  We consider the design of an optimal superlattice thermoelectric generator
via the energy bandpass filter approach. Various configurations of superlattice
structures are explored to obtain a bandpass transmission spectrum that
approaches the ideal ``boxcar'' form, which is now well known to manifest the
largest efficiency at a given output power. Using the non-equilibrium Green's
function formalism coupled self-consistently with the Poisson's equation, we
identify such an ideal structure and also demonstrate that it is almost immune
to the deleterious effect of self-consistent charging and device variability.
Analyzing various superlattice designs, we conclude that superlattices with a
Gaussian distribution of the barrier thickness offers the best thermoelectric
efficiency at maximum power. It is observed that the best operating regime of
this device design provides a maximum power in the range of 0.32-0.46 $MW/m^2$
at efficiencies between 54\%-43\% of Carnot efficiency. We also analyze our
device designs with the conventional figure of merit approach to counter
support the results so obtained. We note a high $zT_{el}=6$ value in the case
of Gaussian distribution of the barrier thickness. With the existing advanced
thin-film growth technology, the suggested superlattice structures can be
achieved, and such optimized thermoelectric performances can be realized.
