Optoelectronics with Carbon Nanotubes

current, suggesting a local increase in the charge density and an accompanying increase in
screening.
We were also able to compare unipolar emission and emission from a p-n junction from
the same tube. The unipolar emission shows a characteristic spectrum that was discussed in
Chapter III, i.e., an inefficient emission and a large width with a slightly asymmetrical shape.
Since ionization by the external field (which explained the broadening at a very high bias
employed in Chapter III) only accounts for a small fraction of the total width, we calculated the
wave function mixing by Franz-Keldysh oscillation 11, 124 . The effect transfers some of the
oscillator strength to the free-carrier interband transition and mixes this state with the excitonic
wave function. The calculated result reasonably reproduces the experimental spectrum (Figure
IV-5, inset).
While the efficiency was two orders of magnitude greater than what has been observed
from conventional CNTFETs, it is still about two orders of magnitude lower than what has been
reported in photoluminescence. This is attributed to the fact that unlike photo-excitation,
electrical excitation populates dark E11 excitons as well as bright excitons, and that the non-
radiative lifetime is comparatively short because of mechanisms such as exciton-exciton
annihilation and the interaction with the substrate and the top dielectric. Nonetheless, a
suspended, bottom-gated CNT p-n junction should be able to show improved the efficiency. Our
work also marks an important step toward realization of nano-scale device application in carbon
nanotube optoelectronics.
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