Determination of the Exciton Binding Energy in Single-Walled Carbon Nanotubes

We report that measurements of the Raman intensity versus applied voltage are sensitive to filling of the density of states and enable us to measure the second band gap in specific semiconducting single-walled carbon nanotubes (SWNTs). Raman scattering preferentially selects sets of SWNTs whose excitonic transitions are resonant with the incident or scattered photon energies. Simultaneous measurement of the electronic gap and exciton resonance allows us to infer binding energies for the exciton of $0.49\pm 0.05$ and $0.62\pm 0.05\mathrm{eV}$ for tubes of $(10,3)$ and $(7,5)$, respectively. Metallic SWNTs exhibit no excitonic feature.