Geometrical and electronic structures of graphene under different vacancy density and configuration

Highlights: • We study geometrical and electronic structures of graphene with different vacancy densities. • Band structure of graphene is influenced by the density and configuration of vacancy. • Formation energy is varied by vacancy configuration under the same vacancy density. - Abstract: We calculated the geometrical and electronic structures of graphene with different vacancy densities and configurations. Vacancy was varied in graphene from mono- to tri-vacancy and configured to zigzag and armchair lattice directions. While di-vacancy in graphene led to a gap in the electronic structure, mono- and tri-vacancies shifted the Fermi level below the valence band maximum irrespective of vacancy configurations. Under the same density of vacancies, di-vacancy to zigzag direction had lower formation energy than defects along armchair direction. Meanwhile, tri-vacancy to zigzag lattice direction led to higher formation energy than defects to armchair direction.