As-vacancy interaction and ring mechanism of diffusion in Si

Vacancy-mediated diffusion of substitutional impurities in Si drastically depends on the character of the impurity-vacancy interaction. The attractive interaction which extends to at least the third nearest neighbors allows a vacancy to move along a ring of Si sites around the impurity. This process enables the impurity-vacancy pair to move and underlies the “ring mechanism” of diffusion. To evaluate the importance of this mechanism for As impurity in Si we performed density functional calculations of the As-vacancy interaction. We also calculated the vacancy migration barriers on the circular path around the impurity. The binding energy of the As-$V$ pair was found to be 1.17 eV. This energy decreases down to 0.36 eV when the vacancy moves onto the third-nearest-neighbor site, which is the most remote site on the ring path. We found that the migration barriers for the vacancy hops around the impurity are an order of magnitude smaller than in a bulk Si. The effective barrier along the ring path is therefore mostly determined by the difference of the binding energies on the first- and the third-nearest-neighbor sites and was found to be about 0.81 eV, in a fairly good agreement with experiment. Using ab initio binding energies and migration barriers we carried out the Monte Carlo simulation of As diffusion in silicon. We found that in a temperature range between 700 K and 1300 K the vacancy-assisted As diffusion is totally dominated by the ring mechanism.