On the effectiveness of the thermoelectric energy filtering mechanism in low-dimensional superlattices and nano-composites

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 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 the maximal power factor for smaller well sizes/smaller grains which are needed to maximize the 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 the 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 between the wells and the barriers along the channel, an event which occurs 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 for 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.