Nano Focus: Quantum model predicts thermoelectric figure of merit for superlattices
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hermoelectric devices could provide a new means for power generation by converting small thermal gradients into electricity. A proven method to increase the performance of bulk thermoelectric materials is through the incorporation of nanostructured superlattices, that is, periodic layers of two or more materials. Because layer composition, thickness, and doping affect the thermoelectric properties, a variety of parameters can be tuned to optimize device performance. It would be useful to have an accurate model that not only screens combinations of such parameters but also provides fundamental insights into the physics at hand. Terence Musho, professor of Mechanical and Aerospace Engineering at West Virginia University, has developed such a model to calculate the thermoelectric properties of superlattice devices. The work is published in a recent issue of the Journal of Materials Research (DOI: 10.1557/jmr.2015.256). Thermoelectric properties arise from both electron and phonon contributions. The thermoelectric figure of merit, denoted ZT, describes both the thermal and electrical contributions to a thermoelectric system. The system’s efficiency depends explicitly on its ZT value. “The novelty of the model is in calculating the full ZT,” says Musho, the sole author of this work. “In much of the literature they’re looking at enhancing one aspect, either the Seebeck coefficient or the electrical conductivity, or they’re trying to decrease the thermal conductivity.” In Musho’s model, the problem is reduced to a single dimension of electron and phonon transport across the superlattice in order to calculate the full ZT for the system. Musho’s model is based on quantum mechanical descriptions of both electrons and phonons using a nonequilibrium Green’s function. “One nice thing about using the nonequilibrium Green’s
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VOLUME 40 • OCTOBER 2015
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Schematic diagram of the thermoelectric device studied in this work to provide proofof-concept validation for the combined phonon and electron quantum model. Source: Journal of Materials Research.
function formalism is that it takes into account some of the wave effects of these species,” says Jeffery Urban, Facility Director at the Molecular Foundry and Head of the Thermoelectrics Program at Lawrence Berkeley National Laboratory, who was not involved in this work. “Often in modeling thermoelectric devices, [phonons and electrons] are treated as particles. This model gets away from a strictly particle-based description, which is appealing particularly for these small feature sizes.” Because a quantum description is used, this model recovers contributions to ZT from quantum phenomena such as tunneling and electron confinement effects. To aid in reproducing such quantum effects, Musho’s model calculates multiple phonon frequencies, rather than relying on the dominant phonon frequency. Calculating multiple phonon frequencies is important because electrons are scattered by phonons during transport. This phonon– electron interaction aids in generating electron t
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