Isovalent dopant-vacancy clusters in silicon: Density functional theory calculations

Isovalent dopants (D) incorporated in the silicon (Si) lattice can readily associate with vacancies to form dopant-vacancy pairs. Theoretical and experimental studies have shown that vacancies (V) tent to accumulate around isovalent dopants to form DVn clusters, where D is carbon (C) germanium (Ge), tin (Sn) and lead (Pb). Using spin polarised density functional theory, we examine the lowest energy structures of D, DV and VDV (D = C, Ge, Sn and Pb) and the energies to form defects and defect clusters from point defects. The results show that substitution of Ge is thermodynamically favourable. Formation of DV and VDV clusters is endoergic for all for dopants. Binding is favourable for all clusters and even more favourable for larger dopants such Sn and Pb. The results are discussed using ionisation energy, structural parameters, Bader charges and electronic structures.