  We study the thermoelectric coefficients of a multi-level quantum dot (QD)
weakly coupled to two electron reservoirs in the Coulomb blockade regime.
Detailed calculations and analytical expressions of the power factor and the
figure of merit are presented. We restrict our interest to the limit where the
energy separation between successive energy levels is much larger than the
thermal energy (i.e., the quantum limit) and we report a giant enhancement of
the figure of merit due to the violation of the Wiedemann-Franz law when
phonons are frozen. We point out the similarity of the electronic and the
phonon contribution to the thermal conductance for zero dimensional electrons
and phonons. Both contributions show an activated behavior. Our findings
suggest that the control of the electron and phonon confinement effects can
lead to nanostructures with improved thermoelectric properties.
