  The thermoelectric power factor of hierarchically nanostructured materials is
investigated using the nonequilibrium Greens function method for quantum
transport, including interactions of electrons with acoustic and optical
phonons. We describe hierarchical nanostructuring by superlatticelike potential
barriers or wells, combined with quantum dot barriers or wells nanoinclusions
as well as voids in the intermediate region. We show that these structures can
be designed in a way that the power factor is not only largely immune to the
presence of the nanostructure features, but under certain conditions benefits
can be achieved as well. Interestingly, we show that these design approaches
are linked to the energy relaxation of the current flow and whether charge
carrier scattering is limited by elastic or inelastic processes. In particular,
when nanostructures form potential barriers, the power factor can be
substantially enhanced under elastic scattering conditions, irrespective of
nanostructuring density and potential barrier heights. When inelastic
scattering processes dominate, however, the power factor is inevitably
degraded. In the case in which nanostructures form potential wells, despite a
slight decrease, the power factor is quite resilient under either elastic or
inelastic scattering processes. These nanostructuring design approaches could
help open the path to the optimization of new generation nanostructured
thermoelectric materials by not only targeting reductions in thermal
conductivity, but simultaneous improvements in the power factor as well.
