Effects of domains in phonon conduction through hybrid boron nitride and graphene sheets

We theoretically investigate the phonon propagation and thermal conductivity $\kappa$ in hybrid boron nitride and graphene sheets. By using a real-space Kubo-computational transport scheme, large and disordered graphene structures are simulated, introducing disk-shaped domains with varying sizes of 2 to 8 nm and concentrations ranging from 0% to 100%. A strong influence of the domain size and concentration on the transport properties is obtained. The mean free paths are minimized at 50% domain concentration, and stronger suppression of $\kappa$ is achieved with smaller domains. It is found to decrease by up to 65% at room temperature when the domain size is 2 nm. These results are beyond the scope of any effective medium approximation.

Figure 1

A schematic representation of the atomic structure of two-dimensional graphene-BN heterostructures. Here, BN clusters with 2-nm diameters are embedded inside the graphene.

Figure 2

Comparison of the phonon dispersions of a single sheet of BN obtained from the fourth-nearest-neighbor force-constant model with Tersoff-type parametrization (data taken from Ref.28) and density-functional-theory calculations. Experimental results are also included for comparison.

Figure 3

Mean free paths for different concentrations at a fixed domain size of 2 nm are plotted for (a) out-of-plane and (b) in-plane modes, separately.

Figure 4

C atoms randomly distributed in the BN host (see the illustration in the inset). MFPs with different concentrations of C atoms for (a) out-of-plane and (b) in-plane modes.

Figure 5

MFPs for different domain sizes at a fixed concentration of 50% for (a) out-of-plane and (b) in-plane modes. MFPs with domains consisting of single hexagons are also plotted for comparison.

Figure 6

MFPs for different B isotopic compositions at a 50% concentration and 2-nm domain size. (a) Out-of-plane and (b) in-plane modes.

Figure 7

Room-temperature thermal conductivity for a 2-nm domain size versus the concentration of BN contributed by out-of-plane modes (blue/dark gray), in-plane modes (red/gray), and all modes (black). Dashed curves are plotted as guides to the eye. At 50% concentration, two additional domain sizes are considered. Circles: 2 nm; squares: 4 nm; and diamonds: 8 nm.