Theoretical Investigation of Traveling-Wave Amplification in Metallic Carbon Nanotubes Biased by a DC Field

Traveling-wave amplification along a carbon nanotube (CNT) under dc-ac fields is theoretically investigated. The ac conductivity of a metallic CNT is found with respect to the applied dc bias. For this purpose, the Boltzmann transport equation (BTE) is solved within the relaxation time approximation (RTA) by separating the ac and dc distributions. The problem is solved both exactly and approximately by semianalytical and analytical means, respectively. It is shown that an absolute negative ac conductivity accompanies a negative differential conductivity beyond a threshold dc field of 3 × 10⁵ V/m. The complex propagation factor of the allowed surface wave modes is found by coupling the BTE current with Maxwell´s equations and solving a transcendental equation. The slow-wave factor and attenuation steadily increase with the dc field amplitude. Beyond the threshold field, amplification occurs, which is a promising result toward enabling traveling-wave amplifiers using CNTs. The amplification is shown to be a result of Bloch-type oscillations.