The dc electrical conductance of ballistic conductors is known to be quantized in units of e2/h. In this paper, we present our measurements of the finite frequency (GHz) electrical conductivity of individual single walled carbon nanotubes (SWNTs). In contrast to the dc conductance, the finite frequency conductance is poorly understood with very little data on which to base realistic models. We have predicted  that the inductance of a 1d quantum wire is approximately 10,000 times larger than expected based on the device dimensions, due to the 1d quantum properties of the system. Additionally, most 1d quantum wires (such as our SWNTs) are capacitively coupled to a nearby gate. We present modeling and measurements of the effects of this kinetic inductance and electrostatic capacitance, as well as the quantum capacitance, on the dynamical impedance of SWNTs. Our measurement technique uses a microstrip coupling circuit to measure the microwave reflection up to 20 GHz ! of individual SWNTs grown by chemical vapor deposition. We measure the complex, frequency dependent microwave reflection coefficient. Using standard microwave network analysis, we determine the nanotube dynamical impedance as a function of frequency, including both the real (i.e. dissipative) and imaginary (i.e. non-dissipative or inductive/capacitive) components, as in . We present RF coupling techniques which address the challenge of measuring devices with high impedances, of order the resistance quantum, at high frequencies. While our measurements are on passive nanotube circuits, the results are important in order to understand, characterize, and control the electronic circuit properties of both freely suspended carbon nanotube nanoelectromechanical RF resonators, as well as the ultimate speed limits of active nanotube transistors.
 Burke, et al, Appl. Phys. Lett. 76(6), 745-747 (2000).
 Burke, IEEE Transactions on Nanotechnology, 2(1), 55-58 (2003).
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