A physics-based flexural phonon-dependent thermal conductivity model for single layer graphene

Abstract

In this paper, we address a physics-based closed-form analytical model of flexural phonon-dependent diffusive thermal conductivity (κ) of suspended rectangular single layer graphene sheet. A quadratic dependence of the out-of-plane phonon frequency, generally called flexural phonons, on the phonon wave vector has been taken into account to analyze the behavior of κ at lower temperatures. Such a dependence has further been used for the determination of second-order three-phonon Umklapp and isotopic scatterings. We find that these behaviors in our model are best explained through the upper limit of Debye cut-off frequency in the second-order three-phonon Umklapp scattering of the long phonon waves that actually remove the thermal conductivity singularity by contributing a constant scattering rate at low frequencies and note that the out-of-plane Gruneisen parameter for these modes need not be too high. Using this, we clearly demonstrate that κ follows a T1.5 and T−2 law at lower and higher temperatures in the absence of isotopes, respectively. However in their presence, the behavior of κ sharply deviates from the T−2 law at higher temperatures. The present geometry-dependent model of κ is found to possess an excellent match with various experimental data over a wide range of temperatures which can be put forward for efficient electro-thermal analyses of encased/supported graphene.