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Electron energy filtering has been suggested as a promising way to improvethe power factor and enhance the ZT figure of merit of thermoelectricmaterials. In this work we explore the effect that reduced dimensionality hason the success of the energy-filtering mechanism for power factor enhancement.We use the quantum mechanical non-equilibrium Green's function (NEGF) methodfor electron transport including electron-phonon scattering to explore 1D and2D superlattice/nanocomposite systems. We find that, given identical materialparameters, 1D channels utilize energy filtering more effectively than 2D asthey: i) allow one to achieve maximal power factor for smaller well sizes /smaller grains (which is needed to maximize phonon scattering), ii) take betteradvantage of a lower thermal conductivity in the barrier/boundary materialscompared to the well/grain materials in both: enhancing the Seebeckcoefficient; and in producing a system which is robust against detrimentalrandom deviations from optimal barrier design. In certain cases we find thatthe relative advantage can be as high as a factor of 3. We determine thatenergy-filtering is most effective when the average energy of carrier flowvaries the most in the wells and the barriers along the channel, an event whichappears when the energy of the carrier flow in the host material is low andwhen the energy relaxation mean-free-path of carriers is short. Although theultimate reason these aspects, which cause a 1D system to see greater relativeimprovement than a 2D, is the 1D system's van Hove singularity in thedensity-of-states, the insights obtained are general and informenergy-filtering design beyond dimensional considerations.

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