Understanding the Frequency- and Time-Dependent Behavior of Ballistic Carbon-Nanotube Transistors

Abstract

The high-frequency and time-dependent behavior of carbon-nanotube (CN) transistors is examined by numerically solving the time-dependent Boltzmann transport equation self-consistently with the Poisson equation. The two-port admittance matrix, containing the transistor's <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">y</i> -parameters, is extracted. At frequencies below the transistor's unity-current-gain frequency <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">fT</i> , the <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">y</i> -parameters are shown to agree with those predicted from a quasi-static description of transistor operation, provided that the partitioning factor for the device charge is extracted through application of an appropriate time-dependent ramp voltage to the gate. The physics of time-dependent transport is described, and by examining the positive- and negative-going components of electron charge in the nanotube, it is shown for an <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">nin</i> device structure that the <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">n</i> regions <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">can</i> add a time delay to the device response, even though these regions do not affect the transistor's extrapolated <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">fT</i> . For very high frequencies, or for very fast transients, it is pointed out that the conventional ldquofloating boundary conditionrdquo approach, which was originally suggested for dc simulations of ballistic Mosfets, becomes questionable when applied to time-dependent simulations of nanotubes. While this paper omits collisions and focuses on an intrinsic transistor structure that excludes external parasitics, it provides a first useful step toward the full frequency- and time-dependent characterization of CN transistors.