Thermal transport in asymmetric sawtooth nanowires was investigated. The boundaries reflect phonons differently depending on the frequency and momentum of the phonon. These systems show thermally rectifying behavior when the boundary reflections are a function of both the direction the phonon is traveling and the frequency of the phonon. This rectifying effect could be useful for thermal management applications at all size scales, but would have to be built up from the nanoscale because of a strong dependence on the device aspect ratio and the Knudsen number of the system. Monte Carlo simulations show an accumulation of phonons at the boundary which emits phonons in a perceived rough direction where those phonons have some probability of diffuse reflections at the boundary while phonons emitted in the smooth direction only experience specular reflections at the boundary and are eventually thermalized at the opposite boundary. In this study the level of rectification of the system was linearly dependent on the device aspect ratio as long as the length of the device was near or below the phonon mean free path of the phonons.

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