The material figure-of-merit for conventional thermoelectrics is micro meff 1.5/beta where micro is the electron or hole mobility, meff its effective mass, and beta the material thermal conductivity. From the electronic point of view, in order to optimize the cooler performance, there is a trade off between electron effective mass and its mobility. While high mobility is inherently important to facilitate electron transport in the material and reduce the Joule heating, a large effective mass is only required due to the symmetry of electronic density-of-states with respect to the Fermi energy in an energy range on the order of thermal energy (k sub b*T) near the Fermi level. It is possible to increase this asymmetry by using doping densities so that the Fermi level is close to the bandedge. In this case there is a small number of electrons participating in the conduction and the net transport of heat is small. We clarify how this trade off is alleviated in high barrier thermionic coolers. Prospects for different material systems to realize bulk and superlattice thermionic coolers are also discussed.