Rare Earth Interstitials in Ge: A Hybrid Density Functional Theory Study

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.