Theory of Raman enhancement by two-dimensional materials: Applications for graphene-enhanced Raman spectroscopy

Abstract

We propose a third-order time-dependent perturbation theory approach to describe the chemical surfaceenhanced Raman spectroscopy of molecules interacting with two-dimensional (2D) surfaces such as an ideal 2D metal and graphene, which are both 2D metallic monolayers. A detailed analysis is performed for all the possible scattering processes involving both electrons and holes and considering the different time orderings for the electron-photon and electron-phonon interactions. We show that for ideal 2D metals a surface enhancement of the Raman scattering is possible if the Fermi energy of the surface is near the energy of either the HOMO or the LUMO states of the molecule and that a maximum enhancement is obtained when the Fermi energy matches the energy of either the HOMO or the LUMO energies plus or minus the phonon energy. The graphene-enhanced Raman spectroscopy effect is then explained as a particular case of a 2D surface, on which the density of electronic states is not constant, but increases linearly with the energy measured from the charge neutrality point. In the case of graphene, the Raman enhancement can occur for any value of the Fermi energy between the HOMO and LUMO states of the molecule. The proposed model allows for a formal approach for calculating the Raman intensity of molecules interacting with different 2D materials.

Introducing Ti-GERS: Raman Scattering Enhancement in Graphene-Mesoporous Titania Films

“…Raman enhancement based on chemical mechanism in graphene has been explained as a resonant Raman scattering process involving electronic states of 2D surfaces. 31 However, in the present case, it should be considered the graphene sensitization of the nanocrystalline titania matrix 32,33 ; silica with exfoliated graphene (green); titania (red); and titania with exfoliated graphene thermally treated at 350°C in air (orange) and 3h at 400°C and further 2h at 450°C under inert atmosphere (blue). b) Bar plots showing the analytical enhancement factors (AEFs) of Rh6G for mesoporous films embedding exfoliated graphene with respect to bare mesoporous silica: silica treated for 2h at 450°C under inert atmosphere (green), titania treated for 2h at 350°C in air (orange) and titania treated for 2h at 450°C under inert atmosphere (anatase phase) with (blue) and without (red) embedded graphene.…”

Understanding and optimising the packing density of perylene bisimide layers on CVD-grown graphene

“…graphene on the Raman signal of organic molecules. 3 It should be noted that this rather defective area of a sample was chosen for display and discussion due to its many interesting features, and that the quality of the graphene/1 films is usually much higher, without defects and with uniform coverage, as indicated in Figure 1c in the main manuscript.…”

“…Since the isolation of single layer graphene by mechanical exfoliation 1 and the subsequent discovery and demonstration of its outstanding electronic 2 and mechanical 3 properties, graphene has attracted an extremely high level of interest. It has been proposed for numerous applications in electronics, 4 photonics, [5][6] sensing, 7 as well as gas barriers 8 and coatings.…”

Reversibility of Graphene‐Enhanced Raman Scattering with Fluorinated Graphene

“…It was shown that GERS exhibits high molecular sensitivity and selectivity, the enhancement depends on the probed molecular vibrational mode, and the Fermi energy of graphene . A theoretical framework that covers all the experimentally observed phenomena was proposed in 2014 . Due to its molecular sensitivity and selectivity, GERS was also suggested for applications in chemical and biological sensing devices …”

“…It is reasonable to expect that for strongly functionalized graphene the conditions for GERS will no longer be fulfilled, because the electronic states (that are also sensitive to sp 3 defects in graphene) are a critical factor in the GERS mechanism. [5,8,9] Graphene with defects has been already studied as a substrate for GERS. It was shown for ozone-treated graphene that for a mild oxidation of graphene the enhancement increased due to p-doping of graphene.…”