The thermoelectric power factor of a semiconductor superlattice with nanoparticle inclusions

We develop a phenomenological theory for cross-plane transport in a semiconductor superlattice (SL) doped with nanostructures to improve the thermoelectric properties. The SL consists of an array of quantum wells equally spaced along a spatial direction separated by narrow barriers, such that, in the presence of inter-well tunneling, a miniband energy structure is established. The semi-metallic ErAs nanoparticles are embedded inside the quantum wells in the process of growth of the SL, as reported in several recent experiments. Their effect on thermoelectric transport is considered through an additional contribution to the electron scattering rate, that is correlated with a process of resonant tunneling through the nanoparticle-semiconductor interface modeled as a Schottky barrier. In a semi-classical approximation of the miniband conduction regime, we calculate the electric conductivity, the thermopower and the power factor as a function of the barrier height and demonstrate the presence of a filtering effect, whereby the Seebeck coefficient is enhanced by the additional scattering.