In many semiconductor nanostructures, characteristic features are shorter than the phonon mean free path for phonon-phonon or mass-difference scattering. However, nanostructures are terminated by atomically rough boundaries and they can incorporate several acoustically mismatched materials separated by imperfect interfaces. I will discuss recent progress and challenges in the simulation of phonon transport in a variety of semiconductor nanostructures where partially diffuse scattering with boundaries or interfaces plays a prominent role, such as nanowires, nanomembrances, superlattices, and polycrystalline materials. I will focus on semiclassical transport techniques based on solving the Boltzman transport equation, such as the relaxatation-time approximation (RTA) and ensemble Monte Carlo (EMC) simulation. I will also discuss the relative merits of various phonon boundary scattering models, from the momentum-dependent specularity parameter to using real-space rough surfaces generated according to experimentally relevant autocorrelation functions.
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