Nonquasi-Static Effects and the Role of Kinetic Inductance in Ballistic Carbon-Nanotube Transistors

Nonquasi-static effects in ballistic carbon-nanotube (CN) FETs (CNFETs) are examined by solving the Boltzmann transport equation self-consistently with the Poisson equation. We begin by specifying the proper boundary conditions that should be employed in time-dependent simulations at high speeds; these are the proper boundary conditions for a characterization of the so-called intrinsic transistor, i.e., the internal portion of the device that is unaffected by the source and drain contacts. A transmission-line model that includes both the kinetic inductance (
L
_K
) and quantum capacitance (
CQ
) is then analytically developed from the Boltzmann and Poisson equations, and it is shown to represent the intrinsic transistor's behavior at high frequencies, including a correct prediction of resonances in the transistor's
y
-parameters. Finally, we show how to represent
L
_K
using lumped elements in the transistor's traditional quasi-static equivalent circuit, and we demonstrate that the resulting circuit is capable of modeling the intrinsic behavior of a ballistic CNFET, including the observed resonances, to frequencies beyond the unity-current-gain frequency
fT
. External parasitics can be easily added for an overall compact model of ballistic CNFET operation.