  Utilizing the non-coherent quantum transport formalism, we investigate
thermoelectric performance across dissipative superlattice configurations in
the linear regime of operation. Using the {\it{dissipative}} non-equilibrium
Green's function formalism coupled self-consistently with the Poisson's
equation, we report an enhanced figure of merit $zT$ in the multi-barrier
device designs. The proposed enhancement, we show, is a result of a drastic
reduction in the electronic thermal conductance triggered via non-coherent
transport. We show that a maximum $zT$ value of 18 can be achieved via the
inclusion of non-coherent elastic scattering processes. There is also a
reasonable enhancement in the Seebeck coefficient, with a maximum of $1000~\mu
V/K$, which we attribute to an enhancement in electronic filtering arising from
the non-coherent transport. Distinctly the thermal conduction is drastically
reduced as the length of the superlattice scales up, although the power factor
shows an overall degradation. While the presence of interfaces is known to kill
phonon thermal conduction, our analysis shows that non-coherent processes in
superlattice structures can effectively kill electronic thermal conduction
also. We believe that the analysis presented here could set the stage to
understand better the interplay between non-coherent scattering and coherent
quantum processes in the electronic engineering of heterostructure
thermoelectric devices.
