Raman spectroscopy is a widely used characterisation technique, and it is well suited to the study of 2D TMD materials. This method is usually non destructive, it doesn’t require elaborate sample preparation, and it provides much information on the crystal structure, thickness and composition of materials.
When a laser is incident on a sample, it is scattered either elastically or inelastically. These scattering mechanisms are visualised in figure 2.8. Scattering involves an interaction between electrons and photons, whereby an electron is excited from its ground state to a virtual level. Most of the time, the electron relaxes back to its ground state via the emission of a photon of the same energy as the incident light (Rayleigh scattering). However a small fraction of photons (≈1 in 107) interact with the molecular vibrational levels of a sample and are inelastically scattered before relaxation. Stokes scattering involves electrons excited from the ground state, with the emitted photons having less energy (longer wavelength) than the absorbed ones, due to the energy transfer needed to excite the molecular vibrations. Anti-Stokes scattering is the opposite, whereby electrons from an excited state interact, and they relax to the ground state, thus the emitted photons have more energy (shorter wavelength) than the incident photons. The difference in frequency between the absorbed and emitted photons is called the Raman shift, and it is used to produce a Raman spectrum, which is simply a plot of the intensity of the shifted lightversusfrequency.
Each band in a Raman spectrum corresponds to a particular molecular vibra- tion induced by the light. In order for a mode to be Raman active, a change in the molecular polarisation potential, with respect to the vibrational coordinate, is required. If a transition is to be allowed, the symmetry of the wave function in the virtual energy state must be the same as the symmetry of the transition
Virtual energy states Ener gy Ground state 1st Excited state Rayleigh scattering Stokes scattering Ani-Stokes scattering
Fig. 2.8 Schematic of different light scattering mechanisms.
moment operator, otherwise the transition moment integral will be zero. In Raman spectroscopy, the operator transforms as a second order term, which can be found in the far right column in a character table.
IR=ν4I0N ∂ α ∂Q (2.2)
Equation 2.2 is an expression for the intensity of a Raman mode, whereν and
I0are the frequency and intensity of the incident laser radiation respectively, N is the amount of molecules being scattered, Q is the vibrational amplitude andα is
the molecular polarisation potential. Due to the quartic relationship between the intensity of a Raman mode, and the frequency of the excitation source, if there is a close match between the excitation energy and an electronic transition, the intensity of the given Raman mode is considered “resonant”, and it can be greatly increased.
Confocal Raman imaging is a technique whereby a confocal Raman micro- scope rasters along a sample, and acquires a complete Raman spectra at each pixel. A schematic of a confocal Raman microscope is given in fig. 2.9. The spatial resolution of such a system is limited by the spot size of the laser, which is approximately 0.61λ/NA (whereλ is the laser wavelength). For a 532 nm laser
and a 100x objective with a NA of 0.95 the spatial resolution is around 300 nm. This technique lends itself to the creation of Raman maps of a sample, which greatly enhances the power of Raman microscopy.
Fig. 2.9 Schematic diagram of a confocal Raman microscope apparatus, with major components labelled. Figure adapted from WITec GmbH116
(a) (b) 150 200 250 300 350 400 450 500 E12g + A1g + 2LA(M) E12g A1g E12g + 2LA(M) A1g Intensity (a.u.) Raman Shift (cm-1) WS2 WSe2 MoS2 MoSe2 E12g A1g (c)
Fig. 2.10 Schematic drawings of (a) the E12g mode and (b) the A1g mode. (c)
Raman spectra of some TMDs, with modes labelled
Raman spectra of TMDs
Each covalently bonded M-X-M structure in a 2D TMD consists of two planar hexagonal chalcogenide layers, sandwiching a plane of metal atoms. For the 2H polytype, the point group of the chalcogenide atoms is C3v, and that of the metal
atoms is D3h, the irreducible representation of C3vand D3his D6h.117 Therefore
bulk samples have D6hpoint group symmetry. Due to the lack of translational
containing even numbers of layers are D3d,118 while odd number layers (and
monolayers) lack inversion symmetry and the point group is D3h.119There are
two main Raman bands with TMDs, the E12gand A1gpeaks. These are present
in all layered TMD materials with a trigonal prismatic 2H crystal structure,i.e.
both MoS2 and WS2, and the corresponding selenides. The positions of the
bands are unique to each material, because of the different bond strengths and atomic masses. The E12g(E1gfor few layer samples) peak is an in-plane vibration corresponding to the chalcogen atoms vibrating in one direction, with the metal atoms moving in the other. The A1g(A21gfor few layer samples) peak is an out of
plane mode, with just the chalcogen atoms vibrating. These modes are depicted in figure 2.10(a) and (b) respectively. Another prominent feature when excitation is with a 532 nm laser, is a second order zone-edge mode which is resonant with the B exciton of WS2 and the A’ exciton of WSe2.120 This 2LA(M) mode is
longitudinal acoustic, and it occurs at the M point in the Brillouin zone. LA(M) phonons are in-plane periodic compressions and expansions of the lattice that occur along the direction of propagation. Fig. 2.10(c) is a plot showing the Raman spectra of MoS2, WS2, MoSe2and WSe2, with the major Raman features labelled.
It clearly illustrates that different TMDs can be easily identified by their Raman spectra.
Transition to monolayer
The Raman signature of layered materials shows variation with layer number. From bulk to monolayer, the dimensional restriction can be seen in several ways. Liet al.described the evolution of the Raman signal of mechanically exfoliated MoS2 flakes upon reducing the number of layers. They observed an upward
respectively, upon going from bulk crystals to monolayers.46 The blue shift of the E12g band is due to stacking induced structure changes and the decreased dielectric screening of long range Coulombic interactions between the effective charges.46,119The red shift observed in the A1gband is due to decreasing restoring
forces as fewer layers are present.46,80 It is generally accepted that more work is necessary to completely clarify these trends.121
An added advantage is that the Raman apparatus can measure photolumines- cence (PL) which is a signature of the direct bandgap associated with monolayer samples.122Splendianiet al. measured PL spectra for MoS2flakes of different
thickness.123In bulk MoS2, with its indirect bandgap, they observed no PL emis-
sion. However, in few- and monolayer crystals they noted PL emissions at the A1 and B1 direct excitonic transitions, these emissions were particularly strong in the monolayer case due to the direct bandgap.