Chapter 2. Graphene
2.2 Electrical and Optical Properties
2.2.2 Optical Properties
One of the biggest reason graphene research became active was the observation of graphene on SiO2/Si wafer by optical microscope (Figure 2.2). Thickness of single layer graphene is 0.2 nm, which is an atomic thickness. It is very unusual to see atomic thickness using an optical microscope with a wavelength of several hundred nm. It is possible to observe with an optical microscope by the interference effect of light by multiple reflection of graphene and SiO2/Si wafer. One of the other properties is that the transmittance of single layer graphene is as high as 97.7%. The transparency of graphene is reduced by exactly 2.3% depending on the number of layers of graphene. So, the
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graphene placed on SiO2/Si wafers can be identified through optical contrast because the contrast changes with graphene layer. The change in the intensity of the absorption spectra is hardly changed in the wavelength range of 300 to 2500 nm. About 0.1% of the incident light in the visible region is reflected from the surface of the single layer graphene. However, it is known that the graphene has a strong absorption characteristic in the ultraviolet region of 200 nm due to the van Hove singularity.
The linear dispersion relationship of Dirac point in graphene means that light of any wavelength can always generate electron-hole pairs. However, the amount of light absorbed depends on the number of photons, not infinity and exhibits nonlinear saturation absorption characteristics. When very few
1500 2000 2500 3000
5000 10000 15000 20000
Raman shift (cm-1) Count
D-mode
G-mode
2D-mode
E 2g A 1 ’
(a)
(b)
Figure 2.3 (a) Raman spectra of graphene. The spectra shows high G-mode and 2D-mode and almost no D-mode. (b) The vibration of G-mode (left) and D-mode (right). Both mode shows a symmetrical vibration.
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photons are incident on graphene, the electrons at the bottom of the Dirac point are excited by the incident photons and move up the Dirac point. The excited electrons lose energy by the two- phonon process. As the number of photons increases, the generated electrons are not allowed to excite more electrons by the principle of Pauli exclusion principle. Thus, the next incident light of a specific wavelength is transmitted through the graphene without being absorbed, which is a reason why it has a high transmittance.
Figure 2.4 (a) Dispersion of phonon energy in graphene [6]. The phonon energy is shown according to the high symmetry points Γ, K and M in the reciprocal lattice Raman scattering process of G-mode (b), 2D-mode (c) and D-mode (d) [23, 24].
(a)
(b) (c)
(d)
G-mode 2D-mode
D-mode
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Information about structure of graphene can be confirmed by using Transmission electron microscopy (TEM) or Scanning tunneling microscope (STM). However, these equipment is difficult to analyze in large area and requires much time to prepare samples. On the other hand, Raman spectroscopy using the optical properties of graphene is the most essential spectroscopic method for graphene research because it can give information about the structure easily and quickly with large area in a non-destructive method. The points of Γ, K, M for the reciprocal lattice are highly symmetric.
Figure 2.4 (a) shows the energy dispersion along the phonon wave vertices for Γ, K, and M in the reciprocal lattice. At points Γ and K, the first derivative of the wave vector is discontinuous. In general, Raman spectroscopy analyzes the energy and symmetry of phonons and obtains information about the crystal structure of the material. When the incident light or scattering light has an energy corresponding to the energy gap existing in the material, a resonance phenomenon occurs in which the Raman signal appears largely. In the case of graphene, the electronic band structure is conical, so that incident light is absorbed over a fairly wide range of energies. This is why a reasonably strong Raman signal can be observed even though graphene is an atomic layer. The resonance phenomenon also provides information on the electronic structure of graphene from Raman spectroscopy. The information obtained from the Raman spectra of graphene is 1350 cm-1 (D-mode), 1580 cm-1 (G-mode) and 2700 cm-1 (2D-mode) (Figure 2.3). The G-mode is a peak commonly found in graphite materials and is called the G-mode. The G-mode corresponds to a mode in which hexagonal carbon atoms vibrate in opposite directions to adjacent carbon, as in Figure 2.3 (b), and has a symmetry of E2g
vibration. This mode corresponds to the case where Raman scattering is possible by symmetry, so it is observed in the primary scattering. As shown in Figure 2.4 (b), the incident light excites the electrons of the valence band into the conduction band, and the excited electrons emit light of energy reduced by the energy of phonons and combine with the holes formed in the original valence band. The difference in energy between the incident light and scattered light corresponds to the phonon energy.
In the case of D-mode, the peak due to crystal defect is observed in the case of graphene. The D-mode is caused by the A1' vibration mode as shown in Figure 2.3 (b), which can’t be observed with Raman scattering in a perfect lattice structure due to symmetry. When the A1' symmetry is broken, D-mode occurs, which means that a hexagonal defect has occurred. So, it is commonly used as an indicator of defects in graphene. The 2D-mode is generated by a two-photon process in which two phonons in D- mode are emitted. The incident light excites the electrons of the valence band into conduction band.
The excited electrons emit phonons and scatter at the other K points (K '). The excited electrons emit phonons of the same energy and return to the original reciprocal lattice and emit light while bonding with the hole left in valence band. Since the 2D-mode emits two phonons at point K instead of point Γ due to the law of momentum conservation, 2D-mode can always be observed unlike D-mode.
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