Optoelectronics with Carbon Nanotubes

elax rapidly to lower non-radiative states 19 . Another factor is an array of phonon modes that
exist in SWNTs; phonons can serve as a valuable measurement tool, but they also make it much
more challenging to understand SWNT optoelectronics. Inelastic scattering of phonons is a
decay mechanism that affects EL and PL efficiency very significantly.
3. Phonon modes in SWNTs
Resonance Raman spectroscopy (RRS) has been a standard tool in the optical
investigation of SWNTs since the first observation of a single-tube RRS in 2001 37 . It is also
commonly used in characterization of bulk samples, but the resonance-dependence of Raman
signal intensities complicates the determination of relative abundance of different tubes. There
are several characteristic phonon modes that are observed in SWNTs using this technique.
Figure I-6 shows an example of phonon dispersion that shows the six branches of phonon modes
in SWNTs. Because of the energy-momentum conservation requirement, one can only observe
phonons near the Γ point in the first order, although secondary processes produce additional
observable peaks. Here, we only discuss some commonly observed modes that are relevant to
PL and EL experiments.
The radial breathing mode (RBM) is the lowest vibrational mode observable in RRS,
ranging in wavenumber from only 100 to 400 cm -1 . It originates from the expansion and
contraction in the radial direction of nanotubes perpendicular to the axis, and is therefore
sensitive to the diameter of the tube. The frequency ωRBM is known to be inversely proportional
to the nanotube diameter; the empirical equation ωRBM = 248 cm -1 nm/d is commonly used to
determine the diameter and even the particular (n, m) assignment of SWNTs on a SiO2 substrate,
as long as the diameter is below ~1.8 nm 37 . For larger diameter tubes, too many SWNTs can be
resonant with the laser energy used in a given Raman measurement, so the identification of a
particular SWNT species is difficult. On the other hand, it is very unlikely that one can get a
strong enough RBM signal from any given individual SWNT if the excitation energy does not
happen to be in resonance with an absorption energy of that specific tube 38 . In addition, larger
diameter tubes have a small ωRBM, so the Raman peak is not easily distinguishable from the laser
excitation line.
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