Absence of Casimir regime in two-dimensional nanoribbon phonon conduction

TL;DR

This paper reveals that boundary scattering in 2D nanoribbons does not produce a finite phonon mean free path or follow the Casimir regime, unlike in 3D nanostructures, affecting thermal conductivity modeling.

Contribution

It demonstrates that 2D nanoribbons do not exhibit the Casimir regime and require a full Boltzmann transport equation solution for accurate phonon scattering analysis.

Findings

Boundary scattering alone does not lead to finite phonon mean free path in 2D nanoribbons.

The Casimir regime is absent in 2D nanoribbons, unlike in 3D nanostructures.

A simple Mathiessen approach is insufficient for 2D nanoribbons, necessitating a full Boltzmann transport solution.

Abstract

In stark contrast with three-dimensional (3D) nanostructures, we show that boundary scattering in two-dimensional (2D) nanoribbons alone does not lead to a finite phonon mean free path. If combined with an intrinsic scattering mechanism, 2D boundary scattering does reduce the overall mean free path, however the latter does not scale proportionally to the ribbon width, unlike the well known Casimir regime occurring in 3D nanowires. We show that boundary scattering can be accounted for by a simple Mathiessen type approach for many different 3D nanowire cross sectional shapes, however this is not possible in the 2D nanoribbon case, where a complete solution of the Boltzmann transport equation is required. These facts have strong implications for the thermal conductivity of suspended nanostructures.