Improving the Power Factor and the Role of Impurity Bands

The thermoelectric figure of merit, Z, is proportional to the ratio of the power factor to the thermal conductivity. In the past, efforts to improve Z have largely been directed towards reduction of the thermal conductivity by lowering the lattice component, lambda (L). This approach has been so successful that lambda (L) is now sometimes no larger than it is in a typical amorphous material. Any further improvement would require the development of thermoelectric materials with larger power factors. Here, we consider some of the ways in which the power factor might be enlarged. The carrier mobilities and density- of-states effective masses for different semiconductors are reviewed briefly, and the relevance of these properties to the power factor is discussed. It is shown that a semiconductor with the mobility and effective mass of electrons in silicon and with the minimum lattice conductivity might have a ZT value of about 6. Preferential scattering to improve the Seebeck coefficient is then considered. Finally, the effect on the power factor of a modification of the density of states through the introduction of impurity bands is calculated. It is found that such bands are not beneficial when they lie close to the edge of a main band. However, they significantly improve the power factor when they lie several kT from the band edge, and their effect can be enhanced by counterdoping.