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. 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.

12 pages, 8 figures

References in corpus (8)

• Energy Dissipation and Transport in Nanoscale Devices
• Channel Length Scaling of MoS2 MOSFETs
• Limits on electron quality in suspended graphene due to flexural phonons
• Electron-phonon heat transfer in monolayer and bilayer graphene
• Imaging, simulation, and electrostatic control of power dissipation in graphene devices
• Mobility enhancement and temperature dependence in top-gated single-layer MoS2
• Near-field radiative heat transfer between closely spaced graphene and amorphous SiO${}_2$
• Theoretical analysis of high-field transport in graphene on a substrate

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• Enhanced Magnetization by Defect-Assisted Exciton Recombination in Atomically Thin CrCl${}_3$