  The structure and properties of vacancies in a 2 nm Si nano-crystal are
studied using a real space density functional theory/pseudopotential method. It
is observed that a vacancy's electronic properties and energy of formation are
directly related to the local symmetry of the vacancy site. The formation
energy for vacancies and Frenkel pair are calculated. It is found that both
defects have lower energy in smaller crystals. In a 2 nm nano-crystal the
energy to form a Frenkel pair is 1.7 eV and the energy to form a vacancy is no
larger than 2.3 eV. The energy barrier for vacancy diffusion is examined via a
nudged elastic band algorithm.
