  The ultralow thermal conductivity $\kappa$ 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 $\kappa$ as a function of the normalized
geometric mean free path $\bar\lambda$ ($0<\bar\lambda<1$); the diffusive
(Casimir) limit corresponds to $\bar\lambda=1/2$. $\kappa$ vs $\bar\lambda$ is
exponential at low-to-moderate roughness (high $\bar\lambda$), where internal
scattering randomly interrupts phonon bouncing across the SiNW, and linear at
high roughness (low $\bar\lambda$), where multiple scattering events at the
same surface results in ultralow, amorphous-limit thermal conductivity.
