In this work, the results of density functional theory calculations for rare
earth (Ce, Pr, Eu, and Er) interstitials in Ge are presented. We employed the
hybrid functional of Heyd, Scuseria, and Ernzerhof (HSE06) for all the calculations.
We calculated the formation energies and charge state transition
levels for the tetrahedral (T) and hexagonal (H) configurations of the Ce, Pr,
Eu, and Er interstitials in Ge. While for the T configuration, the charge states
of the Ce and Pr did not induce any thermodynamic accessible transition state
level within the band gap of Ge, for both the T and H configurations the Eu
and Er interstitials in Ge induce deep levels in the band gap. The H configuration
of the Ce interstitial in Ge induces a shallow donor level at 0.03 eV
below the conduction band. The Eu interstitial exhibits negative-U properties
for the (+2/2) transition level and the Er interstitial displays characteristics
of charge state controlled metastability.