(2 × 1)-(1 × 1) phase transition on Ge(0 0 1): quasi-chemical approximation and Monte Carlo simulations

This paper deals with the (2 × 1)-(1 × 1) phase transition that has been observed on the Ge(0 0 1) surface at temperatures 950–1000 K. The transition is described in terms of ordering and disordering in (2 × 1) arrays of surface Ge dimers. An analytical statistical mechanical theory is presented in the framework of the quasi-chemical approximation. The dimer formation energy allows dimers to dissociate into monomers and the attractive interaction energy between dimers realizes the (2 × 1) ordered array of dimers. The conventional order parameter reproduces at least qualitatively well the experimentally observed drastic disordering with increasing temperature. On the contrary the monomer density remains fairy low and increases quite modestly with temperature around the transition point, which is not in favor to the dimer break-up mechanism for the phase transition. Combined with suitable Monte Carlo simulations, the phase transition can be characterized by exhaustive recombination of dimers triggered by generation of a small number of monomers.