A model of the electronic structure of the Si interstitial, which was consistent with full local-density approximations, was analyzed. The model assumed the existence of 3 charge states. These were: neutral (0), singly (+) and doubly-ionized (++). The (0) interstitial was stable in a shared site, the (++) interstitial was stable in a tetrahedral site, and the (+) state had an energy which was almost independent of position. In thermal equilibrium, the relative occupation of the (0) and (++) states (each near to its stable position) depended upon the electronic Fermi energy. The (+) state had a much lower probability than the (0) or the (++) state; thus making this a negative-U center. However, the predicted diffusion constant for dopant atoms was dominated by motion of the interstitial in the (+) state. It had an activation energy which was equal to about 50% of the band gap, and was also proportional to the total interstitial density. If the interstitial density was established at a high annealing temperature, it depended strongly upon the Fermi energy at that temperature, and was much higher for p-type Si. The moving interstitial also provided the radiationless recombination of excess carriers, at a rate which was calculated by using matrix elements that were derived from the full local-density approximation electronic structure. The recombination rate did not contain a Boltzmann factor, but was proportional to the interstitial density and, at high carrier densities, to the square root of the product of the electron and hole densities. This recombination caused an enhancement of the diffusion rate. At high carrier densities, the enhancement could greatly exceed equilibrium diffusion.

W.A.Harrison: Physical Review B, 1998, 57[16], 9727-35