Atomic scale simulations of donor-vacancy pairs in germanium

Atomic scale calculations have been used to predict the structures and relative energies of defect clusters formed between n-type dopants and lattice vacancies in germanium (Ge). These include phosphorous-vacancy (P-V), arsenic-vacancy (As-V) and antimony-vacancy (Sb-V) pairs as well as larger clusters. The calculations used a plane-wave basis set in conjunction with pseudo-potentials within the generalized gradient approximation (GGA) of density functional theory (DFT). Equivalent defects in silicon (Si) are also predicted, and these demonstrate the excellent correlation of the present simulations to previous experimental and theoretical studies. The calculations highlight similarities and important differences in the formation and binding energies of clusters in Ge compared to Si. Interestingly the binding energies of the donor-vacancy pairs do not scale with dopant size.