Rare earth substitutional impurities in germanium: A hybrid density functional theory study

The Heyd, Scuseria, and Ernzerhof (HSE06) hybrid functional by means of density functional theory has been used to model the electronic and structural properties of rare earth (RE) substitutional impurities in germanium (REGe). The formation and charge state transition energies for the REGe (RE = Ce, Pr, Er and Eu) were calculated. The energy of formation for the neutral charge state of the REGe lies between −0.14 and 3.13 eV. The formation energy result shows that the Pr dopant in Ge (PrGe) has the lowest formation energy of −0.14 eV, and is most energetically favourable under equilibrium conditions. The REGe induced charge state transition levels within the band gap of Ge. Shallow acceptor levels were induced by both the Eu (EuGe) and Pr (PrGe) dopants in Ge. The CeGe and ErGe exhibited properties of negative-U ordering with effective-U values of −0.85 and −1.07 eV, respectively.