Chemistry Reference
In-Depth Information
Fig. 2. The vibration of K point phonon. Two sub-lattice atoms move circularly in
opposite directions.
graphite, diamond, poly-aromatic compounds, fullerenes and carbon nan-
otubes.
8
It has been used uniquely to identify the number of graphene
layers. Raman fingerprints of single and bilayer graphene are different and
have been investigated by many groups.
38-45
The symmetry allowed E
2
g
mode at Γpoint, usually termed as G mode, appears at
1583 cm
−
1
.Other
∼
1350 cm
−
1
(D mode), 1620 cm
−
1
(D
mode),
2680 (2D or D
∗
mode), 2950 (D+G), 3245(2D
) and 4290 cm
−
1
(2D+G).
The mode at
Raman modes seen are at
∼
1350 cm
−
1
, termed as D mode, is disorder activated mode
associated with the TO branch near the K point.
Raman signatures of number of layers in the sample are reflected not
in the G-band but in the line shape of the 2D band.
38-40,44,45
This occurs
because Raman scattering from phonons occurs via electronic states, giving
rise to double resonance Raman process.
46,47
In Fig. 3 we have shown the
second order Raman process for the 2D band in single layer graphene. The
Raman tensor (R) can be written in the fourth order perturbation theory
as:
46
∼
=
a,b,c
M
er
M
e−ph
M
e−ph
M
er
R
(1)
(
E
I
−
E
ai
−
iγ
e
)(
E
I
−
ω
ph
−
E
bi
−
iγ
e
)(
E
I
−
ω
ph
−
ω
ph
−
E
ci
−
iγ
e
)
M
s are the matrix elements. It can be seen from Fig. 3(a) that
there are four steps involved in the second order Raman process. (1) elec-
tron - radiation interaction with matrix element
Here
M
er
, (2) electron-phonon
)tran-
interaction (
M
e−ph
) making a phonon assisted inter valley (
K → K
sition, (3) electron-phonon interaction (
M
e−ph
) making a phonon assisted
