Thermionic phenomena in a nanoscale ring without carrier reservoirs: A thermionic couple

Abstract

We have studied various thermionic processes in a small one-dimensional ring consisting of a metallic wire and an insulator which serves as the potential barrier for the charge carriers in the metallic wire. The ring is not connected to any particle reservoir, but at the two junctions it is attached to two phonon reservoirs with different temperatures. The lengths of both the metallic wire and the insulating part are shorter than the carrier mean free path, and therefore the nonequilibrium electron distribution function was solved using the Boltzmann-equation approach with electron-phonon interaction at the two junctions. We found that there is always a heat current flowing from the hot junction to the cold one. The electric current over the potential barrier increases monotonically as the Fermi energy in the metallic wire approaches the potential barrier height from below. Using a modulation doped semiconductor ring for numerical calculation, the thermionic current is found to be almost linear with respect to the temperature difference between the two junctions. Consequently, our system can be developed into a nanometer scale thermionic couple.