Enhancement of the thermoelectric figure of merit of Si1−xGex quantum wires due to spatial confinement of acoustic phonons

We have theoretically investigated the thermoelectric figure of merit of Si1−xGex quantum wires rigorously taking into account spatial confinement of both electrons and phonons. The calculations were carried out for cylindrical quantum wires with radius View the MathML source and infinite potential barriers. A significant enhancement of the thermoelectric figure of merit is predicted despite the decrease of the carrier mobility in very narrow-quantum wires. The enhancement is mostly due to the drop in the lattice thermal conductivity caused by the spatial confinement of acoustic phonons and the corresponding increase in phonon relaxation rates. The predicted increase is important for the anticipated applications of Si1−xGex nanostructured materials for high-temperature thermoelectric devices.