Optoelectronics with Carbon Nanotubes

By plotting the current as a function of VDS, we can estimate the threshold drain voltage
necessary to overcome Schottky barriers in this particular device, as in Figure III-6 for the data
corresponding to the spectra in Figure III-4, and from which a ~3.5 V threshold voltage is
inferred. The non-linear part as VDS approaches zero was not recorded for this device, but is
expected to resemble the non-linear behavior at small VDS in Figure III-5.
Figure III-6. Average current as a function of applied VDS from the same
measurement as in Figure III-4. Both have been converted to absolute values. The
dotted line is a linear fit and is extrapolated to zero current to show the threshold
voltage of ~3.5 V necessary to overcome the Schottky barrier.
Even though the current threshold is ~3.5 V, the light emission does not occur until |VDS|
= 4.9 V (see Figure III-4 inset), suggesting that the field strength does not immediately reach the
critical value for impact excitation. The field needs to be large enough to accelerate injected
carriers to a kinetic energy sufficient for exciton production. The threshold energy should at
least be equal to E11, but actually it is higher by a factor of ~1.5 because of the energy-
momentum conservation requirement 110 and can be relaxed somewhat depending on the
interaction with the environment such as the substrate 111 . Details of the field at Schottky barrier
at various applied biases can be mapped by high-resolution photovoltage imaging 70 , which is
beyond the scope of this work. Given the channel length of ~0.5 μm for this device and the
estimated threshold drain voltage of 4.9 V, the onset field is at least 10 V/μm, and most likely
higher because the potential drop is not uniformly distributed across the channel in the presence
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