  The functionalization of semiconducting single-wall carbon nanotubes (SWCNTs)
with luminescent sp$^{3}$ defects creates red-shifted emission features in the
near-infrared and boosts their photoluminescence quantum yields (PLQYs). While
multiple synthetic routes for the selective introduction of sp$^{3}$ defects
have been developed, a convenient metric to precisely quantify the number of
defects on a SWCNT lattice is not available. Here, we present a direct and
simple quantification protocol based on a linear correlation of the integrated
Raman D/G$^{+}$ signal ratios and defect densities as extracted from PLQY
measurements. Corroborated by a statistical analysis of single-nanotube
emission spectra at cryogenic temperature, this method enables the quantitative
evaluation of sp$^{3}$ defect densities in (6,5) SWCNTs with an error of $\pm$
3 defects per micrometer and the determination of oscillator strengths for
different defect types. The developed protocol requires only standard Raman
spectroscopy and is independent of the defect configuration, dispersion solvent
and nanotube length.
