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 reconstructed 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. We also show that the use of QM/MM results in much more significant corrections at the saddle points (up to 0.5 eV) that at minima, demonstrating its importance for describing kinetics correctly.

• Received 4 July 2014
• Revised 12 September 2014

DOI:https://doi.org/10.1103/PhysRevB.90.155302