Magic numbers for vacancy aggregation in crystalline Si

Abstract

The stability of small n-atom vacancy clusters ${V}_{n}$ in Si is examined for n\ensuremath{\le}12. The most stable structures occur for ringlike ${V}_{6}$ and ``adamantine cage'' ${V}_{10}$ clusters and the least stable ones for ${V}_{5}$ and ${V}_{8}$ clusters. Electron-paramagnetic-resonance measurements are shown to provide strong support for the assignment of ${V}_{10}$ to the dominant ${P}_{1}$ paramagnetic center in neutron- or ion-bombarded Si.