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 ([Formula: see text] eV/Å). In the final relaxation, the symmetry of [Formula: see text] is [Formula: see text] for AA stacking and [Formula: see text] for AB stacking. The formation energy of AA stacking (1.72 eV) is much lower than that of AB stacking ([Formula: see text] 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 [Formula: see text] (AA stacking) and [Formula: see text] m/s (AB stacking). Those for Ca-doped bilayer graphene are [Formula: see text] (AA stacking) and [Formula: see text] m/s (AB stacking). Phonon calculations revealed that considering the vibrational effect, the defect concentration is [Formula: see text] cm[Formula: see text] in the AA stacking system. Meanwhile, concentration is deficient in the AB stacking system due to the asymmetric defect configuration.