Thermoelectric performance of granular semiconductors

We study the effects of doping and confinement on the thermoelectric properties of nanocrystalline semiconductors. We calculate the thermopower and figure of merit for temperatures less than the charging energy. For weakly coupled semiconducting grains it is shown that the figure of merit is optimized for grain sizes of order 5 nm for typical materials, and that its value can be larger than one. Using the similarities between granular semiconductors and electron or Coulomb glasses allows for a quantitative description of inhomogeneous semiconducting thermoelectrics.