Rare earth interstitial-complexes in Ge: Hybrid density functional studies

We present results of the structural, energetic and electronic properties of rare earth (RE) interstitial-complexes in Ge (REGeGei; for RE: Ce, Pr, Eu, Er and Tm). We used the Heyd, Scuseria, and Ernzerhof (HSE06) hybrid functional within the framework of density functional theory for all calculations. The energy of formation and charge state transition levels of REGeGei complexes were obtained. For the neutral charge state, the results of the formation energy of the REGeGei, were between 0.21 and 8.14 eV. Amongst the REGeGei, while the CeGeGei was energetically the most favourable with a binding energy of 3.90 eV, TmGeGei and ErGeGei were not stable with respect to their binding energies. The CeGeGei induced deep donor level with negative-U ordering, the PrGeGei induced shallow levels close to the valence band maximum and the EuGeGei induced a shallow single donor level.