Phonon Knudsen flow in nanostructured semiconductor systems

TL;DR

This paper investigates how nanoscale structures in semiconductors affect thermal conductivity through phonon boundary scattering, highlighting significant size effects and the breakdown of Fourier's law in certain multilayer systems.

Contribution

It provides a detailed analysis of phonon Knudsen flow effects in nanostructured semiconductors using the Boltzmann transport equation, with new predictions for multilayered SiC systems and experimental validation in Si nanowires.

Findings

Phonon transport is significantly reduced in nanostructures due to boundary scattering.

Knudsen flow effects are most pronounced in Si and SiC systems.

Size-dependent thermal conductivity can be used to monitor SiC oxidation.

Abstract

We determine the size effect on the lattice thermal conductivity of nanoscale wire and multilayer structures formed in and by some typical semiconductor materials, using the Boltzmann transport equation and focusing on the Knudsen flow effect. For both types of nanostructured systems we find that the phonon transport is reduced significantly below the bulk value by boundary scattering off interface defects and/or interface modes. The Knudsen flow effects are important for almost all types of semiconductor nanostructures but we find them most pronounced in Si and SiC systems due to the very large phonon mean-free paths. We apply and test our wire thermal-transport results to recent measurements on Si nanowires. We further investigate and predict size effects in typical multilayered SiC nanostructures, for example, a doped-SiC/SiC/SiO$_2$ layered structure that could define the transport channel in a nanosize transistor. Here the phonon-interface scattering produces a heterostructure thermal conductivity smaller than what is predicted in a traditional heat-transport calculation, suggesting a breakdown of the traditional Fourier analysis even at room temperatures. Finally, we show that the effective thermal transport in a SiC/SiO$_2$ heterostructure is sensitive to the oxide depth and could thus be used as an in-situ probe of the SiC oxidation progress.