Layer-number determination in graphene by out-of-plane phonons

Abstract

We present and discuss a double-resonant Raman mode in few-layer graphene, which has not been interpreted before and is able to probe the number of graphene layers. This so-called N mode on the low-frequency side of the G mode results from a double-resonant Stokes/anti-Stokes process combining an optical (LO) and an out-of-plane (ZO ) phonon. Simulations of the double-resonant Raman spectra in bilayer graphene show very good agreement with the experiments.Raman spectroscopy belongs to the most widely used methods in graphene research. Raman spectroscopy is used for characterizing graphene regarding defects 1-3 , doping 4,5 , strain 6-9 , crystallographic orientation 10,11 , or interaction with the substrate 12 . In view of fundamental physical properties of graphene, Raman spectroscopy gives information on electron-phonon coupling and scattering rates, optical excitations in graphene, thermal and mechanical properties [13][14][15] . Probably the most popular application of Raman scattering in graphene is the distinction of single-layer graphene from few-layer graphene and graphite via the lineshape of the double-resonant 2D mode 16 . On the other hand, few-layer graphene has recently come into focus, as gated bi-and trilayer graphene offer a tunable band gap 17,18 and bilayer graphene has been demonstrated to give much higher on-off ratios in a field-effect transistor than single-layer graphene 19 . Therefore, it is important to establish a reliable method for the determination of the layer number in few-layer graphene and to identify spectroscopic signatures of the layer-layer interaction. So far, typically the evolution of the 2D-mode lineshape or the absolute Raman intensity of the G mode is used in combination with optical contrast measurements. However, the lineshape of the 2D mode depends strongly on the excitation wavelength 16 , and the G-mode amplitude depends not only on the scattering volume 20,21 , but also on the substrate and optical interference effects 22 . Recently, the rigid-layer shear mode, which is the other Raman-active E 2g phonon mode in graphite, was shown to have a strong frequency dependence on the number of layers in few-layer graphene 23 . The frequency of this mode, however, is below 44 cm −1 . Measurement of this low-frequency mode is therefore difficult and requires non-standard equipment.

Interlayer resonant Raman modes in few-layerMoS2

“…The reduced representation of the A 2u and B 2g modes in C 3v is A 1 ; E 1u and E 2g reduce to E. This leads to the same possible symmetries for the few-layer graphene phonons as for few-layer MoS 2 with the same point group (see Table III). Again, the acoustic phonons of single-layer graphene lead to the optical shear and layer breathing like modes [35][36][37][38]. The E 2g phonon, which is responsible for the G mode of graphene, has Raman active counterparts of E g /E symmetry in the few-layer structures.…”

Influence of the buffer layer properties on the intensity of Raman scattering of graphene

“…Although the Raman technique is incapable of measuring the thickness of graphene monolayers directly, it enables differentiation of a single layer from the thicker flakes up to a thickness of 10 monolayers. It also distinguishes between monolayers and graphite via the behavior of the vibrational bands of graphene in the regions of 1500–1740 cm −1 and 2500–2900 cm −1 (see Refs …”

Resonant Raman spectroscopy of twisted multilayer graphene

“…The Raman spectrum of graphite and MLG consists of two fundamentally different sets of peaks. Those, such as D, G and 2D, present also in SLG, and due to in-plane vibrations 14,16,17 , and others, such as the shear (C) modes 18 and the layer breathing modes [19][20][21] , due to the relative motions of the planes themselves, either perpendicular or parallel to their normal. The G peak corresponds to the high-frequency E 2g phonon at G. The D peak is due to the breathing modes of six-atom rings and requires a defect for its activation 16,[22][23][24] .…”