Surface roughness and thermal conductivity of semiconductor nanowires: going below the Casimir limit

TL;DR

This study demonstrates that atomic-level surface roughness can cause silicon nanowires to have thermal conductivities below the classical Casimir limit, especially with deep surface degradation, challenging previous perturbative models.

Contribution

We provide an exact atomic-level analysis of surface roughness effects on nanowire thermal conductivity, contrasting with earlier perturbative approaches and highlighting the need for improved theoretical models.

Findings

Thermal conductivity can be lower than Casimir's limit with deep surface roughness.

Shallow roughness still allows Casimir's formula to be a good approximation.

Perturbative models significantly overestimate scattering rates.

Abstract

By explicitly considering surface roughness at the atomic level, we quantitatively show that the thermal conductivity of Si nanowires can be lower than Casimir's classical limit. However, this violation only occurs for deep surface degradation. For shallow surface roughness, the Casimir formula is shown to yield a good approximation to the phonon mean free paths and conductivity, even for nanowire diameters as thin as 2.22 nm. Our exact treatment of roughness scattering is in stark contrast with a previously proposed perturbative approach, which is found to overpredict scattering rates by an order of magnitude. The obtained results suggest that a complete theoretical understanding of some previously published experimental results is still lacking.