First- and second-nearest-neighbor divacancies in silicon: Origin and ordering of gap levels

Abstract

Two configurations of the silicon divacancy, namely the first- and second-nearest-neighbor divacancies, are examined using a semi-self-consistent Hamiltonian describing the neutral undistorted situation. With Gaussian-type basis orbitals and a supercell containing 686 atoms plus the defect, the energy levels of major interest around the band gap were extracted using the Lanczos algorithm and a continued-fraction representation of the local density of states. The first-nearest-neighbor divacancy is found to introduce two doubly degenerate gap levels. The corresponding wave functions are bonding (g) and antibonding (u) combinations of \ensuremath{\pi}-like monovacancy orbitals, with the ${\ensuremath{\pi}}_{u}$-like state below ${\ensuremath{\pi}}_{g}$. The corresponding combinations of the \ensuremath{\sigma}-like orbitals (${\ensuremath{\sigma}}_{u}$ and ${\ensuremath{\sigma}}_{g}$) are found to be band resonances. By requiring calculated results to be compatible with experimental data, the symmetry of each gap level corresponding to the various charge states in the fully Jahn-Teller distorted system is inferred. We also discuss the possibility that the doubly negative charge state can appear in two lattice-distorted configurations of different symmetries. The second-nearest-neighbor (or split) divacancy, which is an intermediate state in divacancy dissociation and probably also in divacancy migration, is found to introduce five nondegenerate gap states. The results can be summarized in terms of a simple molecular model based on interacting monovacancy orbitals. It is also argued that the particular ordering of these levels is due to a solid-state node in the monovacancy gap-state wave function.