Incoherent scattering can favorably influence energy filtering in nanostructured thermoelectrics

TL;DR

This paper demonstrates that incoherent scattering enhances energy filtering in nanostructured thermoelectrics, leading to increased power generation, and provides design guidelines for optimizing thermoelectric devices.

Contribution

It reveals that incoherent scattering, not ballistic transport, is crucial for energy filtering benefits and analyzes the effects of nanobarrier width and scattering parameters on thermoelectric performance.

Findings

Incoherent scattering enables power enhancement via energy filtering.

Optimal barrier width is just enough to scatter low energy electrons.

Inter sub-band scattering contributes to power increase.

Abstract

Investigating in detail the physics of energy filtering through a single planar energy barrier in nanostructured thermoelectric generators, we reinforce the non-trivial result that the anticipated enhancement in generated power at a given efficiency via energy filtering is a characteristic of systems dominated by incoherent scattering and is absent in ballistic devices. In such cases, assuming an energy dependent relaxation time $\tau(E)=kE^r$, we show that there exists a minimum value $r_{min}$ beyond which generation can be enhanced by embedding nanobarriers. For bulk generators with embedded nanobarriers, we delve into the details of inter sub-band scattering and show that it has finite contribution to the enhancement in generation. We subsequently discuss the realistic aspects, such as the effect of smooth transmission cut-off and show that for $r>r_{min}$, the optimized energy barrier is just sufficiently wide enough to scatter off low energy electrons, a very wide barrier being detrimental to the performance. Analysis of the obtained results should provide general design guidelines for enhancement in thermoelectric generation via energy filtering. Our non-equilibrium approach is typically valid in the absence of local quasi-equilibrium and hence sets the stage for future advancements in thermoelectric device analysis, for example, Peltier cooling near a barrier interface.