Convergence study of neutral and charged defect formation energies in Si nanowires

We present a systematic study of the convergence with the supercell size of the defect formation energy of a substitutional Al impurity in a Si nanowire within density-functional theory. We discuss the case of neutral and charged impurities, highlighting the importance, in the presence of ionized defects and periodic boundary conditions, of including a Madelung-like correction to the total energy in order to get correct results, which cannot be obtained by the simple use of a large vacuum buffer layer or an extrapolation thereof.