Microscopic mechanism of atomic diffusion in Si under pressure

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Abstract
We have performed the first-principles total-energy calculations on the atomic diffusion of group-V impurities in Si, and have revealed the pressure effect on the activation energy of the diffusion. For the vacancy mechanism, the activation energies for P, As, and Sb decrease with pressure. For the interstitial mechanism, on the other hand, the formation energy of the interstitial impurity shows a general tendency to increase with pressure. Combining the results with the experimental data, we have concluded that there is a dominant contribution of the vacancy mechanism for the As diffusion. The microscopic origin of the pressure dependence is clarified in terms of the local strain around the defects. The negative pressure dependence common to the group-V impurities for the vacancy-mediated diffusion is well explained by the peculiar nature of the isolated vacancy: (a) breathing distortion of the surrounding Si atoms toward the vacancy site, which gives rise to a tensile strain around the vacancy, and (b) the characters of the wave function and the lattice distortion originating from the vacancy, which cause the weak vacancy-impurity interaction. The positive pressure dependence for the interstitial-mediated diffusion is closely related to the atomic structures of the interstitial impurities which cause compressive strain to the surrounding Si-Si bonds.