Cluster model calculations for charge states of a silicon vacancy

Abstract

To investigate the charge states of a silicon vacancy, we introduce a cluster model which includes both the Coulomb interaction U between electrons in the dangling bond and the coupling g between the electrons and Jahn-Teller phonons, and solve the model by using the numerical diagonalization method. It is found that, for U > 0 and g = 0, the ground state of the neutral charge state V0 is spin singlet (S = 0) and orbital doublet. When g is varied for a finite U, the ground state changes to the orbital triplet state with S = 1 at an intermediate coupling gc1, and finally changes to the orbital triplet state with S = 0 at a strong coupling gc2. The obtained result for g > gc2 is consistent with the low temperature elastic softening observed in non-doped crystalline silicon.