Exciton Diffusion in Air-Suspended Single-Walled Carbon Nanotubes

Direct measurements of the diffusion length of excitons in air-suspended single-walled carbon nanotubes are reported. Photoluminescence microscopy is used to identify individual nanotubes and to determine their lengths and chiral indices. Exciton diffusion length is obtained by comparing the dependence of photoluminescence intensity on the nanotube length to numerical solutions of diffusion equations. We find that the diffusion length in these clean, as-grown nanotubes is significantly longer than those reported for micelle-encapsulated nanotubes.

Figure 1

(a) A scanning electron microscope image of a typical sample. The scale bar is $1\mu \mathrm{m}$. (b) PL spectra for a carbon nanotube (red curve) and Si substrate (black curve). Blue and green shaded areas indicate the 4 meV wide integration windows that are used to obtain PL images at emission energies of (c) 0.908 eV and (d) 1.116 eV, respectively. The red dot and the black dot indicate the positions of the laser spot where the red and black curves in (b) were taken, respectively. The scale bars in (c) and (d) are $1\mu \mathrm{m}$. For (b)–(d), excitation energy of 1.653 eV and excitation power of 0.36 mW are used. (e) PL excitation map for the same nanotube. Excitation power of $1.5–2.5\mu \mathrm{W}$ is used. The spectra are corrected for the changes in excitation power with tuning of the excitation energy. Inset is the laser polarization angle dependence of the PL intensity showing polarization $p=0.90$ for this nanotube. Blue circles are data and the red line is a fit. Taken at an excitation energy of 1.653 eV and an excitation power of $2.24\mu \mathrm{W}$.

Figure 2

(a) Nanotube emission spectra at excitation powers of $0.47\mu \mathrm{W}$ (circles), $2.32\mu \mathrm{W}$ (squares), and $13.7\mu \mathrm{W}$ (triangles). Data are taken at an excitation energy of 1.553 eV. Data are offset for clarity and lines are Lorentzian fits to data. The same nanotube as in Figs. 1b, 1c, 1d, 1e is used. Panels (b)–(d) show photoluminescence intensity, FWHM of the emission line, and emission energy as a function of excitation power, respectively.

Figure 3

(a) Simulated exciton density spatial profile for $l=0.5\mu \mathrm{m}$ (blue curve), $1.0\mu \mathrm{m}$ (purple curve), and $2.0\mu \mathrm{m}$ (red curve). Exciton diffusion length $L=0.3\mu \mathrm{m}$ is used for obtaining these curves. (b) Simulated PL intensity as a function of $l$ for $L=0.0\mu \mathrm{m}$ (black line), $0.2\mu \mathrm{m}$ (red line), $0.4\mu \mathrm{m}$ (blue line), $0.6\mu \mathrm{m}$ (green line), and $0.8\mu \mathrm{m}$ (orange line).

Figure 4

Panels (a)–(c) show measured PL intensity as a function of nanotube length for $P=0.47$, 2.32, and $13.7\mu \mathrm{W}$, respectively. The solid lines represent the best fits, giving $L=610$, 430, and 280 nm for (a)–(c), respectively. Polarization dependence of the detection efficiency has been corrected. (d) Excitation power dependence of exciton diffusion length. Inset shows $N$ as a function of the excitation power in arbitrary units.