Role of Anharmonicity in Dictating the Thermal Boundary Conductance across Interfaces Comprised of Two-Dimensional Materials

Understanding the fundamental heat-transport mechanisms across interfaces comprised of two-dimensional (2D) materials is crucial for the further development of the next generation of optoelectronic devices based on 2D heterostructures for which one of the main factors affecting the device performance is their poor thermal management. Here we use systematic atomistic simulations to unravel the influence of anharmonicity in dictating the thermal boundary conductance across graphene and ${\mathrm{Mo}\mathrm{S}}_{2}$-based 2D and three-dimensional (3D) interfaces. Specifically, we conduct nonequilibrium molecular dynamics simulations on computational domains with graphene or ${\mathrm{Mo}\mathrm{S}}_{2}$ layers encapsulated between crystalline or amorphous silicon leads across a wide temperature range (of 50--600 K). We show that while the interfacial conductance across a graphene and crystalline silicon interface demonstrates considerable temperature dependence, the conductance across a graphene and amorphous silicon interface has no significant temperature dependence. In contrast, the thermal boundary conductance for the ${\mathrm{Mo}\mathrm{S}}_{2}$-based heterostructures with both the crystalline and amorphous leads demonstrate no significant temperature dependence. Our spectral energy-density calculations along with our spectrally resolved heat-flux accumulation calculations on the various interfaces show that anharmonic coupling across the entire vibrational spectrum as well as the strong hybridization of a broader spectrum of the flexural modes with substrate Rayleigh waves in graphene heterostructures give rise to the relatively higher and drastically different heat-transport mechanisms across these interfaces as compared to the ${\mathrm{Mo}\mathrm{S}}_{2}$-based heterostructures. Through these understandings, we show that one strategy to enhance heat conductance across 2D-3D interfaces is to increase the anharmonic coupling between the acoustic and optic modes in the 2D materials by inducing a stronger interaction strength with the substrates. Our findings elucidate the fundamental heat-transfer mechanisms dictating thermal-boundary conductances across 2D-3D interfaces and will be crucial for heat dissipation in the next generation of optoelectronic devices where the utilization of 2D materials are becoming ubiquitous.