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

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., ${\mathrm{MoS}}_{2})$ 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 ${\mathrm{SiO}}_{2}$-encased single-layer graphene and ${\mathrm{MoS}}_{2}$ on a ${\mathrm{SiO}}_{2}$ substrate, using input parameters from first-principles calculation. The estimated room temperatures TBC for bare (encased) graphene and ${\mathrm{MoS}}_{2}$ on ${\mathrm{SiO}}_{2}$ are 34.6 (105) and 3.10 (5.07) ${\mathrm{MW}\phantom{\rule{0.16em}{0ex}}\mathrm{K}}^{\ensuremath{-}1}{\mathrm{m}}^{\ensuremath{-}2}$, 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 ${\mathrm{SiO}}_{2}$ 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.