Divacancy binding enthalpy and contribution of divacancies to self-diffusion in Si

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Abstract
Recognition of the ‘‘negative-U’’ character of the donor levels of the single vacancy in Si compels one to make a reassessment of the long-range, Coulomb contribution to the Si divacancy binding enthalpy. On the basis of simple models, a revised value of 1.7 eV is obtained, of which 0.8 eV is from Coulomb interaction and 0.9 eV from short-range interaction. This Coulomb attraction serves to explain the previous observation that, below 340 °C, divacancies anneal by long-range migration rather than by dissociation to single vacancies. Recent positron-annihilation measurements by Dannefaer et al. are shown to be consistent with this value of the binding enthalpy and with a vacancy-formation enthalpy of 2.4 eV. Some evidence is given that the positron is bound in a single vacancy with only about 1 eV of energy so that detrapping is significant above 900 K. It also seems likely that divacancy diffusion accounts for a significant fraction of Si self-diffusion above 1300 °C and for the increase in self-diffusion activation energy from 4 to 5 eV between 1200 and 1400 °C.