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.

Heat flow in nanomaterials is an important area of study, with both fundamental and technological implications. However, little is known about heat flow in two-dimensional devices or interconnects with dimensions comparable to the phonon mean free path. Here we find that short, quarter-micron graphene samples reach ~35% of the ballistic thermal conductance limit up to room temperature, enabled by the relatively large phonon mean free path (~100 nm) in substrate-supported graphene. In contrast, patterning similar samples into nanoribbons leads to a diffusive heat-flow regime that is controlled by ribbon width and edge disorder. In the edge-controlled regime, the graphene nanoribbon thermal conductivity scales with width approximately as ~W1.80.3, being about 100 W m−1 K−1 in 65-nm-wide graphene nanoribbons, at room temperature. These results show how manipulation oftwo-dimensional device dimensions and edges can be used to achieve full control of their heat-carrying properties, approaching fundamentally limited upper or lower bounds. Understanding heat flow in two-dimensional nanomaterials has wide-ranging implications. Here, the authors show that the thermal conductance of quarter-micron graphene samples is quasi-ballistic, but patterning the graphene into nanoribbons leads to diffusive heat flow strongly limited by edge scattering.