Simulation of phonon transmission through graphene and graphene nanoribbons with a Green's function method

In this paper, phonon transmission through a graphene sheet and graphene nanoribbons is investigated using an atomistic Green's function method. Best-fit results from first-principles calculations using a fourth nearest neighbor force-constant model are used to establish the matrices that describe interactions among carbon atoms. The effect of carbon isotopes on thermal conductance is investigated, and the results reveal that isotopic doping moderately reduces both phonon transmission function and thermal conductance. The phonon transmission function of each vibrational branch in the heterogeneous interface is also calculated, and comparisons indicate the major and minor channels of phonon transport through graphene. Further, phonon wave effects in zigzag and armchair edge ribbons are investigated. Phonon transmission functions and thermal conductances are found to be sensitive to the edge shape of structures. The phonon transmission functions of nanoribbons with defects are evaluated by artificially creating mismatches at interfaces. By comparing the transmission function of different defect patterns and the corresponding thermal conductances, the reduction in phonon transport is quantified. The length of defects is found to be important to phonon transport. The results herein offer a useful reference and suggest directions for future research on thermal applications of this material. (C) 2010 American Institute of Physics. [doi:10.1063/1.3499347]