RECONSTRUCTIONS AND PHASE-TRANSITIONS OF THE GE(001) SURFACE

We have calculated the energy differences between the four members of the 2 x 1 family (b(2 x 1), c(4 x 2), p(2 x 2) and p(4 x 1) of the Ge(001) surface by taking only electrostatic interactions between the dimers into account. We have found that p(2 x 2) is the lowest-energy reconstruction at zero temperature. The phase transitions from ordered p(2 x 2) to disordered (2 x 1) and ordered c(4 x 2) to disordered (2 x 1) are discussed using our energy calculations, the mean-field approximation, the Ising model and Onsager's exact solution. A second-order phase transition is found at about 200-250 K from an ordered p(2 x 2) (c(4 x 2)) dimer reconstruction to a disordered (2 x 1) dimer reconstruction assuming a charge transfer of 0.08e between the up atom and the down atom of the asymmetric dimer.