Luminescence Decay and the Absorption Cross Section of Individual Single-Walled Carbon Nanotubes

The absorption cross section of highly luminescent individual single-walled carbon nanotubes is determined using time-resolved and cw luminescence spectroscopy. A mean value of $\sim 1\times {10}^{-17}{\mathrm{cm}}^2$ per carbon atom is obtained for $(6,5)$ tubes excited at their second optical transition, and corroborated by single tube photothermal absorption measurements. Biexponential luminescence decays are systematically observed, with short and long lifetimes around 45 and 250 ps. This behavior is attributed to the band edge exciton fine structure with a dark level lying a few meV below a bright one.

Figure 1

(a) Confocal luminescence image of an individual $(6,5)$ nanotube (scale bar is $1\mu \mathrm{m}$). (b) Luminescence spectra recorded before (line) and after (circles) the luminescence decay. (c) Time-resolved luminescence decay from the nanotube shown in (a) and (b). The gray curve represents the instrumental response function. The data were recorded at very low fluence $\sim {10}^{12}\mathrm{\text{photons}}/\mathrm{\text{pulse}}/{\mathrm{cm}}^2$, yielding an average generation of 0.08 exciton per femtosecond pulse and per exciton diffusion range. The decay is fitted by a single [blue line, residuals in (e)] and double [red line, residuals in (f)] exponential function. From the biexponential fit we deduce short and long time constants of 46 and 210 ps, respectively, as well as a short component fractional yield of 78%. (d) Time trace of the luminescence signal recorded while measuring the decay.

Figure 2

(a) Long decay times as function of short ones, deduced from 48 luminescence decays of individual $(6,5)$ SWNTs. (b),(c) The corresponding histograms. Weights of the short decay components (d) and peak emission wavelengths (e) as a function of the short decay times. (f) Three level scheme used in the model.

Figure 3

(a) Luminescence signal of an individual $(6,5)$ nanotube as a function of cw laser intensity (circles: experimental data; solid line: fit using the saturation profile described in the text). The corresponding luminescence decay (circles) and a biexponential fit (red line) are shown in the inset. Knowing the effective decay time of 55 ps, we deduce a resonant absorption cross section of $110{\mathrm{nm}}^2/\mu \mathrm{m}$. (b) Histogram of the absorption cross sections deduced for 27 individual $(6,5)$ SWNTs. Histogram of the photothermal signals measured in the same experimental conditions on nine individual $(6,5)$ SWNTs (c) and 140 individual gold nanoparticles (NPs) with mean diameter of 9.2 nm (d). The Gaussian lines in (b)–(d) are guides to the eye. (e) Plot of the estimated quantum yields as a function of the effective lifetime.