Thermal conductivity of single layer graphene supported on silicon nitride/silicon substrates

We determine the thermal conductivity of single layer graphene supported on silicon nitride layer followed by a silicon substrate using a three dimensional simulation study. Temperature distribution profile along the graphene flake is obtained and heat transmission in graphene layer along with the subsequent layers is investigated by modeling the laser light as heat source. Two types of heat sources of varying shapes (disk heat source and line heat source) are used in the study to explore the effect of the geometry of heat source on thermal conductivity. Thermal conductivity value is found as 1000 Wm-1K-1 and 600 Wm-1K-1 for disk and line heat sources respectively which are lower than the values found previously for suspended graphene as a consequence of phonon leakage across the graphene-substrate interface. Dependence of thermal conductivity on the length of the graphene flake is studied and a growth in thermal conductivity is found with the increase in the length due to long phonon mean free path and reduced boundary scattering.