Calculation of nanowire thermal conductivity using complete phonon dispersion relations

TL;DR

This paper calculates the thermal conductivity of silicon nanowires using complete phonon dispersion relations, achieving good agreement with experiments without adjustable parameters, and discusses related theoretical formulations.

Contribution

It introduces a method to compute nanowire thermal conductivity using full phonon dispersions without needing frequency cutoffs or adjustments.

Findings

Accurate thermal conductivity calculations for nanowires wider than 35 nm.

No external frequency cutoff needed for calculations.

Comparison with the Callaway formula from a dispersion perspective.

Abstract

The lattice thermal conductivity of crystalline Si nanowires is calculated. The calculation uses complete phonon dispersions, and does not require any externally imposed frequency cutoffs. No adjustment to nanowire thermal conductivity measurements is required. Good agreement with experimental results for nanowires wider than 35 nm is obtained. A formulation in terms of the transmission function is given. Also, the use of a simpler, nondispersive "Callaway formula", is discussed from the complete dispersions perspective.