Quantifying thermal boundary conductance of 2D–3D interfaces

Abstract

Heat dissipation in next-generation electronics based on two-dimensional (2D) materials is a critical issue in their development and implementation. A potential bottleneck for heat removal in 2D-based devices is the thermal pathway from the 2D layer into its supporting substrate. The choice of substrate, its composition and structure, can strongly impact the thermal boundary conductance (TBC). Here we investigate the temperature-dependent TBC of 42 interfaces formed between a group of six 2D materials and seven crystalline and amorphous substrates. We use first-principles density functional perturbation theory to calculate the full phonon dispersion of the 2D layers and substrates and then input them into our model for phonon transport across the 2D-3D interface. Our results show that the TBC depends on the overlap between the vibrational frequencies and can be varied by nearly two orders of magnitude, from as low as ∼0.6 MW • m −2 • K −1 (h-BN on diamond) to ∼40 MW • m −2 • K −1 (h-BN on SiO 2), for the same 2D layer by changing the substrate material. We find that amorphous materials significantly boost the TBC relative to their crystalline counterparts, assuming the two interfaces have the same adhesion, owing to the low-frequency Boson peak feature in their vibrational density of states (vDOS). For crystalline substrates, we further correlate constituent material properties with the calculated TBCs and find that the TBC strongly depends on a combination of the speed of sound, Debye temperature, and density of the substrate as well as the bandwidth of the flexural branch in the 2D material. We conclude that softer substrates with sharp low-frequency features in their vDOS, such as amorphous materials, polymers, and nanoparticles, could have higher TBC, leading to a trade-off between TBC and the thermal conductivity of the substrate.

A Review of Experimental and Computational Advances in Thermal Boundary Conductance and Nanoscale Thermal Transport across Solid Interfaces

“…To understand the low conductances associated with interfaces comprised of 2D materials, there have been considerable advances both from atomistic simulations as well as analytical and theoretical frameworks . One of the main findings from the MD simulations is that the conductance across the dimensionally mismatched graphene and substrate can be ascribed to the coupling between flexural acoustic phonons of graphene and the longitudinal phonons in the substrate .…”

“…In this work, the modification in the phonon dispersion relation for the ZA acoustic modes due to interaction with the substrate, which lifts the long wavelength modes near the Brillouin zone center, is accounted for thus capturing the physics and importance of the flexural modes . Furthermore, a thorough review and calculations of h K across six common 2D materials and seven substrates has also been carried out by Foss et al Along with the significance of the flexural modes, this study has emphasized the role of the substrate properties such as mass density and sound speed to be important factors while considering the heat transfer across 2D/3D interfaces.…”

“…[169] To understand the low conductances associated with interfaces comprised of 2D materials, there have been considerable advances both from atomistic simulations [109,[174][175][176] as well as analytical and theoretical frameworks. [50,125,173,[177][178][179][180] One of the main findings from the MD simulations is that the conductance across the dimensionally mismatched graphene and substrate can be ascribed to the coupling between flexural acoustic phonons of graphene and the longitudinal phonons in the substrate. [109] The simulations show that the most efficient thermal transport channel across graphene/ substrate interfaces is the transmission of energy from the acoustic branches (especially the flexural modes) in graphene to the cross-plane longitudinal acoustic and optical modes in the substrate.…”

Reduced thermal conductivity of supported and encased monolayer and bilayer MoS2

“…To better understand thermal transport in supported MoS 2 , we plot the vibrational density of states [82], disrupting thermal transport in the MoS 2 and reducing its thermal conductivity. This phenomenon is similar to that of remote phonon scattering for the reduction of transistor mobility in ultrathin films or silicon inversion layers [83,84].…”

Thermal rectification optimization in nanoporous Si using Monte Carlo simulations

“…1). 3 We compute the thermal conductivity in the materials by solving the phonon Boltzmann transport equation using the Monte Carlo method as we described in our previous works [24][25][26]. The Monte Carlo (MC) approach offers great flexibility of geometrical configurations and parametric control over the scattering mechanisms that the phonons undergo, while still allowing very good accuracy [24,26] and large micrometer size simulation domains.…”