The relative energetic stabilities of high-order reconstructions of the (001) surface were studied by using first-principles calculations. Monte Carlo simulations of the phase transition in the asymmetrical dimer directions were performed after deducing the parameters for the Ising model. The Monte Carlo simulations reproduced quite well the transition temperature which was detected using X-ray-diffraction experiments. The potential-energy curve for dimer flip-flop motion in the p(2 x 1) structure was determined. The deduced geometry of the c(4 x 2) structure also agreed quite well with the results of X-ray diffraction experiments.

Ge(001) Surface Reconstruction Studied using a First-Principles Calculations and a Monte Carlo Simulation Y.Yoshimoto, Y.Nakamura, H.Kawai, M.Tsukada, M.Nakayama: Physical Review B, 2000, 61[3], 1965-70