• Impedance and Capacitance Measurement of Individual Carbon Nanotubes

We experimentally examined the impedance of individual single wall carbon nanotubes (SWNT) in the frequency range of 40 Hz to 110 MHz. The tubes were assembled as a conducting channel of field‐effect transistor (FET) structures from aqueous suspension using dielectrophoresis. At the low frequency limit the impedance is independent of the frequency and equivalent to real resistance. We observe a sharp conductor‐insulator transition at a crossover frequency of about 2.5 MHz, above which the circuit response becomes capacitive. The extracted SWNT capacitance, ${\mathrm{C}}_{\mathrm{SWNT}},$ of about ${\text{4\hspace{0.17em}10}}^{\text{−14}}\hspace{0.17em}\mathrm{F}\mathrm{/\mu }\mathrm{m},$ is independent of the total real resistance, however the ${\mathrm{C}}_{\mathrm{SWNT}}$ value is larger than that theoretically predicted quantum capacitance ${\mathrm{C}}_{\mathrm{QE}}.$ Within this formalism we estimate that the effective Fermi velocity of charge carriers, ${\mathrm{v}}_{\mathrm{F}},$ for our SWNT is about ${10}^3\hspace{0.17em}\mathrm{m}/\mathrm{s},$ which is about two orders of magnitude below ${\mathrm{v}}_{\mathrm{F}}$ of a perfect tube. Our results agree qualitatively with the theoretical impedance characteristic of a SWNT, and furthermore, they imply that the crossover frequency due to quantum capacitance of a perfect SWNT would fall in the range of about 100 GHz.