  We study thermoelectric properties of granular semiconductors with weak
tunneling conductance between the grains, g_t < 1. We calculate the thermopower
and figure of merit taking into account the shift of the chemical potential and
the asymmetry of the density of states in the vicinity of the Fermi surface due
to n- or p-type doping in the Efros-Shklovskii regime for temperatures less
than the charging energy. We show that for weakly coupled semiconducting grains
the figure of merit is optimized for grain sizes of order 5nm for typical
materials and its values can be larger than one. We also study the case of
compensated granular semiconductors and show that in this case the thermopower
can be still finite, although two to three orders of magnitude smaller than in
the uncompensated regime.
