  We investigate thermal rectification in nanoporous silicon using a
semi-classical Monte Carlo (MC) simulation method. We consider geometrically
asymmetric nanoporous structures, and investigate the combined effects of
porosity, inter-pore distance, and pore position relative to the device
boundaries. Two basis geometries are considered, one in which the pores are
arranged in rectangular arrays, and ones in which they form triangular
arrangements. We show that systems: i) with denser, compressed pore
arrangements (i.e with smaller inter-pore distances), ii) with pores positioned
closer to the device edge/contact, and iii) with pores in a triangular
arrangement, can achieve rectification of over 55%. Introducing smaller pores
into existing porous geometries in a hierarchical fashion increases
rectification even further to over 60%. Importantly, for the structures we
simulate, we show that sharp rectifying junctions, separating regions of long
from short phonon mean-free-paths are more beneficial for rectification than
spreading the asymmetry throughout the material along the heat direction in a
graded fashion.
