(373l) Heat Transfer Studies in Supported Graphene Layers
Since being first exfoliated  from graphite, grapheme has received tremendous attention from various areas due to its superior mechanical and thermal properties such as charge mobility  and mechanical strength  compared to the materials in use today. The issue of special interest in electronic industry is the electronic and heat condution ability of graphene layers. As the dimensions of electronic devices decrease significantly, novel materials with enhanced properties are required. Thus, graphene has a huge potential for the next generation devices. Single layer graphene (SLG) at room temperature has shown remarkable heat transfer coefficient of about 3000 W/m.K , which is orders of magnitude higher than copper or other metals. In practical device applications, SLG is supported on a dielectric substrate. This decreases the thermal conductivity of the system, but still is higher than copper. The main carriers of thermal energy in nano-scale systems such as SLG are electrons and lattice vibrations termed as phonons. Atoms in a solid can be visualized as a system of masses separated by springs which are chemical bonds. When the atoms are heated, they get excited and start vibrating, and pass the thermal energy via these springs. The descrete value of vibrational energy is called a phonon. Thus, to fully understand the thermal energy distribution mechanism, it is important to understand the nature of these vibrations.
In our earlier work, we attempted to solve a mesoscopic model  based on Boltzmann transport equation (BTE) for the radiative transport of phonons called equation for phonon radiative transfer (EPRT) by using a descritized version of the BTE known as lattice Boltzmann method (LBM). Our model successfully predicted transient heat transfer in single and multilayer dielectric materials in sub-continuum range, while retaining the computational efficiency and simplicity of boundary conditions of LBM. In this study, we attempt to apply this model to validate the data provided  thermal transport dependence in SLG exfoliated on a dielectric substrate. We also attempt to explain the interesting observations of the authors on the contribution of phonon modes (longitudinal: LA, in-plane transverse: TA, and out-of plane :ZA) to the thermal conductivity. Based on their results, they have reported that the ZA mode, which has been assumed to contribute minimally in SLG, has in fact a large contribution in thermal conductivity. Thus looking at the reduced conductivity for the SLG-substrate system, they deduce that since the SLG partially conforms to the roughness of the substrate surface, the ZA phonon modes leak through the contact points much stronger than TA or LA modes. We investigate in detail the scattering of the phonons at the boundary of SLG and substrate through van der Walls springs to substantially increase the thermal conductivity.
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