First-principles density functional theory for the structural, electronic, and phonon calculations of Ca-doped bilayer graphene

Density functional theory is adopted for the electronic structure and phonon calculation of Ca-doped bilayer graphene. The AA and AB stacking configurations are simulated, and the atoms are relaxed so that the atomic forces working on them are close to zero ([removed]5.0 × 10-3 eV/Å). In the final relaxation, the symmetry of [removed]C8CaC8 is [removed]D2h for AA stacking and [removed]CS for AB stacking. The formation energy of AA stacking (1.72 eV) is much lower than that of AB stacking ([removed]8.07 eV). According to the electronic structure calculations, the Dirac point shifts down from the Fermi level, indicating that the Ca atom behaves as an n-type dopant. The calculated Fermi velocities for pristine bilayer graphene are [removed]7.69 × 105 (AA stacking) and [removed]7.75 × 105 m/s (AB stacking). Those for Ca-doped bilayer graphene are [removed]7.29 × 105 (AA stacking) and [removed]7.22 × 105 m/s (AB stacking). Phonon calculations revealed that considering the vibrational effect, the defect concentration is [removed]1.4 × 1016 cm[removed]-3 in the AA stacking system. Meanwhile, concentration is deficient in the AB stacking system due to the asymmetric defect configuration.