Ab initio study of aluminium impurity and interstitial-substitutional complexes in Ge using a hybrid functional (HSE)

Abstract

The results of an ab initio modelling of aluminium substitutional impurity (AlGe), aluminium interstitial in Ge [IAl for the tetrahedral (T) and hexagonal (H) configurations] and aluminium interstitial-substitutional pairs in Ge (IAlAlGe) are presented. For all calculations, the hybrid functional of Heyd, Scuseria, and Ernzerhof in the framework of density functional theory was used. Defects formation energies, charge state transition levels and minimum energy configurations of the AlGe, IAl and IAlAlGe were obtained for 2, 1, 0, þ1 and þ2 charge states. The calculated formation energy shows that for the neutral charge state, the IAl is energetically more favourable in the T than the H configuration. The IAlAlGe forms with formation energies of 2.37 eV and 2.32 eV, when the interstitial atom is at the T and H sites, respectively. The IAlAlGe is energetically more favourable when the interstitial atom is at the T site with a binding energy of 0.8 eV. The IAl in the T configuration, induced a deep donor (þ2/þ1) level at EV þ 0:23 eV and the AlGe induced a single acceptor level (0/1) at EV þ 0:14 eV in the band gap of Ge. The IAlAlGe induced double-donor levels are at EV þ 0:06 and EV þ 0:12 eV, when the interstitial atom is at the T and H sites, respectively. The IAl and IAlAlGe exhibit properties of charge state-controlled metastability.