Raman spectroscopy

Raman spectroscopy is probably the most powerful, non-destructive technique used to characterize graphene and layered materials[70]. This technique is based on the detection of photons inelastically scattered by phonons. When a photon of energy ~ωph impinges on a sample, an electron may be excited from the ground state at energy E_GS to a state at energy E_GS+ ~ωph. This excited state can be either real, leading to resonant Raman spectroscopy or virtual, leading to non-resonant Raman spectroscopy. Graphene is a broadband absorber, therefore Raman spectroscopy is always resonant. The radiative recombination of the electron, accompanied by emission of a photon with the same energy as that used for excitation, is defined as an elastic scattering phenomenon and referred to as “Rayleigh scattering”. In an inelastic process, the electron interacts with a phonon before radiative recombination, gaining or reducing its energy of an amount ~Ω. This process is termed “Raman scattering”[71]:

~ωsc.ph= ~ωph± ~Ω (2.20)

being ~ωsc.ph the energy of the scattered photon. If the electron loses energy from the interaction with a photon before recombining, the sign in equation2.20 is minus and the process is called “Stokes”. On the opposite, if the electron gains energy, the process is referred to as “Anti-Stokes”. The Raman spectrum is a plot of the energy difference

2.4 Characterization 25

between the incident and scattered photon energies and the shift is usually expressed in cm⁻¹. Excitation frequencies used for Raman spectroscopy are typically in the infrared (IR) to ultraviolet (UV) spectral range[71].

Carbon atoms being active in the 800-2000cm⁻¹range make graphene a good candidate for showing prominent features in the Raman spectrum (Fig. 2.14(a))[70, 72]. The G peak is due to the stretching of carbon atoms bonds and it corresponds to the E_2g phonon (Fig. 2.14(b)), whereas the D peak is due to the breathing modes in six-atom rings and thus its origin is related to the A_1g mode. The D peak process is not Raman active in pristine graphene, hence it requires the presence of disorder, edges or defects to be activated[70].

E

A

(a) (b)

Figure 2.14: (a) Raman spectra of pristine (top) and defective (bottom) graphene (from Ref.[70]). (b) Representation of the E_2g and A_1g modes at the origin of the G and

D Raman peak in graphene, respectively

The activation mechanisms are depicted in Fig.2.15. For the G peak there are three steps: a photon from the excitation beam induces the generation of an electron hole couple; consequently, a phonon of momentum q ∼ 0 may scatter the excited electron in a virtual state; this electron can therefore recombine by emitting a photon with different energy[70, 73]. The activation process for the D peak is an intervalley process and it involves a “double resonance” mechanism, described by the following steps[74, 75]:

excitation through light of an electron-hole pair, scattering with phonon while exchanging a momentum q ∼ K, defect scattering event and electron-hole recombination.

A similar process exists also as intravalley, in which case the peak that arises is called D^′. The 2D and 2D^′ peaks are the overtones of the D and D^′ peaks, respectively. Since

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they originate from a process where momentum conservation is satisfied by the presence of two phonons with opposite wave vectors, no defects are required for their activation and this suggests their presence also in the pristine graphene spectrum.

By analysing the Raman spectrum it is possible to immediately distinguish graphene from few-layer graphene and graphite because of the change in intensity and shape of the 2D peak[72]. Specifically, while the single-layer has a single, sharp 2D peak of Lorentzian shape, in multilayer graphene a shoulder appears in the 2D shape, suggesting that more components arise for the peak formation, due to the appearance of additional energy bands[72].

Figure 2.15: Activation mechanisms for peaks in the Raman spectrum of graphene.

Solid black and red lines indicate photo-excitation of electron-hole pairs and radiative recombination, respectively, while dashed and dotted lines indicate phonon and defect scattering, respectively. Taken from Ref.[73].

Other information can be retrieved from the analysis of the position, shape, intensity and area of the peaks. For instance by studying the G peak position and width, and the variation of position, relative intensities and areas with the 2D peak it is possible to estimate the level of doping[73,76]. The intensity of the D peak relative to that of the G peak and their positions and shape will describe the amount of defects in the sample and the presence of edges[64,77].

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The distinction between mono- and few-layer graphene is rather straightforward.

However trying to determine the exact number of layers in few-layer graphene is chal-lenging if only the G and 2D peaks are used. When atomic layers stack one on top of the other, new modes appear in the low frequency Raman spectrum (<200cm⁻¹). These are the shear (C) and layer breathing modes (LBM), corresponding to the relative motion of atoms in adjacent layer[78, 79]. A relation between C, LBM peak positions versus number of layers can be found if atoms within a layer are considered as a single atomic mass and that layers are connected by springs. This is referred to as the linear chain model. Spring constants are named α∥ for C and α⊥ for LBM. The following equations apply[78, 79]: where c is the speed of light in vacuum, µ_m is the single layer mass per unit area and N is the number of layers. In the case of C modes, for instance, Eq.2.21can be applied in the bulk limit to calculate α∥ and then used to build a calibration curve for the number of layers. Eq.2.21 and Eq.2.22 can be extended to all other layered materials[78, 79].

In the high frequencies range h-BN has only one prominent G peak due to the in plane relative motion of boron and nitrogen atoms (E_2g phonon mode)[80]. In the same frequency range MoS₂ shows two prominent peaks: they are assigned to the E¹_2g mode, corresponding to the in-plane relative motion between molybdenum and sulphur atoms and the A_1g mode, due to the out-of-plane motion of sulphur atoms[81, 82]. Their frequency difference has been used to monitor the number of layers (Fig.2.17): E¹_2g shifts to lower frequencies while the A_1g blue shifts to higher frequencies with increasing N [83].

This method is quite powerful to determine thickness in 1L-MoS₂ and 2L-MoS₂, but the E¹_2g-A_1g frequency difference starts to fall within the instrumental precision for >3L-MoS₂ and it is therefore necessary to resort to the C and LBM peaks.

NbSe₂ has the same structure of MoS₂ and it also possesses E¹_2g and A_1g modes.

However the sensitivity of the material to light when exposed to the environment, has made Raman measurements more complicated[84].

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Figure 2.16: (a) Raman spectra of few layer graphene flakes in the frequency region of the C and G peaks. (b) Plot of the C and G peak positions as a function of the inverse number of layers 1/N . Taken from Ref.[78].

Figure 2.17: (a) Raman spectra of MoS₂ for flakes of different thickness. (b) Plot of the E¹_2g and A_1g peak positions (black line) and the relative frequency difference (red line) as a function of the number of layers. Taken from Ref.[83].

2.4 Characterization 29