Confinement of Excitons for the Lowest Optical Transition Energies of Single Wall Carbon Nanotubes

Abstract

he confinement of excitons in a single wall carbon nanotube (SWNT) is discussed based on an analysis of the environmental effect on the optical transition energies, E_ii, measured by photoluminescence spectroscopy. We use the effective dielectric constant κ as a function of nanotube diameter and exciton size that has also been used to reproduce excitonic transition energies E_ii from resonance Raman spectroscopy experiments. When we focus our attention to the lowest transitions, E₁₁ region, we find a systematic deviation of the κ values for semiconducting type-I and type-II carbon nanotubes. We suggest that the E₁₁ energies observed by photoluminescence are upshifted to the calculated E₁₁ energies due to the confinement of excitons in the SWNTs. Considering this effect, the same energy shift formula for the environmental effect as that for the the Raman spectroscopy results can be used to reproduce experimental E_ii values from photoluminescence spectroscopy within a good accuracy, hence providing an accurate assignment of many nanotube chiralities. [DOI: 10.1380/ejssnt.2010.367]