June 09, 2011

Thermoelectric figure of merit calculations for semiconducting nanowires

It was previously believed that as nanowires became smaller that the the thermoelectric figure of merit would improve, but new work shows that improving heat to electricity conversion in nanowires is not that simple.

The prevailing notion that quantum confinement benefits the thermoelectric power factor is supported by the model when a single-subband dominates transport. When transport involves multiple subbands, the thermoelectric power factor in fact decreases to about 62% of the bulk value as the wire radius is initially reduced. This work correctly models the power factor for wire sizes ranging from the nanoscale to bulk and settles the discrepancies between theoretical and measured thermoelectric power factors in nanowires and other nanoscale systems

"Previous models told us that the use of nanomaterials at small dimensions would lead to an improvement in power generation efficiency," says Cornett. "The models also predicted that the smaller the nanostructure, the more significant the improvement would be. In practice, people weren't seeing the gains they thought they should when they designed thermoelectric devices with nanoscale components, which indicated to us that there might be an issue with the interpretation of the original models."

Cornett and Rabin have presented a revised thermoelectric performance model that confirms that smaller is not always better. Using advanced computer modeling to investigate the potential of thermoelectric nanowires only 100 to 1000 atoms thick (about 1000 times smaller than a human hair), they demonstrate that in the set of the tiniest nanowires, measuring 17 nanometers or less in radius, decreasing their radii does result in the increased thermoelectric performance previous models predict. In nanowires above 17 nanometers in radius, however, an improvement is seen as the radius increases.

"The surprising behavior in the larger size range demonstrates that a different physical mechanism, which was overlooked in previous models, is dominant," says Cornett. "People were looking for solutions in the wrong places," says Rabin. “We've created a better understanding of how to search for the best new materials.”

In summary, we have reported a non-monotonic dependence of the power factor on NW radius for n-type InSb NWs. This behavior is attributed to the increasing number of nearly-degenerate subbands with r, a hypothesis supported by the results of a model based on a weighted count of the subbands that contribute to transport. This phenomenon is not exclusive to InSb—rather, it may explain why for many conventional thermoelectric materials the improvement in PF when moving from bulk to nanoscale has proven to be so elusive. With the assumption of a radius-dependent lattice thermal conductivity, the expected monotonic trend in ZT(r) is recovered. It is important to note, however, that electron and hole transport in semiconductors is dependent on specific materials parameters (i.e., effective mass, mobility, degeneracy of carriers). Thermoelectric systems in which multiple
carrier types are found (including p-type InSb) will likely exhibit more complex radius-dependent behavior.

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