpg 3

where ε = {(ω – ωo)/(Γ/2)}, ωo and Γ denote the phonon frequency and line width, respectively, and q is the Fano parameter and is the inverse of strength of electron–phonon coupling in any given system. Figure 3a,b shows experimentally obtained Raman spectra (discrete data points) for E12g and A1g modes of MoS2, respectively, fitted with the theoretical Fano–Raman line shape function (solid lines) represented by eq 3, for the two excitation wavelengths, namely, 633 and 532 nm. Figure 3 shows a good fit between the experimental Raman data and theoretical line-shape function (Fano–Raman equation) meaning a corroboration between the experimental data and the hypothesized Fano interaction. The values of q obtained, corresponding to the best fit, for both the E12g and A1g modes for 633 and 532 nm laser have been listed in Table 1. The trend of q versus λexc shows the typical Fano-type wavelength dependence as shown in systems containing Fano interference55,59 and is governed by eq 4

graphic file with name pg2c00021_m004.jpg 4

where λo is the critical point energy corresponding to the electronic excitation at k = 0 in the band structure of MoS2 and λexc is the energy of laser excitation. The value of λ0 has been estimated by analyzing the wavelength-dependent trend (by extrapolating the trend) which comes out to be ∼2.91 eV.

Figure 3.

Figure 3

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Theoretical fitting (solid lines) of experimentally observed Raman spectra (discrete points) of MoS2 nano-flakes corresponding to E12g mode (a) and A1g mode (b) recorded using 633 and 532 nm laser excitation represented in red and green colors, respectively.

Table 1. Estimated Fano Parameters (q) for E12g and A1g Modes for Different Excitation Wavelengths Obtained from Theoretical Fitting (Using eq 3) of Different Raman Spectra in Figure 3.

excitation wavelength (nm) q for E12g mode q for A1g mode
633 –7 ± 0.35 7 ± 0.35
532 –12 ± 0.5 12 ± 0.5
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The dependence of the electron–phonon coupling parameter on the excitation wavelength arises from the fact that the electronic continuum generated by A and B excitons depends on the excitation wavelength, and hence, the extent to which this continuum interacts with the discrete phonon also gets affected. A stronger Fano interaction (measured through a smaller q value) for a higher excitation wavelength is a clear signature of the presence of Fano resonance in the system.

Overall, the observed asymmetric Raman line shapes and their dependence on the excitation laser wavelength are due to the exciton quasi-continuum and phonon interaction as quantified using the Fano asymmetry parameter. The asymmetry in Raman line shape for the E12g mode is toward the lower-wavenumber side (higher half width is less than the lower half width) along with the negative q value, representing a destructive interference between the electron continuum and discrete phonon mode. On the other hand, the asymmetry toward the higher-wavenumber side (higher half width is more than the lower half width) and a positive value or Fano parameter q obtained for the A1g mode correspond to the constructive coupling of the electronic continuum with the discrete phonon.60

Conclusions

An asymmetric Raman line shape has been observed from MLMNs due to Fano interaction. Both the characteristic Raman modes of MLMNs, E12g and A1g, exhibit asymmetric spectral line shape and show good fit with the theoretical Fano–Raman line-shape function giving the first indication of possible Fano interaction. The presence of Fano interaction has been validated using wavelength-dependent variation in the Raman line shape which shows stronger Fano coupling for longer wavelengths, a typical observation from any system that possesses Fano interaction. The asymmetric Raman line shape obtained using 633 nm laser excitation is compared with the 532 nm one, and a smaller value of q, the Fano parameter that quantifies the coupling strength, was obtained for 633 nm excitation than for 532 nm, which validates the typical wavelength dependence of Fano interaction. The interaction is likely taking place between the quasi-continuum present by means of A and B excitons and the discrete vibrionic levels. Varying electronic continuum due to different laser excitations appears to be the most likely reason for such wavelength-dependent electron–phonon interaction. Raman line shape analysis, carried out at two different wavelengths, proves to be helpful in gaining an understanding of electron–phonon interaction in 2D materials which may help in better device design and in understanding carrier dynamics. A similar study could be extended for various 2D materials like MoS2 monolayers, WS2, etc. to understand the phonon mechanism in 2D materials.

Acknowledgments

Authors acknowledge financial support from the Science and Engineering Research Board, Govt. of India (Grant no. CRG/2019/000371). Authors are thankful to Er. Nitin Upadhyay for technical support. One of the authors (L.B.) acknowledges the Council of Scientific and Industrial Research (CSIR) for financial assistance [file no. 09/1022(12309)/2021-EMR-I]. Authors T.G. and M.T. acknowledge IIT Indore and the Department of Science and Technology (DST), (file DST/INSPIRE/03/2018/000910/IF180398), Government of India, for providing fellowships. Author C.R. acknowledges the DST (DST/INSPIRE/03/2019/002160/IF190314), and author S.K. acknowledges the UGC (Ref. 1304-JUNE-2018-513215), Govt. of India, for providing fellowships. Facilities received from the DST, Govt. of India, under the FIST scheme (grant number S.R./FST/PSI-225/2016) are highly acknowledged. S. Rani is thankful to DST, New Delhi for the financial aid. I. Sameera & R. Bhatia are thankful to DST, New Delhi (India) for the research grant in the form of Inspire Faculty Awards [DST/INSPIRE04/2017/002776 & DST/INSPIRE/04/2015/000902]. We thank Department of Science and Technology, New Delhi for providing XRD facilities (FIST scheme SR/FST/PSI-089/2005).

Glossary

Abbreviations

FET

field-effect transistor

fwhm

full width at half-maximum

MLMNs

multi-layered MoS2 nanoflakes

The authors declare no competing financial interest.

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