We investigate thermal rectification in nanoporous silicon using a semiclassical Monte Carlo simulation method. We consider geometrically asymmetric nanoporous structures and investigate the combined effects of porosity, interpore 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 interpore distances), (ii) with the pores positioned closer to the device edge/contact, and (iii) with the 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.

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