Measurement of impedance of individual carbon nanotubes

We describe impedance measurements of individual single wall carbon nanotubes (SWNTs) in the frequency range of 40 Hz to 100 MHz. The tubes were assembled on the active channel of field effect transistor (FET) structures from aqueous suspension using dielectrophoresis. The FET channels were made by using photo-lithography. We utilized a resistance-capacitance (RC) lumped element circuit model to describe the observed impedance of the tubes and the corresponding contact resistance. At the low frequency limit the impedance is frequency independent and equivalent to the real resistance. In the high frequency range we observe a sharp conductor-insulator transition at a crossover frequency, above which the circuit response becomes capacitive. The extracted SWNT capacitance, C_SWNT, of about 4 10^-14 F/mum, is independent on the total real resistance, however the C_SWNT value is larger than that theoretically predicted quantum capacitance of a perfect tube. Our observations also indicate that the damping frequency is lower than the theoretically predicted in SWNTs.