Optoelectronics with Carbon Nanotubes

Figure III-9. The temperatures of three different phonon modes as a function of
power measured by Steiner et al. K and G are zone-boundary phonons and optical
phonons, respectively. Notice the saturation-like behavior for acoustic phonons (red
squares) above 25 W m -1 . After Ref. 112.
Another clue that suggests temperature saturation in the higher bias regime comes from
EL spectra of the high-energy E11 peaks (~0.8 eV, see Figure III-10) from two of our CNTFET
devices. Judging from the energy of the main peak, the CNTs used for these have smaller
diameters than that of Figure III-4. When the main peak is fit as Lorentzian and the background
as blackbody, we can extract the temperature corresponding to the blackbody temperature that
results from the heating of the nanotubes, which, we assume, represents the “average lattice
temperature”. Blackbody radiation from CNT heating has been reported by several groups (see,
for example, Refs. 86, 121, 122 ). Although there is no well-defined lattice temperature in our case
because the phonons are not in thermal equilibrium, the kinetic energies of the carbon atoms
manifested as the populations of different phonon modes must have an average value. The
heating of the lattice results in the blackbody emission in the infrared. Although the dimensions
of CNTs are outside the thermodynamic limit for the traditional bulk blackbody, it was recently
shown that Planck’s Law explains well the blackbody emission intensity of multi-wall nanotubes
121 . Therefore, we assume that this broad background is blackbody emission resulting from the
“average temperature” nanotube lattice and investigate the temperature of acoustic phonons at
power greater than 40 W m -1 .
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