Impact of germanium on vacancy clustering in germanium-doped silicon

Abstract

Recent density functional theory calculations by Chen et al. [J. Appl. Phys. 103, 123519 (2008)] revealed that vacancies (V) tend to accumulate around germanium (Ge) atoms in Ge-doped silicon (Si) to form GeVn clusters. In the present study, we employ similar electronic structure calculations to predict the binding energies of GeVn and Vn clusters containing up to four V. It is verified that V are strongly attracted to pre-existing GeVn clusters. Nevertheless, by comparing with the stability of Vn clusters, we predict that the Ge contribution to the binding energy of the GeVn clusters is limited. We use mass action analysis to quantify the relative concentrations of GeVn and Vn clusters over a wide temperature range: Vn clusters dominate in Ge-doped Si under realistic conditions.