Exponential Decay Lifetimes of Excitons in Individual Single-Walled Carbon Nanotubes

The dynamics of excitons in individual semiconducting single-walled carbon nanotubes was studied using time-resolved photoluminescence (PL) spectroscopy. The PL decay from tubes of the same $(n,m)$ type was found to be monoexponential, however, with lifetimes varying between less than 20 and 200 ps from tube to tube. Competition of nonradiative decay of excitons is facilitated by a thermally activated process, most likely a transition to a low-lying optically inactive trap state that is promoted by a low-frequency phonon mode.

Figure 1

(a) Atomic force microscope image of a spin-coated film containing a single SWNT on glass and (b) cross sectional profile. (c) Confocal PL image of a region around a $(6,4)$ tube. The diffraction-limited central spot at the location of the $(6,4)$ tube is about 700 nm in diameter.

Figure 2

Photoluminescence transients (a)–(c) and corresponding spectra (d)–(f) of three different single $(6,4)$ SWNTs observed after femtosecond pulse excitation at 800 nm. Excited state lifetimes $\tau$ were obtained from a monoexponential fit to the experimental data [solid lines in (a)–(c)] taking into account the measured system response [dashed line in (a)]. The excitation density was $6.0\times {10}^{-4}\mathrm{\text{photons}}/(\mathrm{\text{pulse}}{\mathrm{cm}}^2)$ and sample temperatures were 87 K for (a) and (b) and 67 K for (c). (g) Bar graph of the distribution of measured lifetimes at 87 K.

Figure 3

(a) Temperature dependence of PL lifetimes between 48 K and 182 K for two different $(6,4)$ SWNTs. The excitation density was $4.1\times {10}^{14}\mathrm{\text{photons}}/(\mathrm{\text{pulse}}{\mathrm{cm}}^2)$. The solid line represents a fit using the Bixon-Jortner model [19, 20], while the dashed line corresponds to a simple Arrhenius fit. (b) Evolution of the emission spectrum with temperature for tube 1. (c) Schematic illustration of the potential energy landscape used to discuss the dependence of PL intensities and peak shapes as well as the kinetics of thermally activated nonradiative decay. $E_{11}^{\mathrm{eh}}$ and $E_{11}^X$ denote the first subband free carrier and exciton thresholds, respectively.

Figure 4

Power dependence of PL amplitudes (left) and lifetimes (right) for two different $(6,4)$ SWNTs [(a),(b)] at 87 K. Solid lines serve as a guide to the eye.