Stability study of germanene vacancies: The first-principles calculations

Abstract

By using the first-principles density functional theory, stability of mono- and divacancies of germanene is studied. We simulate two configurations of monovacancies (Mo1, and Mo2) and three configurations of divacancies (Di1, Di2, and Di3). The calculated formation energies are 2.03, 2.34, 2.54, 3.38, 3.68 eV for Mo1, Mo2, Di1, Di2, and Di3, respectively. In the case of monovacancies, Mo1 has no broken-bond stabilizing its geometry and forming a fourfold configuration with tetrahedral symmetry. Meanwhile Mo2 forms a C2v symmetry leaving two broken-bonds that make Mo2 less stable than Mo1. As for the divacancies, Di1 and Di2 are more stable than Di3, originating from the absence of broken-bonds. Meanwhile, Di1 is the most stable configuration maintaining the sp2 hybridization. The metastability of Di2 compared with Di1 is that there are two fourfold configurations in Di2 replacing the sp2 by sp3 hybridization which requires higher energies.