Simple parametrized model for Jahn-Teller systems: Vacancy inp-type silicon

We propose a simple and quite general model for charge states and their activated relaxation in localized defects. Applying the model to the analysis of Watkins's electron-paramagnetic resonance and deep-level-transient-spectroscopy observations of vacancies in $p$-type silicon, we obtain two constraints on the model's three parameters. This allows us to conclude (1) that the vacancy is indeed an "Anderson negative-$U$" system as we had earlier calculated, and (2) that the Jahn-Teller stabilization energy of the $V^0$ neutral vacancy cannot substantially exceed 0.8 eV.