  Large efforts in improving thermoelectric energy conversion are devoted to
energy filtering by nanometer size potential barriers. In this work we perform
an analysis and optimization of such barriers for improved energy filtering. We
merge semiclassical with quantum mechanical simulations to capture tunneling
and reflections due to the barrier, and analyze the influence of the width W,
the height Vb, and the shape of the barrier, and the position of the Fermi
level (EF) above the band edge, {\eta}F. We show that for an optimized design,
approx. 40 per cent improvement in the thermoelectric power factor can be
achieved if the following conditions are met: {\eta}F is large; the different
of Vb from EF is somewhat higher but comparable to kBT; and W is large enough
to suppress tunneling. Finally, we show that a smooth energy barrier is
beneficial compared to a sharp (square) barrier for increasing the
thermoelectric power factor.
