  Boundary-engineering in nanostructures has the potential to dramatically
impact the development of materials for high-efficiency conversion of thermal
energy directly into electricity. In particular, nanostructuring of
semiconductors can lead to strong suppression of heat transport with little
degradation of electrical conductivity. Although this combination of material
properties is promising for thermoelectric materials, it remains largely
unexplored. In this work, we introduce a novel concept, the directional phonon
suppression function, to unravel boundary-dominated heat transport in
unprecedented detail. Using a combination of density functional theory and the
Boltzmann transport equation, we compute this quantity for nanoporous silicon
materials. We first compute the thermal conductivity for the case with aligned
circular pores, confirming a significant thermal transport degradation with
respect to the bulk. Then, by analyzing the information on the directionality
of phonon suppression in this system, we identify a new structure of
rectangular pores with the same porosity that enables a four-fold decrease in
thermal transport with respect to the circular pores. Our results illustrate
the utility of the directional phonon suppression function, enabling new
avenues for systematic thermal conductivity minimization and potentially
accelerating the engineering of next-generation thermoelectric devices.
