  Hierarchical material nanostructuring is considered to be a very promising
direction for high performance thermoelectric materials. In this work we
investigate thermal transport in hierarchically nanostructured silicon. We
consider the combined presence of nanocrystallinity and nanopores, arranged
under both ordered and randomized positions and sizes, by solving the Boltzmann
transport equation using the Monte Carlo method. We show that nanocrystalline
boundaries degrade the thermal conductivity more drastically when the average
grain size becomes smaller than the average phonon mean free path. The
introduction of pores degrades the thermal conductivity even further. Its
effect, however, is significantly more severe when the pore sizes and positions
are randomized, as randomization results in regions of higher porosity along
the phonon transport direction, which introduce significant thermal resistance.
We show that randomization acts as a large increase in the overall effective
porosity. Using our simulations, we show that existing compact nanocrystalline
and nanoporous theoretical models describe thermal conductivity accurately
under uniform nanostructured conditions, but overestimate it in randomized
geometries. We propose extensions to these models that accurately predict the
thermal conductivity of randomized nanoporous materials based solely on a few
geometrical features. Finally, we show that the new compact models introduced
can be used within Matthiessens rule to combine scattering from different
geometrical features within approximately 10 per cent accuracy.
