A quasi-two-dimensional four-state planar model was proposed to study the Si(111)-(n x n) (n = 5 or 7) surface reconstructive phase transition. Monte Carlo calculation showed that the model underwent a first-order phase transition that results in the n x n structure at low temperatures. It also showed the onset of stacking ordering at slightly higher temperature than the critical point. By using the model, a natural candidate for the substitution sites of Ge atoms in the Ge/Si(111)-(5 x 5) structure was identified. The origin of the difference between corresponding reconstructions on Si(111) and Ge(111) surfaces was also identified.

Four-State Planar Model of the Si(111) Surface Reconstruction. M.Itoh: Physical Review B, 1996, 54, 5873-80