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Investigating in detail the physics of energy filtering through a singleplanar energy barrier in nanostructured thermoelectric generators, we reinforcethe non-trivial result that the anticipated enhancement in generated power at agiven efficiency via energy filtering is a characteristic of systems dominatedby incoherent scattering and is absent in ballistic devices. In such cases,assuming an energy dependent relaxation time $\tau(E)=kE^r$, we show that thereexists a minimum value $r_{min}$ beyond which generation can be enhanced byembedding nanobarriers. For bulk generators with embedded nanobarriers, wedelve into the details of inter sub-band scattering and show that it has finitecontribution to the enhancement in generation. We subsequently discuss therealistic aspects, such as the effect of smooth transmission cut-off and showthat for $r>r_{min}$, the optimized energy barrier is just sufficiently wideenough to scatter off low energy electrons, a very wide barrier beingdetrimental to the performance. Analysis of the obtained results should providegeneral design guidelines for enhancement in thermoelectric generation viaenergy filtering. Our non-equilibrium approach is typically valid in theabsence of local quasi-equilibrium and hence sets the stage for futureadvancements in thermoelectric device analysis, for example, Peltier coolingnear a barrier interface.

Incoherent scattering can favorably influence energy filtering in nanostructured thermoelectrics