Diameter Dependent Resonance Raman Scattering

In the resonance Raman effect, a large scattering intensity is observed when either the incident or the scattered light is in resonance with electronic tran sitions between vHs in the valence and conduction bands Epp(dt) for a given nanotube (n, m) [4,25,27,28,29,55,56,57,58]. In general, the size of the optical excitation beam is at least 1 |im in diameter, so that many nanotubes with a large variety of (n, m) values are excited by the optical beam simultaneously, as is also the case for the optical absorption measurements discussed above. Since it is unlikely that any information on the nanotube chirality distribution is available experimentally, the assumption of equal a priori probability can be assumed, so that at a given diameter dt the resonance Raman effect is sensitive to the width of the Epp(dt) inter-subband transitions plotted in Fig. 5.

In Fig. 13 are plotted the resonance Raman spectra for SWNT samples using (a) NiY and (b) RhPd catalysts. The left and right figures for each sample (see Fig. 13) show the Raman spectra the phonon energy region of the radial breathing mode and the tangential G-bands, respectively [4]. As a first approximation, the resonant laser energy for the RBM spectra, and the G-band Raman spectra are used to estimate the Epp (dt) transition energies, as shown in Fig. 5, with the diameter distribution for each catalyst. When the nanotube diameter values of dt = 1.24-1.58nm and dt = 0.68-1.00nm are used for the NiY and RhPd catalyst samples, respectively, the resonance for the metallic nanotubes Epp(dt) is seen in the laser energy region around 1.6-2.0 eV and 2.4-2.8 eV, respectively. Hereafter we call this region of laser energy, which is resonant with metallic nanotubes, the "metallic window". This metallic window for the Raman RBM intensity is consistent with the optical density of the third peaks as a function of laser excitation energy, as shown in Fig. 14, where for laser excitation energies greater than 1.5 eV, the optical density (absorption) and the Raman intensity of the RBMs are consistent both for the NiY and RhPd catalyzed samples.

The metallic window for a given diameter distribution of SWNTs is obtained by the third peak of the optical absorption, as discussed in the previous subsection, and more precisely by the appearance of Raman intensity at 1540 cm-1 which can be seen only in the case of a rope sample containing metallic nanotubes, where the spectra are fit to a Breit-Wigner-Fano plot [4,27,28,29] as shown in Fig. 2.4.

It is pointed out here that the phonon energies of the G-band are large (0.2 eV) compared with the RBM phonon (0.02eV), so that the resonant condition for the metallic energy window is generally different according to the difference between the RBM and G-band phonon energy. Furthermore, the resonant laser energies for phonon-emitted Stokes and phonon-absorbed anti-Stokes Raman spectra (see Sect. 2.5) are different from each other by twice the energy of the corresponding phonon. Thus when a laser energy is selected, carbon nanotubes with different diameters dt are resonant between the RBM and G bands and between the Stokes and anti-Stokes Raman spectra, which will be described in more detail in the following subsection.

100 150 200 2501400 1500 1600 1700 -1 -1 Raman shift (cm ) Raman shift (cm )

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Raman shift (cm-1) Raman shift (cm"1)

Fig. 13. Resonance Raman spectra for (a) NiY (top) and (b) RhPd (bottom) catalyzed samples. The left and right figures for each sample show Raman spectra in the phonon energy region of the RBM and the tangential G-bands, respectively [4]

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Raman shift (cm-1) Raman shift (cm"1)

Fig. 13. Resonance Raman spectra for (a) NiY (top) and (b) RhPd (bottom) catalyzed samples. The left and right figures for each sample show Raman spectra in the phonon energy region of the RBM and the tangential G-bands, respectively [4]

Fig. 14. Optical density of the absorption spectra (left scale) and the intensity of the RBM feature in the Raman spectra are plotted as a function of the laser excitation energy greater than 1.5 eV for NiY and RhPd catalyzed SWNT samples. The third peaks correspond to the metallic window [3]
Fig. 15. Breit-Wigner-Fano plot for the Raman signals associated with the indicated G-band feature for the NiY and RhPd catalyzed samples [3]. The difference in the fitting parameters in the figures might reflect the different density of states at the Fermi level D(Ef) which have been reported [59]
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