Theory of the silicon vacancy: An Anderson negative-<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>U</mml:mi></mml:math>system

Abstract

We present a quantitative theory of electron states associated with strongly lattice-coupled localized defects. Using the total energy functional, we derive optical transition energies, occupancy levels, and activation energies. The parameters of this theory are calculated for silicon vacancies. Electron levels and deformation potentials are derived by a self-consistent Green's-function technique. The elastic lattice response is calculated using a modified valence force model. We find that the charge states ${V}^{0}$, ${V}^{+}$, and ${V}^{++}$ form an "Anderson negative-$U$ system," and we predict two-electron transitions between ${V}^{0}$ and ${V}^{++}$. To test these results, the three parameters of our theory are then treated as fully adjustable and fitted to electron paramagnetic resonance and deep-level transient spectroscopy experiments. The fitted values also lead to a prediction of the two-electron transition. Thus, experiment alone strongly suggests that the silicon vacancy is an Anderson negative-$U$ system. The results of the fitting confirm the correctness of our general theory and also demonstrate the accuracy and usefulness of our a priori calculations.