Isovalent dopant-vacancy clustering in germanium

The introduction of isovalent dopants (D = carbon (C), silicon (Si), tin (Sn) and lead (Pb)) in the germanium (Ge) lattice can lead to the association with the prevalent intrinsic defect (vacancy) to form dopant-vacancy pairs (DV) or more extended defects such as (VDV or DVV). Here we employ spin-polarized density functional theory (DFT) calculations to predict the lowest energy structures of D, DV, VDV and DVV (D = C, Si, Sn and Pb) defects in Ge. All the defects considered with the larger isovalent dopants are predicted to be strongly bound. The defects' structural parameters, ionization energy, Bader charges and electronic structures are thoroughly discussed.