Diameter Dependent Optical Absorption

In Fig. 10, the optical absorption spectra of an as-prepared and a purified SWNT thin film sample are shown, respectively, by the solid and dashed curves. Both samples are synthesized using the electric arc method and the NiY catalyst [3]. The three peaks appearing at 0.68, 1.2 and 1.7 eV correspond to the two semiconductor DOS peaks and the metallic DOS peaks discussed in the previous section. When we consider the distribution of nanotube diameters, only the first three peaks of the DOS spectra can be distinguished in relation to the calculation [45], which is consistent with the optical spectra shown in Fig. 10. Since there is no substantial difference in the spectra between the as-prepared and purified samples, we can conclude that the peaks come from the SWNTs. The dotted line denotes the photo-thermal deflection spectrum (PDS) for the same purified sample. The signal of the PDS data is proportional to the heat generated by multi-phonon processes involved in the recombination of the optically pumped electron-hole pairs, and thus the PDS spectra are considered to be free from light scattering by nano-particles [46]. Furthermore, since carbon black is used as a black body reference, the PDS reflects the difference in electronic states between SWNTs and amorphous carbon. These peak structures are more clearly seen in the PDS than in the absorption spectra, while the peak positions are almost the same as in the absorption spectra, which indicates that these peaks are not due to light scattering losses. Thus we understand that the residual nanospheres and metal

Fig. 10. Optical density in the absorption spectra of as-prepared (solid line) and purified (dashed line) SWNT thin film samples synthesized by the electric arc method using a NiY catalyst [3]. The photo-thermal deflection spectrum (PDS, dotted line) is also plotted for the same sample, and the spectral features of the PDS data are consistent with the absorption spectra c

Fig. 10. Optical density in the absorption spectra of as-prepared (solid line) and purified (dashed line) SWNT thin film samples synthesized by the electric arc method using a NiY catalyst [3]. The photo-thermal deflection spectrum (PDS, dotted line) is also plotted for the same sample, and the spectral features of the PDS data are consistent with the absorption spectra

particles in the sample do not seriously affect the optical absorption spectrum in the energy region below 2 eV. This fact is confirmed by the observation of no change in the absorption spectra between purified and pristine samples in which the density of nanoparticles and catalysts are much different from each other.

The purified sample shows a large optical absorption band at 4.5 eV, which corresponds to the n-plasmon of SWNTs observed in the energy loss spectrum [47], which is not so clearly seen in the as-prepared sample. Figure 11 shows the optical absorption spectra of SWNTs with different diameter distributions associated with the use of four different catalysts [3]. For convenience, the large background due to the n plasmon is subtracted. The inset shows the corresponding Raman spectra of the RBMs taken with 488 nm laser excitation. The diameter distributions can be estimated from the peak frequencies using the rule, wrbm rc (1/dt), where dt is the diameter of a SWNT that is in resonance with the laser photons [5,35]. Thus, higher lying Raman

Fig. 11. Optical absorption spectra are taken for single wall nanotubes synthesized using four different catalysts, [3,4] namely NiY (1.24-1.58 nm), NiCo (1.061.45 nm), Ni (1.06-1.45 nm), and RhPd (0.68-1.00 nm). Peaks at 0.55 eV and 0.9 eV are due to absorption by the quartz substrate [3]. The inset shows the corresponding RBM modes of Raman spectroscopy obtained at 488 nm laser excitation with the same 4 catalysts

Fig. 11. Optical absorption spectra are taken for single wall nanotubes synthesized using four different catalysts, [3,4] namely NiY (1.24-1.58 nm), NiCo (1.061.45 nm), Ni (1.06-1.45 nm), and RhPd (0.68-1.00 nm). Peaks at 0.55 eV and 0.9 eV are due to absorption by the quartz substrate [3]. The inset shows the corresponding RBM modes of Raman spectroscopy obtained at 488 nm laser excitation with the same 4 catalysts peaks indicate the presence of smaller diameter SWNTs in the sample. The nanotube diameter distribution can be estimated from the diameter dt dependence of wrbm « 1/dt, once the proportionality between wrbm and one (n, m) nanotube is established, such as for the (10,10) nanotube. Information on the nanotube diameter distribution is available either by TEM or from measurement of the wRBM band for many laser excitation energies Eiaser.

A method for determining E11 (dt) comes from optical spectra, where the measurements are made on ropes of SWNTs, so that appropriate corrections should be made for inter-tube interactions in interpreting the experimental data [29,48,49,50,51,52,53,54]. In interpreting the optical transmission data, corrections for the nonlinear k dependence of E(k) away from the ^-point also needs to be considered. In addition, the asymmetry of the 1D electronic density of states singularities should be taken into account in extracting the energy Epp(dt) from the absorption line shape. Furthermore, the diameter distributions of the nanotubes, as well as the difference in gap energies for nanotubes of different chiralities, but for a given dt, should be considered in the detailed interpretation of the optical transmission data to yield a value for y0. The calculations given in Fig. 5 provide a firm basis for a more detailed analysis.

Another important issue to address here is the so-called antenna effect of nanotubes. Since the diameter of SWNTs is much smaller than the wave length of light, an effective medium theory or other model must be used for describing the dielectric function of the nanotubes within an aligned nanotube bundle, for nanotubes that have an arbitrary polarization with respect to the randomly oriented nanotube bundles, which collectively have an anisotropic £i(w) and e2(w). The optical measurements should determine such fundamental properties for SWNTs.

Kazaoui et al. [24] have reported optical absorption spectra for doped SWNTs as shown in Fig. 12, including both donor (Cs) and acceptor (Br), and they found that the intensity of the absorption peaks decreased, especially for the lower energy absorption peaks with increasing dopant concentration. In the undoped SWNTs, three peaks at 0.68 eV, 1.2 eV and 1.8 eV are found in the absorption spectra in Fig. 12. When the doping concentration x in M^C, (M = Cs, Br) is less than 0.005, the first peak at 0.68 eV decreases continuously in intensity with increasing x without changing the intensity of the second and the third peaks. In subsequent doping in the range 0.005 < x < 0.04, the two peaks of 0.68 eV and 1.2 eV decrease in intensity. At the high doping level shown in Fig. 12b, the peak at 1.8 eV smoothes out and new bands appears at 1.07eV and 1.30eV for CBr015 and CCs010, respectively. These doping-induced absorption peaks may come from the transition between conduction to conduction inter-subband transitions and from valence to valence inter-subband transitions, respectively, for donor and acceptor type SWNTs. The difference between the peak positions 1.07 eV and 1.30 eV for acceptor and donor type SWNTs, respectively, is consistent with the expected magni-

Fig. 12. (a) Optical absorption spectra for Cs and Br doped SWNT samples for various stoichiometries x for CCs^ and CBr^. The entire set of spectra for the CCs^ samples is offset for clarity with a short line indicating the 0 level. * in the figure indicates features coming from the quartz substrate and from spectrometer noise. (b) The absorption spectra for CCs^ and CBr^ for the almost saturated doping regime [24]

Fig. 12. (a) Optical absorption spectra for Cs and Br doped SWNT samples for various stoichiometries x for CCs^ and CBr^. The entire set of spectra for the CCs^ samples is offset for clarity with a short line indicating the 0 level. * in the figure indicates features coming from the quartz substrate and from spectrometer noise. (b) The absorption spectra for CCs^ and CBr^ for the almost saturated doping regime [24]

tude of the asymmetry between the n and n* bands. However, the detailed assignments for the inter-subband transitions which are responsible for the doping-induced peaks are not clear within the rigid band model.

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