Raman intensity mapping of single-walled carbon nanotubes

We report on the measurement of the Raman intensity of radial breathing modes of a relatively large diameter range of single-walled carbon nanotubes (SWNTs) by confocal Raman scattering. Statistical data analysis yielded an intensity distribution within the excitation width of the single laser line at $2.33\mathrm{eV}$. These measurements were compared to recent nonorthogonal tight-binding calculations on the Raman intensity where a match could be found. The mapping allowed for accurate determination of optical transition energies of the nanotubes and their chirality. Higher $E_{33}^{\mathrm{M}}$ and $E_{55}^{\mathrm{S}}$ optical transitions of both metallic and semiconducting SWNTs could be recorded for which intensity calculations were extended to tube diameters up to $2.6\mathrm{nm}$.

Figure 1

(Color online) (a) Raman intensity distribution of the measured RBM frequencies. (b) Histogram of the measured Raman intensities and diameter distribution measured by atomic force microscopy. (c) Histogram convergence of average counts of two RBM’s upon sampling.

Figure 2

(Color online) (a) Optical transition energies $E_{ii}$ as a function of the tube diameter. Shown in red (dark gray) are a selection of high-intensity SWNTs with respect to the excitation line of $2.33\mathrm{eV}$. The complete set is plotted in the background as a guide to the eye (gray filled circles). All calculated data was rigidly upshifted by $0.43\mathrm{eV}$ (see text). (b) Calculated Raman intensities corresponding to the selected dots in (a). The open dots are calculated maximum intensities. The filled dots were multiplied with a normal distribution function to model the distance (in eV) to the laser line. Numbers in parentheses indicate tube families $(2n+m)$. (c) Converted measured histogram from Fig. 1b. The measured data (open circles) were corrected for sample population independence (filled circles). Only large diameters are shown.

Figure 3

(Color online) $\Delta E_{ii}=E_{ii}-E_{\mathrm{L}}$ optical transitions of semiconducting (top) and metallic (bottom) SWNTs. Squares indicate calculations [red (dark gray) squares define the resonant window] while diamonds represent measured data from the $\Delta E=0$ line.