The effective-mass nature of deep-level point-defect states in semiconductors

The basic premise of Effective-Mass Theory (EMT) is that bound-state wavefunctions are constructible from Bloch functions in a small region or regions of k space. In contrast, deep-level wavefunctions are believed to involve Bloch functions from the entire Brillouin zone and several bands. In this paper we analyse the wavefunction of the deep vacancy level in Si obtained recently by self-consistent Green's-function calculations. We find that this wavefunction has a strong EMT character in that it is composed primarily of Bloch functions from the nearest bands and the corresponding coefficients, i.e. the envelope functions, are peaked about the band extrema. As a further check, we have used a spherical average of the self-consistent vacancy potential in the acceptor EMT equations. The resulting energy level is at E_v+0.9 eV, as compared with the Green's-function-theoretic value of E_v+0.8 eV. The resulting wavefunction, on the other hand, does not have the correct form. A check of the correction terms left out by the standard EMT equations reveals that their contributions to the energy level are large and tend to cancel one another.