Optoelectronics with Carbon Nanotubes

inding energy for perpendicular excitation than for parallel excitation, which is responsible for
the blue shift 139 . On the contrary, in our data, no blue shift is observed in the E12 transition
(Figure III-16 (b)). A theoretical work by Uryu et al. predicts a large blue shift of the E12 peak
that depends on the strength of the Coulomb interaction in SWNTs 133 ; their results show that in
the absence of a strong Coulomb interaction, E12 is close to (E11 + E22)/2. In the PL
measurements in which large blue shifts were observed in transverse polarization, the tubes were
suspended structurally or kept in a surfactant suspension in order to reduce interaction with the
environment. In contrast, our devices are directly on the substrate, which significantly increases
the dielectric constant of the environment that screens the Coulomb interaction. In our analysis,
ε = 3.3 is used which includes ε = 3.9 of the silicon oxide substrate. This significantly reduces
the Coulomb interaction in the CNTs on substrate, which could account for the absence of a blue
shift of the E12 transition.
Lastly, E12 and E21 transitions are degenerate in the single-particle framework, but this no
longer applies if the asymmetry between valence and conduction bands are taken into account
140 . Miyauchi et al. has found about a 100 meV difference between the two peaks in
perpendicular excitations 30 . However, as has been discussed, all excitonic peaks are
significantly broadened and we are not able to determine whether what we consider the E12
transition is actually a double peak consisting of E12 and E21 signatures.
64