We have investigated the photophysical properties of electrochemically gate-doped semiconducting single-wall carbon nanotubes (s-SWNTs). A comparison of photoluminescence (PL) and simultaneously recorded absorption spectra reveals that free-carrier densities correlate well with the first sub-band exciton or trion oscillator strengths but not with PL intensities. We thus used a global analysis of the first sub-band exciton absorption for a detailed investigation of gate-doping, here of the (6,5) SWNT valence band. Our data are consistent with a doping-induced valence band shift according to Δϵv = n × b, where n is the free-carrier density, ϵv is the valence band edge, and b = 0.15 ± 0.05 eV·nm. We also predict such band gap renormalization of one-dimensional gate-doped semiconductors to be accompanied by a stepwise increase of the carrier density by Δn = (32meffb)/(πℏ)(2) (meff is effective carrier mass). Moreover, we show that the width of the spectroelectrochemical window of the first sub-band exciton of 1.55 ± 0.05 eV corresponds to the fundamental band gap of the undoped (6,5) SWNTs in our samples and not to the renormalized band gap of the doped system. These observations as well as a previously unidentified absorption band emerging at high doping levels in the Pauli-blocked region of the single-particle Hartree band structure provide clear evidence for strong electronic correlations in the optical spectra of SWNTs.

Doping by chemical or physical means is key for the development of future semiconductor technologies. Ideally, charge carriers should be able to move freely in a homogeneous environment. Here, we report on evidence suggesting that excess carriers in electrochemically p-doped semiconducting single-wall carbon nanotubes (s-SWNTs) become localized, most likely due to poorly screened Coulomb interactions with counterions in the Helmholtz layer. A quantitative analysis of blue-shift, broadening, and asymmetry of the first exciton absorption band also reveals that doping leads to hard segmentation of s-SWNTs with intrinsic undoped segments being separated by randomly distributed charge puddles approximately 4 nm in width. Light absorption in these doped segments is associated with the formation of trions, spatially separated from neutral excitons. Acceleration of exciton decay in doped samples is governed by diffusive exciton transport to, and nonradiative decay at charge puddles within 3.2 ps in moderately doped s-SWNTs. The results suggest that conventional band-filling in s-SWNTs breaks down due to inhomogeneous electrochemical doping.

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Spectroelectrochemical studies were used to investigate the photophysics of electrochemically doped (6,5) SWNTs. The optical properties of SWNT ensembles were here studied by quasi simultaneous absorption and photoluminescence spectroscopy over the NIR and VIS spectral ranges. This allowed correlating changes in the oscillator strength of first and second subband excitons with changes in the photoluminescence signals from the bright singlet exciton. The data thus provides a key link between photoluminescence quantum yields affecting PL measurements and the extent of SWNT p or n doping as evidenced by absorption spectra. The data also provides evidence for a shift of oscillator strength from exciton transitions to free carrier type transitions in higher lying subbands.