  Electron energy filtering has been suggested as a promising way to improve
the power factor and enhance the ZT figure of merit of thermoelectric
materials. In this work we explore the effect that reduced dimensionality has
on the success of the energy-filtering mechanism for power factor enhancement.
We use the quantum mechanical non-equilibrium Green's function (NEGF) method
for electron transport including electron-phonon scattering to explore 1D and
2D superlattice/nanocomposite systems. We find that, given identical material
parameters, 1D channels utilize energy filtering more effectively than 2D as
they: i) allow one to achieve maximal power factor for smaller well sizes /
smaller grains (which is needed to maximize phonon scattering), ii) take better
advantage of a lower thermal conductivity in the barrier/boundary materials
compared to the well/grain materials in both: enhancing the Seebeck
coefficient; and in producing a system which is robust against detrimental
random deviations from optimal barrier design. In certain cases we find that
the relative advantage can be as high as a factor of 3. We determine that
energy-filtering is most effective when the average energy of carrier flow
varies the most in the wells and the barriers along the channel, an event which
appears when the energy of the carrier flow in the host material is low and
when the energy relaxation mean-free-path of carriers is short. Although the
ultimate reason these aspects, which cause a 1D system to see greater relative
improvement than a 2D, is the 1D system's van Hove singularity in the
density-of-states, the insights obtained are general and inform
energy-filtering design beyond dimensional considerations.
