A hybrid functional calculation of Tm3+ defects in germanium (Ge)

In this work, we present ab-initio calculation results for the Tm3+ interstitial (Tmi3+), vacancy–interstitial complex (VGe-Tmi3+) and substitutional (TmGe3+) defects in germanium (Ge) as determined by the density functional theory (DFT) using the Heyd, Scuseria, and Ernzerhof (HSE06) hybrid functional. We calculated the formation energies and the charge state transition levels of different configurations. Our results show that the Tm3+ interstitial exists in the hexagonal configuration with low formation energy. The formation energies for VGe−Tmi3+ and TmGe3+ were as low as 0.84 eV. The most energetically favourable defects were the VGe−Tmi3+ in the axial   configuration and the TmGe3+. The TmGe3+ and VGe−Tmi3+ introduced a single acceptor ϵ(0/−1)ϵ(0/−1) charge state transition level that was positioned deep in the middle of the band gap. The majority of the levels induced by the defects under investigation, were either shallow donor or acceptor level lying close to the band gap edges.