Ab-initio study of germanium di-interstitial using a hybrid functional (HSE)

Abstract

In this work, we present ab-initio calculation results of Ge di-interstitials (I2(Ge)) in the framework of the density functional theory (DFT) using the Heyd, Scuseria, and Ernzerhof (HSE) hybrid functional. The formation energy, transition levels and minimum energy con gurations were obtained for I2(Ge) -2, -1, 0, +1 and +2 charge states. The calculated formation energies shows that for all charge states of I2(Ge), the double tetrahedral (T) con guration formed the most stable defect with a binding energy of 1.24 eV in the neutral state. We found the (+2/+1) charge state transition level for the T lying below the conduction band minimum and (+2/+1) for the split[110]-tetrahedral con guration lying deep at 0.41 eV above the valence band maximum. The di -interstitials in Ge exhibited the properties of both shallow and deep donor levels at (+2/+1) within the band gap and depending on the con gurations. I2(Ge) gave rise to negative-U, with e ective-U values of -0.61 and -1.6 eV in di erent con gurations. We have compared our results with calculations of di -interstitials in silicon and available experimental data.