Impact of energy filtering and carrier localization on the thermoelectric properties of granular semiconductors

Energy filtering has been widely considered as a suitable tool to increase the thermoelectric performances of several classes of materials. In its essence, energy filtering provides a way to increase the Seebeck coefficient by introducing a strongly energy-dependent scattering mechanism. Under certain conditions, however, potential barriers may lead to carrier localization, that may also affect the thermoelectric properties of a material. A model is proposed, actually showing that randomly distributed potential barriers (as those found, e.g., in polycrystalline films) may lead to the simultaneous occurrence of energy filtering and carrier localization. Localization is shown to cause a decrease of the actual carrier density that, along with the quantum tunneling of carriers, may result in an unexpected increase of the power factor with the doping level. The model is corroborated toward experimental data gathered by several authors on degenerate polycrystalline silicon and lead telluride. - Graphical abstract: In heavily doped semiconductors potential barriers may lead to both carrier energy filtering and localization. This may lead to an enhancement of the thermoelectric properties of the material, resulting in an unexpected increase of the power factor with the doping level. Highlights: ► Potential barriers are shown to lead to carrier localization in thermoelectric materials. ► Evidence is put forward of the formation of a mobility edge. ► Energy filtering and localization may explain the enhancement of power factor in degenerate semiconductors.