Optoelectronics with Carbon Nanotubes

and we still do not know the actual temperature. A direct measurement of the electronic
temperature, perhaps similar to the method used by Steiner et al. 112 , is needed to investigate the
degree of contribution to the broadening by electron heating.
Lifetime shortening due to exciton-exciton annihilation (EEA) also needs to be
considered. EEA is an interaction process between excitons in which the excitation energy is
transferred from one exciton to another, thereby annihilating the first exciton and making the
other exciton a higher-energy exciton (from E11 to E22, for example). Evidence for EEA in
SWNTs has been observed in PL 127, 128 and femtosecond absorption spectroscopy 129 ; a
saturation in intensity and a sudden increase in the linewidth were observed in PL spectroscopy,
for example 127 . Unfortunately, there are too many unknowns (such as the exciton generation
rate by impact excitation and the optical phonon scattering rate) to evaluate quantitatively the
contribution by this process in our devices. However, the lack of saturation in E11 and E22
intensity (Figure III-13 (a), inset) suggests that exciton-exciton annihilation is not a major
contributor to broadening. Since this is a very fast process (800 fs at the linear exciton density of
2 μm -1 127 ) compared to the radiative exciton decay (10 to 100 ns at room temperature 33, 34, 78 ) or
nonradiative decay due to phonons (20 to 200 ps 130 ), if there is Auger-type decay of excitons by
another exciton, we expect to see its signature in the saturation of EL intensity, at least for the
E11 peak (exciton-exciton annihilation of E11 excitons can populate the E22 peak), which is absent
(Figure III-13 (a), inset).
Figure III-13 shows another device in which both E11 and E22 peaks are observed. As
before, we assign E11 based on the diameter distribution of the sample and the fact that it is the
main peak, and E22 from the position of the peak and the fact that it is the second dominant peak
in the spectra. Also, the E22 peak intensity has a higher power threshold than E11, as expected
(see III-13 (a) inset). The energy ratio of E22 to E11 is about 1.8, similar to what has been
observed in PL, which has led to the “ratio problem” discussed in the Introduction. E22 peak is
broader than E11 peak, also expected from a calculation by Qiu et al 27 . E22 transition is expected
to be much broader than E11 because of its coupling to the first free-particle continuum state.
The weak peak appearing at higher VDS between the E11 and E22 peaks is considered to be from
the E12 and/or E21 transitions for the reasons we now examine in the polarization of the EL
emission.
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