Minimum length scales for enhancement of the power factor in thermoelectric nanostructures

It is shown, through a comparison of the respective electron density distribution and the density of states (DOS), that there exists an optimal length scale only below which the thermoelectric power factor of nanostructures is enhanced over the bulk value. The comparison is done for an optimal value of the Seebeck coefficient in three, two, and one dimensions for Si/SiGe, Bi(2)Te(3), PbTe, and SrTiO(3) with various scattering mechanisms. It is then concluded that the increase in the magnitude of the integrated DOS and not the change in shape, as is commonly believed, to be most responsible for the increases in the power factor. (C) 2010 American Institute of Physics. [doi: 10.1063/1.3359659]