  We propose a cooling scheme for fermionic quantum gases, based on the
principles of the Peltier thermoelectric effect and energy filtering. The
system to be cooled is connected to another harmonically trapped gas acting as
a reservoir. The cooling is achieved by two simultaneous processes: (i) the
system is evaporatively cooled and (ii) cold fermions from deep below the Fermi
surface of the reservoir are injected below the Fermi level of the system, in
order to fill the 'holes' in the energy distribution. This is achieved by a
suitable energy dependence of the transmission coefficient connecting the
system to the reservoir. The two processes can be viewed as simultaneous
evaporative cooling of particles and holes. We show that both a significantly
lower entropy per particle and faster cooling rate can be achieved than by
using only evaporative cooling.
