The role of dimensionality on the electronic performance of thermoelectric devices is clarified using the Landauer formalism, which shows that the thermoelectric coefficients are related to the transmission, T(E)T(E), and how the conducting channels, M(E)M(E), are distributed in energy. The Landauer formalism applies from the ballistic to diffusive limits and provides a clear way to compare performance in different dimensions. It also provides a physical interpretation of the “transport distribution,” a quantity that arises in the Boltzmann transport equation approach. Quantitative comparison of thermoelectric coefficients in one, two, and three dimensions shows that the channels are utilized more effectively in lower dimensions. To realize the advantage of lower dimensionality, however, the packing density must be very high, so the thicknesses of the quantum wells or wires must be small. The potential benefits of engineering M(E)M(E) into a delta function are also investigated. When compared with a bulk semiconductor, we find the potential for ~50% ~50% improvement in performance. The shape of M(E)M(E) improves as dimensionality decreases, but lower dimensionality itself does not guarantee better performance because it is controlled by both the shape and the magnitude of M(E)M(E). The benefits of engineering the shape of M(E)M(E) appear to be modest, but approaches to increase the magnitude of M(E)M(E) could pay large dividends.
Date of this Version
J. Appl. Phys. 105, 034506 (2009)