▎ 摘　　要

Boron and nitrogen doping in graphene has important implications in graphene-based devices. We investigate systematically the vibrational properties of B- and N-doped graphene with vacancies using forced vibrational method. We have calculated the phonon density of states (PDOSs), typical mode patterns and phonon localization length for different concentration of B, N and vacancies. We find that the interference between native point defects and B or N dopant break down the phonon degeneracy at the Gamma point of the LO and TO modes, distort and shift down the PDOSs significantly. We observe a broadening and softening of the Raman active E-2g phonon mode with an increase of B and N atoms. The PDOS peaks for the mixture of vacancies and B or N atoms show the remarkable increase in the low-frequency region induced by their defect formations. Our computer experiments demonstrate that the disordered graphene show the spatially localized vibrations due to the resonant vibrations of the impurity atoms relative to the main C atoms. The calculated typical mode patterns for in-plane K point optical phonon modes indicate that the phonon is localized strongly within a region of several nanometers in the random disordered graphene structures. In particular, a typical localization length is on the order of approximate to 9.5 nm for B- and N-doping, approximate to 9 nm for mixture of B-doping and vacancy, and approximate to 8.5 nm for mixture of N-doping and vacancy concentrations of 20%. This study provides a useful basis for the understanding of a wide variety of physical properties such as thermal conductivity, specific heat capacity, and electron-phonon interaction, as well as in the experiments of infrared, Raman, and neutron-diffraction spectra of doped-graphene. (C) 2014 Elsevier B.V. All rights reserved.