Mode dependent lattice thermal conductivity of single layer graphene

Molecular dynamics simulation is performed to extract the phonon dispersion and phonon lifetime of single layer graphene. The mode dependent thermal conductivity is calculated from the phonon kinetic theory. The predicted thermal conductivity at room temperature exhibits important quantum effects due to the high Debye temperature of graphene. But the quantum effects are reduced significantly when the simulated temperature is as high as 1000 K. Our calculations show that out-of-plane modes contribute about 41.1% to the total thermal conductivity at room temperature. The relative contribution of out-of-plane modes has a little decrease with the increase of temperature. Contact with substrate can reduce both the total thermal conductivity of graphene and the relative contribution of out-of-plane modes, in agreement with previous experiments and theories. Increasing the coupling strength between graphene and substrate can further reduce the relative contribution of out-of-plane modes. The present investigations also show that the relative contribution of different mode phonons is not sensitive to the grain size of graphene. The obtained phonon relaxation time provides useful insight for understanding the phonon mean free path and the size effects in graphene.