In this paper, the phonon scattering mechanisms of single-layer graphene are investigated based on the complete phonon dispersion relations. According to the selection rules that a phonon scattering process should obey the energy and momentum conservation conditions, the relaxation rates of combining and splitting umklapp processes can be calculated by integrating the intersection lines between different phonon mode surfaces in the phonon dispersion relation space. The dependence of the relaxation rates on the wave vector directions is presented with a three-dimensional surface over the first Brillouin zone. It is found that the reason for the optical phonons contributing little to heat transfer is attributed to the strong umklapp processes but not to their low phonon group velocities. The combining umklapp scattering processes involving the optical phonons mainly decrease the acoustic phonon thermal conductivity, while the splitting umklapp scattering processes of the optical phonons mainly restrict heat conduction by the optical phonons themselves. Neglecting the splitting processes, the optical phonons can contribute more energy than that carried by the acoustic phonons. Based on the calculated phonon relaxation time, the thermal conductivities contributed from different mode phonons can be evaluated. At low temperatures, both longitudinal and in-plane transverse acoustic phonon thermal conductivities have T2 temperature dependence, and the out-of-plane transverse acoustic phonon thermal conductivity is proportion to T3/2. The calculated thermal conductivity is on the order of a few thousands W/(m K) at room temperature, depending on the sample size and the edge roughness, and is in agreement well with the recently measured data in the temperature range from about 350 K to 500 K.

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