Theory of substrate-directed heat dissipation for single-layer graphene and other two-dimensional crystals

TL;DR

This paper develops a theoretical model for phononic thermal resistance at the interface between single-layer 2D crystals like graphene and substrates, highlighting the effects of flexural phonon damping and encasement on heat transfer.

Contribution

It introduces a modified heat transfer model accounting for flexural phonon damping and extends it to encased 2D crystals, providing quantitative predictions of thermal boundary conductance.

Findings

Estimated room temperature TBC for bare graphene: 34.6 MWK$^{-1}$m$^{-2}$.

Encasement with SiO$_{2}$ significantly reduces Kapitza resistance.

Identifies a phonon frequency crossover affecting energy dissipation.

Abstract

We present a theory of the phononic thermal (Kapitza) resistance at the interface between graphene or another single-layer two-dimensional (2D) crystal (e.g. MoS$_{2}$) and a flat substrate, based on a modified version of the cross-plane heat transfer model by Persson, Volokitin and Ueba [J. Phys.: Condens. Matter 23, 045009 (2011)]. We show how intrinsic flexural phonon damping is necessary for obtaining a finite Kapitza resistance and also generalize the theory to encased single-layer 2D crystals with a superstrate. We illustrate our model by computing the thermal boundary conductance (TBC) for bare and SiO$_{2}$-encased single-layer graphene and MoS$_{2}$ on a SiO$_{2}$ substrate, using input parameters from first-principles calculation. The estimated room temperature TBC for bare (encased) graphene and MoS$_{2}$ on SiO$_{2}$ are 34.6 (105) and 3.10 (5.07) MWK$^{-1}$m$^{-2}$, respectively. The theory predicts the existence of a phonon frequency crossover point, below which the low-frequency flexural phonons in the bare 2D crystal do not dissipate energy efficiently to the substrate. We explain within the framework of our theory how the encasement of graphene with a top SiO$_{2}$ layer introduces new low-frequency transmission channels which significantly reduce the graphene-substrate Kapitza resistance. We emphasize that the distinction between bare and encased 2D crystals must be made in the analysis of cross-plane heat dissipation to the substrate.