Optoelectronics with Carbon Nanotubes

phonon temperature in broadening. Steiner et al. found phonon temperatures to be proportional
to input power 112 , and using this parameter also allows us to compare different devices with
different I-VDS characteristics. The spectrum in Figure III-4 is fit with a following equation,
A{ [1 ( x x )]}
f ( x) y
0
{ [1 (
x
2
x0)]} 0
( x
2
x0)
48
(Eq. III.1)
where x is the photon energy. Equation III.1 is a modified form of the Lorentz distribution to
account for asymmetry in the spectrum with the parameter η 113 . Γ is the equivalent of half-
width-at-half-maximum (HWHM) in the Lorentz function. Figure III-8 shows the FWHM as a
function of applied power calculated as the product of VDS and IDS. We find that a linear
function fits the data reasonable well.
Figure III-8. Electroluminescence spectrum width as a function of power and a linear
fit (solid line), showing a minimum width at zero power of 170 meV for this device.
The vertical axis corresponds to FWHM(2Γ) from the fit shown in Figure III-4, which
comes from Equation III.1.
One of the most salient characteristics of the spectrum is its broad width. In room-
temperature photoluminescence experiments, the single-tube width is significantly smaller than
kBT (~25 meV) 114-116 , which agrees with the low acoustic phonon scattering rate in CNTs. One