Monte Carlo simulation of temperature dependence of X-ray diffraction intensity of Ge(0 0 1) surface with defects

We perform Monte Carlo simulations (MCS) to study the influence of surface defects on the order–disorder phase transition of Ge(0 0 1) surface. Coupling constants among the buckling of the dimers given by the recent first-principles calculations are used in the MCS. The feature of the phase transition is remarkably changed by a low density of defect. The magnitude of the long-range order parameter is much reduced at low temperatures as compared to the defect-free system. The temperature dependence of the X-ray diffraction intensity for the quarter-order spot specific to the c(4×2) structure becomes broad. The influence of defects on the formations of local domains of Ge(0 0 1) is well understood by analogy with that of Si(0 0 1). The experimental temperature dependence of the X-ray diffraction intensity is well reproduced by the present MCS.