Thickness-dependent Kapitza resistance in multilayered graphene and other two-dimensional crystals

The Kapitza or thermal boundary resistance (TBR), which limits heat dissipation from a thin film to its substrate, is a major factor in the thermal management of ultrathin nanoelectronic devices and is widely assumed to be a property of only the interface. However, data from experiments and molecular dynamics simulations suggest that the TBR between a multilayer 2-dimensional (2D) crystal and its substrate decreases with increasing film thickness. To explain this thickness dependence, we generalize the recent theory for single-layer 2D crystals by Ong, Cai and Zhang [Phys. Rev. B 94, 165427 (2016)], which is derived from the theory by Persson, Volokitin, and Ueba [J. Phys.: Condens. Matter 23, 045009 (2011)], and use it to evaluate the TBR between bare $N$-layer graphene and SiO$_{2}$. Our calculations reproduce quantitatively the TBR thickness dependence seen in experiments and simulations as well as its asymptotic convergence, and predict that the low-temperature TBR scales as $T^{-4}$ in few-layer graphene. Analysis of the interfacial transmission coefficient spectrum shows that the TBR reduction in few-layer graphene is due to the additional contribution from higher flexural phonon branches. Our theory sheds light on the role of flexural phonons in substrate-directed heat dissipation and provides the framework for optimizing the thermal management of multilayered 2D devices.