Full-dispersion Monte Carlo simulation of phonon transport in micron-sized graphene nanoribbons

Abstract

We simulate phonon transport in suspended graphene nanoribbons (GNRs) with real-space edges and experimentally-relevant widths and lengths (from submicron to hundreds of microns). The full-dispersion phonon Monte Carlo (PMC) simulation technique, which we describe in detail, involves a stochastic solution to the phonon Boltzmann transport equation with the relevant scattering mechanisms (edge, three-phonon, isotope, and grain boundary scattering) while accounting for the dispersion of all three acoustic phonon branches, calculated from the fourth-nearest-neighbor dynamical matrix. We accurately reproduce the results of several experimental measurements on pure and isotopically modified samples [S.

Phonon transport effects in one-dimensional width-modulated graphene nanoribbons

“…7 and Fig. 8 that the more realistic saturation value could be much higher, closer to 6000 W/m-K, attributing this to their calculation that 20% of the phonon mean-free-paths are even larger than 100 μm [41]. The important point we would like to make, however, is that since the MFPs are so long, all experiments to date are performed in the ballistic or quasiballistic regime, and in such channel lengths our conclusions (which are based on the wave nature of transport) will be more valid and not influenced significantly by phononphonon scattering, thus wave effects are the ones which will dominate transport in these…”

“…Several studies have shown that armchair edge GNRs (AGNRs -the ones considerd in the main text) and zig-zag-GNRs (ZGNRs) differ in thermal conductivity [41,[59][60][61][62]. Thus, we find it instructive to present the corresponding simulation results as in Fig.…”

“…2c). We need to point out here that the geometries of the structures we employ contain very small feature sizes, which can be experimentally difficult to realize (although the armchair edges we use are shown to be stable [41,48]). Our intention, however, is to provide fundamental understanding and information about the nature of phonon transport at the nanoscale in the presence of channel width-modulation and generic conclusions.…”

“…Graphene and GNRs have huge thermal conductivities in their pristine form, reaching values as high as 3080-5150 W/mK at room temperature [9,[34][35][36][37][38][39][40]. Recent theoretical works even suggest values up to ~6000 W/mK, with a large proportion of phonon mean-free-paths beyond 10μm [41][42][43]. Previous works indicated that under certain conditions, GNRbased channels could provide very high thermoelectric performance as well [44,45].…”

Rayleigh waves, surface disorder, and phonon localization in nanostructures

“…In 3D, the density of states g 3D (ω) ∝ ω 2 , so lim ω→0 N 3D (ω) = 0, i.e., there are relatively few phonons in the continuum limit in 3D [23]. In contrast, the continuum limit of in-plane 2D modes yields the density of states g 2D (ω) ∝ ω, so lim ω→0 N 2D (ω) is nonzero [54,55]. The result is clear in graphene at 300 K [ Fig.…”