Mobility in semiconducting carbon nanotubes at finite carrier density

TL;DR

This paper calculates the mobility of semiconducting carbon nanotubes as a function of carrier density and electric field, revealing complex behaviors like non-monotonic mobility and velocity saturation at certain densities.

Contribution

It provides a detailed analysis of how mobility varies with carrier density, electric field, tube diameter, and temperature in semiconducting nanotubes, including novel insights into velocity saturation phenomena.

Findings

Low-field mobility varies non-monotonically with carrier density.

Drift velocity exhibits negative differential mobility at low densities.

Velocity saturation occurs at a critical density around 0.35-0.5 electrons/nm.

Abstract

Carbon nanotube field-effect transistors operate over a wide range of electron or hole density, controlled by the gate voltage. Here we calculate the mobility in semiconducting nanotubes as a function of carrier density and electric field, for different tube diameters and temperature. The low-field mobility is a non-monotonic function of carrier density, and varies by as much as a factor of 4 at room temperature. At low density, with increasing field the drift velocity reaches a maximum and then exhibits negative differential mobility, due to the non-parabolicity of the bandstructure. At a critical density $\rho_c\sim$ 0.35-0.5 electrons/nm, the drift velocity saturates at around one third of the Fermi velocity. Above $\rho_c$, the velocity increases with field strength with no apparent saturation.