Existence of an upper limit on the density of excitons in carbon nanotubes by diffusion-limited exciton-exciton annihilation: Experiment and theory

Through an investigation of photoemission properties of highly photoexcited single-walled carbon nanotubes, we demonstrate that there is an upper limit on the achievable excitonic density. As the intensity of optical excitation increases, all photoluminescence emission peaks arising from different chirality singlewalled carbon nanotubes showed clear saturation in intensity. Each peak exhibited a saturation value that was independent of the excitation wavelength, indicating that there is an upper limit on the excitonic density for each nanotube species. We propose that this saturation behavior is a result of efficient exciton-exciton annihilation through which excitons decay nonradiatively. In order to explain the experimental results and obtain excitonic densities in the saturation regime, we have developed a model, taking into account the generation, diffusion-limited exciton-exciton annihilation, and spontaneous decays of one-dimensional excitons. Using the model, we were able to reproduce the experimentally obtained saturation curves under certain approximations, from which the excitonic densities were estimated. The validity of the model was confirmed through comparison with Monte Carlo simulations. Finally, we show that the conventional rate equation for exciton-exciton annihilation fails to fit the experimentally observed saturation behavior, especially at high excitonic densities.