Universal features of phonon transport in nanowires with correlated surface roughness

The ultralow thermal conductivity $κ$ observed experimentally in intentionally roughened silicon nanowires (SiNWs) is reproduced in phonon Monte Carlo simulations with exponentially correlated real-space rough surfaces similar to measurement [J. Lim, K. Hippalgaonkar, S. C. Andrews, A. Majumdar, and P. Yang, Nano Lett. 12, 2475 (2012)]. Universal features of thermal transport are revealed by presenting $κ$ as a function of the normalized geometric mean free path $\barλ$ ($0<\barλ<1$); the diffusive (Casimir) limit corresponds to $\barλ=1/2$. $κ$ vs $\barλ$ is exponential at low-to-moderate roughness (high $\barλ$), where internal scattering randomly interrupts phonon bouncing across the SiNW, and linear at high roughness (low $\barλ$), where multiple scattering events at the same surface results in ultralow, amorphous-limit thermal conductivity.

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