Temperature dependence of the optical excitation lifetime and band gap in chirality assigned semiconducting single-wall carbon nanotubes

The temperature dependence of optical excitation lifetime $1∕\Gamma$ and transition energies $E_{ii}$ were measured for bucky papers of single-wall carbon nanotubes (SWCNTs) and inner tubes in double-wall carbon nanotubes (DWCNTs) using resonant Raman scattering on the radial breathing mode. The temperature dependence of $\Gamma$ and $E_{ii}$ is the same for both types of samples and is independent of tube chirality. The data suggest that electron-phonon interaction is responsible for the temperature dependence of $E_{ii}$ and $\Gamma$. The temperature independent contribution to $\Gamma$ is much larger in SWCNT than in DWCNT samples. This is explained by the different nanotube environment in the two types of samples. $\Gamma$ for the inner tubes of the DWCNTs is only $\sim 30\mathrm{meV}$ below $150\mathrm{K}$, which is comparable to that found for individual SWCNTs and is considered as intrinsic to the tubes.

Figure 1

(Color online) Energy dispersive Raman contour plot for SWCNT (CoMoCat) and DWCNT samples at $80\mathrm{K}$. The vertical bar shows the color coding for the observed intensities on a logarithmic scale in arbitrary units. Lower panels show individual Raman spectra with $2.10\mathrm{eV}$ laser energy.

Figure 2

Raman resonance profile for the $(6,4)$ tubes in the SWCNT (CoMoCat) and DWCNT samples $∎$: $80\mathrm{K}$, $엯$: $300\mathrm{K}$, $▴$: $600\mathrm{K}$. Solid curves show fits with the RRS theory. Dashed curve is a simulation for the $80\mathrm{K}$ SWCNT data with $\Gamma =10\mathrm{meV}$. Arrows indicate the incoming and outgoing resonance energies. Note the much narrower widths for the DWCNT sample.

Figure 3

Temperature dependence of the optical transition energy shift $E_{22}\left(T\right)-E_{22}\left(80\mathrm{K}\right)$ and the damping parameter $\Gamma$ for the $(6,5)$ and $(6,4)$ inner tubes of DWCNTs, HiPco tubes, and CoMoCat tubes. Open and closed symbols are for the $(6,4)$ and $(6,5)$ tubes, respectively. $▵$: CoMoCat, $◻$: HiPco, $엯$: DWCNT. Solid curves are calculated values of $\Gamma \left(T\right)$ as explained in the text. Dashed curve is the calculated redshifting $E_{22}$ for a $(6,5)$ tube as explained in the text. Representative error bars for both parameters are shown. The error bars are similar to the symbol size for $\Gamma \left(T\right)$ of inner tubes.