Transition level dependence of Raman intensities in carbon nanotubes: Role of exciton decay

We present a direct comparison of intensities of Raman scattering from the radial breathing mode of semiconducting single-walled carbon nanotubes under excitations resonant with different electronic transitions. Incident light frequency in our experiments is tuned to be resonant with either $E_{11}$ or $E_{22}$ transitions. We find that the difference in measured Raman intensities varies from one to several orders of magnitude, depending on the nanotube chiralities. The results are interpreted using the recently developed model for chirality dependence of the Raman cross section and taking into account the difference in decay rates for the exciton states excited by the $E_{11}$ and $E_{22}$ transitions. From our data it follows that the exciton state excited by the $E_{22}$ transition decays $3$ to $10$ times faster than the state excited by the $E_{11}$ transition. This conclusion is supported by the observation that $E_{22}$ Raman excitation profile linewidths are significantly broadened compared to those for $E_{11}$ excitation, which show a two-peak structure. These results provide additional evidence that dark excitonic states and trapping sites may contribute strongly to observed emission decay rates.

Figure 1

Experimental resonance Raman peak intensity (squares) for (a) $E_{11}$ and (b) $E_{22}$ excitation, multiplied by the fourth power of the nanotube radius [and scaled by the optical absorption matrix elements, Eqs. (4, 5)] plotted as a function of the parameter $A$ for specific $(n,m)$ chiralities. The solid line is a fit to the data using Eqs. (6, 7).

Figure 2

Experimental resonance Raman intensities (circles) as a function of excitation energy with theoretical fit (solid line) to the data for (a) $E_{11}$ excitation of (6,5) and (9,1) chiralities with ${\Gamma }_{11}=21\mathrm{meV}$ and $22\mathrm{meV}$, respectively; (b) $E_{22}$ excitation of (6,5) chirality with ${\Gamma }_{22}=90\mathrm{meV}$ (fit using fixed values of RBM frequency and $E_{22}$ from Table ); (c) $E_{22}$ excitation of (9,1) chirality with ${\Gamma }_{22}=79\mathrm{meV}$.

Figure 3

$E_{11}$ excitation profiles for the (9,1) chirality (normalized to peak intensity) from different production batches. Experimental points are shown as circles, with best fit profiles shown as the solid line. Fitting linewidths are as follows: (a) HPR162, ${\Gamma }_{11}=23\mathrm{meV}$, (b) HPR107, ${\Gamma }_{11}=23\mathrm{meV}$, (c) HPR120, ${\Gamma }_{11}=23\mathrm{meV}$.

Figure 4

$E_{11}$ excitation profiles (normalized to peak intensity) for the following chiralities: (a) (5,4), ${\Gamma }_{11}=35\mathrm{meV}$, (b) (6,5), ${\Gamma }_{11}=23\mathrm{meV}$, and (c) (8,3), ${\Gamma }_{11}=23\mathrm{meV}$. Experimental data shown as circles, with a best fit profile shown as the solid line.

Figure 5

$E_{22}$ excitation profiles (normalized to peak intensity) with best fit (solid line) to the experimental data (circles) for a number of chiralities. (a) (12,1), ${\Gamma }_{22}=61\mathrm{meV}$, (b) (10,5), ${\Gamma }_{22}=73\mathrm{meV}$, (c) (9,7), ${\Gamma }_{22}=67\mathrm{meV}$, (d) (10,2), ${\Gamma }_{22}=82\mathrm{meV}$, (e) (9,4), ${\Gamma }_{22}=57\mathrm{meV}$, and (f) (8,6), ${\Gamma }_{22}=74\mathrm{meV}$.

Figure 6

Model $E_{11}$ excitation profiles for the (9,1) chirality (with $E_{11}$ as $1.359\mathrm{eV}$ and RBM frequency as $304{\mathrm{cm}}^{-1}$), showing the effect on observed structure as gamma is varied. (a) ${\Gamma }_{11}=23\mathrm{meV}$, (b) ${\Gamma }_{11}=30\mathrm{meV}$, (c) ${\Gamma }_{11}=35\mathrm{meV}$, and (d) ${\Gamma }_{11}=60\mathrm{meV}$.