  Conventional thermionic power generators and refrigerators utilize a barrier
in the direction of transport to selectively transmit high-energy electrons.
Here we show that the energy spectrum of electrons transmitted in this way is
not optimal, and we derive the ideal energy spectrum for operation in the
maximum power regime. By using suitable energy filters, such as resonances in
quantum dots, the power of thermionic devices can, in principle, be improved by
an order of magnitude.
