Diffusion-limited exciton-exciton annihilation in single-walled carbon nanotubes: A time-dependent analysis

Abstract

To provide physical insight into the recently observed photoluminescence saturation behaviors in single-walled carbon nanotubes implying the existence of an upper limit of exciton densities, we have performed a time-dependent theoretical study of diffusion-limited exciton-exciton annihilation in the general context of reaction-diffusion processes, for which exact treatments exist. By including the radiative recombination decay as a Poissonian process in the exactly-solvable problem of one-dimensional diffusion-driven two-particle annihilation, we were able to correctly model the dynamics of excitons as a function of time with different initial densities, which in turn allowed us to reproduce the experimentally observed photoluminescence saturation behavior at high exciton densities. We also performed Monte Carlo simulations of the purely stochastic, Brownian diffusive motion of one-dimensional excitons, which validated our analytical results. Finally, we consider the temperature-dependence of this diffusion-limited exciton-exciton annihilation and point out that high excitonic densities in SWNTs could be achieved at low temperature in an external magnetic field.

6 pages, 4 figures

References in corpus (5)

• Stepwise Quenching of Exciton Fluorescence in Carbon Nanotubes by Single Molecule Reactions
• Photon Antibunching in the Photoluminescence Spectra of a Single Carbon Nanotube
• Diameter and Chirality Dependence of Exciton Properties in Carbon Nanotubes
• Magnetic Brightening of Carbon Nanotube Photoluminescence through Symmetry Breaking
• Nonlinear Photoluminescence Excitation Spectroscopy of Carbon Nanotubes: Exploring the Upper Density Limit of One-Dimensional Excitons

Cited by in corpus (13)

• Uncooled Carbon Nanotube Photodetectors
• Statistical mechanics of the coagulation-diffusion process with a stochastic reset
• Exciton diffusion, end quenching, and exciton-exciton annihilation in individual air-suspended carbon nanotubes
• Existence of an upper limit on the density of excitons in carbon nanotubes by diffusion-limited exciton-exciton annihilation: Experiment and theory
• High efficiency dark-to-bright exciton conversion in carbon nanotubes
• Asymptotic exchange coupling of quasi-1D excitons in carbon nanotubes
• Polarization dependence of coherent phonon generation and detection in highly-aligned single-walled carbon nanotubes
• Exact two-time correlation and response functions in the one-dimensional coagulation-diffusion process by the empty-interval-particle method
• Exact correlations in the one-dimensional coagulation-diffusion process by the empty-interval method
• First-passage theory of exciton population loss in single-walled carbon nanotubes reveals micron-scale intrinsic diffusion lengths
• Configuration space method for calculating binding energies of exciton complexes in quasi-1D/2D semiconductors
• Cross-over between diffusion-limited and reaction-limited regimes in the coagulation-diffusion process
• Exact correlation functions in particle-reaction models with immobile particles