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 E11 or E22 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 E11 and E22 transitions. From our data it follows that the exciton state excited by the E22 transition decays 3 to 10 times faster than the state excited by the E11 transition. This conclusion is supported by the observation that E22 Raman excitation profile linewidths are significantly broadened compared to those for E11 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.