Lattice thermal transport in large-area polycrystalline graphene

We study lattice thermal transport in large-area polycrystalline graphene, such as the samples grown by chemical vapor deposition (CVD) of carbon on Cu. These systems are composed of single-crystalline grains with a broad range of sizes and crystal orientations, separated by atomically rough grain boundaries. We solve the phonon Boltzmann transport equation and calculate the thermal conductivity in each grain, including scattering from the grain boundary roughness. Thermal transport in the large-area sample is considered in the Corbino-membrane geometry, with heat flowing through a network of thermal resistors and away from a pointlike heat source. The thermal transport in polycrystalline graphene is shown to be highly anisotropic, depending on the individual properties of the grains (their size and boundary roughness), as well as on grain connectivity. Strongest heat conduction occurs along large-grain filaments, while the heat flow is blocked through regions containing predominantly small grains. We discuss how thermal transport in CVD graphene can be tailored by controlling grain disorder.

Figure 1

Grains in polycrystalline graphene computed based on the 2D Voronoi tessellation. Inset shows a phonon traveling through a polycrystalline sample, encountering rough grain boundaries. Grain boundaries are shown with $\Delta =1$ nm rms roughness. $D$ denotes the distance a phonon mode with wave vector $\vec{q}$ has traveled inside a particular grain.

Figure 2

Histogram of a grain-size distribution obtained based on the Voronoi tessellation, which corresponds closely with experiment. The distribution represents a $10\times 10$ $\mu {\mathrm{m}}^2$ polycrystalline graphene sheet with 5000 grains and an average grain diameter of about 120 nm.

Figure 3

Steady-state temperature profile, represented by color (red is high, blue is low; color bar is in degrees Kelvin) in the $10\mu \mathrm{m}\times 10\mu \mathrm{m}$ polycrystalline graphene sample. Black lines show the grain boundaries. Temperature is resolved at the level of individual grains.

Figure 4

Polar plot of the directional dependence of thermal conductivity in large-area polycrystalline graphene, showing large anisotropy due to the variation in the relative positions and sizes of grains. The polar angle $\Theta$ denotes the direction of heat propagation with respect to the $x$ axis from Figs. 3 and 6, while the radial coordinate corresponds to the magnitude of thermal conductivity (concentric circles with radii in 500 W/m K increments are shown).

Figure 5

Comparison of the calculated thermal conductivities (curves) with experimental data for suspended CVD graphene taken from Ref. [21] (symbols). The two sets of experimental data (triangles and circles) were obtained from micro-Raman spectroscopy using two different objectives to focus the laser. The black solid curve corresponds to the grain size distribution depicted in Fig. 3 and ${\kappa }_{\mathrm{eff}}$ was obtained upon the temperature iteration described in Sec. 3c. For the same collection of grains, the upper limit to thermal conductivity would be obtained by connecting them in parallel (dashed blue line). The lower limit corresponds to the same collection of grains in series (dashed red line). Results from the effective medium theory (a single grain having the same average diameter) are presented by the black dash-dot curve.

Figure 6

Spatial profile of the normalized heat flux magnitude, represented by color (red is high, blue is low). The grain distribution is the same as in Fig. 3.