Strain effects and intermixing at the Si surface: Importance of long-range elastic corrections in first-principles calculations

Abstract

We investigate Ge mixing at the Si(001) surface and characterize the $2\times N$ Si(001) reconstruction by means of hybrid quantum and molecular mechanics calculations (QM/MM). Avoiding fake elastic dampening, this scheme allows to correctly take into account long range deformation induced by reconstruted and defective surfaces. We focus in particular on the dimer vacancy line (DVL) and its interaction with Ge adatoms. We first show that calculated formation energies for these defects are highly dependent on the choice of chemical potential and that the latter must be chosen carefully. Characterizing the effect of the DVL on the deformation field, we also find that the DVL favors Ge segregation in the fourth layer close to the DVL. Using the activation-relaxation technique (ART nouveau) and QM/MM, we show that a complex diffusion path permits the substitution of the Ge atom in the fourth layer, with barriers compatible with mixing observed at intermediate temperature.