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research-article

Diffusive Phonons in Nongray Nanostructures

[+] Author and Article Information
Giuseppe Romano

Department of Mechanical Engineering, Massachusetts Institute of Technology, 77 Massachusetts Avenue, Cambridge, MA 02139, USA
romanog@mit.edu

Alexie Kolpak

Department of Mechanical Engineering, Massachusetts Institute of Technology, 77 Massachusetts Avenue, Cambridge, MA 02139, USA
kolpak@mit.edu

1Corresponding author.

ASME doi:10.1115/1.4040611 History: Received October 16, 2017; Revised June 12, 2018

Abstract

Nanostructured semiconducting materials are promising candidates for thermoelectrics due to their potential to suppress phonon transport while preserving electrical properties. Modeling phonon-boundary scattering in complex geometries is crucial for predicting materials with high conversion efficiency. However, the simultaneous presence of ballistic and diffusive phonons challenge the development of models that are both accurate and computationally tractable. Using the recently developed first-principles Boltzmann transport equation (BTE) approach, we investigate diffusive phonons in nanomaterials with wide mean-free-path (MFP) distributions. First, we derive the short MFP limit of the suppression function, showing that it does not necessarily recover the value predicted by standard diffusive transport, challenging previous assumptions. Second, we identify a Robin type boundary condition describing diffuse surfaces within Fourier's law, extending the validity of diffusive heat transport in terms of Knudsen numbers. Finally, we use this result to develop a hybrid Fourier/BTE approach to model realistic materials, obtaining good agreement with experiments. These results provide insight on thermal transport in materials that are within experimental reach and open opportunities for large-scale screening of nanostructured thermoelectric materials.

Copyright (c) 2018 by ASME
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