Theoretical Analysis of Thermal Transport in Graphene Supported on Hexagonal Boron Nitride: The Importance of Strong Adhesion Due to $\pi$-Bond Polarization

One important attribute of graphene that makes it attractive for high-performance electronics is its inherently large thermal conductivity ($\kappa$) for the purposes of thermal management. Using a combined density-functional theory and classical molecular-dynamics approach, we predict that the $\kappa$ of graphene supported on hexagonal boron nitride ($h$-BN) can be as large as 90% of the $\kappa$ of suspended graphene, in contrast to the significant suppression of $\kappa$ (more than 70% reduction) on amorphous silica. Interestingly, we find that this enhanced thermal transport is largely attributed to increased lifetimes of the in-plane acoustic phonon modes, which is a notable contrast from the dominant contribution of out-of-plane acoustic modes in suspended graphene. This behavior is possible due to the charge polarization throughout graphene that induces strong interlayer adhesion between graphene and $h$-BN. These findings highlight the potential benefit of layered dielectric substrates such as $h$-BN for graphene-based thermal management, in addition to their electronic advantages. Furthermore, our study brings attention to the importance of understanding the interlayer interactions of graphene with layered dielectric materials which may offer an alternative technological platform for substrates in electronics.

Figure 1

(a) Schematic of the simulation cell used in DFT calculations and representations of the three stacking orientations. (b) Schematic of the graphene (Gr) and hexagonal boron nitride ($h$-BN) heterostructures used in MD simulations. Gray, pink, and blue balls represent C, B, and N atoms, respectively.

Figure 2

Charge-density difference plots for monolayer $h$-BN/graphene for (a) ${\mathrm{AB}}_{\mathrm{B}}$, (b) ${\mathrm{AB}}_{\mathrm{N}}$, and (c) AA stacking orientations. The pink, blue, and gray balls denote B, N, and C atoms, respectively. The yellow (blue) shaded regions depict isosurfaces with positive (negative) charge at a value of $0.0002e/{\mathrm{bohr}}^3$. Energetically optimal separation distances between $h$-BN and graphene are used in each case (around 3.1, 3.3, and 3.4 Å, respectively).

Figure 3

Comparison of the computed interlayer binding energy ($E_b$) at varying interlayer distances for (a) ${\mathrm{AB}}_{\mathrm{B}}$, (b) ${\mathrm{AB}}_{\mathrm{N}}$, and (c) AA orientations using DFT D2 (black squares) and optimized Mie parameters from this work (blue open circles).

Figure 4

(a) Thermal conductivity ($\kappa$) and thermal conductance ($G$) of the listed systems at 300 K; the vertical bars represent the standard error.

Figure 5

Comparison between the listed $\text{graphene}/h$-BN heterostructures of the (right) phonon lifetimes for the three acoustic modes at $k=(2/11)(2\pi /a_1,2\pi /a_2)$ extracted from spectral energy density analysis and (left) effective total mean free path (MFP) of phonons from Eq. (4). The $k$ point is chosen to be close enough to the Brillouin-zone center to sample acoustic branches with high group velocity while being far enough to clearly distinguish the three branches. The up-shift in the phonon mode frequency compared to the graphene case is less than 7% for the ZA branch and less than 2% for the TA and LA branches.

Figure 6

Comparison between the (a) out-of-plane ZA and (b) combined in-plane TA and LA phonon lifetimes to the variance of the atomic forces experienced by the graphene sheet in the out-of-plane ($\sigma |f_z|$) and in-plane ($\sigma |f_{xy}|$) directions.