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Understanding the limits of phononic heat dissipation from a two-dimensional layered material (2DLM) to its hexagonal boron nitride (h-BN) substrate and how it varies with the structure of the 2DLM is important for the design and thermal management of h-BN-supported nanoelectronic devices. We formulate an elasticity-based theory to model the phonon-mediated heat dissipation between a 2DLM and its h-BN substrate. By treating the h-BN substrate as a semi-infinite stack of harmonically coupled thin plates, we obtain semi-analytical expressions for the thermal boundary conductance (TBC) and interfacial phonon transmission spectrum. We evaluate the temperature-dependent TBC of the N-layer 2DLM (graphene or MoS2) on different common substrates (h-BN vs. a-SiO2) at different values of N. The results suggest that h-BN is substantially more effective for heat dissipation from MoS2 than a-SiO2 especially at large N. To understand the limitations of the our stack model, we also compare its predictions in the N=∞ limit to those of the more exact atomistic Green’s function model for the graphite–BN and molybdenite–BN interfaces. Our stack model provides clear insights into the key role of the flexural modes in the TBC and how the anisotropic elastic properties of h-BN affect heat dissipation.

The role of flexural coupling in heat dissipation from a two-dimensional layered material to its hexagonal boron nitride substrate