Stability study of germanene vacancies: The first-principles calculations

By using the first-principles density functional theory, stability of mono- and divacancies of germanene is studied. We simulate two configurations of monovacancies (Mo<inf>1</inf>, and Mo<inf>2</inf>) and three configurations of divacancies (Di<inf>1</inf>, Di<inf>2</inf>, and Di<inf>3</inf>). The calculated formation energies are 2.03, 2.34, 2.54, 3.38, 3.68 eV for Mo<inf>1</inf>, Mo<inf>2</inf>, Di<inf>1</inf>, Di<inf>2</inf>, and Di<inf>3</inf>, respectively. In the case of monovacancies, Mo<inf>1</inf> has no broken-bond stabilizing its geometry and forming a fourfold configuration with tetrahedral symmetry. Meanwhile Mo<inf>2</inf> forms a C<inf>2v</inf> symmetry leaving two broken-bonds that make Mo<inf>2</inf> less stable than Mo<inf>1</inf>. As for the divacancies, Di<inf>1</inf> and Di<inf>2</inf> are more stable than Di<inf>3</inf>, originating from the absence of broken-bonds. Meanwhile, Di<inf>1</inf> is the most stable configuration maintaining the sp² hybridization. The metastability of Di<inf>2</inf> compared with Di<inf>1</inf> is that there are two fourfold configurations in Di<inf>2</inf> replacing the sp² by sp³ hybridization which requires higher energies. © 2019 Elsevier Ltd