Simulation of Heat Conduction in Suspended Graphene Flakes of Variable Shapes

Graphene is a novel material that reveals many remarkable properties. Academic and industry research groups around the globe are carrying out theoretical and experimental studies to discover and investigate characteristics of graphene. Due to its outstanding properties, graphene has a potential to revolutionize technology. Particularly, graphene was found to be one of the best known heat conductors [Balandin et al., Nano Lett. 8, 902 (2008)], which suggests that it can be used in nanoelectronic and optoelectronic devices as a heat spreader component. The extremely high thermal conductivity was found for single layer graphene, which consisted of one crystalline plane of Sp(2)-bound carbon atoms. In that experiment a method of measuring G peak position of the Raman spectrum as a function of both the temperature of the graphene sample and the power of the heat source was used to compute the thermal conductivity. The sample in the experiment had approximately rectangular geometry and a simple model was used to extract the thermal conductivity under certain assumptions about the nature of the thermal transport. In this work we used finite-element simulations to model the heat spreading in graphene flakes of variable shapes. We also investigated how the thermal transport is influenced by the geometry of the heat source and flake width. We found that all mentioned factors impact heat propagation and have to be included in the experimental data extraction. The simulations also proved that for the rectangular geometry of the flake and specific conditions of the experiment, e.g., ratio of the flake width to the laser spot size, the simple one-dimensional model data extraction was adequate. The developed simulation procedure can be further used for investigation of thermal transport in graphene multi-layers and graphene-heat sink structures. The latter is required in order to study the feasibility of application of graphene multi-layers for the lateral hot-spot removal and other device-level thermal management applications.