Phonon transport in silicon nanowires: The reduced group velocity and surface-roughness scattering

Abstract

Using a linear-scaling Kubo simulation approach, we have quantitatively investigated the effects of confinement and surface roughness on phonon transport in silicon nanowires (SiNWs) as thick as 55 nm in diameter $R$. The confinement effect leads to significant reduction of phonon group velocity $v$ in SiNWs compared to bulk silicon except at extremely low phonon frequencies $f$, which very likely persists in SiNWs several hundreds of nanometers thick, suggesting the inapplicability of bulk properties, including anharmonic phonon scattering, to SiNWs. For instance, the velocity can be reduced by more than 30% for phonons with $fg4.5$ THz in 55-nm-thick nanowires. In rough SiNWs Casimir's limit, which is valid in confined macroscopic systems, can underestimate the surface scattering by more than one order of magnitude. For a roughness profile with Lorentzian correlation characterized by root-mean-square roughness $\ensuremath{\sigma}$ and correlation length ${L}_{r}$, the frequency-dependent phonon diffusivity $D$ follows power-law dependences $D\ensuremath{\propto}{R}^{\ensuremath{\alpha}}{\ensuremath{\sigma}}^{\ensuremath{-}\ensuremath{\beta}}{L}_{r}^{\ensuremath{\gamma}}$, where $\ensuremath{\alpha}\ensuremath{\sim}2$ and $\ensuremath{\beta}\ensuremath{\sim}1$. On average, $\ensuremath{\gamma}$ increases from 0 to 0.5 as $R/\ensuremath{\sigma}$ increases. The mean free path and the phonon lifetime essentially follow the same power-law dependences. These dependences are in striking contrast to Casimir's limit, i.e., $D\ensuremath{\sim}vR/3$, and manifest the dominant role of the change in the number of atoms due to roughness. The thermal conductivity $\ensuremath{\kappa}$ can vary by one order of magnitude with varying $\ensuremath{\sigma}$ and ${L}_{r}$ in SiNWs, and increasing $\ensuremath{\sigma}$ and shortening ${L}_{r}$ can efficiently lower $\ensuremath{\kappa}$ below Casimir's limit by one order of magnitude. Our work provides different insights to understand the ultralow thermal conductivity of SiNWs reported experimentally and guidance to manipulate $\ensuremath{\kappa}$ via surface roughness engineering.